8 Chrysler, Irvine, CA 92618. USA. 1 Introduction. When an optical wavefront passes through an aerodynamic flow, its phase and amplitude are modulated, ...
New Interferometry Tools for AeroOptics James Trolinger and Vladimir Markov MetroLaser Incorporated 8 Chrysler, Irvine, CA 92618 USA
1 Introduction When an optical wavefront passes through an aerodynamic flow, its phase and amplitude are modulated, resulting in distortion and loss of optical information and energy. Its phase is modulated by diffraction and spatial and temporal variations in refractive index. These effects deteriorate the ability to transmit and focus a beam onto a target. Refractive effects cause 1) image shift, also known as boresight error, 2) wavefront distortion (image blur) and 3) beam jitter (a kind of time varying boresight error). The ability to store and compare wavefronts directly provided by holography led to quantum leaps in understanding how turbulence affects optical imaging, and holographic interferometry provided one of the very first direct quantitative and visual observations of aero optical effects. MetroLaser has moved this powerful tool to a new level, incorporating digital techniques and producing unique diagnostics methods that enhance tests designed to study and correct aero-optical effects on imaging and energy projection. The fundamental concept is built around a wavefront sensor/recorder that records and reconstructs optical wavefronts known as the PhaseCam™. The PhaseCam is a digital phase shifting holographic interferometer that produces four simultaneous phase shifted interferograms that are solved to produce an instantaneous phase map of the wavefront. As a part of the diagnostics capability we developed supporting software and procedures to collect and analyze PhaseCam™ data and extract aero-optical parameters (e.g. Strehl ratio, point spread function, wavefront error) as well as software for simulating, modeling and interpreting such data. This paper describes the concepts and methods including applications in wind tunnel turret tests of optical systems. A wavefront is projected from the PhaseCam™ through a flow field to a mirror, which returns the beam double passed through the same flow field. The PhaseCam™ then records the aero optically modulated wavefront and
W. Osten, M. Kujawinska (eds.), Fringe 2009, DOI 10.1007/978-3-642-03051-2_72, © Springer-Verlag Berlin Heidelberg 2009
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analyzes it to deduce all of the data required to fully characterize the aerooptical nature of an optical system. Examining a single wavefront provides the required input for an adaptive optical system to correct aero-optical effects. Recording two wavefronts and subtracting one from the other and varying the time separation, provides the temporal response required of the adaptive optics. Examining the detailed nature of the wavefront and its changes in time quantifies the flow structure. Aero optics tests of flow control and flow field effects must provide: • Strehl ratio or RMS wavefront distortion (i.e., wavefront quality) and Bore site error (BSE), (the tilt of the wavefront). • Structural changes in the flow and/or wavefront, i.e., coherence, size, and regularity of structures. • Temporal characteristics of the flow structure, i.e., decorrelation time.
2 Aero Optical Measurements Parameters of merit that are commonly employed to describe the deterioration of a propagating wavefront are: • σ, RMS wavefront variance; • S, Strehl Ratio (peak intensity loss) which can be computed from σ; • Image size at the focus of an ideal lens ( also known as blur circle, encircled energy, diffraction limited spot size, point spread function, far field pattern, energy in the bucket), which also can be computed from σ. When the aperture is large compared to the extent of spatial variation in refractive index (mean turbulence structure size) these are approximately related by S = I/Io = exp(-k2σ2), where S - Strehl Ratio, I - beam intensity, I0 - beam intensity on the axis, k = 2π/λ, σ - RMS deviance of the wavefront. The far field intensity, If, can be estimated as If = S(πPD2/4λ2R2) where P - power, R - distance to the target, D - aperture diameter. Therefore, possibly the most useful and important fundamental measurement is that of σ, which characterizes the wavefront statistically. Therefore the required wavefront sensor captures wavefronts and determines σ. Some wavefront sensors are capable of capturing pieces of
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wavefronts and inferring σ. Only one of these, interferometry, is capable of capturing the whole wavefront with high spatial resolution. Conventional interferometry is too sensitive to vibration to be employed in aero optics experiments. However, the “PhaseCam™” solves the usual problem with robustness and enables interferometry to be employed in harsh, high vibration environments. Still, the job is not without problems related to high vibration in the measurement. The makeup and technical details of the PhaseCam, itself, are discussed elsewhere and are not repeated here. The system has the capability to capture and reconstruct an entire wavefront (phase and amplitude) in the instant during which it enters the instrument, including the following data required to fully characterize the aero optical nature of an optical system. • Examining a single wavefront provides the required instantaneous input into an adaptive optical system for correction for aero optical effects. This determines the spatial requirements of adaptive optics required to correct the wavefront. • Recording two wavefronts and subtracting one from the other and varying the time separation provides the exact settings and temporal response required of an adaptive optical system to correct for aero optical effects. This tells how fast the adaptive optics must be. • Measuring wavefront quality reveals how much you have improved or degraded the wavefront. This reveals the aero optical effect of flow control. • Examining the detailed nature of the wavefront and its changes in time quantifies the aero optical flow structure effects. This shows what the flow control is doing, aero optically, to the flow. • When we subtract one wavefront from another that passes through the flow at a later time, the extremes are 1) that the time difference is large so that the wavefronts are uncorrelated, and 2) the time difference is small so the wavefronts are similar and correlated. • By varying the time difference of the two compared waves from zero to a larger value we can determine the correlation distance or turbulence scales. By keeping the time separations small, we can subtract out all steady flow effects and slower time varying effects such as room air currents. To get good statistics, since we are dealing with turbulence and random flow states, ten or more data sets per test condition is adequate. Upon receipt, manuscripts and illustrations become the property of ITO and will not be returned to the author. With the submission of the manuscript authors assign to ITO and Springer copyright ownership in their paper including all used artwork, drawings and photographs.
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3 Experimental Data Examples We have applied these methods in a variety of aeroptical tests including flows over cavities and optical turrets. The following provides a sample of some of the data for flow over a hemispherical turret. The most obvious flow feature observed at the 90 degree angle was the normal shock. It is best seen in Figure 1. This is most easily seen from a wrapped phasemap. Two of these are shown in Figure 1. Several conclusions can be drawn from these figures. The shock is dynamic. In 180 microseconds it moves from right to left. In some recordings it cannot be seen at all. The wavefront itself is much smoother at 90 degree look angle. However, a considerable boresight error still exists. This may be due to both mirror vibrations as well as the flow. Interferograms for a wide range of conditions were examined to demonstrate the usefulness in aero optical assessment. We demonstrated the ability to measure boresight error, Strehl ratio, turbulence scale, and the temperal characteristics of these parameters. Figure 2 illustrates how the system can quantify the temporal characteristics of a wavefront and also quantify the turbulence structure and scale. Two wavefronts with a 180 µsec time spacing differ only in tilt (beam jitter) whereas two wavefronts spaced in time by 440 µsec show a significant difference caused by turbulence. Examining more data, turbulence effects were seen to come and go as expected and without considering the statistics, general conclusions about turbulence may be premature. The quantity of available data will allow us to do the statistics that can lead to more general conclusions. Normal Shock
(a) Wrapped phase map Fig. 1. Wavefront aero optics at 90 degree look angle
(b) 180 µsec later.
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b) ∆t = 440 µsec
Fig. 2. Phase difference map showing very low, small-scale turbulence effects on aero optics at (a) the 180 µsec rates but increasing the time difference to 440 µsec (b) brings in the effects of turbulence thus defining the speed at which adaptive optics must operate
4 Conclusions In the foregoing we have described the application of digital holographic interferometry in aero optical testing. A digital holocamera based on instantaneous phase shifting interferometry provides all of the information needed to aero optically characterize and optical system including and defines the requirements of an adaptive optical system that would be required to correct the problems caused by deleterious aero optical effects.
5 Acknowledgments The work reported in this paper was supported by an SBIR program from Wright Patterson Air Force Base, Wright Laboratories. The project officer was Don Saunders.
6 References 1. Trolinger, J.D., “Aero-Optical Characterization of Aircraft Optical Turrets by Holography, Interferometry, and Shadowgraph,” Aero-
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Optical Phenomena, Editors: Keith G. Gilbert and Leonard J. Otten, American Institute of Aeronautics and Astronautics, Inc., 1982, p. 200. Trolinger, J.D., Craig, J.E. & Rose, W.C. "Propagation Diagnostic Technique for Turbulent Transonic Flow," AIAA No. 84-0104, AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, 9-12 January 1984. Anderson, C. and Trolinger, J.D., “New Developments in Digitial Electronic Flow Diagnostics Methods,” SPIE Proceedings, International Conference, San Diego, CA (July 2001). Trolinger, J.D., “Interferometric Flow Measurement,” Chapter 3 in Optical Diagnostics in Fluid and Thermal Flows, edited by Carolyn Mercer, Kluewer Press International (May 2003). Brock, N.J., Millerd, J.E., and Trolinger, J.D. “A Simple and Versatile, Real-Time Interferometer for Quantitative Flow Visualization,” AIAA99-0770; 37th Aerospace Sciences Meeting and Exhibit, Reno, NV (January 1999). Smythe and Moore, “Instantaneous Phase Measuring Interferometry,” Opt. Eng. vol. 23, p. 361 (1984). Trolinger, J., “A Digital Wavefront Sensor for Aero-Optics and Flow Diagnostics,” ICIASF Congress on Laser Flow Diagnostics, 2003.
