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Point diffraction interferometer for fluids study in microgravity environment
Point Diffraction lnterferometer for Fluids Study in Microgravity Environment S. Musazzi U. Perini F. Trespidi CISE Technologie Innovative SpA, Segrate, Milan, Italy
• We present an interferometric apparatus for fluids study that will be used for experiments in microgravity onboard Spacelab in the IML2 mission (scheduled for early 1994). The point diffraction interferometer (PDI) was selected from among various types of interferometers because of its simplicity and inherent stability. Furthermore, because of the environmental conditions in which the instrument has to operate, and to reduce the manipulations of the Spacelab payload specialist, the main technical objective was to design a system where the most delicate operation, the control of the alignment of the optical components, is made by an active servosystem. The servosystem also allows the interferometer to work properly in the presence of large refractive index gradients. Furthermore, when the perturbation becomes so great that the use of interferometric equipment becomes questionable, the interferometric assembly can easily be switched to a schlieren system; which is more appropriate for observing strong index of refraction variations. A laboratory prototype of the instrument has been developed and successfully tested. The instrument that will be mounted onboard Spacelab is under construction and is to be completed by the end of 1992.
Keywords: Point diffraction interferometer, transparent fluids diagnostic, microgravity INTRODUCTION Scientific and technological interest in the behavior of fluids in a low-gravity environment has greatly increased since the beginning of scientific experimentation in space. In space, in fact, unlike ground laboratories, very low gravity levels can be reached and maintained for relatively long periods. Microgravity is a quite interesting environment because it implies a drastic reduction of hydrostatic pressure, sedimentation, buoyancy, and consequently thermal and solutal convection. This has consequences for virtually all processes involving fluid phases, and a number of experiments dealing with the influence of gravity on capillarity phenomena, solidification, heat and mass transfer, critical point phenomena, etc. have already been performed or are planned for the near future [1]. The consequence of this increasing interest in spaceborne experiments is the demand from the scientific community for appropriate instrumentation. It must be emphasized that conventional instruments and techniques can not usually be used in space applications because they do not fulfill the very tough and stringent requirements imposed by such activities, so the demand is now for a new class of space-dedicated instruments that are not commercially available. An interesting group of optical techniques, very promis-
ing for the analysis of fluids, is represented by interferometric methods. They are, in fact, noninvasive measuring systems that allow quantitative monitoring of index of refraction variations. Among the various types of interferometric techniques the point diffraction interferometer (PDI) [2-4] shows very interesting features that make it very attractive for space applications. The most important one is that the reference is taken from the test beam; thus interferograms are immune from disturbances such as those produced by environmental mechanical vibrations or caused by random phase modulations in the reference beam path. When compared with other interferometric techniques, the advantages of using a PDI for space applications become evident. All the conventional two-beam interferometers [5], in fact, show a high sensitivity to environmental conditions such as mechanical vibrations and thermal stress. Only differential interferometers [5, 6] are intrinsically stable because the two beams travel on the same path. Unfortunately, for many applications this technique does not offer any advantage over direct interferometry, being actually less sensitive and the interferograms more complex to interpret. Holographic interferometry [7] presents the advantage of giving an enormous amount of information because the interferograms generated offer a three-dimensional mapping of the fringes. Furthermore it is possible to perform
Address correspondence to Dr. S. Musazzi, CISE SpA, P.O. Box 12081, 1-20134 Milano, Italy.
Experimental Thermaland Fluid Science 1993; 6:49-55 © 1993 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
0894-1777/93/$5.00 49
50 S. Musazzi et al. interferometric measurements on test samples that have no stringent requirements in terms of optical quality. This would be a decisive factor if one had to investigate systems with awkward geometry. However, the holographic technique does not have the simplicity and inherent stability of a PDI arrangement. In this paper we discuss the work we have done to develop a PDI-based optical arrangement to be used during space missions. It must be anticipated that PDI (as described in the literature) does not work properly in the presence of large refractive index gradients and hence cannot be used in its basic configuration. Much of our activity has been dedicated to this problem, which has been solved by implementing the PDI scheme with a servo-system alignment-control loop. Since the instrument was conceived to reduce the manipulations of the payload specialist, the same servo system controls the alignment procedure during the start up periods in the mission. Another important aspect of this instrument is the possibility of changing configuration and switching from a PDI scheme into a schlieren mode of operation. A laboratory prototype of this instrument has been developed and successfully tested (some results will be presented). An engineering version of the same apparatus is now under construction and will be part of the BDPU (Bubble, Drop and Particle Unit) facility that will be flown onboard Spacelab in the IML2 mission (scheduled for early 1994).
a small pinhole in the center. The size of the pinhole is a fraction of the theoretical unaberrated point-spread function of the lens. By diffraction this small aperture generates a spherical wave-front that will interfere with the wave-front transmitted through the semitransparent plate. If no aberrations occur in the test region and the focusing lens is a perfect one, in the plane of the PDI we will obtain a diffraction-limited spot. In this case, under the assumption that the PDI pinhole is positioned in correspondence with the optic axes, no interference fringes are generated. If the plate is now displaced along the optic axis away from the focal plane, circular interference fringes appear because the two wave fronts have longitudinally displaced centers of curvature. For a displacement orthogonal to the axis, straight fringes are produced. This behavior is similar to that of other interferometers, such as the TwymanGreen interferometer. When an aberrated test wave front is focused onto the PDI plate, the resulting interference pattern provides a direct measurement of the wave-front distortions. The fringes, in fact, map regions of equal optical path difference, the optical path difference between adjacent fringes being one wavelength. Angular directions define the correspondence between fringes and positions on the region under test. A second lens can also be used to give an image of the region under test. PDI Servo System for Fluids Analysis
POINT DIFFRACTION INTERFEROMETER FOR FLUID MOTION
Principle of Point Diffraction Interferometer The point diffraction interferometer, which was first described by Smartt and Strong in 1972 [2], is based on the interference of the test beam with a reference beam obtained from a small portion of the test beam itself. It is used mostly to test optical elements, lenses, and telescopes [3, 4], but it can also be used to detect wave-front distortions caused by a perturbation of the refractive index in the test beam path. The PDI principle of operation is illustrated in Fig. 1. A collimated light beam, after crossing a test region, is focused via a lens onto a plane P where the PDI plate is positioned. The PDI plate is a semitransparent plate with
When the PDI has to be used to study fluids it cannot be arranged in the simple geometry described in the previous section. A more sophisticated system has to be implemented. To understand how the original PDI setup has to be modified to allow reliable fluids analysis it is necessary to first briefly consider the behavior of the intensity distribution in the plane of the PDI plate (the focal plane) as refractive index gradients are created in the fluid test sample. Let us suppose we progressively distort the test beam wave-front and follow in a qualitative manner the way in which the intensity distribution is correspondingly modified in the focal plane. If we assume that distortions are everywhere small compared with the wavelength of light, the resulting interferogram contains one or a few fringes, and the intensity distribution in the focal plane
PDI
TEST) WAVEFRONT
\
!rlt_n D
(a)
(REFERENCE) WAVEFRONT
PLATE
x
(b)
Figure 1. PDI principle of operation. (a) Interference between the transmitted beam and the self-generated spherical reference beam; (b) PDI plate transmission function.
Point Diffraction Interferometer 51 displays only one peak whose diameter is larger than the diffraction-limited spot. For small distortions one can show that the widening of the focal spot does not depend on the actual shape of the deformation, but depends solely on the rms wave distortions [8]. As the wave distortion is increased, the broadening becomes more pronounced and irregular, departing in general from axial symmetry. In the limit of a highly distorted wave-front, the focal plane intensity distribution tends to assume a speckle-type form, that is, one with areas of relatively high intensity surrounded by low-intensity areas. It may happen in this case that a "dark speckle" overlaps the PDI pinhole, thus preventing the reference beam from being generated and causing the interferogram to lose visibility. To maintain adequate power in the reference beam, a servo-system alignment-control loop has been implemented. The scheme of the servo is shown in Fig. 2. A beamsplitter is placed before the PDI plate. The reflected part of the beam falls on the center of the PDI plate while the transmitted portion is collected by a microscope objective that forms an enlarged image of the focal plane intensity distribution on the surface of a position-sensing device (a quadrant detector) whose center is optically conjugate with the PDI pinhole. The ratio of the magnified diffraction spot diameter to the sensor diameter is a critical parameter. The diameter of the sensor must be large enough to span a few speckles so that a bright speckle will always be present in its active area. Displacements of the intensity distribution in the plane of the quadrant detector (and consequently in the plane of the PDI) are obtained by means of a steering element. This component is a tilting mirror positioned on a gimbal mount. Rotations around the horizontal and vertical axes are provided by two piezoceramic actuators whose driving voltage is proportional to the signal difference between opposing sensor elements of the quadrant detector. The signals coming from the four elements are summed, thus providing a signal proportional to the total intensity falling over the entire area of the sensor. When the perturbations on the test wave front become sufficiently
=ZT
Y
CELL
TILTING MIRROR LASER BEAM
PDI [ ' ~ - "PLATEU MICROSCOPE OBJECTIVE
BEAM SPLITTER CUBE
<) SERVO UNIT
DETECTOR
E
-1
Figure 2. Servo-system alignment-control loop.
l
large, the spread of the (averaged) intensity distribution in the focal plane becomes substantial. Many speckles are created, and consequently the peak intensity is low. Dividing the error signals by the sum signal, it is possible to normalize the error signal amplitude fluctuations to the total amount of light impinging on the sensor so as to have an error signal that is independent of the degree of perturbation. When the sum signal falls below a properly set threshold (as in the case of a very strong perturbation or a misalignment), an automatic search mode of operation is activated. A two-dimensional scan is performed by the tilting mirror, and the system seeks for any prominent feature in the focal plane intensity distribution. The search continues until a new peak of adequate intensity is found. The servo then resumes its normal function and latches onto the newly found peak. Incidental strong mechanical shocks on the optical bench, can cause a temporary misalignment of the interferometer. To avoid a useless and time-consuming activation of the search mode of operation, which would cause an interruption in the measurement, a shock detector circuit (working on the sum signal) disables the search mode when a shock is revealed.
PDI Instrument for Spacelab The PDI-based optical equipment is shown in Fig. 3. The light emerging from a 2 mW He-Ne laser source is expanded by means of a custom-made spatial filter assembly directly clamped to the laser support. The diverging beam is reflected by two mirrors (flatness A/20) so as to follow a folded path, then is collimated by an achromat doublet that is placed at a distance from the spatial filter pinhole equal to its focal length (0.5 m). The plane wave (a 0.07 m diameter parallel beam) propagating from the achromat doublet crosses the region of the fluid test container and is focused by a second achromat doublet identical to the first. After reflection onto a mirror (flatness A/20), the focused beam impinges on the tilting mirror (flatness A/20). The tilting mirror mount is a custom-made ballbearing playless gimbal mount provided with air dampers and balancing masses. Positioning of the two frames rotating around the vertical and horizontal axes is performed by means of piezoelectric transducers whose driving voltage is provided by a voltage amplifier controlled by a servo unit (operating in the integral configuration). The description of the PDI servo loop optical scheme was given in the previous subsection and will not be repeated here. To have a system capable of performing other kinds of fluid diagnostics, both a vertical and a horizontal blade for schlieren observation are mounted, on the same PDI plate support. Selection of the diagnostic apparatus (PDI, vertical blade, horizontal blade) is attained by positioning the selected tool in correspondence with the optic axes. Displacement of the diagnostic tools is performed by means of a translation stage driven by a dc motor. The actual position of the translation stage is detected by an optical encoder (solidly mounted to the translation stage mount) whose output is fed to a motor control unit. Observation of the output from the three diagnostic
52
S. Musazzi et al. VERT. BLADE
HORIZ. BLADE
PDI LASER
SPATIAL FILTER MIRROR
TILTING MIRROR POSITION DETECTOR TRANSLATION STAGE
~----~CCD CAMERA LENS
TEST CELL
LENS!
;
1
MIRROF Figure 3. PDI general layout.
equipments (interferograms, schlieren patterns) is performed by a CCD camera. The main technical characteristics of the instrument are as follows. • The tilting mirror has been designed to compensate for beam angular displacements caused by both vertical and horizontal constant gradients (in the test fluid) of _+ 120 K in water, which correspond to a beam deflection of + 12 mrad. The tilting mirror angular position sensitivity is on the order of 10 -6 of the total compensating capability angular range. • During startup operations, the average time required by the system for alignment is 20 s. • The alignment control system bandwidth is about 10 Hz. This means that the time constant of the system is about 0.02 s, which is typically smaller than the time constant of a perturbation in a fluid. • The dynamic range is 104; that is, the system maintains alignment until the light level measured by the quadrant detector is as low as 10 4 of the intensity measured when no perturbation is present in the test region. • The instrument can work in three different configurations: as a PD! interferometer; in the vertical schlieren configuration; and in the horizontal schlieren configuration. The average time required to switch from one configuration to another is less than 40 s. • The field of view is 0.04 m × 0.06 m and can be increased to a circular region 0.07 m in diameter by changing the CCD camera objective.
EXPERIMENTAL RESULTS A number of tests have been performed to check the system capabilities. Some video hard copies of the most significant interferograms are presented in Figs. 4-6. It must be pointed out that interferograms show a twodimensional index of refraction distribution, and consequently fringes describe index of refraction variations averaged along the direction of propagation of the probe beam. The interferogram in Fig. 4 shows the temperature gradient distribution close to a soldering tip in air. (The tip length in the figure is about 5 cm.) Because of the low dn/dT of the air, only a few fringes surrounding the soldering tip are observed. With the tip temperature being about 500 K we can appreciate a temperature difference between two adjacent fringes of about 70 K. Optical disturbances in the picture are caused by the CCD camera objective because a commercial camera with nonoptimized lens coating was used for these tests. The results of a test on a pure liquid are shown in the sequence reported in Fig. 5. A cylindrical test cell (0.07 m long, 0.065 m diameter) with the cylinder axes parallel to the optic axes is filled with water and warmed by a heater (100 W, 3 12 resistor) placed below the cell bottom. About 60 s after the heater is switched on, a hot plume rises from the cell bottom (see Fig. 5a). Successively other convective motions appear as shown in Figs. 5b and 5c. These interferograms were recorded about 90 and 120 s, respectively, after the beginning of the heating process. Once the heater is turned off the fringes inside the test cell tend to become horizontal (Fig 5d); that is, a vertical temperature gradient is now present in the liquid. It can be noticed that in this test the revealed temperature gradients (AT) are much smaller than in the previous
Point Diffraction Interferometer 53 alcohol into a water-filled cell (the cell is the same one used for the test on a pure liquid). At the beginning the perturbation in the fluid is on a spatial scale too small to be resolved by the system, and no fringes can be observed (Fig. 6a). After a few seconds the two fluids tend to mix, and the fringes become visible as shown in Figs. 6b, 6c, and 6d (recorded about 30, 180, and 600 s, respectively, after the injection of alcohol into the test cell). It must be emphasized that because of the very strong perturbation in the test fluid the intensity distribution in the plane of the PDI becomes very broad, and consequently the intensity of the beam actually impinging on the PDI (and consequently on the quadrant detector) becomes dramatically small. Nevertheless the dynamic range of the instrument is so wide that the measurement has been performed without activation of the automatic search mode of operation. PRACTICAL USEFULNESS OF T H E PDI-BASED OPTICAL A R R A N G E M E N T As anticipated, the optical arrangement described in this paper will be used in the IML2 Spacelab mission (scheduled for 1994) as part of the Bubble Drop and Particle Unit (BDPU) facility. This is a facility dedicated to the study of the behavior of bubbles, drops, and particles in transparent fluids. Examples of experiments to be performed by means of this facility and requiring interferometric/schlieren analysis are:
Figure 4. Interferogram showing the refractive index distribution around a hot soldering tip in air. case. Knowing the test cell thickness L along the optic axis • (0.07 mm) and d n / d T for water (9 x 10- 5 in the range of temperatures of interest), we can calculate the AT necessary to produce one fringe. A dark fringe appears when the optical path difference between reference and measurement beams is equal to A/2. Thus, A n L = A/2 where An is the variation of the refractive index due to a thermal gradient. We obtain A n = A / 2 L = 4.5 X 10 - 6
Since A n ~ A T
=9 x 10 -5, we have AT
An 9 × 10 -5
0.05 K
This means that since a fraction of a fringe can easily be evaluated, temperature variations smaller than 0.05 K can be measured in water. As the third example, we show the mixing of two fluids with different indices of refraction. The sequence in Fig. 6 shows the interferograms generated after an injection of
• Bubble, drop, and particle behavior in fluids under the influence of temperature and concentration gradients and electric fields • Formation and dynamics of solidification fronts • Interaction between inclusions and solidification fronts • Flow phenomena such as Marangoni convection • Crystal growth from solutions It must be pointed out, however, that apart from application of this system to space activities, the described instrumentation can conveniently be used in any laboratory where experiments on transparent fluids are performed. CONCLUSIONS In this paper we have described a new interferometric equipment for the study of fluids. It is based on a point diffraction interferometer implemented by an active servo system designed to allow the system to work in the presence of large refractive index gradients. A laboratory demonstration unit has been constructed, and experimental results of tests performed on pure fluids and liquid mixtures have been presented. The interferometric equipment has been designed taking into account the criteria set for space applications; for example, it is completely automatic to minimize manipulations of the payload specialist, only materials a n d / o r treatments allowed for space applications have been selected, and optical and mechanical components have been designed to survive (both from the structural and functional point of view) thermal and mechanical stresses
54
S. Musazzi et al.
(a)
(b)
(c)
(d)
Figure 5. Sequence of interferograms showing the evolution of the index of refraction distribution in a water-filled cell heated from below. during the mission. The flying model of the instrument is now under construction and will be flown o n b o a r d Spacelab in the IML2 mission. Future developments of the P D I apparatus that can be
(a)
(c)
foreseen at this m o m e n t mainly concern the laser source. New and more reliable laser sources such as laser diodes, not available (or reliable) when the instrument was designed, can now be used. Not only are laser diode sources,
(b)
(d)
Figure 6. Sequence of interferograms showing the evolution of the index of refraction distribution in a liquid mixture obtained after the injection of alcohol into a water-filled cell.
Point Diffraction Interferometer in particular, a d e q u a t e for space application (they are m o r e compact and robust than H e - N e lasers and do not require a high driving voltage, thus reducing safety problems), but also they offer a n u m b e r o f advantages from the experimental point of view. By using two laser diodes, in fact, it will be possible to obtain interferograms at two different wavelengths so as to p e r f o r m studies on both t e m p e r a t u r e and concentration distributions in a fluid at the same time. The use of two different wavelengths will also allow the d e t e r m i n a t i o n of the sign ( + or - ) of the m e a s u r e d index of refraction gradients. We wish to thank Prof. M. Giglio, UniversitA degli Studi of Milan, for his essential contribution during the first stages of the work and for useful discussions. This work was supported by the ESA-ALENIA contract BDPU.
NOMENCLATURE L T A n
test cell length, m temperature, K wavelength, m index of refraction, dimensionless
55
REFERENCES 1. Walter, H. U., Fluids Sciences and Material Science in Space, Springer-Verlag, Berlin, 1987. 2. Smartt, R. N., and Strong, J., Point Diffraction Interferometer, J. Opt. Soc. Am., 62, 737, 1972. 3. Viswanathan, V. K., Liberman, I., Lawrence, G., and Seery, B. D., Optical Analysis of Laser Systems Using Interferometry, Appl. Opt., 19, 1870-1873, 1980. 4. Koliopoulos, C., Kwon, O., Shagan, R., Wyant, J. C., and Hayslett, C. R., Infrared Point Diffraction Interferometer, Opt. Lett., 3, 118-121, 1987. 5. Fran§on, M., Optical Interferometry, Academic, New York, 1966. 6. Fran~on, M. H., and Mallick, S., Polarization Interferometers: Applications in Microscopy and Macroscopy, Wiley-Interscience, London, 1971. 7. Vest, C. M., Holographic Interferometry, Wiley, New York, 1979. 8. Born, M., and Wolf, E., Principles of Optics, Pergamon, London, 1959.
Received Nov. 19, 1991; revised June 30, 1992
• We present an interferometric apparatus for fluids study that will be used for experiments in microgravity onboard Spacelab in the IML2 mission (scheduled for early 1994). The point diffraction interferometer (PDI) was selected from among various types of interferometers because of its simplicity and inherent stability. Furthermore, because of the environmental conditions in which the instrument has to operate, and to reduce the manipulations of the Spacelab payload specialist, the main technical objective was to design a system where the most delicate operation, the control of the alignment of the optical components, is made by an active servosystem. The servosystem also allows the interferometer to work properly in the presence of large refractive index gradients. Furthermore, when the perturbation becomes so great that the use of interferometric equipment becomes questionable, the interferometric assembly can easily be switched to a schlieren system; which is more appropriate for observing strong index of refraction variations. A laboratory prototype of the instrument has been developed and successfully tested. The instrument that will be mounted onboard Spacelab is under construction and is to be completed by the end of 1992.
Keywords: Point diffraction interferometer, transparent fluids diagnostic, microgravity INTRODUCTION Scientific and technological interest in the behavior of fluids in a low-gravity environment has greatly increased since the beginning of scientific experimentation in space. In space, in fact, unlike ground laboratories, very low gravity levels can be reached and maintained for relatively long periods. Microgravity is a quite interesting environment because it implies a drastic reduction of hydrostatic pressure, sedimentation, buoyancy, and consequently thermal and solutal convection. This has consequences for virtually all processes involving fluid phases, and a number of experiments dealing with the influence of gravity on capillarity phenomena, solidification, heat and mass transfer, critical point phenomena, etc. have already been performed or are planned for the near future [1]. The consequence of this increasing interest in spaceborne experiments is the demand from the scientific community for appropriate instrumentation. It must be emphasized that conventional instruments and techniques can not usually be used in space applications because they do not fulfill the very tough and stringent requirements imposed by such activities, so the demand is now for a new class of space-dedicated instruments that are not commercially available. An interesting group of optical techniques, very promis-
ing for the analysis of fluids, is represented by interferometric methods. They are, in fact, noninvasive measuring systems that allow quantitative monitoring of index of refraction variations. Among the various types of interferometric techniques the point diffraction interferometer (PDI) [2-4] shows very interesting features that make it very attractive for space applications. The most important one is that the reference is taken from the test beam; thus interferograms are immune from disturbances such as those produced by environmental mechanical vibrations or caused by random phase modulations in the reference beam path. When compared with other interferometric techniques, the advantages of using a PDI for space applications become evident. All the conventional two-beam interferometers [5], in fact, show a high sensitivity to environmental conditions such as mechanical vibrations and thermal stress. Only differential interferometers [5, 6] are intrinsically stable because the two beams travel on the same path. Unfortunately, for many applications this technique does not offer any advantage over direct interferometry, being actually less sensitive and the interferograms more complex to interpret. Holographic interferometry [7] presents the advantage of giving an enormous amount of information because the interferograms generated offer a three-dimensional mapping of the fringes. Furthermore it is possible to perform
Address correspondence to Dr. S. Musazzi, CISE SpA, P.O. Box 12081, 1-20134 Milano, Italy.
Experimental Thermaland Fluid Science 1993; 6:49-55 © 1993 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
0894-1777/93/$5.00 49
50 S. Musazzi et al. interferometric measurements on test samples that have no stringent requirements in terms of optical quality. This would be a decisive factor if one had to investigate systems with awkward geometry. However, the holographic technique does not have the simplicity and inherent stability of a PDI arrangement. In this paper we discuss the work we have done to develop a PDI-based optical arrangement to be used during space missions. It must be anticipated that PDI (as described in the literature) does not work properly in the presence of large refractive index gradients and hence cannot be used in its basic configuration. Much of our activity has been dedicated to this problem, which has been solved by implementing the PDI scheme with a servo-system alignment-control loop. Since the instrument was conceived to reduce the manipulations of the payload specialist, the same servo system controls the alignment procedure during the start up periods in the mission. Another important aspect of this instrument is the possibility of changing configuration and switching from a PDI scheme into a schlieren mode of operation. A laboratory prototype of this instrument has been developed and successfully tested (some results will be presented). An engineering version of the same apparatus is now under construction and will be part of the BDPU (Bubble, Drop and Particle Unit) facility that will be flown onboard Spacelab in the IML2 mission (scheduled for early 1994).
a small pinhole in the center. The size of the pinhole is a fraction of the theoretical unaberrated point-spread function of the lens. By diffraction this small aperture generates a spherical wave-front that will interfere with the wave-front transmitted through the semitransparent plate. If no aberrations occur in the test region and the focusing lens is a perfect one, in the plane of the PDI we will obtain a diffraction-limited spot. In this case, under the assumption that the PDI pinhole is positioned in correspondence with the optic axes, no interference fringes are generated. If the plate is now displaced along the optic axis away from the focal plane, circular interference fringes appear because the two wave fronts have longitudinally displaced centers of curvature. For a displacement orthogonal to the axis, straight fringes are produced. This behavior is similar to that of other interferometers, such as the TwymanGreen interferometer. When an aberrated test wave front is focused onto the PDI plate, the resulting interference pattern provides a direct measurement of the wave-front distortions. The fringes, in fact, map regions of equal optical path difference, the optical path difference between adjacent fringes being one wavelength. Angular directions define the correspondence between fringes and positions on the region under test. A second lens can also be used to give an image of the region under test. PDI Servo System for Fluids Analysis
POINT DIFFRACTION INTERFEROMETER FOR FLUID MOTION
Principle of Point Diffraction Interferometer The point diffraction interferometer, which was first described by Smartt and Strong in 1972 [2], is based on the interference of the test beam with a reference beam obtained from a small portion of the test beam itself. It is used mostly to test optical elements, lenses, and telescopes [3, 4], but it can also be used to detect wave-front distortions caused by a perturbation of the refractive index in the test beam path. The PDI principle of operation is illustrated in Fig. 1. A collimated light beam, after crossing a test region, is focused via a lens onto a plane P where the PDI plate is positioned. The PDI plate is a semitransparent plate with
When the PDI has to be used to study fluids it cannot be arranged in the simple geometry described in the previous section. A more sophisticated system has to be implemented. To understand how the original PDI setup has to be modified to allow reliable fluids analysis it is necessary to first briefly consider the behavior of the intensity distribution in the plane of the PDI plate (the focal plane) as refractive index gradients are created in the fluid test sample. Let us suppose we progressively distort the test beam wave-front and follow in a qualitative manner the way in which the intensity distribution is correspondingly modified in the focal plane. If we assume that distortions are everywhere small compared with the wavelength of light, the resulting interferogram contains one or a few fringes, and the intensity distribution in the focal plane
PDI
TEST) WAVEFRONT
\
!rlt_n D
(a)
(REFERENCE) WAVEFRONT
PLATE
x
(b)
Figure 1. PDI principle of operation. (a) Interference between the transmitted beam and the self-generated spherical reference beam; (b) PDI plate transmission function.
Point Diffraction Interferometer 51 displays only one peak whose diameter is larger than the diffraction-limited spot. For small distortions one can show that the widening of the focal spot does not depend on the actual shape of the deformation, but depends solely on the rms wave distortions [8]. As the wave distortion is increased, the broadening becomes more pronounced and irregular, departing in general from axial symmetry. In the limit of a highly distorted wave-front, the focal plane intensity distribution tends to assume a speckle-type form, that is, one with areas of relatively high intensity surrounded by low-intensity areas. It may happen in this case that a "dark speckle" overlaps the PDI pinhole, thus preventing the reference beam from being generated and causing the interferogram to lose visibility. To maintain adequate power in the reference beam, a servo-system alignment-control loop has been implemented. The scheme of the servo is shown in Fig. 2. A beamsplitter is placed before the PDI plate. The reflected part of the beam falls on the center of the PDI plate while the transmitted portion is collected by a microscope objective that forms an enlarged image of the focal plane intensity distribution on the surface of a position-sensing device (a quadrant detector) whose center is optically conjugate with the PDI pinhole. The ratio of the magnified diffraction spot diameter to the sensor diameter is a critical parameter. The diameter of the sensor must be large enough to span a few speckles so that a bright speckle will always be present in its active area. Displacements of the intensity distribution in the plane of the quadrant detector (and consequently in the plane of the PDI) are obtained by means of a steering element. This component is a tilting mirror positioned on a gimbal mount. Rotations around the horizontal and vertical axes are provided by two piezoceramic actuators whose driving voltage is proportional to the signal difference between opposing sensor elements of the quadrant detector. The signals coming from the four elements are summed, thus providing a signal proportional to the total intensity falling over the entire area of the sensor. When the perturbations on the test wave front become sufficiently
=ZT
Y
CELL
TILTING MIRROR LASER BEAM
PDI [ ' ~ - "PLATEU MICROSCOPE OBJECTIVE
BEAM SPLITTER CUBE
<) SERVO UNIT
DETECTOR
E
-1
Figure 2. Servo-system alignment-control loop.
l
large, the spread of the (averaged) intensity distribution in the focal plane becomes substantial. Many speckles are created, and consequently the peak intensity is low. Dividing the error signals by the sum signal, it is possible to normalize the error signal amplitude fluctuations to the total amount of light impinging on the sensor so as to have an error signal that is independent of the degree of perturbation. When the sum signal falls below a properly set threshold (as in the case of a very strong perturbation or a misalignment), an automatic search mode of operation is activated. A two-dimensional scan is performed by the tilting mirror, and the system seeks for any prominent feature in the focal plane intensity distribution. The search continues until a new peak of adequate intensity is found. The servo then resumes its normal function and latches onto the newly found peak. Incidental strong mechanical shocks on the optical bench, can cause a temporary misalignment of the interferometer. To avoid a useless and time-consuming activation of the search mode of operation, which would cause an interruption in the measurement, a shock detector circuit (working on the sum signal) disables the search mode when a shock is revealed.
PDI Instrument for Spacelab The PDI-based optical equipment is shown in Fig. 3. The light emerging from a 2 mW He-Ne laser source is expanded by means of a custom-made spatial filter assembly directly clamped to the laser support. The diverging beam is reflected by two mirrors (flatness A/20) so as to follow a folded path, then is collimated by an achromat doublet that is placed at a distance from the spatial filter pinhole equal to its focal length (0.5 m). The plane wave (a 0.07 m diameter parallel beam) propagating from the achromat doublet crosses the region of the fluid test container and is focused by a second achromat doublet identical to the first. After reflection onto a mirror (flatness A/20), the focused beam impinges on the tilting mirror (flatness A/20). The tilting mirror mount is a custom-made ballbearing playless gimbal mount provided with air dampers and balancing masses. Positioning of the two frames rotating around the vertical and horizontal axes is performed by means of piezoelectric transducers whose driving voltage is provided by a voltage amplifier controlled by a servo unit (operating in the integral configuration). The description of the PDI servo loop optical scheme was given in the previous subsection and will not be repeated here. To have a system capable of performing other kinds of fluid diagnostics, both a vertical and a horizontal blade for schlieren observation are mounted, on the same PDI plate support. Selection of the diagnostic apparatus (PDI, vertical blade, horizontal blade) is attained by positioning the selected tool in correspondence with the optic axes. Displacement of the diagnostic tools is performed by means of a translation stage driven by a dc motor. The actual position of the translation stage is detected by an optical encoder (solidly mounted to the translation stage mount) whose output is fed to a motor control unit. Observation of the output from the three diagnostic
52
S. Musazzi et al. VERT. BLADE
HORIZ. BLADE
PDI LASER
SPATIAL FILTER MIRROR
TILTING MIRROR POSITION DETECTOR TRANSLATION STAGE
~----~CCD CAMERA LENS
TEST CELL
LENS!
;
1
MIRROF Figure 3. PDI general layout.
equipments (interferograms, schlieren patterns) is performed by a CCD camera. The main technical characteristics of the instrument are as follows. • The tilting mirror has been designed to compensate for beam angular displacements caused by both vertical and horizontal constant gradients (in the test fluid) of _+ 120 K in water, which correspond to a beam deflection of + 12 mrad. The tilting mirror angular position sensitivity is on the order of 10 -6 of the total compensating capability angular range. • During startup operations, the average time required by the system for alignment is 20 s. • The alignment control system bandwidth is about 10 Hz. This means that the time constant of the system is about 0.02 s, which is typically smaller than the time constant of a perturbation in a fluid. • The dynamic range is 104; that is, the system maintains alignment until the light level measured by the quadrant detector is as low as 10 4 of the intensity measured when no perturbation is present in the test region. • The instrument can work in three different configurations: as a PD! interferometer; in the vertical schlieren configuration; and in the horizontal schlieren configuration. The average time required to switch from one configuration to another is less than 40 s. • The field of view is 0.04 m × 0.06 m and can be increased to a circular region 0.07 m in diameter by changing the CCD camera objective.
EXPERIMENTAL RESULTS A number of tests have been performed to check the system capabilities. Some video hard copies of the most significant interferograms are presented in Figs. 4-6. It must be pointed out that interferograms show a twodimensional index of refraction distribution, and consequently fringes describe index of refraction variations averaged along the direction of propagation of the probe beam. The interferogram in Fig. 4 shows the temperature gradient distribution close to a soldering tip in air. (The tip length in the figure is about 5 cm.) Because of the low dn/dT of the air, only a few fringes surrounding the soldering tip are observed. With the tip temperature being about 500 K we can appreciate a temperature difference between two adjacent fringes of about 70 K. Optical disturbances in the picture are caused by the CCD camera objective because a commercial camera with nonoptimized lens coating was used for these tests. The results of a test on a pure liquid are shown in the sequence reported in Fig. 5. A cylindrical test cell (0.07 m long, 0.065 m diameter) with the cylinder axes parallel to the optic axes is filled with water and warmed by a heater (100 W, 3 12 resistor) placed below the cell bottom. About 60 s after the heater is switched on, a hot plume rises from the cell bottom (see Fig. 5a). Successively other convective motions appear as shown in Figs. 5b and 5c. These interferograms were recorded about 90 and 120 s, respectively, after the beginning of the heating process. Once the heater is turned off the fringes inside the test cell tend to become horizontal (Fig 5d); that is, a vertical temperature gradient is now present in the liquid. It can be noticed that in this test the revealed temperature gradients (AT) are much smaller than in the previous
Point Diffraction Interferometer 53 alcohol into a water-filled cell (the cell is the same one used for the test on a pure liquid). At the beginning the perturbation in the fluid is on a spatial scale too small to be resolved by the system, and no fringes can be observed (Fig. 6a). After a few seconds the two fluids tend to mix, and the fringes become visible as shown in Figs. 6b, 6c, and 6d (recorded about 30, 180, and 600 s, respectively, after the injection of alcohol into the test cell). It must be emphasized that because of the very strong perturbation in the test fluid the intensity distribution in the plane of the PDI becomes very broad, and consequently the intensity of the beam actually impinging on the PDI (and consequently on the quadrant detector) becomes dramatically small. Nevertheless the dynamic range of the instrument is so wide that the measurement has been performed without activation of the automatic search mode of operation. PRACTICAL USEFULNESS OF T H E PDI-BASED OPTICAL A R R A N G E M E N T As anticipated, the optical arrangement described in this paper will be used in the IML2 Spacelab mission (scheduled for 1994) as part of the Bubble Drop and Particle Unit (BDPU) facility. This is a facility dedicated to the study of the behavior of bubbles, drops, and particles in transparent fluids. Examples of experiments to be performed by means of this facility and requiring interferometric/schlieren analysis are:
Figure 4. Interferogram showing the refractive index distribution around a hot soldering tip in air. case. Knowing the test cell thickness L along the optic axis • (0.07 mm) and d n / d T for water (9 x 10- 5 in the range of temperatures of interest), we can calculate the AT necessary to produce one fringe. A dark fringe appears when the optical path difference between reference and measurement beams is equal to A/2. Thus, A n L = A/2 where An is the variation of the refractive index due to a thermal gradient. We obtain A n = A / 2 L = 4.5 X 10 - 6
Since A n ~ A T
=9 x 10 -5, we have AT
An 9 × 10 -5
0.05 K
This means that since a fraction of a fringe can easily be evaluated, temperature variations smaller than 0.05 K can be measured in water. As the third example, we show the mixing of two fluids with different indices of refraction. The sequence in Fig. 6 shows the interferograms generated after an injection of
• Bubble, drop, and particle behavior in fluids under the influence of temperature and concentration gradients and electric fields • Formation and dynamics of solidification fronts • Interaction between inclusions and solidification fronts • Flow phenomena such as Marangoni convection • Crystal growth from solutions It must be pointed out, however, that apart from application of this system to space activities, the described instrumentation can conveniently be used in any laboratory where experiments on transparent fluids are performed. CONCLUSIONS In this paper we have described a new interferometric equipment for the study of fluids. It is based on a point diffraction interferometer implemented by an active servo system designed to allow the system to work in the presence of large refractive index gradients. A laboratory demonstration unit has been constructed, and experimental results of tests performed on pure fluids and liquid mixtures have been presented. The interferometric equipment has been designed taking into account the criteria set for space applications; for example, it is completely automatic to minimize manipulations of the payload specialist, only materials a n d / o r treatments allowed for space applications have been selected, and optical and mechanical components have been designed to survive (both from the structural and functional point of view) thermal and mechanical stresses
54
S. Musazzi et al.
(a)
(b)
(c)
(d)
Figure 5. Sequence of interferograms showing the evolution of the index of refraction distribution in a water-filled cell heated from below. during the mission. The flying model of the instrument is now under construction and will be flown o n b o a r d Spacelab in the IML2 mission. Future developments of the P D I apparatus that can be
(a)
(c)
foreseen at this m o m e n t mainly concern the laser source. New and more reliable laser sources such as laser diodes, not available (or reliable) when the instrument was designed, can now be used. Not only are laser diode sources,
(b)
(d)
Figure 6. Sequence of interferograms showing the evolution of the index of refraction distribution in a liquid mixture obtained after the injection of alcohol into a water-filled cell.
Point Diffraction Interferometer in particular, a d e q u a t e for space application (they are m o r e compact and robust than H e - N e lasers and do not require a high driving voltage, thus reducing safety problems), but also they offer a n u m b e r o f advantages from the experimental point of view. By using two laser diodes, in fact, it will be possible to obtain interferograms at two different wavelengths so as to p e r f o r m studies on both t e m p e r a t u r e and concentration distributions in a fluid at the same time. The use of two different wavelengths will also allow the d e t e r m i n a t i o n of the sign ( + or - ) of the m e a s u r e d index of refraction gradients. We wish to thank Prof. M. Giglio, UniversitA degli Studi of Milan, for his essential contribution during the first stages of the work and for useful discussions. This work was supported by the ESA-ALENIA contract BDPU.
NOMENCLATURE L T A n
test cell length, m temperature, K wavelength, m index of refraction, dimensionless
55
REFERENCES 1. Walter, H. U., Fluids Sciences and Material Science in Space, Springer-Verlag, Berlin, 1987. 2. Smartt, R. N., and Strong, J., Point Diffraction Interferometer, J. Opt. Soc. Am., 62, 737, 1972. 3. Viswanathan, V. K., Liberman, I., Lawrence, G., and Seery, B. D., Optical Analysis of Laser Systems Using Interferometry, Appl. Opt., 19, 1870-1873, 1980. 4. Koliopoulos, C., Kwon, O., Shagan, R., Wyant, J. C., and Hayslett, C. R., Infrared Point Diffraction Interferometer, Opt. Lett., 3, 118-121, 1987. 5. Fran§on, M., Optical Interferometry, Academic, New York, 1966. 6. Fran~on, M. H., and Mallick, S., Polarization Interferometers: Applications in Microscopy and Macroscopy, Wiley-Interscience, London, 1971. 7. Vest, C. M., Holographic Interferometry, Wiley, New York, 1979. 8. Born, M., and Wolf, E., Principles of Optics, Pergamon, London, 1959.
Received Nov. 19, 1991; revised June 30, 1992