fluid flow measurements

Int. Comm. Heat Mass Transfer, Vol. 25. No. 1, pp. 1-8, 1998

Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/98 $19.00 + .00

Pergamon

P H S0735-1933(97)00132-2

PRACTICAL COMMON-PATH INTERFEROMETRY FOR REAL-TIME THERMAL/FLUID FLOW MEASUREMENTS

Depang Yant and Soyoung S. Cha Department of Mechanical Engineering University of Illinois at Chicago 2039 ERF, 842 West Taylor Street Chicago, Illinois 60607-7022 U.S.A.

(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT Interferometric technique can be a useful gross-field diagnostic tool for quantitative and qualitative evaluation of thermal/fluid flow phenomena. Here, we present a practical interferometric approach based on a common-path configuration of the interfering beams with some results for demonstration. It incorporates advances in the modern optical technology to fully exploit the potential of interferometric techniques for on-site applications. The results of the initial testing are encouraging. The approach can allow one to build a simple and compact system insensitive to external disturbances for real-time monitoring with good measurement accuracy. The system errors contributed by low-quality optics can be eliminated by employing a moire technique. The approach based on the numerical moire, which utilizes the images directly captured by a solid-state camera to avoid wet chemical processing, appears to be promising. © 1998 Elsevier ScienceLtd

Introduction Interferometric techniques have been frequently employed for measurements of heat/mass transfer and fluid flow fields [1-3].

Interferometric techniques can offer advantages over other

conventional techniques, including gross-field capture, nonintrusive remote sensing, high measurement sensitivity and accuracy, and real-time monitoring capability. In the areas of nondestructive testing for measuring or inspecting solid objects including commercial products, interferometric techniques have already become an indispensable tool. They are now in great utility and demand for industrial precision measurements [4]. In order to fully exploit their potential in thermal/fluid engineering, however, some

t: Currently, a visiting scholar at the University of Illinois at Chicago.

2

D. Yan and S.S. Cha

Vol. 25, No. 1

problems for practical applications need to be resolved in both hardware and software. The hardware and software are closely related. It is important for the hardware to produce appropriate type and quality of data, which are amenable to software processing. The software can in turn minimize the effects associated with hardware deficiencies including noise, thus, to enhance the overall performance. Firstly, the hardware needs to be simple and compact for easy installation and operation. The system should be tolerable of external disturbances including vibration for on-site applications. It is desirable to build a economical system by allowing the use of inexpensive low-quality optics. Secondly, the gross-field information extraction is computation-intensive. The software should provide required processing efficiency for expeditious display without compromising the high accuracy intrinsic to interferometric techniques. The advances in both hardware and software in recent years, however, have provided means in resolving these problems associated with practical applications of interferometric techniques. Currently, small diode-lasers and fast solid-state array sensors are available to build an inexpensive compact system without using bulky lasers as a coherent light source and without going through wet chemical processing for interferometric image capture and analysis. The processing speed of personal computers and software efficiency for interferogram reduction have also been substantially improved in recent years. Traditionally, the Mach-Zehnder interferometry has been employed for thermal/fluid engineering [1,5]. This technique can offer a real-time capability; however, it is based on the interference of two separate beams, which in turn requires isolation from external vibration and use of high-quality optics. It is thus difficult to build a compact inexpensive system. Holographic techniques [6] became available with the advent of lasers as coherent light sources. It offers some merits as compared with the MachZehnder interferometry while also posing some limitations. Utilizing interference of the reconstructed beams that have passed through the same path, it can eliminate the phase errors generated by low-quality optics. However, it is sensitive to external vibration during hologram recording. A pulsed laser can be incorporated to avoid the vibration effects but with only added complexity and cost. Real-time imaging is possible but at the expense of image quality.

Here, we present the concept of common-path

interferometry with some measurement demonstration. It incorporates the advances in the modem optical technology to fully exploit the potential of interferomeric techniques for practical applications in heat/mass transfer and fluid flow.

Vol. 25, No. 1

INTERFEROMETRY FOR FLOW MEASUREMENTS

3

Experimental Setup~ Operation and Data-Processing Principle, and Measurement Demonstration

It is well known that the Fabry-Perot interferometry [7] can be used for measuring phase objects. The interferometric setup presented here is a modification of the Fabry-Perot configuration.

The

schematic of the common-path interferometer is shown in Fig. 1. In the setup, the laser beam is expanded by microscope and spatial filter assembly LI and collimated by lens L 2. The beam is then further expanded by lenses L 3 and L4. The expanded and collimated beam passes through the test section with optical windows W 1 and W 2, which contains the flow to be measured. The beam is then narrowed down to a small size by lenses L 5 and L 6 for gross-field capture by a solid-state detector array. The optical elements that generate fringes, that is, interfering beams, are the beam splitters B 1 and B2, with their coated surfaces facing each other. The beam splitters produce a directly-transmitted beam together with the multiply-reflected and transmitted beams. These beams interfere each other to produce an interferogram of the flow field. Bright fringes thus appear wherever the phases differ by an inter multiple of 2m If it is possible to use large beam splitters or a small field is measured, the lenses L2 and L3 can be removed by inserting the beam splitters directly between lenses L4 and L 5. If the beam splitters are parallel, an infinite-fringe pattern is formed. A finite-fringe pattern can be produced by tilting a beam splitter.

W 1

L,

W2

Detector

"ql L4 F1//owfield

Ls

[ ] ~=:=

B: B e a m Splitter L: Lens W: Optical W i n d o w

FIG. 1 Schematic of the common-path interferometer.

Computer

[

4

D. Yan and S.S. Cha

Vol. 25, No. 1

Assume inclination angle a of B 1. By neglecting the contributions by the optical windows and the test flow field, it can be shown [7] that the effective phase difference 8,, due to different optical pathlengths of the directly-transmitted and the mth reflected-transmitted beams is 8 m = 4~ d s i n m a cosmc~ )~o tanc~

(1)

where d is the effective optical pathlength between the two beam splitters. For small angle c~, Eq. (1) reduces to a m = m( 47~ d o + A S ~ ) .

(2)

Xo where AS0~ due to the tilt of a bean splitter is ABet = 4 r t noCtX. ~o

(3)

Here, x is the distance from the reference point along the inclination direction.

In Eq. (2), the

relationship of d = d o + noc~X is used. As indicated similarly to ordinary interferometry, fringes of the same intensity appear wherever the phase difference 81, which corresponds to the phase difference in each round-trip reflection, becomes an integer multiple of 2r~. However, the fringe intensity becomes the Airy distribution [7] due to the interference of multiple beams. With a flow field added, 81 becomes 81 (x, y) = A8c¢ + 2q~(x, y)

(4)

where ~(x,y) is the phase change in a single path through the flow field. As seen, the sensitivity is doubled in the common-path interferometry. Without a flow, the carrier fringe interval Ax is thus Ax-

;~o 2nor

(5)

Figure 2 shows the interference pattern thus formed by tilting a beam splitter. As expected, the fringes are parallel with an equal interval. If the reflectance of the beam splitters is greater than 0.5, the fringe sharpness becomes greater than common sinusoidal patterns, In our experiments, the reflectance ranging from 0.6 to 0.7 was tested even though other values were feasible, depending on experimental conditions and optimization,

For these values, only the directly-transmitted and first few reflected-transmitted

beams were important. When low-quality optics including test section windows W 1 and W 2 are deployed, wavefronts, that is, fringe patterns, become distorted to produce system errors of E(x,y) in interferometric phase measurements.

Figure 3 demonstrates an interferogram formed by using inferior plexiglas as the test

section windows, which produced serious distortions. In order to eliminate the system errors, a moire technique can be employed. For example, an initial interferogram without a flow is recorded with carrier fringes on a photographic film, i.e., glass-backed holographic plate.

After developing the film, the

Vol. 25, No. 1

INTERFEROMETRY FOR FLOW MEASUREMENTS

FIG. 2. Interferogram formed by tilting a beam splitter without a flow field.

FIG. 3 Erroneous fringe pattern contributed by low-quality test-section windows.

5

6

D. Yan and S.S. Cha

Vol. 25, No. 1

interferogram is placed at its original position. The second interferogram formed with the flow in the test section is then detected through a transparency of the initial interferogram, that is, by superimposing the two interferograms.

If so, by assuming sinusoidal fringe patterns, the normalized superimposed

intensity l(x,y) becomes I ( x , y ) = I~(x,y) + I2(x,y ) = {1 + cos[e(x, y) + A6 a 1} + {1 + cos[e(x, y) + A~Sct + 2qb(x, y)]}

(6)

= 2 + 2 cos[~:(x, y) + A6 a + ~(x, y)] cos d~(x, y). In Eq. (6), only the cosine-term containing a low frequency of ~(x,y), which represents only the disturbance by a flow, is detectable by a solid-state camera. The high-frequency term containing A5 a and c(x,y) is either invisible or can be averaged out. In this manner, the system errors that exist in both interferograms can be substracted out. Our experimental measurements based on the photographic moire worked well to obtain good-quality interferograms. Since the interfering beams follow the same paths as indicated, the common path interferometer can be made compact for easy setup and insensitive to external vibrations. The phase errors by lowquality optics can also be substracted out and real-time-monitoring is possible. In order to make the interferometer truly practical without wet-chemical processing and remounting of a photographic transparency, a simple approach based on numerical moire was tested as explained below.

In the

approach, the initial and second interferograms of l l(x,y ) and 12(x,y ) without and with a flow, respectively, were captured directly by a CCD array of 512 x 480 pixels and their intensity values were stored on a computer. These images were then numerically added and displayed on the monitor to form a digital moire pattern, as represented by Eq. (5) with only the low-frequency cosine-term of ~(x,y) detectable.

For experiments, an argon-ion laser and a thermal plume generated by a heater were

employed as a coherent light source and a test field, respectively. Carrier fringes of about 8 fringeshnm in frequency were generated by tilting a beam splitter as explained before. The test section windows were those shown in Fig. 3. The moire interferogram thus formed by a computer is shown in Fig. 4. We can see that the fringes representing iso-phase lines appear without the system errors contributed by the windows. The image quality is reasonably good even with the CCD sensor of limited resolution. It is believed that the image quality can be substantially improved if a high-resolution camera, i.e., 2,000 x 2,000 pixels is employed. The photographic moire can be adopted if ultimate image quality is needed. Interferogram reduction accuracy strongly depends on processing algorithms.

Interferograms

can be captured in a single frame or multiple frames through phase stepping for each flow moment. Typical processing algorithms [8] can be those based on a single frame, that is, fringe tracking, Fourier transform, and regression approaches, and those based on phase-stepped multiple frames. The fringe

Vol. 25, No. 1

INTERFEROMETRY FOR FLOW MEASUREMENTS

7

tracking that has been frequently employed in thermal/fluid flow provides limited accuracy less than X/10 in pathlength but the regression can offer accuracy close to Z/100, which can be sufficient for most applications.

These techniques are relatively slow in processing.

The phase stepping for ultimate

processing speed and accuracy better than X/100, however, can be achieved with slight modification of the hardware shown in Fig. 1. For example, a liquid-crystal phase retarder can be inserted and phase stepped frames can be rapidly captured in sequence for each flow instance.

Conclusions

The experimental concept and test demonstration of the common-path interferometry, which is based on the Fabri-Perrot configuration, have been presented. The technique can provide a simple and compact system, which is insensitive to external disturbances and allows for real-time monitoring with good measurement accuracy. The system errors contributed by low-quality optics can be eliminated by employing a moire technique. As seen in demonstration, the approach based on convenient numerical moire produced good images even with low-quality test-section windows and a low-resolution CCD camera.

It is believed that the image quality can be substantially enhanced when a high-resolution

camera is deployed. Future investigation can be testing of the systems that incorporate phase-stepping techniques.

FIG. 4 Computer-generated moir6 fringes of a thermal plume by common-path interferometry.

8

D. Yan and S.S. Cha

Vol. 25, No. 1

Nomenclature

d do no C~

8m

effective optical pathlength d at the reference point refractive-index of the ambient medium tilt angle of a beam splitter phase difference of the ruth ray

Ax ASct ~b )~o

fringe interval contribution by carrier fringes error contribution by the optical system phase change due to a flow laser wavelength in vacuum

References

1. K. J. Choi and S. Cha, J. ThermophysicsHeat Transfer, 4, 228 (1990). 2. L. W. Carr and Y. H. Yu, Opt. Lasers Engng. 17, 121 (1992). 3. S. Bahl and J. A. Liburdy, Int, J. Heat Mass Transfer 34, 949 (1991). 4. Hologram Interferometry and Speckle Metrology, Proceedings' of Society for Experimental Mechanics, Baltimore, MD (1990). 5. R. Boyce, J. Morton, F. Houwing, C. Mundt, and D. J. Bone, CFD Validation Using Multiple Interferometric Views of Three-Dimensional Shock Layer Flows over a Blunt Body, Paper 94-0282, AIAA 32nd Aerospace Sciences Meeting & Exhibit, Reno, NV (1994). 6. C. M. Vest, Holographic Interferometry, Wiley, New York (1979). 7. M. Born and E. Wolf, Principles of Optics, 5th ed,, chap. 7, Pergamon, New York (1975). 8. J. S. Slepicka and S. S. Cha, Appl. Opt. 34, 5039 (1995).

ReceivedAugust 7, 1997