Molecular filter based planar Doppler velocimetry

Progress in Aerospace Sciences 35 (1999) 799 } 845

Molecular "lter based planar Doppler velocimetry Gregory S. Elliott!,*, Thomas J. Beutner" !Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA "Air Force Ozce of Scientixc Research, Arlington, VA 22203, USA

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Motivation for planar velocimetry systems . . . . . . . . . . . . . . . . . . . . . 1.2. Intrusive and nonintrusive techniques . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Modern advancements in optical diagnostics . . . . . . . . . . . . . . . . . . . . 1.4. Expansion of measurements beyond single points . . . . . . . . . . . . . . . . . 1.5. General description of planar Doppler velocimetry . . . . . . . . . . . . . . . . 1.6. History of the introduction of molecular "lters to experimental #uid dynamics 2. Basic science and technologies behind PDV . . . . . . . . . . . . . . . . . . . . . . . 2.1. Scattering from particles and molecules . . . . . . . . . . . . . . . . . . . . . . . 2.2. The absorption processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. PDV systems and processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. PDV components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Absorption cell design considerations . . . . . . . . . . . . . . . . . . . . 3.1.2. Laser and sheet forming optics . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. Frequency monitoring system . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Camera and receiving optics . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Iodine "lter calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. PDV image calibration and mapping . . . . . . . . . . . . . . . . . . . . . 3.2.3. Determination of frequency shifts . . . . . . . . . . . . . . . . . . . . . . . 4. The development and application of PDV . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Instrument development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Flow "eld measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Axisymmetric jet studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. Supersonic wind tunnel measurements . . . . . . . . . . . . . . . . . . . . 4.2.3. Subsonic large-scale wind tunnel measurements . . . . . . . . . . . . . . 5. Uncertainty analysis of PDV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Bias errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Random errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Current reported levels of uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 6. Future trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

* Corresponding author. Tel.: 732-445-3282; fax: 732-445-3124. E-mail address: [email protected] (G.S. Elliott) 0376-0421/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 6 - 0 4 2 1 ( 9 9 ) 0 0 0 0 8 - 1

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Nomenclature a F *f D f 0 f 8

mapping coe$cients f-number of optical system Doppler shift frequency laser frequency Rayleigh scattering thermal broadening frequency width half maximum I intensity k Boltzmann constant k observation unit light-wave vector 4 k incident unit light-wave vector 0 k spectral absorption l K transition linestrength ji ¸ cell length m magni"cation ratio M molecular mass P pressure R reference camera image S signal camera image ¹ temperature ¹ temperature of iodine 12 TR transmission V velocity vector x, y, z Spatial coordinates x independent variable contributing to bias i uncertainty

*x i *x y j *y j y >(l) Greek d j l f h l

uncertainty of independent variable contributing to bias average sixe of camera pixels independent variable contributing to random uncertainty uncertainty of independent variable contributing to the random uncertainty collisional frequency to acoustic spatial frequency ratio line pro"le letters absorption linewidth laser wavelength frequency frequency function angle between the incident and scattered wave vectors viscosity

Subscripts B background image D data image G #at-"eld image

Abstract Molecular "lter based diagnostics are continuing to gain popularity as a research tool for investigations in areas of aerodynamics, #uid mechanics, and combustion. This class of diagnostics has gone by many terms including Filtered Rayleigh Scattering, Doppler Global Velocimetry, and Planar Doppler Velocimetry. The majority of this article reviews recent advances in Planar Doppler Velocimetry in measuring up to three velocity components over a planar region in a #ow"eld. The history of the development of these techniques is given with a description of typical systems, components, and levels of uncertainty in the measurement. Current trends indicate that uncertainties on the order of 1 m/s are possible with these techniques. A comprehensive review is also given on the application of Planar Doppler Velocimetry to laboratory #ows, supersonic #ows, and large scale subsonic wind tunnels. The article concludes with a description of future trends, which may simplify the technique, followed by a description of techniques which allow multi-property measurements (i.e. velocity, density, temperature, and pressure) simultaneously. ( 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction 1.1. Motivation for planar velocimetry systems Considerable work has been undertaken during the past decade on the development of velocimetry systems designed to capture data over entire planes in a #ow "eld simultaneously. These systems represent a signi"cant advancement over point-measurement systems, and their

development has been motivated by both scienti"c and economic considerations. Of particular interest, in this review, are a class of velocimetry systems which are based on using molecular "lters to measure Doppler shifts of scattered laser light collected from the #ow under investigation. These measurements allow the velocity to be determined throughout the #ow. A review of these techniques at this time is particularly appropriate since the techniques are maturing to the point that accurate,

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

reliable measurements may be made in realistic #ow "elds. This class of diagnostic techniques share several important characteristics: (1) the measurements are nonintrusive, (2) velocities over an entire plane of the #ow "eld, can be captured, (3) three-component velocity measurements are feasibility, (4) instantaneous measurements in unsteady #ow "elds are possible, (5) applications in both small and large scale facilities have been demonstrated. The motivation for a planar velocity measurement technique is at least twofold. First, from an economic viewpoint, a planar technique capable of capturing thousands of velocity measurements simultaneously allows #ow "eld data to be characterized rapidly. Since run-time costs of large wind tunnels may be tens or hundreds of thousand of dollars per day, these types of velocimetry systems, even if expensive to construct, may pay for themselves in a single test. In practice, this not only reduces the wind tunnel run time required for detailed measurements by orders of magnitude, resulting in a tremendous cost savings to research e!orts, but it may make detailed #ow "eld measurements possible in cases where traditional measurement surveys were cost-prohibitive. This new capability provides a wealth of #ow-"eld data to the aircraft designer or #uid dynamics researcher. Secondly, as a scienti"c tool, a diagnostic technique which provides simultaneous, instantaneous data throughout a #ow "eld is desirable for investigating unsteady #ows. The ideal measurement technique would be capable of characterizing (with measurements of all physical properties) a #ow "eld globally in space, continuously and instantaneously in time, by a means that is nonintrusive to the #ow. No currently available diagnostic techniques satisfy all these criteria, but, as will be discussed here, molecular-"ltered-based diagnostics represent an advance toward this end.

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are limited either to surface measurements, or they raise the possibility that the probe or its support may disturb the very #ow "eld which is being measured. Even small perturbations due to the probe can dramatically change some #ow "elds of aerodynamic interest. This is particularly true for sensitive or unstable #ows, such as turbulent transition or vortex bursting. A probe may obviously in#uence the downstream #ow causing wakes or shocks, but it may also cause pressure gradients which in#uence even the upstream #ow "eld for the subsonic case. Additionally, the measurement of multiple points in the #ow "eld requires either a rake of probes, or a scanning apparatus. Such systems may be di$cult to implement, especially in large wind tunnel applications, and scanning systems will generally result in long run times to provide su$cient resolution of the #ow "eld. These problems have motivated the development of a wide variety of nonintrusive diagnostic techniques. Examples of nonintrusive techniques include a variety of optical diagnostics (schlieren, shadowgraph, laser velocimetry, particle image velocimetry, two-spot velocimetry, spectroscopic techniques, etc.) which use light as the interrogator. Some of the more simple lineof-sight techniques have been used mainly for qualitative #ow visualization and are based on the changes in the index of refraction caused by changes in gas density or composition. This group of techniques includes shadow photography, schlieren photography, and conventional interferometry. One weakness of these techniques is that the beam of light is passed across the #ow-"eld, so that the resulting measurement is integrated across the #ow. Therefore, three-dimensional details of the #ow can be masked. Despite this, these techniques have led to many signi"cant discoveries, particularly in compressible #ows. Holographic interferometry has also been extended into a quantitative three-dimensional technique, but typical systems are extremely sensitive to vibrations and window distortions making them di$cult to implement in largescale facilities.

1.2. Intrusive and nonintrusive techniques 1.3. Modern advancements in optical diagnostics Experimental techniques to measure #ow quantities may be generally classi"ed as intrusive or nonintrusive. Those techniques in which a mechanical probe must have contact with the #ow are considered intrusive. Alternatively, nonintrusive techniques are those in which the measurement apparatus is located outside the #ow and does not signi"cantly perturb the #ow. For many years #uid dynamicists have used intrusive techniques such as pitot-static probes, thermocouples, "ve-hole probes, and hot-wire/"lm anemometry. In general these techniques provide an accurate measure of #ow properties (velocity, pressure, temperature, or mass #ux) and can provide continuous if not instantaneous measurements. In practice, however, intrusive techniques

Since the late 1960s, the #uid dynamics community has incorporated the laser into a variety of nonintrusive diagnostic techniques. These techniques have been made possible by the laser characteristics of coherence, single frequency, and polarization. Although these techniques may still require some interaction with or modi"cation to the #ow (e.g. seeding with particles or gasses, or absorption of laser energy by the gas) which can be done without signi"cant alteration of the #ow "eld. The laserbased techniques can be divided into those which focus the laser beam to a `single-pointa or line, and those which spread the laser beam out to a sheet of laser light. One group of point measurement techniques, that

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have been utilized widely in the combustion community, include Rayleigh, Raman, absorption, and laser-induced #uorescence methods that are all based on the signal collected from molecules in the #ow [1,2]. In general these techniques have the ability to measure multiple #ow properties including temperature, pressure, density, gas composition, and velocity. It should be noted, however, that these techniques may su!er from low signal levels, the need to seed toxic or corrosive #uorescence species into the #ow, and can have complex optical arrangements. One of the most popular and widely applied techniques for #ow velocity measurements is Laser Doppler Velocimetry (LDV), also called Laser Doppler Anemometry (LDA). Most current LDV systems use two beams which are focused and crossed at a point in space creating a small measurement volume containing an interference fringe pattern. When a small particle passes through the probe volume, the scattered signal intensity varies in amplitude due to the fringe pattern. This beat frequency is measured with a photomultiplier tube and "ltered using FFT analyzers. Since the fringe spacing is known, the velocity can be easily calculated from the beat frequency. By using multiple beams, each having a di!erent frequency, multiple fringe patterns may be established in the same probe volume, allowing two or three-component velocity measurements to be made. The LDV technique is well developed and commercial o!the-shelf systems are available. The greatest di$culty with LDV is that it is a point technique and beam alignment issues make it di$cult to traverse the probe volume e$ciently in a large wind tunnels. Also, issues with signal strength and velocity dynamic range become problematic when distances between the transmitting or receiving optics is large. 1.4. Expansion of measurements beyond single points A new category of techniques has emerged which provides more spatial detail about the #ow "eld by spreading the laser beam into a two-dimensional sheet of laser light and interrogating an entire plane in the #ow "eld. Initially these techniques were limited to #ow visualizations made by seeding the #ow with smoke or a #uorescence species. These laser light-sheet techniques are widely used in all classes of wind tunnels, and are useful in visualizing qualitative #ow features, such a vortex trajectories. In order to obtain quantitative information about the #ow, these techniques were enhanced to included Rayleigh and Raman scattering measurements. Planar Laser Induced Fluorescence (PLIF), has also been accomplished by seeding #uorescent species into the #ow or sometimes by exciting species naturally present in the #ow. These quantitative techniques have been primarily limited to small-scale facilities, due to the low signal levels, seeding requirements, and the toxicity or corrosive

nature of some of the seeding materials, but a judicious choice of the laser and #uorescent species can reduce these problems (for example oxygen can be used with ArF lasers). Currently the most popular quantitative velocimetry technique based on laser sheet measurements is Particle Image Velocimetry (PIV). This technique is also referred to as DPIV when a digital camera is used. PIV is a timeof-#ight method based on measuring particle displacements between two sequential images, separated by a known time interval. These displacements may be readily determined by correlations between the two images, however, the PIV technique requires that individual seed particles be resolved in each image. This requirement may be di$cult to achieve when large interrogation regions are involved. In high-speed facilities an additional complication may arise since particles small enough to follow the #ow may be so small that they do not scatter enough light for the detector systems typically used in PIV. Also, large velocity components in the direction normal to the illuminating light sheet can destroy the correlation between PIV images, since the particles imaged in the "rst frame are carried out of the light sheet by the out-of-plane motion and replaced by di!erent particles during the second frame. In highly three-dimensional #ow "elds, such out-of-plane velocity components may be di$cult to avoid. This problem may be addressed by an extension to the PIV technique which uses stereo imaging to resolve the out-of-plane velocity component. Additionally, holographic PIV systems have been demonstrated which provide a truly global measurement technique. However, both the stereoscopic and holographic extensions to the PIV technique signi"cantly increase the complexity of the measurement apparatus and the data processing. A complete discussion of the current state of PIV technologies is given by Ra!el et al. [3] and a comparison of PIV and the molecular "lter based techniques to be described is given by Samimy and Wernet [4]. Of course, no one measurement technique is ideal for all applications. Each technique has strengths and weaknesses * particularly when ease of use, cost, and measurement uncertainties are fully considered. The molecular-"lter-based techniques to be discussed here are no exception. However, these techniques have some unique characteristics which make them particularly appropriate for some applications. 1.5. General description of planar Doppler velocimetry Molecular/atomic "lter techniques o!er the potential of making quantitative and multi-component two-dimensional velocity measurements. Furthermore, they appear well suited to applications in large-scale facilities. As such, considerable interest in these techniques has been generated during the past several years.

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803

Fig. 1. Vector relationships of incident and scattered light and the measured velocity component.

The basis of these techniques lies in measuring the Doppler shift of laser light scattered o! of moving particles. These particles may either be molecules in the #ow, or seed particles (such as smoke, fog, aluminum oxide, condensation, etc.) which occur naturally or are introduced into the #ow. When the laser light is scattered by a moving particle, the frequency of the light is shifted according to the Doppler shift equation: 1 *f " (k !k ) ) V D j 4 0

(1)

where k and k are the observation and incident unit 4 0 light-wave vectors, respectively, V is the #ow velocity vector, and j is the wavelength of the incident light. As illustrated in Fig. 1, the direction of velocity sensitivity of Eq. (1) is de"ned by the bisector of the directions de"ned by k and negative k . It is the presence of this Doppler s 0 shift that allows the molecular-"lter-based diagnostic techniques described below to measure velocity. The Doppler shift of light is well known and has been used by astronomers for years to determine the velocity of stars based on the shift in emission spectra. Indeed, in #ow applications, where a #uorescent species is present and excited, a similar technique may be applied [5,6]. What is novel in this new class of diagnostic techniques, however, is that they do not depend on a #uorescent species being present in the #ow: instead they operate with light scattered by particles in the #ow with the absorption species located in the detection system. Over the last "fteen years many di!erent acronyms have been given to essentially similar molecular-"lterbased techniques. These include PDV [7] Doppler Global Velocimetry (DGV [8,9]), Filtered Planar Velocimetry [10,11], Absorption Filter-Planar Doppler Velocimetry [12], and Filtered Rayleigh Scattering (FRS) Velocimetry [13]. Although each research group has their preference and each acronym represents di!erent characteristics of the technique, PDV seems to be gaining wider acceptance in the literature [4]. Before describing the technique in detail, a general description is given here. PDV uses a narrow-linewidth

Fig. 2. Planar Doppler Velocimetry (PDV) general optical arrangement.

laser to illuminate a plane in the #ow "eld as illustrated in Fig. 2. As illustrated, the laser sheet is imaged by one camera which views the illuminated plane through a molecular "lter, termed the signal camera (or signal image), and a second camera which views the plane without a "lter, termed the reference camera (or reference image). The molecular "lter is simply an optical cell (glass cylinder with windows on each end) containing a molecule having an absorption line in the frequency tuning range of the illuminating laser. This results in a "lter that has a transmission pro"le with "nite sloping edges as shown in Fig. 3a. The term I /I is the spectral transmission of l 0l the molecular "lter, with I de"ned as the spectral intenl sity (intensity at frequency l) after the cell, and I de0l "ned as the spectral intensity before entering the cell. The #ow "eld contains small particles which are seeded into the #ow or occur naturally (such as condensation) and scatter the illuminating light from the laser sheet. The spectral intensity of the light which passes through the molecular "lter is the convolution of the scattered spectral intensity from the particles illuminated in the #ow "eld, and the absorption pro"le of the molecule present within the cell (as illustrated in Fig. 3b). As an example, consider a case where the laser frequency, f , is tuned to 0 the midpoint of the transmission pro"le. The scattered light experiences a change in frequency, due to the Doppler shift (Eq. (1)), causing the transmission from the scattered light to either increase or decrease depending on whether the frequency increases or decreases. Note, also, that there is no ambiguity in the direction of the shift: positive and negative frequency shifts are distinguished by the increase or decrease in transmission respectively. The pixels of the signal camera CCD array, record the integrated spectral intensity which is

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camera records I , which is the integrated spectral inten0 sity of the un"ltered light (i.e. I ":I dl). 0 0l The integrated transmission through the cell (TR) is obtained by dividing the intensities of the signal (I) and reference (I ) cameras at corresponding pixels. Fig. 3c 0 shows a plot of the integrated transmission as the independent variable and the frequency shift (or frequency function, f determined from the given "lter) as the dependent variable with points taken from Fig. 3b highlighted. In an experiment, once the integrated transmission (TR) is determined from the two cameras at each corresponding pixel, the Doppler shift can be found at each pixel using the frequency function of the "lter used (Fig. 3c). The velocity is then calculated at each pixel of the image using this measured Doppler shift and Eq. (1). As may be noted in Eq. (1), the measured Doppler shift is dependent on the angle between the illumination and observation directions, respectively. This fact may be exploited in order to make multi-component velocity measurements * either by viewing the #ow "eld from more than one direction (changing the observed unit light-wave vector k ), or by illuminating the #ow "eld 4 from multiple directions (changing the incident light wave vector, k ). Both approaches have been used by 0 researchers in order to make multi-component measurements. Before continuing with a detailed discussion of this technique, a brief review of the history of the planar, molecular-"lter techniques will be presented. Following this, a review of particle scattering and absorption processes will be given. A summary of the typical aspects of measuring and processing data using these techniques will then be given, followed by examples from several researchers showing applications of these techniques in a variety of #ows. A brief discussion of important error sources and emerging trends in these techniques is given at the end of this review. 1.6. History of the introduction of molecular xlters to experimental yuid dynamics Fig. 3. Schematic of intensity spectra of PDV process showing the (a) transmission pro"le of the atomic/molecular "lter, (b) laser and Doppler shifted signals with transmission pro"le, and (c) frequency function.

transmitted through the molecular "lters absorption pro"le and is given by I (i.e. I":I dl with the limits on the l integration dependent on the spectral sensitivity of the camera and optics). The second reference camera (or a separate portion of the same camera) is used to collect images of the #ow "eld without the molecular "lter. The reference camera is used to account for intensity #uctuations due to laser energy (and/or sheet energy distribution) or seed-concentration variations. The reference

It is interesting to begin our discussion of molecular"lter-based velocimetry techniques with a brief history of how these techniques were initially developed. Two groups independently introduced the use of molecular "lters to #ow diagnostics at approximately the same time, and each received patents on the techniques. One group, headed by Hiroshi Komine, was organized at Northrop [14]. This group was primarily composed of experts in spectroscopy. They were asked to develop a method for their company to measure the air velocity in wind tunnels and #ight tests. With an expertise in spectroscopy and unincumbered with the requirement of using existing aerodynamic measurement technologies, they proposed that the transmission through a molecular "lter could be used to measure the Doppler shift of light

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scattered from particles seeded into the #ow "eld. Their initial approach used an iodine "lter with both an argonion laser operated in single-frequency mode with a etalon, and an injection-seeded Nd : YAG laser [8,15]. The transmission was recorded by analog division of two camera signals, aligned pixel-by-pixel and viewing the same #ow region * one camera imaging the #ow directly, and the other imaging the #ow through the iodine "lter cell. This program was later supported through NASA Langley. NASA researchers collaborated on the research extending prototypes to three-component systems and utilizing digital algorithms to align and calibrate the "ltered and reference cameras [9]. It should be noted that even though systematic problem existed in initial tests, many of the processing algorithms and basic setups seen today were derived from the methodologies and demonstrations of Komine and Meyers. The other group responsible for the early developments of molecular-"lter-based techniques was headed by Richard Miles at Princeton University [16]. This research group originally concentrated on the application of molecular "lters to improve #ow visualizations in cases where the signal is low and in the Rayleigh Scattering regime. They also initiated a research program to measure simultaneous average thermodynamic properties in a two-dimensional plane (which will be discussed in detail shortly). According to Miles and associates, the initial idea of using molecular "lters in these applications formed out of discussions on the use of Planar Laser Induced Fluorescence (PLIF) to measure thermodynamic quantities. As discussed previously, the di$culty with these techniques is that the #uorescent species either must be naturally present or seeded into the #ow "eld. Unfortunately many of the species used in these measurements are toxic, corrosive, or reactive with the #ow "eld itself. Because of this, Miles and colleagues considered the idea that it may be possible to take the #uorescence species out of the #ow and use its absorption properties to modify the scattered light collected by the receiving optics. This was "rst attempted using an available injection seeded Nd : YAG laser and a molecular iodine "lter [13]. Fig. 4 illustrates the potential a!orded by FRS to reduce the surface scattering in a #ow visualization of a Mach 8 boundary layer [17]. The signal is from CO 2 clusters which naturally form when CO is seeded into 2 the hypersonic #ow (the intensity in this image is inverted so the free stream is dark). To optimize this technique, an absorption "lter with a sharp sloping edge is utilized and the laser is tuned to the center of the absorption well. Light scattering from the CO particles experiences 2 a Doppler shift out of the absorption well, while the unshifted background light and re#ections are absorbed by the "lter. This allows the boundary layer to be visualized without being overwhelmed by strong surface scattering. Since the "rst use of FRS for #ow visualizations,

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Fig. 4. Flow visualization of a Mach 8 boundary layer taken using FRS. Flow is from left to right [17].

several other #ow "elds have been studied, including supersonic shear layers [18], compressible boundary layer through an expansion [19], and shock boundary layer interactions [20]. Later, Forkey et al. [21] concentrated on quantitative measurements of #ow properties. Although the research groups under the direction of Komine and Miles brought the use of molecular "lters to the application of wind tunnel #ow diagnostics, they were preceded by an earlier application of molecular "lters in Light Detection and Ranging (LIDAR) applications. In the early 1980s, Shimizu et al. proposed the combination of molecular/atomic "lters and lasers to create the High Spectral Resolution LIDAR (HSRL), an instrument used to remotely sense atmospheric properties based upon scattered laser light [22,23]. Light in the atmosphere is scattered by both the gas molecules that constitute the atmosphere and by particles (eg. Dust, water droplets, etc.). Because the thermodynamic information about the atmosphere is contained in the molecular scattering, not the particle scattering, it is crucially important to be able to spectroscopically separate these two scattering sources. The line-shape of the scattering from the particles is nearly the same as that of the incident light, and at typical atmospheric conditions, frequency shifts of no more than 100 MHz arise due to air currents. Scattered light from the gas molecules, on the other hand, exhibits thermal broadening on the order of 2 GHz. The innovation of Shimizu et al. [22] was to suggest the use of a molecular "lter to spectroscopically separate light scattered from gases from that of aerosols. The outgoing laser light was tuned to the frequency of an absorption line of the "lter * the narrow line-width scattering from the aerosols was therefore blocked, while the broadened light from the molecular scattering was passed. The signal from the gases could then be used to determine such atmospheric properties as temperature and pressure.

2. Basic science and technologies behind PDV Before continuing with descriptions of common molecular "lter based diagnostic systems, a brief review of

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the particle scattering and absorption processes on which these processes depend is in order. This overview is by no means complete, but rather serves to point out several critical aspects of these processes so that the basis of these techniques may be better understood. 2.1. Scattering from particles and molecules All of the molecular "lter techniques which will be discussed depend on imaging light which has been scattered by either seed particles or molecules in the #ow. This scattering arises when an incident light ray encounters a perturbation due to a small particle or molecule. When this happens, a portion of the energy reradiates in all directions centered at the particle. Fig. 5 illustrates the two types of scattering common in current molecular "lter diagnostic techniques * particle Rayleigh/Mie scattering and molecular Rayleigh scattering. It is common, as in our discussions, to separate Mie scattering and Rayleigh scattering by the relative diameter of the particle (although Mie scattering theory is fully capable of describing the scattering in the Rayleigh regime). Mie scattering is generally de"ned as scattering from particles which are greater than 1/10 of the incident light wavelength (j) and Rayleigh scattering is de"ned as scattering from particles with diameters less than 1/10 j [24]. Particle scattering can be in either the Mie or Rayleigh regime, depending on the size of the particles. In the Mie regime, the scattering will have a dominant forward direction, and nonuniform `lobeda scattering towards the sides, typical of Fig. 5a. These scattering distributions will depend upon the particle size, incident light wavelength, and polarization. It should be noted that if the light is linearly polarized, the Mie scattering pattern

tends to go nearly to zero (due to depolarization) in the direction normal to the incident light polarization direction. If the particle scattering is in the Rayleigh regime, it will exhibit the toroidal shaped scattering pattern when the light polarization direction oriented through the center as shown in Fig. 5b. Not only will the importance of the scattered intensity become apparent in the use of molecular "ltered diagnostics, but the relevance of the polarization and spectral content of the scattered light will also be demonstrated. For particle scattering, two spectral characteristics are important in the following discussion as illustrated in Fig. 6. First, the scattering from particles is generally not broadened due to thermal motions, therefore it has approximately the same line width as the illuminating laser light (Fig. 6a). Secondly, the particle Mie/Rayleigh scattering will exhibit a Doppler shift in frequency which is given by Eq. (1). The second class of scattered light which is used in molecular "lter based diagnostics is molecular Rayleigh scattering. Light scattered from molecules falls into this regime and exhibits the toroidal scattering pattern of Fig. 5b if the incident light is linearly polarized. For Rayleigh scattering, the intensity of the scattered light varies as the sixth power of the equivalent particle diameter and as the inverse of the incident wavelength to the fourth power [24]. The strong dependence on wavelength results in a signi"cant improvement in scattered signal levels when shorter wavelengths are used. Unlike scattering from particles, the scattering from molecules will be a!ected by the thermal motions of the #uid. Therefore, the spectral pro"le of the molecular/scattered light is changed from the incident light spectra as illustrated in Fig. 6b. The scattered intensity is

Fig. 5. Scattered intensity contours for scattering from particles larger than the wavelength of light in the Mie Scattering regime (a) and particles smaller than the wavelength of light in the Rayleigh regime (b).

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807

where P is the pressure and l is the viscosity. Writing the y parameter for air with dimensional units Eq. (3) becomes y"0.2308

T[K]#110.4 P[atm]j[nm] ) . ¹2[K] sin(h/2)

(4)

It is recognized that for y of order unity or greater (the kinetic regime), Brillouin components become important and kinetic models must be used. For y@1 (low pressures or high temperatures) the scattering spectrum is Gaussian and the Brillouin components can be neglected [29]. As y is increased (typical of air at atmospheric conditions), Brillouin lobes become more apparent in the Rayleigh scattering frequency pro"le. The importance of these characteristics of Rayleigh scattering will become apparent when future trends of molecular "lter based diagnostics are discussed below. 2.2. The absorption processes

Fig. 6. Schematic of scattered intensity spectrum from (a) particles and (b) molecules. Note the pro"les are not to scale.

proportional to the density. The Rayleigh scattering frequency line-width (FWHM) is a function of the temperature (due to thermal induced molecular motions) and is given by [25]: 2sin(h/2) f " 8 j

S

8k¹ ln(2) M

(2)

where j is the wavelength of the incident light, h is the angle between the incident and scattered wave vectors, k is the Boltzmann constant, ¹ is the temperature of the gas, and M is the molecular mass. The shape of the scattered spectrum (as illustrated in Fig. 6b) is governed by the y-parameter which is also a function of the density and governs the onset of Brillouin scattering e!ects. Since many #ow"elds studied are at or above atmospheric pressure, Brillouin scattering e!ects should be considered. Several di!erent models exist for calculating the Rayleigh/Brillouin scattering spectral pro"le (for example see Refs. [26,27]), and these have been con"rmed by experimental measurements [28]. The y parameter, which is the ratio of the collisional frequency to the acoustic spatial frequency is given by jP y" 4l sin(h/2)

S

M 2k¹

(3)

A brief review of absorption processes is also presented here, preliminary to the discussion of the basics of molecular "lter based diagnostics. This concept can be introduced by considering a cylindrical glass cell "lled with a molecular/atomic species. This molecule may have multiple absorption lines within the frequency tuning range of a narrow-linewidth laser. For example (and due to their relevance to the discussion which follows) the absorption lines of iodine are given in Fig. 7 which are a result of overlapping vibration-rotation transitions in the resonant B(0`u3%)QX(0#g1R) electronic band [7,30]. The transition frequencies and intensities are reported by Gerstenkorn and Luc [31]. As calculated by the model of Forkey [32], a portion of this spectra is accessible by an argon ion-laser (Fig. 7a) or a Nd : YAG laser (Fig. 7b). Within the tuning range of these lasers are some optical frequencies at which the molecular species will absorb the laser light to varying degrees. For example Fig. 7c gives the absorption lines of iodine measured by tuning a Nd : YAG laser through a 10 cm long optical cell with iodine at a partial pressure of 1.03 torr and a cell body temperature of 373 K. As can be seen, the absorption lines are not discrete, but have a varying line pro"le. The absorption pro"le or spectral transmission (I /I ) of each line is related to the path l 0l length through Beer's law I /I "ekl L l 0l

(5)

where, as de"ned previously, I is the spectral intensity 0l of the incoming light, I is the spectral intensity of the l transmitted light, ¸ is the length of the cell, and k is the l spectral absorption which is given by k "K >(l) l ji

(6)

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Fig. 7. Absorption lines of I in the visible wavelengths (a) 2 frequency region accessible by argon-ion, (b) Nd : YAG laser as calculated by the model of Forkey (1996) and (c) the experimentally measured spectra using a Nd : YAG laser [42].

where K is the linestrength of the individual transition ji (electronic, vibrational, rotational) and >(l) is the line pro"le which is determined by the manner in which the line is broadened. For the molecular "lter based

diagnostics, there are three broadening processes which should be considered [33,34]: 1. Natural broadening, due to the "nite lifetime of the excited energy state results in a Lorentz pro"le. 2. Temperature (Doppler) broadening, due to random thermal motion of the molecules as they absorb the incident light (resulting in a Gaussian line shape). 3. Pressure (collisional) broadening, due to collisions with foreign non-absorbing gases (Lorentz broadening), molecules of the same kind (Holtsmark broadening) or electrons and ions (Stark broadening). Pressure broadening also results in a Lorentz line pro"le. In general all three of these processes may be present, resulting in a Voigt pro"le (the convolution of the Lorentzian and Gaussian pro"les) when they are combined. Furthermore, what may appear as a single absorption line is actually multiple individual hyper"ne lines broadened together. The transmission characteristics of a molecular-"lter cell may be varied by a careful choice of cell length, operating temperature and pressure, and by the introduction of a second, nonabsorbing, gas species. Fig. 8 shows an individual transmission pro"le taken by passing a beam from an injection seeded Nd : YAG laser through a 22 cm long optical cell "lled with iodine and operated at various thermodynamic conditions. The absorption line center is located at 18789.28 cm~1. Fig. 8a shows the e!ect of varying the number density. The number density, or partial pressure of the iodine is changed by accurately regulating the temperature at the coldest point in the cell, termed the side-arm temperature and identi"ed in Fig. 8 as T . Iodine will condense in the I2 side arm and, in a properly regulated cell, will not condense in the cell body which is maintained at a higher temperature. As the number density increases, the cell goes from an optically thin operation, in which it passes considerable light even at the minimum transmission frequency, to optically thick operation, in which rejection of several orders of magnitude may be achieved at minimum transmission. It is clear that the optically thick line results in the maximum transmission curve slope * a desirable feature in some applications such as reducing the background light in #ow visualizations as mentioned previously. Also, it should be noted that if the transition is not saturated, the absorption pro"le will not change with incident intensity. For iodine absorption in the 500}600 nm range, an additional nonresonant continuum absorption [due primarily to a di!use 1u(1%)QX band and A(1u3%)QX band] causes the uniform background absorption to increase as the number density of the iodine is increased [7]. Due to the strong variation in the absorption pro"le as the side arm temperature changes (or iodine partial pressure changes), this temperature must be carefully regulated. Fig. 8b shows the e!ect of temperature of the iodine in the vapor phase on the pro"le. This results in an increase of

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809

pro"le and stretch the transmission curve over a wider frequency range which may be desirable for some applications where a large velocity range is expected in a #ow. Forkey developed a widely used theoretical absorption model showing the same e!ects as those measured experimentally and shown above for iodine in the tuning range of Nd : YAG and argon-ion lasers [21,35]. The theoretical model accounts for varying cell length, sidearm temperature, and iodine gas temperature (also referred to as the cell body temperature). The theoretical model used by Forkey was based on spectroscopic constants published by Gerstenkorn and Luc [31,36], Tellinghuisen [37,38], and Luc [39]. This model was later modi"ed by adding the nonresonant continuum bands, discussed previously, and "nite laser bandwidth e!ects [7]. The stability of the transmission pro"le is critical in making accurate measurements using PDV. Several laser systems and molecular or atomic "lters may be used for these measurements. Table 1 gives examples of possible combinations. Aside from choosing a molecule or atom with absorption lines accessible by current lasers, the choice of absorbing molecule in the cell is determined by some additional considerations as discussed by Miles et al. [40]: 1. Molecular weight and temperature: For many molecular "lter based diagnostic techniques, including PDV, one would prefer to have the maximum slope possible of the absorption line. Obviously as the slope is increased the maximum sensitivity to frequency is realized. This slope may be reduced, if necessary, by pressure broadening or operating the cell in the optically thin regime. The absorption slope can be shown to be inversely proportional to the thermal linewidth as the light passes through the cell [40]. This linewidth is given by 1 d" j

Fig. 8. E!ects of cell conditions on "lter performance. Nominal conditions are 373 K body temperature; 313 K side-arm temperature, and no bu!er gas. Varied conditions are (a) partial pressure of iodine; (b) temperature of "lter body; (c) partial pressure of nitrogen.

Doppler broadening although as seen here over the operating range of the cell this change is barely perceivable. Fig. 8c shows the e!ect of introducing a small amount of a nonabsorbing species (nitrogen) into the cell and the resulting e!ect on the absorption pro"le. In this case, the pressure broadening (Lorentz pro"le) begins to dominate, resulting in more gradual slopes of the pro"le. This makes it possible to reduce the slope of the absorption

S

2k¹ . M

(7)

Table 1 Possible laser and absorbing atom/molecule combinations Laser

Atom/Molecule

Wavelength (nm)

Reference

Ti : Sapphire Ti : Sapphire Diode Dye Alexandrite Doubled Alexandrite Doubled Dye Nd : YAG Argon-ion

Hg K Cs Ba Rb Cs

253.7 769.9 852.0 553.7 780.0 388.9

[51] [53] [54] [22] [22] [22]

Pb I 2 I 2

283.3 532.2 514.5

[22]

810

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Therefore, it would be preferable to use a gas with a high molecular weight and operate the cell at a low temperature. In order to have a su$cient number of absorbers (i.e. high gas density), it would be preferable to use a molecule with a high vapor pressure, again at low temperatures. The number density should be kept low enough to avoid excessive pressure broadening which decreases the slope of the absorption pro"le (see Fig. 8c). 2. Isolation of the absorption lines: The absorption lines should be separated by regions with relatively constant absorption. These `plateausa in the absorption pro"les are very useful in calibration processes for #at "eld corrections and on-line system checks. Furthermore, they help reduce the possibility that a user may inadvertently collect light on one transmission pro"le while thinking they are tuned to an adjacent line. 3. Strength of the absorption lines: In order to access the full dynamic range of the camera, an absorption line should provide the greatest possible di!erence between minimum and maximum transmission. 4. Wavelength of absorption lines: Although the Doppler-shift equation applies for any wavelength of light, certain applications may be better suited to visible, infrared, or ultra violet (UV) wavelengths. The reasons for selecting molecules with absorption lines in the visible wavelengths is that current detectors, lenses, and wind tunnel windows generally are intended for this regime. Also, the visible wavelengths are inherently safer since the beams and scattering can be seen, reducing the possibility of accidental injury. Infrared (IR) absorption lines have a major advantage in that they are accessible by inexpensive, narrow-linewidth laser diodes. Ultra violet wavelengths o!er an advantage in signal intensity when the scattering is in the Rayleigh regime. These advantages may be o!set, however, by: (1) the need to use quartz or fused silica optics (particularly the camera lenses) and windows, (2) lower UV energy in current lasers, and (3) lower quantum e$ciency of UV-sensitive cameras. Using the above criteria, iodine has been the most common choice for use in molecular "lter based diagnostic techniques. It has a molecular weight of 254 and a high vapor pressure at moderate temperatures. Additionally, it is accessible by two di!erent narrow linewidth lasers: CW argon-ion lasers operated with an etalon (514.5 nm), and pulsed frequency-doubled injectionseeded Nd : YAG lasers (532 nm). Both of these lasers are relatively mature systems and are available from several manufacturers.

3. PDV systems and processing While simple in concept, the PDV technique can be di$cult to implement. It is notable that this technique

depends both on intensity measurements and frequency measurements. Furthermore, these measurements are made simultaneously by multiple electro-optic components, and they depend on the stable operation of a laser source, often in a harsh environment. In order to provide quantitative velocity measurements, care must be taken to ensure the stable operation of cameras, iodine cells, photodiodes and lasers, as well as the stable placement of all optical elements. Furthermore, in processing the data, attention must be paid to all corrections applied, including corrections for perspective distortions, background light, image normalization, etc. Several examples of data sets corrupted by a single problem, noise source or uncertainty can be found in the literature. Indeed, many contributions to the state-of-the-art have been made by researchers who identi"ed an error source or problem by careful analysis of data-collection and processing procedures. 3.1. PDV components Most groups currently conducting research in PDV have unique aspects of their system hardware, data collection process, and post-processing procedures. Furthermore, since PDV is still a relatively new technique, these di!erences are still evolving and typically change from one application to the next. In the discussion which follows, a typical system and processing procedure will be discussed. Some notable exceptions to these components are mentioned, but the noted exceptions are by no means exhaustive. The outline for the system and processing described here relied extensively on the work of Mosedale [41,42] and Beutner [43,44]. A schematic of a typical PDV system is shown in Fig. 9. This system is made up of a laser and light-sheetforming optics, a frequency-monitoring system, cameras and receiving optics. This schematic shows a system for measuring a single velocity component. Before describing these three sub-systems, a discussion of the critical aspects of absorption-cell design is given. 3.1.1. Absorption cell design considerations A variety of iodine cell designs have been used by researchers developing PDV systems [10,21,45]. In choosing a cell design, some consideration must be given to both the ease and cost of manufacture, as well as the stability and versatility of the cell in applications. The simplest cells are typically composed of a glass barrel with optical windows on each end, and a side-arm protruding from the side of the barrel [21]. Control of the cold "nger temperature determines the number density of the iodine in the cell. The barrel temperature is generally independently controlled, and controls the temperature of the iodine vapor. The barrel temperature must be su$ciently high to prevent condensation on the optical windows, which are typically the next coldest point on

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811

Fig. 9. Planar Doppler Velocimetry experimental arrangement.

the barrel aside from the side-arm. As previously illustrated in Fig. 8, the cell transmission is very sensitive to the side-arm temperature (controlling the number density), but much less so to the barrel temperature (controlling the amount of temperature broadening). While such cells are relatively easy to construct, the requirement of precise temperature control on the side-arm can be problematic, particularly if the system is to be used in a wide variety of operating environments. Fig. 10 gives a schematic of a versatile iodine cell design [10,42]. This cell has some additional features which help stabilize the transmission pro"le and allow for pressure broadening the pro"le as well. Again, this cell is basically a glass cylinder with optical quality windows on both ends. A small side-arm and a cold-tip extends from the cylindrical body, as seen in Fig. 10. Iodine crystals are placed in the cell, and the cell is then attached to a vacuum pump and evacuated. The cylindrical portion of the cell can be wrapped with heating tape and insulation, or with copper cladding and strip heaters, and maintained at an elevated temperature * typically 340}380 K. This temperature is usually maintained via a closed-loop temperature controller. As can be seen in Fig. 8b, the temperature of the cell body is not critical provided the iodine does not collect on the windows, but should still be controlled as well as possible. The side-arm, which is connected to the body of the

Fig. 10. Schematic of iodine cell.

cell, is maintained at a lower temperature, typically 310}325 K. Since the cell operation is particularly sensitive to the side arm temperature, this temperature is usually maintained by a precision system, such as

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a constant temperature waterbath. The coldest point in the cell regulates the partial pressure of iodine (number density) in the cell and is given by [46] 2867.028 LOG (P [Torr])"9.75715! (8) 10 I2 254.180#¹ [3C] I2 After solid}vapor equilibrium is established in the side arm, a valve is closed shutting o! the side arm from the body of the cell. At this point, no iodine crystals are present in the cell barrel and therefore, the number density of the iodine vapor in the barrel of the cell is "xed. Such a "lter is termed a starved cell because all of the iodine is in a gaseous state in the cell body. Some experimenters have used simpler cell designs that do not allow the side arm to be closed o!. These cells are called saturated cells and require continuous temperature control of the side arm by means of a waterbath or some other device in order to maintain a constant number density in the cell, and therefore a stable transmission pro"le. In practice, saturated cells are easier to construct, and avoid the possibility of leaks through valves. However, saturated cells are more susceptible to variations in environmental conditions. The diameter of the cell is governed by the collection angle of the camera lens so that the cell does not aperture the collected light, causing image distortion or vignetting on the image boundaries. The diameter should be small enough, however, to avoid a cold spot at the center of the window which would be su$cient for the iodine crystals to start forming, thus changing the number density of the gas-phase iodine. The length of the cell should be long enough to minimize any density gradients which may exist along the optical path through the cell. A typical cell may be on order of 7.5 cm in diameter and 10}20 cm in length, although there are no standard cell dimensions. McKenzie [7] has studied iodine "lters with the goal of optimizing their performance. He developed criteria for the design of a "lter without a bu!er gas. His concerns were dynamic range (the di!erence between maximum and minimum transmission of the "lter) and sensitivity (the slope of the "lter, expressed as change in transmission per change in wave number and having units of 1/cm). These quantities are important because they determine the range of velocities over which measurements can be made and the extent to which errors in the transmission are propagated into errors in frequency and hence velocity. McKenzie showed that for a given "lter length and body temperature, a judicious choice of spectral feature and side arm temperature must be made to yield high sensitivity with adequate dynamic range. In general, the limit on the dynamic range becomes more severe with an increase in the sidearm temperature because this increases the iodine number density, which in turn increases the continuum (non-resonant) absorption

and lowers the maximum transmission. Thus, a sidearm temperature su$cient to provide high sensitivity without degrading the dynamic range of the "lter is desired. Elliott et al. [10,11] investigated the e!ects of introducing nitrogen as a bu!er gas in iodine cells. This is generally done to extend the range of measurable frequencies and velocities which are possible. The "lter can therefore be tailored to measure a greater range of velocities. This ability to pressure broaden the "lter is particularly attractive in high-speed #ows and was utilized in several supersonic studies [10,11,47}50]. In general, the nonabsorbing gas introduced is nitrogen (&20 Torr). The nitrogen is added after forcing essentially all of the iodine into the solid state by submerging the cold tip in a dryice acetone bath. When the nitrogen is added, the pressure measured using a vacuum gage is almost entirely due to the nitrogen, since the iodine vapor pressure is very low. Once the desired pressure of the nitrogen is set, the cold tip can once again be heated and wrapped in heat tape. After equilibrium is established, the side arm is shut o! from the "lter body, creating a pressurebroadened starved cell. Whether the absorption cell is used in the frequencymonitoring system or camera system, one should check if the absorption transition used is saturated. Saturation is a local phenomena occurring at the molecular level when the transition is populated to the point that stimulated emission competes with absorption. This results in a condition where the transmission is a function of intensity (in addition to frequency), leading to inaccuracies in calculating the velocity. One method of checking for saturation is to record detector signals with a neutral density "lter inserted in the beam path "rst before the iodine "lter (S ) and then after the iodine "lter (S ) when the " ! laser is tuned to the 50% transmission frequency. If S is " greater than S (rather than equal to S ) the absorption ! ! line is saturated (due to stimulated emission) and the irradiance (W/cm2) of the beam introduced into the cell should be reduced. If S and S are the same then the " ! absorption "lter is not saturated. Beam irradiance may be reduced by expanding the beam going into the cell, or placing neutral density "lters in front of the cell. Problems with saturation are generally encountered in "lter calibration systems and monitoring systems when a collimated beam is directed into the cell. 3.1.2. Laser and sheet forming optics Several considerations govern the choice of the laser system to use in PDV. Among these are: 1. frequency overlap with absorption lines of the molecular "lter, 2. a narrow linewidth, 3. frequency tunability, 4. integration with other system components, 5. desired temporal resolution of data.

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

Two laser systems have been widely used with PDV systems which utilize iodine in the molecular "lter. These systems are the argon-ion laser and the frequency-doubled Nd : YAG laser. Other laser systems have been used in limited cases for measurements at near infrared (IR) and UV wavelengths [51}55]. Because the majority of the work in PDV has been performed with argon-ion and Nd : YAG lasers, only the relative merits of these systems will be discussed here. Argon-ion lasers are widely available, having been popular for use in LDV systems and may be an economical choice for use with PDV systems. When used in PDV, the 514.5 nm line from the argon-ion laser is used. The argon-ion laser simpli"es the requirements for synchronization with cameras and photodiodes, since it operates in continuous wave mode. Since PDV uses a laser sheet, instead of a focused beam, and since this sheet is typically viewed in a side-scattering direction for which scattering intensity may be low (see Fig. 5), consideration must be given to the power requirements for the laser. When operated in single frequency mode with an etalon, argon-ion lasers produce only about 20}25% of the rated power for the laser. The laser frequency may then be changed by discrete intervals } the mode hop frequency } by either heating or tilting the etalon to change its thickness in the laser cavity. This mode hop frequency is determined by the thickness of the etalon and the length of the laser cavity. Typical mode hop values range from 70 to 130 MHZ. This may be troublesome if the transmission pro"le of the iodine cell is to be determined by tuning the laser through the absorption line, since only rather large discrete changes in the frequency may be achieved, and then only by mechanical manipulation of the etalon. In practice, this may allow only several points to be measured experimentally in the transmission pro"le, and would therefore require that some sort of curve"tting algorithm be used to approximate the remainder of the transmission pro"le. Curve "tting algorithms used by PDV researchers have been based on either the theoretical iodine absorption pro"le, or on appropriately shaped analytic functions [21,56}59]. This problem may also be addressed by customized argon-ion laser systems which utilize feedback frequency monitoring and control (described below). Although cylindrical lenses may be used to form the light sheet with an argon-ion laser, the resulting light sheet will show the same Gaussian intensity distribution as the source beam. For this reason, many researchers have used a scanning mirror system to form a light sheet with argon-ion lasers. Provided the beam scan rate is su$ciently high, this system may result in a more uniform illumination of the #ow than a lens system. Since the argon-ion laser operates in continuous wave mode, the collected signal is obviously integrated over the exposure time of the camera. This makes instantaneous measurements more di$cult, since the signal

813

level drops directly with the exposure time. However, this does have the bene"t of reducing speckle in the resulting image, since the speckle pattern will change during typical exposures. When operated with an intercavity etalon, the argon-ion laser also has an inherently narrow linewidth of approximately 10 MHz. The other widely used laser system for PDV measurements is the Q-switched frequency-doubled, injectionseeded Nd : YAG laser. This laser typically produces pulses of approximately 10 ns in duration at an operating wavelength of approximately 532 nm. The light sheet must be formed using a combination of cylindrical and spherical lenses, since the pulse duration is too short to allow for any type of spatial scanning over the #ow "eld. The high power associated with the pulsed beam may require high-quality glass windows in the wind tunnel, whereas the argon-ion lasers may usually be directed through acrylic windows without damage. The Nd : YAG laser frequency is controlled by the injection seeder which is a continuous-wave laser. The seed laser provides a narrow linewidth (approximately 10 KHz) seed beam which is directed through the Nd : YAG oscillator and ampli"er cavities. Since the seed beam intensity is several orders of magnitude greater than spontaneous emission in the oscillator, its frequency is more readily ampli"ed by the Nd : YAG rod. The resulting emission has a reported linewidth of approximately 50 MHz in the IR (1064 nm). When this beam is doubled in frequency to 532 nm, the linewidth increases to approximately 100 MHz. The seed beam frequency and subsequent host laser frequency is adjusted by applying a bias voltage on the temperature control circuit of the injection seeder. Typical seeder systems allow the frequency to be changed by approximately 100 GHz. By adjusting the bias voltage, repeatable scans with frequency increments as small as 2 MHz may be made of the transmission pro"le. Generally there is a potentiometer on the seeder controlling the gain of the bias voltage. This should be adjusted so that the jitter in the bias voltage from a power supply does not a!ect the frequency stability of the laser. Recent experiments with an etalon installed in the oscillator cavity have shown that improved line center absorption can be obtained in molecular "lter based diagnostics by suppressing frequencies lying outside the iodine absorption line [60]. The short pulse duration of the Nd : YAG laser allows unsteady #ows to be interrogated without the inherent time-averaging of the argon-ion laser system. However, this feature also results in higher levels of noise in the data images due to laser speckle. It should be noted here that several investigators have reported a chirp, or spatial variation in frequency, for the Nd : YAG laser of up to 100 MHz [48,61,62]. One solution to this problem is to use only the center of the laser pro"le which has been reported to reduce the variation to less than 4 MHz [48]. Alternatively, this chirp could be

814

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

accounted for by calibration, assuming that it is steady from pulse to pulse. Other experimenters have reported relatively low levels of chirp [42,44]. Recently, it has been found that a major source of chirp may be related to misalignment of the seeder within the host laser platform and therefore may be laser speci"c [41]. 3.1.3. Frequency monitoring system Since the velocity measured using PDV is based on the frequency change due to the Doppler shift of the scattered light, the laser operating frequency must be known. Both argon-ion lasers and Nd : YAG lasers have a longterm frequency drift, which may vary greatly depending on the laser system or operating environment. In addition to long term drifts, a Nd : YAG laser has a pulse to pulse frequency #uctuation on the order of 20 MHZ due to the cavity mirror dither used to maintain the frequency overlap with the seed laser. An argon-ion laser may experience undesired mode hops in frequency. Typical wind tunnel operating environments may involve daily temperature #uctuations of up to 20 K, high mechanical vibration and acoustic noise levels, and cooling water temperature and pressure #uctuations. All these e!ects aggravate attempts at laser frequency stabilization, and therefore many researchers have used systems to continuously monitor the laser operating frequency. The most common method of monitoring the laser frequency is to use an additional molecular "lter which is stabilized and isolated from the environment as much as possible. Since the absorption line and its pro"le can only be modi"ed by changing the cell's thermodynamic conditions (which is addressed in the starved-cell design) or the presence of a strong magnetic "eld, the absorption "lter provides an excellent frequency reference. Ideally, this "lter is calibrated simultaneously with the "lter which is used in front of the camera, yielding separate transmission pro"les tied together by the same frequency scan. Some of these reference "lter based systems are only used for monitoring the long-term drift of the laser while others are capable of recording the instantaneous laser frequency with each image [8,43}45,50,62}67]. A description of a typical reference "lter frequency monitoring system used by Mosedale et al. [42] and Beutner et al. [43,44] is described here and illustrated in Fig. 9. During data collection, a portion of the laser beam is directed to the frequency monitoring system. The frequency monitoring system divides this beam, sending a portion through the iodine cell. The two beam paths are directed to separate photodiodes, and the ratio of the signals from these photodiodes gives the transmission of the "lter, and thus the frequency of the laser beam. Additional features in this system may include lenses to expand the beam before it passes through the iodine cell, and optical di!users in front of the photodiodes. The beam expander reduces the possibility of saturating the iodine transition, and the optical di!user reduces the

sensitivity of the system to slight beam wandering e!ects. For pulsed systems, a direct measurement of the photodiode readings may be a!ected by the linearity of the photodiodes and background signal. A common means of addressing this is to use integrating circuits which are gated to a period slightly greater than the pulse signal. The reference system frequency must be recorded with each image in order to correct for frequency #uctuations during the test. This system, when used with additional beam paths and photodiodes, may also be used to calibrate multiple iodine cells simultaneously. This allows the transmission pro"le for each of the iodine cells used in front of a camera, and the iodine cell used in the frequency reference system to be measured and tied together by the same laser frequency scan. As an example of the need for a frequency monitoring system, Fig. 11 shows a plot of pulse-to-pulse variations measured by a frequency monitoring system for a frequency-doubled, injection seeded Nd : YAG laser. This laser was operated in the vicinity of the Subsonic Aerodynamics Research Laboratory (SARL) wind tunnel at Wright-Patterson Air Force Base. The SARL facility was expected to have turbulent #uctuations of less than 0.1%, resulting in a Doppler shift #uctuation of less than 0.5 MHz. Pulse-to-pulse rms variations in the frequency measured by the laser monitoring reference system were approximately 41 MHZ for the 66 pulses shown. Also shown in this "gure is a plot of the frequency variations for scattered light in an empty tunnel run, as recorded by a PDV camera system. The di!erence, however, between the PDV frequency and the laser frequency remains relatively constant (equal to the Doppler shift induced by the uniform #ow). The standard deviation of the di!erence is less than 4 MHz, demonstrating the e!ectiveness of the frequency monitoring system in tracking laser frequency #uctuations. This is by no means the only method in which the laser frequency has been monitored or controlled. Some investigators have used o! the shelf etalons [10,12] and wavemeters [68] although the resolution can be limited. Using a Fabry-Perot etalon, McKenzie [7] developed a photodiode-based system for measuring velocity at a point rather than in a plane, in which a time delay provided by "ber optics permitted sequential collection of the frequency monitoring signals and the #ow measurement signals deriving from a single laser pulse. In a later work describing a CCD-based planar measurement system, McKenzie [69] included a reference tab in the "eld of view of the camera system. Fiber optics directed laser light from each pulse onto this stationary tab. Signals collected from this region of the camera images were then used to establish the unshifted laser frequency associated with each Doppler image. Investigators using argon-ion lasers typically can achieve greater stability than those who use Nd : YAG lasers. For example, Roehle and Schodl [66] have implemented

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

815

Fig. 11. Frequency for 66 laser pulses as measured by the frequency monitoring system and by the PDV camera system in a uniform Mach 0.2 #ow. Notice that the laser displays relatively large #uctuations (RMS"41 MHZ), but that the di!erence in frequencies between the two plots has a RMS variation of less than 4 MHz [42].

a feedback control system that yields a reported stability of better than 1 MHz for their argon-ion laser. A consensus appears to have developed among PDV researchers that frequency monitoring of the laser system is at least desirable, and in many applications essential (particularly in the subsonic regime) in order to make measurements with acceptable accuracy. While implementations of frequency-monitoring systems have varied, the most widely used systems currently use a separate beam path and separate iodine cell for the frequency monitoring function. While this adds some complexity to the data-collection system and requires an additional iodine cell and associated photoelectric devices, it adds versatility to the system, since no portion of the camera image is required for frequency monitoring. 3.1.4. Camera and receiving optics Typical camera and receiving optics for PDV are also illustrated in Fig. 9. Many notable variations exist on this setup, but some elements of the optical setup are common to virtually all researchers making PDV measurements. The receiving optics illustrated in Fig. 9 incorporate two features designed to reduce the system sensitivity to polarization e!ects. Polarization e!ects may contribute to random or bias errors in the measured signal. These e!ects occur due to the depolarizing e!ect of the scattering processes, and the spatial variation in

the relative intensity of parallel and perpendicular polarization of the scattered light. These e!ects lead to system sensitivities since most beam splitting devices split incoming light of di!erent polarizations with di!erent ratios. This e!ect has been addressed by researchers in at least three ways. First, systems have been demonstrated which use two cameras placed side-by-side, and no beam splitting optics. This eliminates the sensitivity to polarization, but may make the system even more susceptible to spatial variations of scattered light intensity depending on the particle size. To maintain nearly identical viewing angles, a beam splitter can be used in the receiving optics system. Nonpolarizing beam splitters o!er a means of reducing the sensitivity to polarization in the system. These beam splitters have reduced sensitivity to polarization, i.e. the re#ectance-to-transmission ratio for incoming light of di!erent polarizations is more constant. As a further means of reducing this sensitivity, a polarizing element may be placed in front of the beam splitting cube, thereby allowing only one polarization component to enter the receiving optics. Fig. 9 shows a typical arrangement for a polarizer and beam splitter used in combination. When collecting the scattered light from particles, one should always be aware of the polarization direction of the laser so that the intensity of the Mie scattering is optimized and the polarizer is oriented correctly. This arrangement provides for separate optical paths to two

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cameras, and allows for those paths to be matched in optical path length and viewing angle. Also, this arrangement ensures that the signal is divided consistently between the two cameras. As discussed previously, an iodine "lter is placed in the optical path leading to the signal camera, providing the frequency sensitivity of the signal image. A neutral density "lter is shown in the optical path for the reference camera. This is used to balance the signal intensity reaching the two cameras. The intensity imbalance exists, even for frequencies at which the transmission through the iodine cell is at a maximum, since broad-band absorption due to non-resonant continuum absorption of the iodine reduces the intensity of the light reaching the signal camera. Additional reductions in this intensity occur due to cell window re#ective losses. The arrangement results in a system that will allow the dynamic range of the two cameras to be matched so that the reference camera will not be saturated at lower scattered light levels than the signal camera. A band-pass "lter, corresponding to the laser wavelength used, is also shown placed in front of each camera. This "lter may be used to reduce the intensity of background light as much as possible. Fig. 9 shows a two-camera arrangement. In this con"guration, the signal camera views the #ow "eld through the iodine cell while the reference camera views the same region of the #ow without a "lter. Intensity variations due to seeding density and laser intensity are normalized by use of the reference camera image. Slight di!erences in the optical path and imaging lenses for the two cameras may be corrected by recording #at "eld images from the two cameras. There is no universal agreement on the issue of camera quality required for PDV measurements. Measurements have been made by researchers using a variety of di!erent cameras systems, ranging from 8-bit video cameras with interlaced 30 Hz framing rates, to 16 bit thermoelectrically cooled scienti"c-grade cameras. A primary advantage of lower-quality cameras is their associated lower cost. Some researchers have argued that the current level of uncertainties in PDV measurements do not warrant the greater accuracy in signal measurements achievable with scienti"c-grade cameras. Other considerations have led some researchers to conclude the use of scienti"c grade cameras is justi"ed. Not only do scienti"c grade cameras reduce the uncertainties associated with the signal intensity measurement, but they also typically o!er greater well depth and have greater dynamic range. These may be important considerations for some PDV applications since seeding intensity in many wind tunnels may vary dramatically in both space and time. These variations can simultaneously cause some regions of the CCD to be saturated while other regions will have signals too low to be useful. In these situations, a reduced camera dynamic range may lead to many images * and there-

fore many hours of wind tunnel run time * being discarded. In large wind tunnels, scienti"c-grade cameras may quickly pay for themselves in wind-tunnel run-time savings. The issue of camera quality is further quanti"ed in the uncertainty analysis section to follow. Instead of the two camera system illustrated in Fig. 9, single camera systems have been used by some researchers [7,12,48,69,70]. A typical arrangement for the receiving optics in a single camera system is shown in Fig. 12 as used by McKenzie [7]. This system uses three mirrors, combined with a nonpolarizing beam splitter, to provide two optical paths for a common image on the camera CCD array. The placement of the mirrors results in the reference and signal images appearing on opposite sides of the camera image. In later single camera arrangements, McKenzie [69] added a polarizing beam splitter

Fig. 12. Single camera split image arrangement for PDV measurements [7].

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

right before the camera. This was found to minimize errors in the normalized image and reduce background scattering (which is largely depolarized) while passing the particle scattering (which, like the incident laser light, is mostly linearly polarized) with no signi"cant loss. Obviously single-camera split image systems reduce the system cost; however, they have some draw-backs by reducing the resolution by a factor of 2, and imagesplitting invariably results in some image overlap [7]. Mosedale [41] quanti"ed this e!ect showing that at small f-numbers, the overlap can cover a signi"cant portion of the image. As McKenzie [7] has pointed out, this overlap is not a cause for concern. If the illuminated region is con"ned to a small portion of the "eld of view near the center, as it is for a jet, the aperture is reduced, or the portion of the #ow being measured can be masked by making the rest of the "eld dark, then the overlapping portions of the image will be dark and will create little interference with one another. 3.2. Data processing After the above components are selected and arranged into a PDV system, the entire system must be aligned and calibrated. Every current investigator using PDV has a slightly di!erent scheme for calibrating their system, recording images, and processing the recorded data to velocity data [10,12,42}45,48,58,63,69}71]. The scope of this paper does not allow a thorough review of all processing schemes in use; furthermore, some researchers have not provided su$cient details of their processing and calibration schemes to allow a thorough review. However, many common elements exist in the processing schemes of virtually all researchers using the PDV technique. In some cases, the di!erence lies in the order in which steps are performed, the type of curve "tting or type of digital "ltering used, etc. In order to provide some insight into the necessary steps in processing PDV data, a single procedure for PDV processing is outlined here. A more detailed description of similar imaging processing routines are given by Mosedale [41,42,45,48,67,58]. The procedure described here is attributable to Beutner et al. [44]. Some notable variations or exceptions to this process as performed by other researchers are identi"ed. In the most general terms, the calibration of the PDV system, and subsequent processing of data requires the following steps: 1. Iodine "lter calibration. This calibration measures the transmission of the iodine cell "lters as a function of frequency. 2. Image calibration and mapping. This step corrects for intensity (o!set and gain) and spatial di!erences between the signal and reference cameras while also correcting for perspective and magni"cation variations.

817

3. Determination of velocity. Geometric information (positions of cameras, light-sheet origin, and imaged #ow "eld coordinates) is used together with camera images and the calibration data to determine velocities in a plane. 3.2.1. Iodine xlter calibration The physical arrangement for calibration of the iodine cells was outlined previously. This procedure has also been performed by some researchers using the camera systems with the iodine cells in place. In either case, the purpose of this calibration is to provide a measurement of the iodine cell transmission as a function of frequency. When using a seeded Nd : YAG laser system, the frequency of the laser may be changed with frequency increments as small as a few Megahertz. This is accomplished by changing the temperature of the seed laser by means of a bias voltage applied to the seed laser heating circuit. After a bias voltage change is made, several seconds may be required for the laser to lock on the new frequency. Monitoring the Q-switch delay time on a pulsed Nd : YAG laser provides a check on whether the laser has locked on a frequency or is operating in multimode. By tuning through the frequency range of the laser (approximately 100 GHz), the transmission pro"le of the iodine cells may be measured experimentally. Tuning through several absorption lines allows the absolute frequency to be determined, since the frequency of these lines may be compared to known values. This step also provides a check on the linearity of the frequency change of the seeder system with applied bias voltage. Several other methodologies have been used to calibrate the frequency axis including the use of etalons [10,12], a wavemeter [68], and heterodyne techniques with a second stabilized laser [32]. Typically, multiple samples are taken at each frequency setting to determine the transmission of the iodine cell. With proper attention to the details of this data collection, these transmission pro"les are very repeatable, even after time intervals as long as a year. However, to ensure that the laser, iodine cells and photoelectronic devices are operating correctly, these frequency scans are typically performed at the beginning and end of each day of wind tunnel testing. If these frequency scans are performed using su$ciently small steps in frequency, the resulting transmission pro"les for the iodine cells may be used directly as a look-up table in the data processing which follows. When using an argon-ion laser, the frequency is typically adjusted by tilting or heating the intercavity etalon. This generally results in a much coarser frequency adjustment than is typical of frequency scans with the Nd : YAG laser. For these coarser scans, a curve "tting algorithm must be used to interpolate between measured points on the transmission pro"le [58]. This type of curve "tting has also been used to "t multiple scans in

818

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R@ "R !R , D D B

(9)

S@ "S !S . D D B

(10)

`green-carda images, to distinguish them from more common `white carda #at "eld correction images. While a white-light #at-"eld correction could be used to normalize the images, the transmission of the iodine cell for broadband `white lighta is not, in general, the same as the local maxima for the cell transmission in the vicinity of the absorption line used during the test. A number of variations are used by di!erent researchers to obtain these images. Some researchers used a card illuminated by laser light, as described above, while others use the laser sheet and seed particles typical of those used in the experiment [11,49,42]. This may be accomplished by introducing seed particles into this region with a very low velocity. If the region around the maximum transmission frequency does not vary signi"cantly in transmission, and the velocity of the seed particles does not shift the light scattered out of this region, these images may be taken at run conditions. This approach has the appealing characteristic that the conditions used to calibrate the cameras are identical to the conditions used to take the data. Whether or not it is used for #at "eld corrections, there is a compelling reason to acquire data with the laser tuned to the local iodine transmission maxima during the wind tunnel run. When this data is processed as outlined below, no frequency-dependent absorption e!ects should be present in the image. Thus, the resulting processed image should show a relatively constant transmission ratio over the entire image. This can serve as an on-line check during testing to determine if the system is operating correctly. Typically, a series of images, R and S for the referG G ence and signal cameras, respectively, are recorded and averaged for these #at-"eld corrections. Background images are also recorded corresponding to this same setup. As with the data shots, the background images are subtracted, resulting in corrected #at-"eld images:

Flat-"eld corrections are also performed to account for optical path di!erences between the two cameras. For these calibrations, the laser beam is expanded and directed onto a white card placed in the position of the original light sheet. The laser is tuned to a frequency outside the absorption curve identi"ed as a local maxima in the iodine cell calibration (for example at l"18789.3 cm~1). It is not necessary that the illumination used in these #at "eld corrections be perfectly uniform. Since the #at "eld correction is used only for a frequency-independent camera-to-camera correction, variations in the illumination of the card will be removed by the process of ratioing the signal and reference camera images. Intensity variations having a high-frequency spatial variation, such as laser speckle, will not cancel perfectly in this process. To reduce the speckle in the #at"eld images, an optical di!user may be used in the beam path. These type of calibration images are typically called

R@ "R !R , (11) G G B S@ "S !S , (12) G G B Some researchers have also included an extra processing step to normalize pixel sensitivity. This may be performed, for example, by using an integrating sphere, or by di!use, unfocused illumination of the CCD array. This step may be used to normalize the gain of individual pixels in the array, and may also be useful in identifying any bad pixels in the array. Depending on the details of the processing procedure, however, the correction for individual pixel gains may be normalized out by the #at-"eld corrections. The processing procedure must also detect pixels which are near the saturation limit of the camera, or which have too low a signal level. These pixels must not be used in processing. The data from the signal and reference cameras must be mapped into overlying images to allow for a

systems which have greater uncertainties in the measurement of the transmission pro"les [72,73]. Another method of calibrating the frequency axis in argon-ion systems is to employ the use of a rotating wheel to provide known frequency shifts in the calibration process [56]. Di!erences in the performance of the beam splitters, the optical paths, and photodiodes mean that the signal ratios representing the transmission of the "lters have undetermined scales. As an aid to the later use of these transmission pro"les, these values are typically normalized by a local maxima in the transmission pro"le. The frequency of this local maxima is recorded, and the same frequency is later used for normalizing camera images. This procedure results in normalized transmissions that vary from approximately 0 to unity. 3.2.2. PDV image calibration and mapping Since the PDV technique is based on intensity measurements, care must be applied throughout the processing to preserve the accuracy of the intensity measurements on a pixel-by-pixel basis. Background camera images are typically collected and subtracted from the signal images. This step removes stray light illumination and re#ections from tunnel walls, windows and model surfaces. This step also accounts for camera dark currents on a pixel-by-pixel basis. Letting the data images be denoted by R and S , for D D the respective reference and signal cameras, and the background images be denoted by R and S for the B B respective reference and signal cameras, then R@ and D S@ are data images corrected for background and dark D current:

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

pixel-by-pixel determination of the iodine-cell transmission. Although steps may be taken to align signal and reference cameras during setup to provide a nearly identical view of the #ow "eld, the resulting images will invariably contain di!erences arising for the separate optical paths to the two cameras. Furthermore, in order to resolve three-component velocity measurements, the perspective and magni"cation di!erences between the di!erent camera pairs must be removed. This is accomplished most e!ectively by mapping all camera images into a common, orthonormal view of the #ow "eld. This mapping is typically accomplished using an image of a dot card placed in the data plane. Images of this dot card are taken with each camera, and the dots provide tie-points in the images which can be used to map the di!erent camera views onto a common grid. In multiplecomponent PDV systems, it may be desirable for this dot card to be made of a translucent material so that the dots may be seen from either side of the card. The images are typically processed digitally to determine the centroid of the dots recorded in the camera images. A variety of algorithms have been used by di!erent researchers to determine dot centroid. These algorithms are typically capable of "nding the centroid of a dot to subpixel accuracy. This produces a set of ordered coordinates, (x@ , y@ ), which correspond to the dot centroid in the raw i i data image. A second set of ordered coordinates, (x , y ), i i corresponds to the centroid locations in a mapped, normal view of the dot-card-plane. Typical mapping programs used by PDV researchers have used bilinear interpolation to locate a source pixel location in the unmapped image for every pixel in the mapped image. The relationship between a pixel location in the source image, (x@ , y@ ), and that in the mapped image, (x, y), is given by i i x@"a x#a y#a xy#a , 1 2 3 4 (13) y@"a x#a y#a xy#a , 5 6 7 8 where the mapping coe$cients, a , were found for each i sub-region of the image by solving two sets of four simultaneous equations based upon the tie-points provided by the dot-"nding program. These tie-points de"ne the corners of the sub-region. The equations are

CD C CD C

x@ x 1 1 x@ x 2 " 2 x@ x 3 3 x@ x 4 4 and

y

1

y

2

y

3

y

y@ x 1 1 y@ x 2 " 2 y@ x 3 3 y@ x 4 4

DC D DC D

1

4

x y 1 1 x y 2 2 x y 3 3 x y 4 4

y 1 y 2 y 3 y 4

x y 1 1 x y 2 2 x y 3 3 x y 4 4

1

1 1

1

1 1 1

a 1 a 2 a 3 a 4

(14)

a 5 a 6 a 7 a 8

(15)

819

where the points (x@ , y@ ), and (x , y ) are the known tiei i i i points. The (x@ , y@ ), location in the source image correi i sponding to a pixel location (x, y) in the mapped image, is not generally an integer value. Therefore, the intensity value assigned to the mapped image must be calculated as a weighted average of the nearest four pixels. This bilinear mapping algorithm is typically applied on a piecewise basis for each square in the mapped image bounded by four dots. Once the mapping coe$cients are determined using the dot card image, they are used to map all data images to a common orthonormal view. This mapping procedure results in a new set of images SA , RA , SA , and RA in which perspective distortions and D D G G magni"cation di!erences have been removed. 3.2.3. Determination of frequency shifts Once the images are mapped, the next step in the processing procedure is to determine the transmission through the iodine cell on a pixel-by-pixel basis. The transmission is determined by dividing the signal and reference camera images, and normalizing by the #at"eld images. The resulting image gives the pixel-by-pixel variation in the transmission, TR, of the iodine cell for the imaged light: TR"(SA /RA )x(RA /SA ). D D G G

(16)

Some investigators have used a calibrated linear least square curve-"t for each pixel instead of the #at-"eld normalization method shown here to verify camera linearity [42]. Once the value of the transmission, TR, is known for a given pixel, the frequency of the imaged light may be determined by use of a lookup table, generated from the iodine cell calibration. This lookup table provides the frequency as a function of transmission of the iodine cell. Similar information is obtained from the reference system, providing the frequency of the unshifted laser light. The di!erence between these frequencies gives the relative Doppler shift of the scattered light. This Doppler shift may then be converted to velocity through the Doppler shift equation expressed as: j [f(TR)!f ]. <" 0 2 sin(/)

(17)

In PDV systems the Doppler shift, the term in brackets, can be expressed in terms of the frequency function, f and the laser frequency, f . The frequency function takes its 0 argument from the transmission, TR, recorded by the signal and reference PDV cameras after they have been calibrated and mapped. The frequency function may be thought of as the absorption pro"le with the transmission as the independent variable and the frequency as the dependent variable. The laser frequency ( f ) is deter0 mined from the frequency monitoring system. The lefthand side of this equation is the velocity component

820

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in the direction of system sensitivity with / de"ned as the angle between the laser propagation direction and the scattering direction. For multiple-component systems the above process is repeated for each reference-signal camera pair. This will provide multiple velocity components since the system sensitivity will vary as a function of / for each camera pair. Mosedale [41] suggested several test conditions in the process outlined to help identify problems and ensure that the calibration and processing are done correctly. Before leaving our discussion of image processing for PDV images, one "nal processing step must be considered. Images contain a level of spatially random intensity #uctuations which may be due to characteristics of the scattered signal (e.g. speckle), camera noise, mapping errors, or calibration errors. These sources of error are discussed in detail below, but there are two processing techniques which may reduce them. First, the data can be time averaged, either by using a CW laser and a long camera exposure, or by averaging individual single-shot images (with the expectation that the random noise will decrease with the square root of the number of samples taken). Additionally, random #uctuations may be reduced by either low-pass "ltering of the image, or by pixel binning in the image. These last two processes are typically performed during digital processing of the data, although pixel binning may also be accomplished during readout for some CCD arrays. Di!erent researchers have taken a wide variety of approaches to the application of low-pass "ltering and pixel binning. These procedures may be performed on the raw data, accomplished as part of the image mapping process, or performed on the "nal velocity images. Furthermore, the type of "lter used for low-pass "ltering varies. A rolling n]n digital "lter is typical with values of n ranging from 3 to as much as 7. In this "lter, all pixels are weighted equally in an n]n pixel cell in the image, and the average value is assigned to the central pixel. Binning is similar except now all the pixels are added together and replaced by a single `super-pixela at that spatial location. McKenzie [69] reports that for a typical PDV image which has a noise-to-signal ratio (NSR) of 0.16, the NSR is reduced to 0.035 by a 3]3 binning and to 0.011 by a 5]5 binning. It should be noted that other more complicated "ltering algorithms, such as the Weiner "lter used by Clancy et al. [70] have reported similar levels of NSR improvement.

4. The development and application of PDV Numerous researchers have worked on various aspects of the Planar Doppler Velocimetry techniques. What follows is a brief description of some of the applications investigated with the PDV technique and the contributions to particular aspects of instrument development which have been made by various researchers. It is often

di$cult to give a comprehensive review of all work done in a particular "eld. The area of Planar Doppler Velocimetry techniques is no exception. Where omissions have occurred in this review, it is not due to the perceived quality of the work, but rather the accessibility of the results. In the review that follows, we have divided the work into research devoted primarily to instrument development and research focused on applying the technique to the measurement of given #ow "elds. 4.1. Instrument development Komine and Brosnan [8], Komine et al. [15], and Meyers and Komine [9] were among the "rst researchers to introduce molecular "lters to aerodynamic measurement, developing a technique called Doppler Global Velocimetry (DGV) that pioneered several of the features common to many current PDV systems. Komine and Brosnan [8] and Komine et al. [15] developed two DGV systems, one using a cw argon-ion laser, which measured velocity time-averaged over the 33 ms exposure of video-rate cameras, and the other using a pulsed Nd : YAG laser, which measured velocity time-averaged over the 15 ns pulse of the laser. The latter system demonstrated the ability of PDV to make essentially instantaneous measurements of velocity. The system of Komine and Brosnan used six cameras in order to resolve three velocity components simultaneously. The system was tested on near-sonic jets seeded with 1.5 lm olive oil droplets. The one-component system of Meyers and Komine [9], based on a cw laser, featured an analog image normalization circuit so that the transmission could be displayed at video rates, but re"ned the system so that each camera was digitized independently. These works outlined many of the basic ideas of DGV and PDV and stand as the original proofs-of-concept, although it would be years before all the uncertainties in the system were known and reduced to make PDV a reliable, quantitative instrument. Most of the researchers who have developed PDV systems have devoted considerable energy to assessing the accuracy of their techniques. A common approach to experimental veri"cation of the technique has been the measurement of a known velocity "eld, such as a rotating wheel, to quantify the absolute accuracy of PDV systems. Meyers and Komine [9] published one of the "rst rotating wheel measurements using a PDV system and continued to improve the system using the rotating wheel in later experiments [56,74]. Reported results with this system indicated a mean error of approximately 1 m/s (where velocities ranged from about !50 to 50 m/s) and a standard deviation from the expected linear velocity pro"le of 3.6 m/s. This latter quantity was attributed to the charge transfer noise of the video-rate CCD cameras utilized. In a more recent study, Meyers performed three-component planar measurements on a rotating

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wheel using an argon-ion laser, and reported results consistent with a solid body of revolution [71,74]. The evolution of the development of the PDV system used by Meyers is outlined in Refs. [71}74] which summarize their discovery and correction of system errors. In another early work, Elliott [10] validated his onecomponent PDV system using a laser-line on a rotating wheel with velocities ranging from !83 to #83 m/s. The system of Elliott utilized a frequency-doubled Nd : YAG laser and 14-bit intensi"ed slow-scan CCD cameras. Absolute accuracies of 10 m/s were reported with this system, irrespective of the velocity magnitude [10,11]. A temporal RMS variation in velocity of 15 m/s was measured at all radial stations. Most of this was attributed to pulse-to-pulse laser frequency variations, as was discussed above, which were not accounted for in this early PDV arrangement. Elliott [10,11] also conducted a theoretical uncertainty analysis of the major system components, identifying major uncertainty contributions from random intensity variations due to speckle and camera noise, least-signi"cant-bit errors, angular uncertainty, and laser frequency stability. The bene"ts of pixel binning were also demonstrated in these studies. McKenzie [7] used a one-component point measurement system to measure velocities on a rotating wheel in a range from 5 to 56 m/s. This system did have the ability to track the laser frequency variations, and McKenzie reported RMS variations in his measurements of 2.5 m/s. These variations were constant for all speeds above 10 m/s. This was within the digital truncation uncertainty of his photodiode system [7]. In a later study involving a planar system, he found that RMS velocity values from 2 to 5 m/s were achievable over the same velocity range of his previous study, and he characterized these as the minimum velocity resolution of his system [69]. In the planar measurements, laser speckle was cited as a signi"cant additional source of measurement uncertainty. Like Elliott [11], McKenzie used a Nd : YAG laser and slow-scan cameras. Using an argon-ion laser and video-rate cameras, Naylor and Kuhlman presented results for 2-component planar measurements of a wheel, reporting mean velocity errors of 2 m/s (where the nominal velocity range was 32.2 m/s), with an unexplained o!set of !20 m/s [45]. Beutner et al. [44] also used rotating wheel experiments to characterize a PDV system performance with varying apertures in the camera-lens system. These measurements utilized a two-camera system with starved iodine cells and 16-bit cameras. Bias errors of approximately 2 m/s were noted with this system and attributed to uncertainties associated with camera and iodine cell calibrations. As expected, RMS errors varied with aperture, and were also dependent on the digital "ltering used in post-processing data. The optimum system arrangement could measure velocities of less than 2 m/s in a single shot. McKenzie has pointed out that results obtained

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from rotating wheels may not be representative of results obtained from seed particles due to polarization e!ects and the role of secondary scattering; however, he found that the results from a rotating wheel and from a lowspeed seeded turbulent jet were consistent. Similarly, Beutner et al. [44] made empty tunnel measurements showing comparable bias and RMS errors to those obtained with a rotating wheel. There have been several di!erent camera arrangements which have been used to collect the PDV images. Initially, Komine et al. [15] used separate reference and signal cameras to record the "ltered and reference images by collecting the scattered signal with a single lens, followed by a beam splitter which separated the signal to the two cameras. Initially they developed a real time analog circuit to normalize the signal with the reference camera and apply the "lter pro"le to obtain the velocity. This arrangement required the optics to be aligned perfectly to produce a pixel-by-pixel correspondence between the two images. This system would also allow a real time visualization of the recorded velocity "eld, but did not allow any post processing to be performed on the measurements. Meyers [9] improved upon this system by digitizing each camera image independently * allowing the images to be mapped, calibrated, and smoothed, and allowing the absorption "lter pro"le to be applied in post processing. Although this resulted in a slower measurement, it gives the researcher more control over the data allowing for algorithms to be applied which reduce the uncertainty in the measurements. Elliott et al. [10,11] and Arnette et al. [49] eliminated the beam splitter by orienting cameras side-by-side. This has the e!ect of increasing the signal level to the reference and signal cameras and eliminates concerns about inconsistent division of the scattered light by the beam splitter. This system was acceptable since the scattering was in the Rayleigh regime, in which the angular variations in scattered light intensity are predictable (see Fig. 5b). Smith et al. [12] and McKenzie [7] were the "rst to combine the signal and reference images on a single camera in what they term a split-image arrangement; this arrangement was also utilized by Clancy et al. [48,70]. This has the advantage of reducing system costs, but may not be applicable for some #ow "elds due to image overlap problems as mentioned previously. Other investigators have demonstrated two camera systems using a beam splitter placed ahead of separate lens systems for the signal and reference cameras. McKenzie [69], Beutner et al. [44], and Mosedale [41] have incorporated nonpolarizing beam splitters and polarizing elements in the optical systems to minimize the e!ects of polarization nonuniformities for particle scattering in the Mie regime. Perhaps the most compelling reason for developing the PDV technique is the capability of extending the planar measurements to multiple velocity components. Since the

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early development of PDV, researchers have recognized the possibility of measuring multiple components of velocity simultaneously. The initial systems of Komine [8] and Meyers et al. [56] demonstrated the potential to measure three velocity components with PDV by using three reference and signal camera systems. Similar systems were used by Beutner et al. [63] and Reinath [67]. Since these cameras viewed the light sheet from di!erent directions, each is sensitive to a di!erent component of velocity when measuring the Doppler shift of the scattered light. Once three independent velocity components are measured, they can be combined to give normal velocity components aligned with either a tunnel or model coordinate system. It should be noted that velocity components measured by single-component systems are never contained in the plane of the light sheet, and are rarely aligned with a tunnel or model coordinate direction. Clancy and Samimy have studied the accuracy of two- and three-component split image PDV systems in measurements of a Mach 2 free jet [48,70]. Clancy [62] also demonstrated that by appropriately locating the position of the cameras, one could reduce problems with laser frequency drift in velocity components which are calculated by the di!erence of two observation directions. Another approach to obtain multiple average velocity components utilized by Roehle and Schodl [66,75] is to use a single reference and signal camera system and illuminate the #ow from three di!erent directions sequentially. This requires that the three sheets of illuminating laser light overlap; however, it also reduces the cost of the system since only one recording system is required. This procedure has been successfully implemented in both small- and large-scale experiments. Beutner et al. [44] extended the single component system of Mosedale [41] (illustrated in Fig. 9) to measure two components of velocity over a Boeing boundary layer interference model in a large-scale wind tunnel. In empty-tunnel measurements, they were able to measure velocities with bias and random errors of less than 1.5 m/s. 4.2. Flow xeld measurement As the accuracy, precision, and reliability of PDV has improved, the research has turned from system development to applying PDV to study the #uid dynamics of a given #ow "eld. The following are a summary of the #ows which have been studied using PDV and the highlights of some of the measurements. 4.2.1. Axisymmetric jet studies One popular #ow "eld studied in the course of system development is the axisymmetric jet. This #ow "eld has been studied in both the subsonic [8,9,58,66,69,75,76] and supersonic [10}12,35,42,48,65,70] regimes. Although many of these studies were focused on instrument development, some further understanding of the turbulent

structure within this #ow "eld has been made. Smith et al. [12] used PDV to measure a sonic and underexpanded jet. Fig. 13 show examples of the instantaneous velocity images (Figs. 13a and b) with the resulting average (Fig. 13c), and RMS (Fig. 13d) images calculated for an under-expanded jet issuing from a sonic nozzle with an equivalent Mach number of 1.9. Single-velocity-component measurements were taken with an orientation of 453 with respect to the streamwise direction. The instantaneous images show the velocity content of the largescale turbulent structures in the shear layer region of the jet as they interact with the ambient air. Surprisingly there is little clear evidence of shock diamonds in the instantaneous images. However in the average velocity image (Fig. 13c), the velocity changes due to the shock and expansion diamonds are clear in the core of the jet. Smith [12] acquired over 1000 images allowing for RMS velocities to be calculated in addition to the average velocity. The RMS images clearly show the level of turbulent #uctuation of the jet due to the shear layer and the interaction with the shock/expansion diamonds which #uctuate in the core of the jet. Also, they were able to use the spatial information provided by PDV in order to quantitatively study the evolution of the turbulent structures within the jet using correlation algorithms. Probably the most complete supersonic axisymmetric jet data taken with PDV is the three component data taken by Clancy et al. [70] of a Mach 2.0 jet. Fig. 14 shows a vector plot of the average streamwise and lateral velocity with the average and RMS pro"les through the core of the jet given in Fig. 15 (compared to LDV measurements taken at the same conditions). Since all three velocity components were measured, Clancy et al. [70] were not constrained to measure an oblique velocity direction, but could calculate and display the 2-D vectors in a single image. As shown in Fig. 15, PDV and LDV velocities are in good agreement with an error of 25 m/s (5% of the core velocity of 500 m/s) in all three components. Fig. 15 also shows the mean velocity pro"les with and without the frequency drift monitoring system and spatial "ltering which they incorporated. They found that due to their optical arrangement only the z component of the velocity needed to be corrected for frequency drift. The uncertainty in the instantaneous velocity measurements varied from 40 to 80 m/s (8% to 16% of the core velocity), resulting in more deviation between the RMS measured using PDV than LDV. In addition to this initial study Clancy [62] also applied PDV to study the streamwise vorticity created by applying small tabs to the exit of the jet. These are similar to the uncertainties quoted by Mosedale et al. [42] for a Mach 1.36 jet which were also veri"ed using LDV. Mosedale et al. [42] reported bias and random uncertainties of 7 m/s (2.5%) and 6 m/s (2.4%) respectively.

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Fig. 13. Instantaneous ((a) and (b)), average (c), and RMS (d) measurements of an under expended jet issuing from a sonic nozzle with an equivalent Mach number of 1.9 [12].

4.2.2. Supersonic wind tunnel measurements One of the greatest advantages of PDV over other techniques is observed as the velocities are increased to

the supersonic regime. This is because the dominant uncertainties in the measurement are constant and independent of velocity. Therefore the higher the velocity the

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Fig. 14. Average velocity vector plot of a Mach 2.0 jet measured using a three component PDV system [70].

lower the percentage of error. The supersonic regime also demonstrates the need to use pressure broadening so that the Doppler shifted light always stays within the absorption pro"le. One of the "rst PDV applications to a supersonic #ow was by Elliott et al. [10,11,47] who investigated compressible free shear layers. The blow-

down supersonic wind tunnel had a test section cross section of 152 mm]152 mm. Water condensation through the expansion created small particles, placing the scattering in the Rayleigh regime. Single-velocitycomponent measurements allowed comparison of the e!ect of compressibility on the instantaneous large-scale structures present in supersonic/subsonic shear layer with supersonic Mach numbers of 1.8 and 3.0. One interesting aspect of this study was that since the velocity in the #ow "eld was supersonic, the measured velocities ranged from 125 to 600 m/s throughout the #ow"eld. As a result, the measured Doppler shifts were always positive. This allowed the use of a second thermally broadened "lter in front of the reference camera so that background scattering from walls and windows in the #ow was totally eliminated, while all of the scattered signal from the #ow passed outside the absorption pro"le resulting in little frequency dependence. The PDV system developed by Elliott et al. [11] was extended to measure two velocity components by Arnette et al. [19,49] in the same wind tunnel. This system was used to study the e!ect of a centered expansion on a Mach 3.0 boundary layer. The mean velocity measurements showed excellent agreement with LDV results, and it was demonstrated that velocities could be measured to within 0.4 mm of the model surface using PDV. However, the uncertainties in the instantaneous measurements were on the same order as the #ow turbulence levels, so turbulence levels along the wall could not be measured.

Fig. 15. Average ((a)}(c)) and RMS ((d)}(f)) pro"les of the three velocity components taken using a three component PDV system and LDV [70].

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Fig. 16. Spanwise views of the mean streamwise velocity for circular jet imaged in an orientation shown in (a). The streamwise locations are x/d "!2 (b), !1 (c), 0 (d), and 4 (e). In all images the #ow is out of the page [50]. %&&

Fig. 16 shows the mean streamswise velocity images taken by Elliott et al. [50] in a circular transverse jet issuing normally into a Mach 2.0 free stream. The imaging plane was oriented spanwise to the #ow direction (across the width of the tunnel) as shown in Fig. 16a. The supersonic wind tunnel in this experiment had a 131 mm]152 mm cross section and could be run continuously. Air was transversely injected through a 6.35 mm diameter injector with circular and elliptical geometries. A velocity component close to the streamwise direction was achieved by retro-re#ecting the laser sheet back through the tunnel. The velocity images were taken at various streamwise locations showing the velocity in di!erent regions of the #ow "eld, including the incoming boundary layer (Fig. 16b), separation region (Fig. 16c), and downstream of the three dimensional bow shock (Figs. 16d and e). Unfortunately the normal jet was not seeded and therefore could not be imaged until it was entrained into the freestream and the data required extensive image processing to eliminate background processing problems. Turbulence intensity measurements

were also taken and indicated increased velocity #uctuation levels in the boundary layer and bow shock regions of the #ow. A research e!ort headed by Meyers and colleagues at NASA Langley utilized the Unitary Plan Wind Tunnel making velocity measurements above a #at plate at !153 angle-of-attack and a 753 delta-wing at various angles of attack and Mach numbers [56,77]. The Unitary Plan Wind Tunnel has a 1.2 m]1.2 m test section and can generate Mach numbers ranging from 1.5 to 4.6. As in other supersonic PDV wind tunnel studies, naturally occurring condensation particles (approximately 0.2 lm in diameter) were used as the scattering medium. Fig. 17a shows a side view of the vertical velocity component measured above a #at plate at !153 angle-of-attack using PDV. Although there is a slight velocity nonuniformity in the free stream (due to the changing incident light vector direction from sweeping the laser beam), the variation in vertical velocity across the oblique shock is consistent with the theoretical value. This #ow"eld also provided an opportunity to study the

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Fig. 17. Map of the vertical velocity component measured by PDV (also termed DGV) of the #ow above a #at plate inclined to !153 at Mach 2.5 (a). Map of the velocity component: !0.90I#0.31j#0.32k measured by the PDV of the vortical #ow above a 75-degree delta wing at the 95-percent chord location at Mach 2.8 (b) [77].

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particle lag time through the oblique shock created by the inclined #at plate. It was demonstrated that the particle lag time was small enough to be masked by the modulation transfer function of the PDV cameras. For the supersonic delta-wing experiments, Meyers [56,77] demonstrated that the PDV technique could successfully measure the vortex structure and the shock patterns which were produced. Fig. 17b gives a spanwise view above one side of a 753 delta wing at 243 angle of attack at the 95% chord location in a Mach 2.8 free stream. The velocity vector measured is de"ned by !0.90i# 0.31j#0.32k. Clearly visible is the vortex formed as well as the complex shock and expansion waves created in this #ow. 4.2.3. Subsonic large-scale wind tunnel measurements Beginning with some of the earliest PDV studies, tests have been conducted in subsonic wind tunnels on various models of research interest. During the development of PDV, Meyers conducted experiments employing a multicomponent PDV instrument to investigate #ow "elds over a delta-wing [9,78,79], F/A-18 model [56,80], reingest of a powered model engine [81], wing-tip vortex interaction with a trailing model [72], and #ow around a helicopter tail rotor and main blade tip vortex [73,82]. These experiments were not only multicomponent, but generally conducted in very large scale facilities such as the NASA Ames 40]80 foot National subsonic wind tunnel, NASA Langley 30]60 foot Full Scale Wind Tunnel, and NASA Langley 14]22 foot Subsonic Tunnel. Although Meyers reported that early images did not have su$cient quality to provide quantitative data with acceptable accuracy [71], several system improvements were discovered for use in largescale production wind tunnel facilities. Meyers and coworkers describe the evolution of system improvements in several recent articles [71}74,77] which are useful for research groups considering development of a PDV system. Fig. 18 shows a spanwise image of the velocity "eld above a F/A 18 prototype at an angle-of-attack of 253 [56,80]. These multicomponent measurements were conducted in the Basic Aerodynamic Research Tunnel (BART) which has a test section area of 0.71 m]1.02 m and a free stream velocity of 67 m/s. Measurements were taken at two streamwise locations: one shortly after the strake (location 440: Fig. 18a) and one just upstream of the vertical stabilizers (location 524: Fig. 18b). The direction of velocity sensitivity was oriented in the upstream direction at !6.53 elevation. The velocity measurements indicated that for the 440 location, the primary streamwise vortices were in transition and were fully burst by the 524 location. It is also interesting to note that the PDV results took a few minutes of run time while LDV measurement of the same region took 8 h for one location [56,80].

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In collaboration with Meyers, Beutner and coworkers used a three-component PDV system in the 7]10 foot Subsonic Aerodynamics Research Laboratory (SARL) wind tunnel at Wright- Patterson Air Force Base [63,64]. This system was used to investigate the interaction of leading edge vortices on a delta wing at high angle of attack with twin tails placed in the vortex trajectory. Unfortunately problems with tunnel vibrations, camera cross-talk, and absorption "lter variations prohibited accurate measurements in these studies. However, the tests were useful in producing qualitative, velocity discriminated, descriptions of the #ow "eld. These descriptions were useful in tracking the vortex trajectory, and in identifying the unsteady nature of the #ow "eld when tails were present on the model. Furthermore, these tests provided insights into several problems in the system which were addressed in subsequent studies. The delta wing model has been studied by several investigators using PDV due to the relative simplicity of the model, the strong vortical structures which develop on the delta wing, and the interest in understanding vortex bursting with application to twin-tailed "ghter aircraft [9,78]. The same delta wing model has been investigated in the SARL facility by di!erent researchers to serve as a benchmark for assessing PDV system improvements [42}44,63,64]. Fig. 19 shows a typical PDV arrangement with the delta wing in the test section of this facility. The model was a 703 sweep delta-wing with sharp leading edges, and was set at an angle-of-attack of 233. Measurements were obtained on the wing at various chord locations at a free-stream Mach number of 0.2. This corresponded to a free-stream velocity of 68 m/s. Measurements were also made on the same model equipped with vertical tails having a planform characteristic of the F-15 tails. These tails were positioned to lie along the vortex core trajectory for the clean delta wing. One of the motivations for testing this model was to provide a database for comparisons to a computational #uid dynamics (CFD) simulation of a similar #ow "eld by Rizzetta [83]. An appealing aspect of PDV is its ability to provide measurement resolution which is typically "ner than the grid spacing in CFD simulations. Early measurements of this delta wing #ow "eld used a three-component PDV system, described previously. To simplify the measurement and concentrate on system development and accuracy issues, Mosedale et al. [42] and Beutner et al. [43] repeated the measurements for a single velocity component. As seen in Fig. 19, the laser sheet was oriented normal to the surface of the model. The direction of PDV sensitivity, based on this geometry, was !0.210i! 0.003j#0.978k, with i, j, and k oriented in the tunnel streamwise, spanwise and vertical directions. Fig. 20 show frame-averaged PDV measurements at locations of 97.1 (Fig. 20a) and 114.3 (Fig. 20c) percent chord. A plot of the velocity along a line drawn through

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Fig. 18. Spanwise velocity images above an F/A 18 prototype shortly after the wing strake (a) and just upstream of the vertical stabilizers (b) [56].

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Fig. 19. Optical arrangement for PDV delta wing measurement.

the cores is also given for each image. The nearly linear region between the velocity peaks in these pro"les is indicative of the vortex cores. The trajectories of the vortices can be calculated based upon the average images. A strengthening of the vortices with streamwise location is seen in the images. Note that far from the cores, the recorded velocity approaches the value obtained in the empty tunnel run at Mach 0.2. A CFD solution using a Baldwin-Lomax turbulence model was computed for a similar #ow "eld and is shown beneath each of the PDV measurements (Figs. 20b and d [83]). The overall #ow structure and the ranges of velocity found in the #ow are in approximate agreement, but the vortex-core diameters measured by PDV are only onethird to one-half what the CFD solution indicates. This di!erence may be due to insu$cient grid resolution in the CFD solution, failure to adequately resolve secondary separation on the delta wing, or the turbulence model used in the solutions [43]. It is interesting to note that other details of the #ow "eld, such as the free-shear-layer roll-up at the leading edge, can be observed in both the PDV data and the CFD solution. Measurements were also taken for the delta wing with tails to investigate the bursting vortex #ow"eld. The CFD solution was not able to predict the burst location correctly [42]. Providing detailed, instantaneous measurements of unsteady or complex #ow "elds continues to be a primary motivation for the development and application of PDV. These results point out the value of such data for CFD development. Subsequent large wind tunnel PDV tests by Beutner et al. [44] have used the PDV technique to make measurements of the #ow around a Boeing Boundary Layer Interference Model. This model has a complex geometry with a fuselage, high aspect ratio main wing, and a highly swept strake. PDV was used to investigate the interaction of the forebody vortex, strake vortex, and wing #ow "eld. A schematic of the model geometry is shown in Fig. 21 and representative results from the PDV measurements are shown in Figs. 22a and b. Fig. 22a

shows PDV measurements on a full-span plane, 3.8 cm upstream of the wing-strake junction. The instrument was sensitive to a velocity component in the direction (!0.273i, 0.0j, 0.962k). In this "gure, the strong vortex which has developed o! the strake leading edge can clearly be seen and has already coalesced with the weaker forebody vortex. This vortex interacts with the pressure gradient "elds over the wing, and ultimately with the tail surface. Fig. 22b shows measurements on a semi-span plane which intersects the tail root. In this case, the instrument was sensitive to a velocity component in the direction (!0.264i, 0.022j, 0.964k). This "gure shows some secondary re#ections o! the tail leading edge, which appear as a diagonal line in the image. More importantly, however, these images capture the interaction of the strake vortex with the tail, as well as a smaller, weak vortex shed o! the bottom corner of the fuselage which appears in the bottom left portion of the image. These measurements were able to resolve complex #ow interactions with multiple vortices and multiple lifting surfaces. This test demonstrates another signi"cant motivation for developing the PDV instrument: for complex #ow "elds, PDV can provide fast, detailed measurements of complex #ow interactions. The resolution of these #ow "elds by point-measurement techniques would require prohibitively long test times, and the complexities of the #ow "elds are beyond the capability of the typical Reynolds-averaged CFD codes commonly used in industry. Therefore, PDV represents a powerful tool not only for the CFD developer, but also for the aircraft designer. Roehle has applied the PDV technique to the swirling #ow from a fuel-spray nozzle, engine inlet, and the wake region behind an automobile model in a wind tunnel [75]. For the 1:5 scale automobile model, three-component mean velocity measurements were obtained using three laser sheet positions imaged separately and one PDV receiving system. The experiment was conducted in a 1.8 m]1.3 m low-speed wind tunnel. Measurements showed the velocity vector "eld 150 mm behind the

Fig. 20. Average PDV measurements [42] of delta wing at 97% (a) and 114% (c) root chord with comparison to CFD (b,d) result of [83].

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Fig. 21. Boeing boundary layer interference model [44].

model indicating the vortex created in the wake region of the automobile. The PDV measurements were found to have an error of approximately 5 m/s with this system. The PDV results acquired in the measurement plane were made in 30 s and demonstrated considerably greater spatial resolution than LDV measurements made over a two hour period. Reinath [67] has used multicomponent PDV in the large wind tunnels at NASA Ames Research Center on `production-typea models. This three-component PDV system used an argon-ion laser and 8-bit cameras. Models investigated include a jet engine simulator, advanced "ghter model, high-speed civil transport model, and an airfoil with a #ap edge. A majority of the tests conducted by Reinath [67] concentrated on the velocity content of the vortex structures in these #ows. These tests were conducted in the 40 by 80 foot and 7 foot by 10 foot wind tunnels at NASA Ames. Reinath [67] provides a complete description of this system along with an experimental and theoretical error analysis. Uncertainties were predicted to be approximately $5 m/s for all three velocity components; this uncertainty reduces to 0.5 m/s when several images are averaged together. Fig. 23 gives an example of one of the measurements conducted by Reinath [67] on a model which simulates

a jet exhaust plume. These tests were conducted in the 40 foot by 80 foot wind tunnel. Fig. 23a shows the mean axial velocity from the jet exhaust plume operated at a nozzle pressure ratio of 3.4, free stream Mach number of 0.244 and exhaust total temperature of 1033 K. One unique feature of #uid dynamic interest, aside from the mean velocity pro"le, was the wavy appearance of the plume edge which is attributed to the WidnallSullivan instability. A cross-section through the PDV velocity image is shown in Fig. 23b, and indicates that the velocity approaches the free stream value of 83 m/s outside the plume. Measurements of this #ow"eld were also compared with pitot rake surveys showing a slight velocity bias drift of the PDV system due to the unstable temperatures of the iodine "lter which were corrected in later tests.

5. Uncertainty analysis of PDV In order to develop PDV as a viable scienti"c instrument, research has been conducted to investigate the uncertainties associated with the technique. Several researchers have reported on the level of PDV uncertainty, sources that contribute to the uncertainty, the formal

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Fig. 22. PDV measurements on a full-span plane, 3.8 cm upstream of the wing-strake junction (a). The instrument was sensitive to a velocity component in the direction (!0.273i, 0.0j, 0.962k). PDV measurements on a semi-span plane intersecting at the tail root (b). The instrument was sensitive to a velocity component in the direction (!0.264i, 0.22j, 0.964k) [44].

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Fig. 23. PDV mean axial velocity image (a) and vertical velocity pro"le (b) for a jet simulator exhaust plume [67].

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uncertainty analysis, and ways to mitigate or reduce the uncertainties [7,10,11,21,32,41}44,48,62,67,69,70,84}88]. Although a generic uncertainty analysis is di$cult (due to the di!erences in PDV systems), the following is a general discussion of the major sources of uncertainty, their level, and mitigation methodologies. This section concludes with a summary of the total uncertainty levels in the velocity as reported by current investigators and expectations for the limits of the technique. Uncertainty in any measurement technique can be classi"ed as bias or random. The bias uncertainty is consistent from measurement to measurement and degrades the accuracy of each individual measurement and of the average of a series of measurements to an equal extent. Due to this consistency, it is sometimes possible to reduce the bias error through calibration if the error is the same in the calibration procedure and experiment. The random error #uctuates from measurement to measurement and degrades the precision of individual measurements. When measurements are averaged, the random error is reduced in proportion to the square root of the number of samples averaged. Thus, by averaging a great many samples, the random error associated with the mean measurement may be reduced. However, in the study of turbulence, statistics are calculated based upon a series of individual measurements, and random errors in the individual measurements will appear as spurious turbulence. Therefore, it is desirable to minimize the random error and to quantify it, if possible. In order to understand the sources which lead to the uncertainty in the velocity measured using PDV, we turn to the Doppler shift equation repeated here for convenience given as

calculate the velocity uncertainty. The following analysis is a summary of the methodology used by McKenzie [7], Mosedale et al. [42], and Beutner et al. [44]. According to the standard practice of error propagation, the contributions of uncorrelated (i.e. independent) error sources are added in quadrature to determine the total measurement error; thus, the bias and random velocity errors may be expressed as

j <" [f(TR)!f ] 0 2 sin(/)

1. uncertainty in the wavelength of the incident laser light, j, 2. uncertainty in the angle between incident and scattered laser light, /, 3. uncertainty in characterization of the "lter frequency function, f, 4. uncertainty in laser frequency, f , 0 5. uncertainty in the measured transmission after calibration and mapping, TR.

(18)

where / is the angle between the incident and observation vectors and the term in brackets is the Doppler shift. In PDV systems the Doppler shift can be expressed in terms of the frequency function, f, and the relative laser frequency, f . The frequency function takes its argument 0 from the transmission, TR, recorded by the signal and reference PDV cameras after they have been calibrated and mapped. Recall the frequency function is the transmission pro"le with the transmission as the independent variable and the relative frequency in GHz as the dependent variable (see Fig. 3c). Since every PDV system has slightly di!erent ways of monitoring the laser frequency, processing the images, calibrating the cameras, etc., this equation will serve as a base to understand how the errors propagate throughout the system in general. It should be noted that sometimes the uncertainty due to a particular source is given in terms of frequency so that the wavelength and angle / can be supplied for a given physical arrangement to

SA B SA B

*< " B*!4

L< 2 + *x , i Lx i i

(19)

L< 2 + *y , j Ly (20) j j where the *x are the uncorrelated sources of bias error i in the independent variables and the *y are the uncori related sources of random error in the independent variables. It should be noted that the total error in the instantaneous velocity combines both the bias and random error added in quadrature. The individual sources which contribute to bias uncertainty and random uncertainty will be discussed separately in the following two sections. *< " R!/$0.

5.1. Bias errors Several mechanisms for bias error have been identi"ed and modeled. The contribution of each of these mechanisms to the total bias error in velocity, is denoted by a subscript corresponding to its independent variable when expressed in mathematical form. The sources of uncertainty leading to bias are:

Although in general it is di$cult to evaluate the uncertainty which is consistent for the variety of documented PDV systems, this is not true for the "rst two items. Uncertainty in the wavelength of the incident laser light is a negligible error source for the following reason. The e!ect of wavelength on velocity is given by standard error propagation as < *j L< *j" *j"< . *< " j Lj j j

(21)

Clearly, the relative uncertainty introduced to the velocity measurement by this term is equal to the relative

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

uncertainty in the wavelength itself. The wavelength of incident laser when using iodine as the absorbing molecule is 532.218 nm for an Nd : YAG laser and 514.5 nm for an argon-ion laser. For the PDV technique to be possible, generally, a variation well below 0.5 GHz (0.00047 nm) is required by the laser. For most #ows measured using PDV (in the supersonic regime and below), variations in wavelength greater than this would shift the laser frequency away from the sloping region making the technique di$cult to implement. This results in an error to the velocity of less than 0.0001%, therefore bias error due to uncertainty in j is negligible and does not need to be considered for most PDV systems. The argument is the same for the random uncertainty and therefore the uncertainty due to wavelength will not be considered further. Uncertainty in the angle / arises from how accurately it can be measured and from variations which exist across the "eld of view which are dependent on the experimental arrangement. There are a variety of methods of measuring the angle between the incident light-propagation direction and the scattered light observation direction ranging from simple protractors, measuring several points to "xed hard-point locations on the experiment, or using surveying equipment with laser locators. No matter what the method, there is some uncertainty in the accuracy of these measurements. The uncertainty in the velocity due to the angle / can be expressed as L< !< ( */" ( */. *< " (22) ( L 2 tan (//2) ( Note that this expression shows that the uncertainty in the velocity introduced by this term is proportional to the velocity itself. Therefore, the relative error is constant. It can be observed in Eq. (22) that the maximum error is found when the incident and scattered light vectors are close together, going to in"nity at /"0 degrees when the system is insensitive to velocity. The error is reduced as / approaches 1803, but for planar measurements the system is typically set up with an angle / close to 903 in order to provide a view of the #ow "eld with minimal distortion. As was mentioned previously, depending on the collection f-number (distance from the laser sheet to the lens divided by the lens diameter) there may be a signi"cant variation in / across the image, but this e!ect can be calculated and reduced in data processing [7,11,77]. Turning to the uncertainty in velocity associated with the frequency function, f, the source of the uncertainty can have two major sources. First, is the accuracy in which the transmission pro"le used to calculate f is measured, and second is the change in f from the time of calibration to conditions which may exist while the data is being collected during the actual experiment. In general researchers have measured the transmission pro"le

835

and calculated f using the laser systems which are used in testing, thus the laser will have the same frequency linewidth as the experiment. Di$culties exist when using an argon ion laser since through the sloping region of the "lter the laser generally has only 5 to 10 mode hops as the etalon is tilted, therefore researchers have either scanned the laser for several minutes (&30 min) over the same region to "ll in the transmission pro"le [45], or used the Doppler shift of a rotating wheel to "ll in the transmission pro"le used to calculate the frequency function [56]. Some researchers further smooth the pro"le by "tting the curve to a Boltzmann distribution [58] or to theoretical absorption curves. Using a Nd : YAG laser for measuring the transmission pro"le and calculating the frequency function usually involves providing a bias voltage to the temperature control circuit on the injection seeder. Care must be taken during the scan so that the laser does not unlock, furthermore, the scan should be performed over a time short enough that the laser does not vary in temperature signi"cantly. The frequency axis of the frequency function may be determined by comparing two or more line positions with theoretical values [11,70,42,44], the free spectral range of an etalon [10,12], a commercial wavemeter [68], and heterodyne techniques with a second stabilized laser [32]. As mentioned previously, one should take care to make sure that the transition used is not saturated when calibrating the iodine "lter; this can potentially lead to large errors. The second source of error in the frequency function is caused by di!erences in the function during the iodine cell calibration and during the measurement. Errors can occur, for example, if there are any leaks in the cell, if the iodine concentration changes due to #uctuations in the cold "nger temperature (see Fig. 8), or if unexpected secondary cold points develop in the cell (i.e. windows, stopcock stem). Since at times the PDV system cell is operated in environments which are not temperature controlled, such as wind tunnels or near cold supersonic #ows, steps should be taken to ensure that the iodine cell is properly isolated from environmental changes using cell designs discussed previously. Although the cell-body temperature also may change the frequency function by e!ecting the thermal broadening of the iodine, this is generally a small e!ect if the cell is properly heated, as demonstrated by the overlapping "lter curves of Fig. 8. Due to the fact that the frequency function may change during an experiment, some researchers conduct periodic scans of the cell to insure unexpected changes have not occurred [10,42,44]. Another di!erence which can occur in the frequency function is due to the path-length change of rays through the cell when the collection f-number is small. Forkey et al. [21] have modeled this e!ect and shown that it is negligible if the collection f-number is above 10. Also, it is possible that the linewidth of the laser may #uctuate, but this is also considered to be a minimal e!ect.

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It is clear that if the frequency function is not properly measured or if it changes during the experiment, the measured velocity will be in error, but the exact level depends on the individual experimental conditions such as the absorption line selected, slope of the absorption line, temperature control of the cell, laser, calibration accuracy, cell design, and optical arrangement. Researchers who have evaluated the e!ect of uncertainties associated with the frequency function report errors less than 5 MHz [42,44,48]. The next source of uncertainty which may cause bias errors in the PDV velocity measurement is from the laser set point frequency, f , as seen in Eq. (18). 0 Since in PDV the Doppler shift is measured relative to the laser frequency, any change in the laser frequency will cause the Doppler shift to be biased. The level of uncertainty in the velocity is dependent on the angle between the laser and scattered light (/). There are two sources of laser frequency change which can cause a bias error: frequency chirp, and long-term drift of the frequency of the laser. Since the time scales of these two sources of error are relatively long and do not vary pulse to pulse, they are considered bias errors in most analysis. Frequency chirp was discussed earlier and can be reduced to less than 4 MHz through calibration, by using only the center of the beam, or by better seeder alignment. The second source of bias error is long-term laserfrequency drift. Most lasers (i.e. argon-ion and Nd : YAG) are a!ected by thermal variations from the environment. Even though much e!ort is made to control this e!ect, lasers tend to drift in frequency over long periods of time (as well as pulse-to-pulse for the Nd : YAG laser). This drift must either be tolerated as an uncertainty in the measurement or monitored during the test. For argonion lasers this drift is typically much smaller than that for Nd : YAG lasers. Overall, drifts and shot-to-shot variations reported by di!erent researchers vary from a few MHz to as much as one GHz per hour. Obviously these values are dependent on the temperature stability of the operating environment and on the design of the laser. As discussed earlier, methodologies of monitoring the laser frequency can be e!ective in reducing this uncertainty to a few MHz for both short- and long-term frequency variations. The last bias uncertainty considered here is that due to the transmission, TR. The bias error in the intensity ratio can stem from three sources: camera nonlinearity, image calibration/processing, and scattering discrepancies. Unfortunately, the bias errors in TR are highly dependent on the frequency function and geometry of the particular experiment. Generally CCD cameras used in PDV are inherently linear. Scienti"c-grade cameras can have nonlinearities of less than 1% which may be ignored [7,62]. The error associated with nonlinearities may increase for less expensive video cameras requiring their behavior to

be accurately modeled in the signal analysis. As a general practice, the linearity of all cameras should be veri"ed to ensure against unexpected manufacturing problems. The second source of bias uncertainty, contributing through TR, is due to the image processing/calibration step which is done to properly align the cameras spatially and enable them to have the same sensitivity. Depending on the processing/calibration routine, bias errors can be introduced if the light used for calibration is di!erent than that which is gathered in the experiment (i.e. scattering type, laser vs. ambient light). Also, bias uncertainties in the intensity ratio can occur if there are systematic changes from the time of calibration to the time when the data is taken. These can include changes in the background signal and misalignment due to camera movement, for example. A "nal source of bias in TR is secondary scattering e!ects from particles seeded into the #ow [7,42,43]. It should be noted that one could consider secondary scattering in the random uncertainty evaluation, since these errors depend on the instantaneous position and density of the scattering particles. We will consider it here since, in general, no level of averaging will reduce these errors. Secondary scattering can cause uncertainties by re#ecting additional light onto surfaces causing the background measured during camera calibration to be biased. Also, multiple-particle scattering errors can cause the incident light direction to be altered. Generally the level of these uncertainties is di$cult to evaluate and quantify and therefore researchers try to minimize these errors through experimental design [7]. One additional uncertainty, which should be mentioned in the discussion of transmission errors, is due to the laser impingement on surfaces. Generally this causes saturation of the CCD if the laser impingement location is within the camera "eld of view; additionally, this strong scattering may illuminate other parts of the model. When this problem is severe, some regions of the image must be discarded [41]. Again this can be minimized by proper experimental design, for instance by having the laser sheet glance surfaces instead of impinging normal to surfaces, or by minimizing surfaces in the image "eld which are strongly illuminated by secondary scattering. For more complex model geometries, some surface impingement may be unavoidable of the laser sheet. 5.2. Random errors Returning to Eq. (18), we now consider the sources of random error which contribute to the terms in the equation. Some of the terms of the equation only contribute to the bias uncertainty. The angle / does not contribute to random uncertainties because it is speci"ed once for all measurements, and therefore errors propagate systematically, not randomly. The frequency function, f, is determined before measurements of the #ow "eld are

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undertaken. Errors associated with the frequency function may be either bias or random errors, depending on whether the characteristics of the "lters change slowly or quickly relative to the time of the experiment. We have classi"ed the errors arising from sidearm- and cell-temperature drift as bias errors, since, in general, averaging will not eliminate the error in the frequency function. The only remaining uncertainties are the laser frequency ( f ) 0 and transmission (TR). As with the bias error, the random uncertainty in the laser frequency is dependent on the method used to monitor it. Manufactures of Nd : YAG lasers seeders generally quote a random uncertainty of 10}20 MHz due to the dither induced on the laser cavity mirror (illustrating the requirement of frequency monitoring). This random uncertainty may be increased to 150 MHz if the laser experiences #uctuations in temperature, vibrations, or even excessive acoustic noise in the wind tunnel environment. For an argon-ion laser, the random frequency #uctuation is generally on the order of 10 MHz [87] with longer term drifts and mode hops which can be much larger, and therefore must be monitored. When frequency monitoring is employed, the random uncertainty due to the laser frequency is determined by the frequency measurement methodology. For example when iodine-"lter reference systems are used, the random uncertainty has been quoted to be on the order of 10 MHz [62] to lower than 4 MHz [42]. A second approach was employed by McKenzie [69]; here a reference tab was placed within the "eld of view of the camera reducing the random uncertainty of the laser frequency below the unmonitored value. For the heterodyne system of Forkey [32], a random uncertainty of 2 MHz was quoted. Frequency #uctuations in an argon-ion laser may be reduced by stabilizing the laser on a hyper"ne structure of a molecular iodine reference absorption cell. Roehle and Schodl [66,75] were able to achieve stabilities of less than 1 MHz in this way. It is clear that any of these frequency-monitoring methods greatly improves the velocity measurements by reducing the random uncertainty in the laser frequency. The following mechanisms have been identi"ed as sources of random error in the transmission (TR):

837

analog to digital conversion. Basing his calculations on a minimum un"ltered signal level of 1/10 of full-scale while tuning the laser frequency to the 50% transmission point, McKenzie reports that the radiometric noise in the Doppler shift is less than 2 MHz over a 300 MHz range for a scienti"c grade 16 bit camera (note that in this analysis a 15 cm cell was used with a body temperature of 373 K and iodine side-arm temperature of 313 K with a given iodine absorption line). At these conditions McKenzie reported that it was the photon-statistical component that dominated the radiometric noise. As the bit resolution is decreased, however, the digital truncation becomes the more dominant source of radiometric noise. Fig. 24 shows the e!ect of digital resolution on the random uncertainty of the Doppler shift for a constant un"ltered signal level of 100,000 photoelectrons and varying Doppler shift (velocity) with conditions given previously. As observed here, the digital resolution becomes the dominant source of random uncertainty in the Doppler shift for 8-bit cameras. Although these trends will generally be true for any PDV arrangement, they are dependent on the cell conditions and camera. In general, the only way to reduce radiometric noise is by using better cameras or binning pixels together. Researchers using PDV to obtain instantaneous measurements have reported that a major component to random uncertainty in the velocity is due to laser speckle [7,41,70] with the most extensive analysis given by Smith

1. radiometric noise associated with the CCD cameras, 2. laser speckle noise associated with imaging narrow line-width laser light, 3. image alignment uncertainties. The "rst of these noise sources, CCD radiometric noise, has been analyzed in PDV applications in great detail by McKenzie [7,69]. He describes radiometric noise in terms of three components; the ampli"ed-circuit noise of the detector system (readout noise and dark charge), the inherent photon-statistical noise of the detection process, and the truncation of the signal in the

Fig. 24. The e!ect of digital resolution on the single-pulse Doppler-shift RMS uncertainties for a signal level of 100,000 photoelectrons. The A/D gain values (electrons/count) corresponding to each value of N-bit are indicated [7].

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[85] and McKenzie [69]. Speckle noise is introduced when laser light is scattered o! a surface or from a cloud of particles; small di!erences in path length cause threedimensional interference patterns. In the PDV technique, ratios are taken of signal images and reference images. If the speckle pattern in these image pairs were perfectly correlated, then the ratio step would remove the speckle noise. However, the speckle pattern does not exhibit perfect correlation (and in fact may be completely uncorrelated) due to slight mapping misalignments and minute di!erences in path length between the signal and reference images (since speckle patterns are three dimensional). As reported by Smith [85] and McKenzie [69] the noise-to-signal ratio (NSR) due to speckle is given by NSR"1.2(1#m)jF/*x

(23)

where F is the f-number of the optical system (focal length/aperture of lens), m is the magni"cation ratio (image size/object size), and *x is the average size of the camera pixels. This equation implies that a large camera aperture (small f-number), a small magni"cation ratio, and large CCD pixels tend to reduce the speckle noise. In most PDV experiments m is relatively small compared to unity and often controlled by optical access limitations. Therefore the magni"cation ratio does not o!er much potential to reduce the speckle noise. The most obvious

and simple way to reduce the speckle noise is to increase the aperture of the imaging system. As presented by Mosedale [41], Fig. 25 shows the strong e!ect of aperture size on speckle noise. The "gure shows instantaneous images of a seeded Mach 1.36 supersonic jet taken at indicated camera lens f-stops of 32, 16, 5.6 and 2.8 with natural seeding and no data processing. The noise-tosignal ratios in a core region of the jet are, correspondingly, 0.35, 0.22, 0.076 and 0.042. McKenzie has also pointed out that for speckle-dominated noise, the noiseto-signal ratio is constant with respect to intensity [69]. This is one method of determining if the random uncertainty is dominated by speckle noise since radiometric noise does not exhibit this trend. Other than using the lowest possible f-number, the e!ects of speckle can be reduced by using a small magni"cation factor, and a CCD array with the largest possible "ll factor [85]. Speckle may also be reduced by time averaging data, either by using a cw laser and a long camera exposure, or by averaging multiple pulses from a pulsed laser, with the expectation that the random speckle noise will decrease with the square root of the number of samples. Additionally, speckle may be reduced by either low-pass "ltering of the image, pixel binning, or more complex "lters discussed previously (see the image processing section for additional details). Investigators have reported random uncertainties in the velocity due to

Fig. 25. Images of light scattering from condensation particles in a supersonic jet taken at di!erent camera lens f-numbers and the associate NSR [41].

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

laser speckle ranging from 18 to 80 MHz [62] to 7 MHz as reported by Mosedale [41] when spatial smoothing is applied. The "nal source of random uncertainty is associated with image alignment during the mapping procedure. Despite the dot-"nding and mapping procedures, some residual error exists in overlaying the images. Investigators typically quote values of from 30% to less than 10% of a pixel for the accuracy of image mapping, but this may increase if the signal and reference cameras experience misalignments due to vibrations during the test. The low-pass "ltering (smoothing) or binning procedure which most investigators employ reduces this error source, which is not expected to be particularly signi"cant compared to other sources of error described above. In a simple experiment to show the e!ect of binning to reduce the random uncertainty in TR (due to speckle, image alignment, etc.), McKenzie [69] showed that the NSR ratio could be reduced from 0.16 for no binning to 0.035 and 0.011 when 3]3 binning and 5]5 binning are used, respectively. Thus, binning or image smoothing has been the most common method of reducing all sources of random uncertainty to TR. Few researchers have addressed the topic of the propagation of the mapping error quantitatively. This may be due to the fact that the mapping error is dependent on the intensity and velocity gradients between adjacent pixels as well as the di!erence in calibrated gain curves between adjacent pixels. Clancy et al. [70] made an attempt to estimate the residual misalignment expressed as a fraction of a pixel, combined with a representative gradient in signal intensity to calculate the associated errors in the transmission, the Doppler shift, and the velocity. They quote values on the order of 3}16 MHz assuming a 30% accuracy on the pixel alignment. Morrison and Gaharan [76] also conducted an uncertainty propagation analysis and reported an average uncertainty in the velocity due to mapping ranging from 0.1% to 16% over the image. 5.3. Current reported levels of uncertainty Given the above uncertainty levels there have been a variety of estimates on the bias and random uncertainty levels of current PDV systems. Table 2 gives the bias and random uncertainty as reported by various investigators. It should be noted that some of these estimates have been measured from deviations of known #ow "elds instead of detailing individual error sources which contribute to the total error. In addition, some of these error estimates have been based on limited error analysis based on a presumed dominate error source. As a trend it appears that most systems are closing in on bias errors on the order of 1 m/s, and random errors on the order of 2 to 10 m/s, depending on the magnitude of the velocity. In the future these uncertainties may be reduced, but may require new

839

Table 2 Bias and random error levels from various experiments Velocity (m/s)

Bias error (m/s)

Random error (m/s)

Reference

600 18.9 20.2 500 !83}83 380 500 60 !50}50 0.115}20 14.2 20.2 260 59 42 60 40}130

30 1.0}1.51 0.5 25 10 15 35 2}5 1 2.3 1.7 0.5 7 5 4 0.4}0.7 3

30 0.35}0.95 1.3 40}80 15 32 Less than 20 2 3.6

[49] [44] [43] [62] [10] [11] [50] [69] [9] [76] [42] [42] [42] [58] [58] [67] [66]

3.8 3.0 6 4 4 4}7

camera, laser, frequency monitoring, image processing, and/or "lter technologies.

6. Future trends The future trends of molecular-"lter diagnostics can be separated by improvements to PDV systems, technologies aimed at providing time resolved measurements, and the implementation of techniques to measure one or more properties (i.e. temperature, density, concentrations, pressure, etc.). As for PDV techniques reviewed in this article, most of the research is focussed on reducing the measurement uncertainty and improving the usability of the system as well as investigating other laser/ molecular "lter combinations [52,89]. Also the technique is continuing to "nd uses in large scale facilities when the velocity "eld is needed over a large planar area. PDV is particularly attractive in these cases when through plane velocities (velocities normal to the laser sheet plane) are high making PIV impossible since individual particles cannot be resolved and high through plane velocities may not allow particles to be tracked or correlated. Beyond the improvements of PDV systems and image processing techniques discussed previously, Arnette et al. [90] have suggested a two color system to simplify the optical arrangement. The two-color PDV system uses a Nd : YAG laser and splits the beam, sending 50% of the intensity to drive a dye laser which shifts the wavelength to the red (618 nm). The two laser beams are then recombined and formed into a single laser sheet which passes through the measurement region. The scattered light

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from particles seeded into the #ow is then collected through an iodine "lter placed in front of a high resolution color CCD camera. As in the PDV techniques described above, the Doppler shift from the #ow"eld causes the intensity from the injection-seeded green sheet to shift into and out of the iodine absorption well. The red scattered signal from the dye laser is not absorbed by the iodine. As a result, the recorded red signal can be used to normalize the scattering signal from the narrow-band green laser sheet. Since the camera records the colors separately, the transmission ratio can be calculated, followed by the determination of the Doppler shift and resultant velocity. Fig. 26 shows an example of the velocity "eld of a Mach 1.36 supersonic jet measured using two-color PDV including the raw, red, and green images, as well as the processed velocity. As seen here, even without processing, a pseudo-color representation of the velocity is indicated, due to the e!ect of the Doppler shift on the green image. Although this technique has some implementation advantages, since there is no need for mapping or separate signal and reference cameras, there is still a need to calibrate the red and green pixel sensitivity of the camera and the intensity of the red and green laser sheets. It should be noted that there is still more development needed for this technique to be fully functional. In order to provide temporally resolved measurements, investigators have turned to point measurement techniques where continuous or high-frequency lasers can provide a detectible signal for photodiodes or photomultiplier tubes. Using an argon-ion laser and iodine "lter, Kuhlman [86] developed a two-component point system. Fig. 27 show two component point measurements across the exit of a fully development turbulent

pipe. Axial mean velocities agree well with pitot probe measurements, but radial velocities have a bias on the order of 2}4 m/s. Grinstead et al. [53] developed a point technique which uses one laser to lock the Rayleigh scattered signal to an absorption line of iodine, while locking a second Nd : YAG laser to a reference iodine cell. The velocity is then determined using an optical heterodyne technique to measure the frequency di!erence of the two signals. Several other investigators have used a Cesium-vapor Faraday cell and actively stabilized laser diode to measure the Doppler-shifted light [54,55,91,92]. The Cesium-vapor Faraday cell is placed between a pair of crossed polarizers. In the presence of a magnetic "eld and with the laser tuned near the atomic resonance lines, the rotation of the polarization plane shows a strong frequency dependence. Detecting the Doppler shifted scattering signal from the #ow and unshifted light through a Cesium vapor Faraday cell, the Doppler shift can be deduced using a harmonic detection technique. Crafton et al. [92] has indicated bias uncertainties of 0.5 m/s and random uncertainties of 0.05 m/s for a velocity measurement range of 20 m/s for systems employing one Cesium-vapor Faraday cell. Another future trend is the use of molecular Rayleigh scattered signal to measure additional thermodynamic quantities. As seen in the equations governing molecular Rayleigh scattering (Eqs. (1)}(4) and Figs. 5 and 6), Rayleigh scattering contains information about the temperature, density, velocity, pressure and composition of the #ow. Filtered Rayleigh Scattering systems have utilized molecular "lters to measure these properties. Also, molecular "lters are used to decrease the scattering of unshifted background light and particles when measuring the much weaker Rayleigh scattered signal as

Fig. 26. Contents of a color Planar Doppler Velocimetry realization of a Mach 1.34 supersonic jet: (a) two-color "ltered image, (b) extracted red image, (c) extracted green image, and (d) resulting velocity image. The #ow is from right to left and the measurements are taken in a region after the jet core has collapsed [90].

G.S. Elliott, T.J. Beutner / Progress in Aerospace Sciences 35 (1999) 799 } 845

841

Fig. 27. Two-component point PDV mean velocity pro"les at the exit of a 1.5A diameter fully-developed turbulent pipe #ow [86].

discussed previously. Miles and Lempert [13,93] "rst proposed the FRS technique to measure thermodynamic properties from the Rayleigh scattered signal. Forkey et al. [21] used the FRS technique to measure the thermodynamic properties of a Mach 2.0 axisymmetric jet. In order to measure multiple properties, images are acquired of the Nd : YAG laser sheet illuminating the #ow"eld as the laser is slowly scanned in frequency through the absorption line of iodine. The result for each pixel is a spectrum for the Rayleigh scattered signal convoluted with the absorption pro"le of the iodine "lter. By the convolution of a Rayleigh scattering model, such as the kinetic Rayleigh-Brillouin scattering model of Tenti [27], and the iodine absorption pro"le, the thermodynamic properties are deduced. Due to laser tuning and camera framing limitations, the FRS technique is limited to average measurements; however, future camera and laser technologies may enable instantaneous measurements to be made within the time scales of some #ow "elds [94]. By reducing the measurement volume to a point, Shelly and Winter [68] demonstrated that the instantaneous mass #ux could be measured using an anamorphic optical system that observes the measurement volume simultaneously from di!erent directions. Since the Doppler shift is dependent on the direction of the scattered light vector, the intensity variation at di!erent angles has a similar e!ect as tuning the laser across the absorption "lter. Elliott and Samimy [95] extended the anamorphic optical system to measure instantaneous

temperature, density, pressure, and velocity simultaneously using a similar optical system. Again this is done using a computer model to "t the anamorphic intensity pro"le to deduce the thermodynamic properties. Another method of obtaining instantaneous property measurements is to reduce the sensitivity of the system to some of the properties. For example Ho!man et al. [96] and Elliott et al. [97,98] have obtained instantaneous temperature measurements using FRS in combustion environments. These temperature measurements are possible if the pressure is constant in the #ame, the Doppler shift sensitivity of the system is not aligned with the #ow "eld, and the Rayleigh scattering cross section and molecular weight is approximately constant (i.e. using a premixed #ame where nitrogen is the dominant species). With these assumptions Elliott et al. [97] were able to measure the temperature of a #ame above a Henken burner to within 2% of the temperature measured using coherent anti-Stokes Raman spectroscopy (CARS). Fig. 28 shows an average and instantaneous images of the two-dimensional temperature "eld above a copperholed-array burner operated at an equivalence ratio of 1.21. Although the average image (Fig. 28a) indicates a relatively uniform #ame, almost all the instantaneous images (Figs. 28b}d) show buoyantly driven vortices rolling up on the edge of the #ame with an associated temperature variation within them. In a later study, Elliott et al. [98] were able to measure the temperature close to surfaces and in particle-laden #ames. This is not possible with standard, un"ltered Rayleigh scattering

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Fig. 28. Average and instantaneous temperature "elds of an unsteady premixed methane #ame taken using FRS [97].

since the unwanted scattering from particles and surfaces can dominate the signal.

7. Conclusions A review of molecular "lter based diagnostic techniques has been presented with an emphasis on Planar Doppler Velocimetry techniques. The background science was discussed along with typical system components and the image processing needed to obtain accurate measurements. Several examples were given of the application of PDV to measure subsonic and supersonic #ows in large- and small-scale facilities. The trend of current PDV system developments indicate that uncertainties on the order of 1 m/s are becoming possible. PDV is also being extended to enable turbulence measurements to be made with an uncertainty of less than 1%. Future trends are likely to be focused on reducing systematic errors, providing more user-friendly systems, developing time resolved point measurements, and measuring multiple thermodynamic properties simultaneously.

Acknowledgements The authors would like to thank Dr. Campbell Carter and Dr. Robert McKenzie for their help in reviewing the manuscript as well as all of the researchers who provided "gures, technical, and historical information to the authors. Dr. Elliott would like to acknowledge the support of the Air Force Research Laboratory with Mr. Harold Baust and Dr. Mark Gruber and the National Science Foundation with Dr. John Foss for funding his research in this area.

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