A MHz rate Shack-Hartmann sensor has been built which allows the measurement of wavefront phase distortion in high speed flows. It is capable of obtaining 30 ...
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CHARACTERIZATION OF OPTICAL WAVEFRONT DISTORTIONS DUE TO A BOUNDARY LAYER AT HYPERSONIC SPEEDS C.M. Wyckham, S.H. Zaidi, R.B. Miles, A.J. Smits Princeton University
34th AIAA Plasmadynamics and Lasers Conference
23-26 June 2003 / Orlando, Florida
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Characterization of optical wavefront distortions due to a boundary layer at hypersonic speeds C.M. Wyckham*, S.H. Zaidi**, R.B. Miles***, A.J. Smits**** Department of Mechanical and Aerospace Engineering Princeton University, Princeton NJ 08540 Abstract A MHz rate Shack-Hartmann sensor has been built which allows the measurement of wavefront phase distortion in high speed flows. It is capable of obtaining 30 frame movies at up to 500 kHz or 1 MHz with a 2 s pause at every fifth frame. The sensor was used to obtain the distortion due to flow over a wedge at Mach 2.4 at a 7.8 kHz framing rate. It was also used at 500 kHz to measure the optical path difference due to a nitrogen free jet and due to a hypersonic boundary layer at Mach 8. Results are promising and the system is still under further development. atmospheric turbulence, and has been studied at some length in the context of ground based astronomical telescopes. Astronomers are now able to measure and compensate for these distortions in real time, effectively ‘detwinkling’ the stars. Aero-optics is, by comparison, at a nascent stage of development.
Introduction Performance of on-board optical systems for high-speed vehicles is seriously degraded by variations in local fluid properties. The main causes for this degradation are the changes in the index of refraction due to the density discontinuities across shock waves and density variations across turbulent boundary layers along the vehicle surfaces. The density fluctuations in the boundary layer can distort the images – the break-up and the rapid movement of these images results in poor resolution. These aero-optic effects are a serious problem for systems designed to image or project energy from a high-speed aerial platform.
Both aero-optics and atmospheric propagation arise due to fluctuations in density, , and the concomitant variations in the index of refraction, n, described by the Gladstone-Dale relation1,
n = 1 + ρK GD
(1)
where KGD is the Gladstone-Dale ‘constant’ which depends on both wavelength and type of fluid. The effect of the index of refraction field is integrated as the light travels through the index of refraction field. The optical path length, OPL, will vary across an initially flat wavefront:
Aero-optics is the study of the interaction between light and air. More specifically, the distortion of light due to propagation through an index of refraction field characterised by high spatial and temporal frequencies due to local vorticity, often surrounding an airframe. A closely related field, atmospheric propagation, involves much lower spatial and temporal frequencies due to
y2
OPL( x, z , t ) = n( x, y, z , t )dy y1
(2) *Graduate Student, Member AIAA **Research Staff, Member AIAA ***Professor, Fellow AIAA ****Professor, Fellow AIAA
In most cases, the optical path difference, OPD is the quantity of interest, not the optical path length:
OPD( x, z , t ) = OPL( x, z , t ) − OPL( x, z , t )
Copyright 2003 by authors. Published by the American Institute of Aeronautics and Atronautics, Inc., with permission.
(3)
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The OPD is also much simpler to measure than the OPL.
focuses a spot on the CCD array. Our lenslet array provides 14 x 14 spots on the CCD. The location of this spot depends on the average local wavefront tilt across the lenslet. Data taken during a run is compared to calibration data, so that the system is relatively insensitive to misalignment and optical aberrations. The result is an array of slopes that can then be used to reconstruct the original wavefront shape using quadrature or least squares techniques. We determine spot centroid locations to sub-pixel accuracy using a Guassian fit, and then recover the phase by fitting the data to a bi-quadratic surface using singular value decomposition4,5.
Aero-optic effects can result in either a gain or loss of information. In the familiar case of shlieren or shadowgraphy, information about the density of the fluid is extracted from the wavefront distortions. On the other hand, if an attempt is made to image through a compressible boundary layer or shock wave, the image will be degraded and information will be lost. Mitigating the latter effect is the focus of our current work. Due to computing and hardware limitations, conventional adaptive optic systems used on terrestrial telescopes are very slow compared to the timescales of hypersonic (or even much slower) boundary layer turbulence. Instead of the real-time measurement, computation and compensation required of adaptive optics systems, an attempt will be made to mitigate aero-optic distortion by modifying the boundary layer using slot helium injection to create stationary, highly organised longitudinal structures in the flow2. The majority of the distortion is then stationary and can be known a priori, therefore enabling its removal by postprocessing of the image or by the use of deformable optics. Figure 1 shows these stable longitudinal structures in a volumetric boundary layer reconstruction created using filtered Rayleigh scattering at Mach 8 at Princeton2.
Until recently, Shack-Hartmann sensors were limited by CCD readout time to 1 kHz. The fastest competing technique, Small Aperture Beam Technique, is capable of speeds of up to 100 kHz, but at a greatly reduced spatial resolution6. Characteristic supersonic boundary layers vary on a microsecond time scale. In order to follow the boundary layer structures, we have developed a high resolution ShackHartmann sensor capable of framing rates of up to 500 kHz (or 1 MHz with a 2 s pause at every fifth frame). Our approach uses a fast framing CCD camera developed by Princeton Scientific Instruments. This camera employs on-chip memory to produce 30 frame movies. A single representative pixel with an adjacent 30 frame storage array is shown in Figure 2. The camera has 180 x180 pixels and a fill factor of 13.5%8. The solid state camera head is kept at approximately -25°C to reduce dark current, and the chip readout occurs over many seconds to reduce readout error. The 15 ms response time of the mechanical shutter was too slow for our purposes at framing rates greater than 7.8 kHz, so we added an electronic shutter with an 80 s response to the laser and slaved it to the camera’s mechanical shutter. This camera (less the electronic shutter) has been used extensively at Princeton for the visualization of high speed flows2,7,8.
Currently available instrumentation can be used to obtain statistical measures of aerooptic distortion. However, these measures have recently been shown to underestimate the farfield effects of the distortion by orders of magnitude3. It is therefore important to capture real-time wavefront data and calculate the farfield effects directly. The first step in finding a way to reduce or correct for wavefront distortions is to be able to measure them. This can be done in a number of ways. Our choice was the use of a ShackHartmann sensor, described below.
A similar Shack-Hartmann sensor is being independently developed at Ohio State9. To our knowledge, these two systems are the only ones of their kind, and represent an increase in speed of three orders of magnitude for high resolution wavefront sensors.
The Shack-Hartmann Sensor Shack-Hartmann sensors have been used for many years and are simple and robust devices consisting of an array of small lenslets and a CCD camera. Each tiny lenslet (ours have a diameter of 400 m and focal length of 71 mm)
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three minutes, depending on Reynolds number. Reynold’s numbers of between 3 and 21 million per meter are achievable.
Test Facilities This system is still under active development. During the design and verification process, progressively more challenging flow fields were used. The first was supersonic flow over a wedge at a slower (7.8 kHz) framing rate. We then progressed to a full mock-up of the Mach 8 condition using a nitrogen jet at the full framing rate, and finally to a Mach 8 boundary layer.
The data presented here was taken with a stagnation pressure and temperature of 8.2 MPa and 683 K, respectively. The Reynold’s number (Rex) at the measurement position was approximately 13×106. No attempt was made to control the temperature of the plate, which started at room temperature. A flat plate model, shown in figure 5, was built for use in the hypersonic facility. A 50 mm diameter window is inserted into the plate at a distance of 356 mm from the leading edge. The laser is coupled into a single mode optical fiber and then focused through a small hole in a laminar flow plate and into the mean flow. This configuration was chosen to limit distortion due to the tunnel’s boundary layer and because it is insensitive to tunnel vibration.
In all cases, the optical source was the 514 nm (green) component of an air cooled argon-ion laser. Laser power was only 3 mW. The Mach 2.4 blow-down tunnel used for initial development is shown in figure 3. The test section static pressure is one atmosphere and the pressure ratio is 14.62. The throat area is 10.6 cm2 and the test section is 15 cm long, 5.46 cm wide and 4.83 cm high. A 1.5 cm long 20 degree wedge was placed in the flow.
The light then passes through the flat plate boundary layer and the window in the model. From there it is collimated by a lens and passes inside the sting to the Shack-Hartmann sensor. Between the tunnel and the wavefront sensor are two lenses in a 4f configuration. This configuration eliminates diffraction of the signal by exploiting the Fourier transforming property of lenses. By varying the focal length ratio of the two lenses, the beam can also be expanded or contracted to allow a trade-off between sensitivity and spatial sampling frequency. The data presented here was taken using a 2:1 focal length ratio, so that we imaged a 1 cm square area on the plate with our roughly 0.6 mm square CCD chip. This also had the effect of amplifying the wavefront slopes by a factor of 2.
The optical beam was expanded and passed through windows both into and out of the flow, so that the optical distortion includes that due to the turbulent boundary layer on both of the windows. No optics were used in the approximately 1.5 m between the tunnel and the Shack-Hartmann sensor. As a result, the imaged wavefront was somewhat diffracted during its travel to the sensor. This diffraction is undesirable for wavefront sensing as the measured phase-front depends on the distance from the flow at which the measurement was taken. This effect was mitigated in subsequent experiments as outlined below. The hypersonic facility is a Mach 8 cold flow blowdown facility, shown in figure 4. Air is compressed, filtered and dried and stored in four tanks with a total capacity of 60 m3 at 21 MPa. The air is then regulated down to a stagnation pressure of between 1.7 and 10.3 MPa. The air passes through a resistively heated coil where it can be heated as high as 870 K to prevent condensation of the air. The air then passes through an axisymmetric nozzle with a throat area of 1.79 cm2 and into a 23 cm diameter test section with four large optical access ports. In order to achieve low back pressures, one or two stage ejectors with active cooling are used. These can achieve back pressures as low as 3.4 kPa. These ejectors consume the vast majority of the stored air, limiting run times to one to
The hypersonic data set was taken with a 2.4 mm boundary layer trip at 59 mm from the leading edge and a 9.5 mm radius hemispherical vortex generator at 70 mm from the leading edge. Results and Discussion The Shack-Hartmann sensor was first tested using flow over a wedge in the Mach 2.4, tunnel. The approximate field of view is indicated in figure 6. The first frame (of thirty) of the measured wavefront is shown in figure 7, along with typical raw data from that run. The effect of the shockwave on the wavefront is
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such simple items as altering the focal ratio of the 4f lens system.
clear. The increased density behind the shock results in a significant phase lag (lag is indicated by increasing height of the phase surface on all plots). This data was taken at 7.8 kHz during system verification.
Conclusions and Future Work Hypersonic wind tunnels are demanding environments for wavefront sensing. Due to its inherently robust nature, a Shack-Hartmann sensor is well suited for use in these facilities, and these preliminary results show that wavefront sensing in hypersonic boundary layers is feasible, though further work is required to increase the signal to noise ratio.
To verify the Mach 8 model’s optical system, an under-expanded sonic nitrogen jet was blown on the plate at a glancing angle 2 cm upstream of the window. The resulting wavefront distortion can be seen in figure 8. This data was taken at 500 kHz. Turbulent structures can be clearly seen propagating downstream in the four frames shown. For example, a bowl shaped feature can be seen moving along the centerline from the left edge towards the right in the direction of flow. Every component of the system used to take this data was identical to that used in the hypersonic case (in fact, the data was taken through an access port while the model was installed in the tunnel). The density of the nitrogen was, of course, several orders of magnitude greater than the air in the Mach 8 flow conditions.
Once fully developed, the sensor will be used to examine the effect of helium injection into the boundary layer on aero-optic distortion. Although helium’s low index of refraction may nominally worsen the distortion, the repeatable regularization of the flow field which occurs will allow this distortion to be corrected for using only a priori information, resulting in a net improvement in the ability to project light or image through a compressible boundary layer.
Figure 9 is the first of 30 frames of the hypersonic data. The large curvature seen in the figure is likely due to the shockwave from the vortex generator. Unfortunately, the spot movement on the sensor due to this shock wave exceeded the dynamic range of the sensor. By matching a distinctively shaped spot on the calibration and run shots, the calibration was adjusted to allow the data to be used. However, this leaves the correct overall tilt of the figure undetermined.
Acknowledgements This work was sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under Grant Number F-49620-00-1-0319. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. We would also like to thank Phil Kang for his hard work in helping us in the Mach 8 facility, and Larry McIntyre and Barry Runner for their efforts in machining the Mach 8 model.
The large average wavefront distortion due to the shockwave in figure 9 serves to mask the turbulence. To highlight the dynamic component of the wavefront, the average of all 30 frames was subtracted from each frame. The result, shown in figure 10, showed some evidence of turbulent structures convecting downstream as well as significant noise. The signal to noise ratio is on the order of one. Turbulent hypersonic boundary layers can have very large relative density fluctuations, on the order of 40% of the average density. However, since the average density in our facility is very low, the absolute difference in density is small, resulting in small phase distortions. Nevertheless, there are a number of steps that can be taken to improve the signal to noise ratio by a significant factor in future runs, including
References
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1.
E.J. Jumper and E.J. Fitzgerald, “Recent Advances in Aero-Optics,” Progress in Aerospace Sciences 37, 299–339, 2001
2.
B. Auvity, M.R. Etz, and A.J. Smits, “Effects of Transverse Helium Injection on Hypersonic Boundary Layers,” Physics of Fluids, V 13, No. 10, Oct. 2001.
3.
J.M. Cicchiello and E.J. Jumper, “FarField Optical Degradation Due to NearField Transmission Through a Turbulent Heated Jet,” Applied Optics, Vol. 36, No. 25, 1997.
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W.H. Southwell, “Wavefront Estimation from Wavefront Slope Measurements,” Journal of the Optical Society of America, Vol. 70, No. 8, 998-1006, 1980.
5.
E. J. Fitzgerald and E. J. Jumper, "Further Consideration of Compressibility Effects on Shear Layer Optical Distortion," AIAA Paper 993617, 1999.
6.
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“Influence of Upstream Pulsed Energy Deposition on a Shockwave Structure in Supersonic Flow,” AIAA Paper 20022703, Proceedings of 22nd AIAA Aerodynamics Measurement Technology and Ground Testing Conference, 2002.
E. J. Fitzgerald and E. J. Jumper, "Extension of the Small-Aperture Beam Technique to the Measurement of Full, 2-Dimensional Optical Wavefronts," SPIE Paper 3172-11, Proceedings of the Optical Technology in Fluid, Thermal, and Combustion Flow III, SPIE-The International Society of Optical Engineering, 1997. S.H. Zaidi, M.N. Shneider, D.K. Mansfield, Y.Z. Ionikh, and R.B. Miles,
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M.B. Huntley, P. Wu, R.B. Miles, and A.J. Smits, “MHz Rate Imaging of Boundary Layer Transition on Elliptic Cones at Mach 8,” AIAA Paper 000379, Proceedings of 38th Aerospace Sciences Meeting and Exhibit, 2000.
9.
B. Thurow, M. Samimy, and W. Lempert, “Simultaneous MHz Rate Flow Visualization and Wavefront Sensing for Aero-Optics,” AIAA Paper 2003-0684, Proceedings of 38th Aerospace Sciences Meeting and Exhibit, 2003.
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(a)
(b)
Figure 1: Three Dimensional Construction of hypersonic boundary Layer (a) without Helium injection and (b) with Helium injection. Flow is from left to right. From Auvity et al., 2001.
Photo Detector
Storage Array
Figure 2: Schematic of one pixel on the PSI fast framing CCD camera.
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Test Section Diffuser
Pressure regulator Nozzle Plenum
To Ejector
Gas
Field of view:1.5 inches
Figure 3: Mach 2.4 Experimental Facility.
Figure 4: Mach 8 Experimental Facility, Princeton University
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Figure 5: Experimental layout of the test section in Mach 8.0 test facility.
Field of View
Figure 6: Shadowgraph showing approximate field of view of Shack-Hartmann sensor in figure 7.
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Figure 7: Raw data (left) and the recovered phase (right). Flow over a wedge at Mach 2.4. All axes in the plot on the right are in meters and flow is from right to left.
Figure 8: Four frames from 30 showing phase from light passing through a sonic, underexpanded nitrogen jet. All axes in meters.
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Figure 9: Phase front measured in a Mach 8 boundary layer. Flow is from right to left, all axes in meters.
Figure 10: Phase front from figure 9, minus the average phase of 30 frames. All axes are in meters.
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