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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 5 — Mar. 2, 2009
  • pp: 3447–3460
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Emulation of dynamic wavefront disturbances using a deformable mirror

Ross A. Conrad, William E. Wilcox, Timothy H. Williams, Steven Michael, and Jeffrey M. Roth  »View Author Affiliations


Optics Express, Vol. 17, Issue 5, pp. 3447-3460 (2009)
http://dx.doi.org/10.1364/OE.17.003447


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Abstract

Boundary-layer turbulence resulting from uneven airflow around window interfaces can impact airborne laser communications (lasercom). In the focal plane, these distortions can produce fast jitter and beam break-up, posing challenges for tracking and communications. We demonstrate an experimental emulator that reproduces aircraft aero-optical distortions using a deformable mirror. This boundary-layer emulator resides in a hardware testbed that experimentally mimics air-to-space lasercom links in a controlled, laboratory environment. The boundary-layer emulator operates in the 1.55-μm band and accurately recreates aero-optical distortions at a rate of 2 kilo-frames per second.

© 2009 Optical Society of America

1. Introduction

Free-space laser communications (lasercom) can provide mobile platforms with rapidly deploy-able, high-rate links. For example, airborne platforms such as commercial jet liners, could exploit lasercom to obtain high-speed connectivity to space- or ground-based backbone networks. Compared to radio-wave-frequency (RF) communications, lasercom utilizes higher carrier frequencies (200 – 300 THz), enabling extremely broad modulation bandwidths. Lasercom’s high carrier frequencies correspond to short wavelengths (1 – 1.5 μm), providing benefits over RF communications of low probability of interception, high power on target, and high antenna gain with relatively small aperture sizes. Furthermore, lasercom is largely unaffected by common impairments associated with terrestrial fiber-optic communications such as dispersion and nonlinearities.

To realize these advantages, airborne lasercom systems must address a number of challenges. The high antenna gain associated with narrow beamwidths in turn leads to stringent pointing requirements necessary to maintain links. Pointing a narrow beamwidth in most cases must be actively controlled to deliver sufficient power to the remote terminal. Therefore, lasercom systems often require a tracking system using the incoming beam as a reference to reject platform jitter and vibrations that might otherwise mis-point a beam off its target [1

1. S. G. Lambert and W. L. Casey, Laser Communications in Space (Artech House, Norwood, MA, 1995), Chap. 3.

]. Second, propagation delays can require point-ahead-angle adjustments and latency tolerance [1

1. S. G. Lambert and W. L. Casey, Laser Communications in Space (Artech House, Norwood, MA, 1995), Chap. 3.

]. Third, the dynamics of atmospheric non-uniformities result in scintillation that causes fading dropouts, impacting both tracking and communications performance [2

2. R. Parenti, R. J. Sasiela, L. C. Andrews, and R. L. Phillips, “Modeling the PDF for the irradiance of an uplink beam in the presence of beam wander,” Proc. SPIE 6215, 621508.1–13 (2006).

]. Finally, boundary-layer distortions may be present for certain window interface geometries, leading to further challenges for tracking and communications.

Aircraft boundary-layer turbulence results from uneven airflow around an aircraft and leads to time-varying and spatially-varying fluctuations in the index of refraction. The degree of boundary-layer phase distortions depends on factors such as view angle through the boundary layer, window interface geometry, air speed, and altitude. The fluctuations can produce nonuniform, time-varying phase shifts across the aperture, as shown in the snapshot of Fig. 1. These phase fluctuations translate to intensity fluctuations at the terminal’s focal plane. Light boundary-layer distortions produce primarily tilt, while severe boundary-layer effects resulting from more stressing view angles lead to higher-order perturbations, faster dynamics, and possibly beam break-up. Boundary-layer distortions on the received optical beam can affect performance of optical tracking used to provide line-of-sight stabilization against platform jitter. In addition to loss of bits from time-varying fading, boundary-layer turbulence can also reduce Strehl and impair high-rate communications based on single-mode-fiber receivers.

This work addresses the challenges of boundary-layer phase distortions by providing an experimental emulation capability to provide insight into the impact of boundary-layer phase distortions on airborne lasercom. We have designed and built a boundary-layer emulator (BLE) which recreates boundary-layer distortions in a laboratory environment using a micro-electromechanical systems deformable mirror (MEMS DM) actuated by electrostatic forces. This article discusses the development of a displacement look-up table to calibrate the response of the boundary-layer emulator and the mirror’s performance at emulating boundary-layer phase distortions.

2. Deformable mirror

Fig. 1. Example of boundary-layer-induced optical path difference (OPD) variation across a 100-mm (4-in.) aperture for an airborne platform. Computational fluid dynamics simulation is for a hyper-hemispherical turret geometry, a 29-kft altitude, a Mach 0.7-aircraft velocity, and a view angle of 120° azimuth and 45° elevation.
Fig. 2. Diagram showing integration of the boundary-layer emulator into a testbed system for evaluating air-to-space links in the presence of environmental impairments. The testbed is described further in Refs. 4 and 5. MEMS DM: micro-electro-mechanical systems de-formable mirror, QWP: quarter wave plate, PBS: polarization beam splitter, DRM: directional rotation module. The deformable mirror is used at normal incidence and requires the bidirectional signals to be co-polarized; the DRM allows the two directions of propagation to be separated into orthogonal polarizations, allowing polarization splitting to be used in the aircraft terminal to separate transmit and receive beams [6].

3. Look-up table development

Recreation of the optical path difference (OPD) variations generated from computational fluid dynamics (CFD) simulations requires characterization of the DM actuators. Since the system is designed to function in an open-loop manner without wave-front-sensing feedback, a look-up table (LUT) is generated to correlate displacements, or OPD, with applied voltage. We chose a simple method that generates the LUT in an iterative manner, forming flat DM surfaces with varying displacement. The BL distortions are decomposed into a grid of displacements, and then projected onto the DM using the LUT. This approach is simple and straightforward to implement; however, it neglects the inter-actuator coupling effects. More complicated models, for example in Refs. 7

7. Y. Zhou and T. Bifano, “Characterization of Contour Shapes Achievable with a MEMS Deformable Mirror,” Proc. SPIE 6113, 123–130 (2006).

and 8

8. Y. Zhou and T. Bifano, “Adaptive optics using a MEMS deformable mirror,” Proc. SPIE 6018, 350–356 (2005).

, have shown performance improvements of approximately 30% when removing Zernike shapes for adaptive optics. Since we are using the DM to introduce simulation-generated distortions, as opposed to removing distortions, we are less concerned with achieving precise fidelity and therefore use the simpler, uncoupled model.

Fig. 3. Photograph of deformable mirror installed in the laboratory testbed for evaluating air-to-space links in the presence of boundary-layer turbulence.

Once developed, the LUT is used to create a voltage file that corresponds to a time series of boundary-layerOPD data, gridded to the mirror array. This voltage file is ultimately streamed to the mirror at rates up to 2 kilo-frames per second (kfps) to match the boundary-layer dynamics.

3.1. Actuator mapping

The mirror’s surface is characterized using a Fizeau interferometer (ZYGO, 1.55-μm model Mark IV). The image of the reflected wavefront produced by the Fizeau is a 316×232-pixel format, providing OPD data in waves for the DM surface. This raw data includes native tilt from the wedged cover glass used to protect the DM. Therefore, the native tilt of the DM is measured using the reflective, flat mounting surface surrounding the membrane. This tilt is removed from the interferometer OPD image of the DM using numerical computation steps in MATLAB. The native tilt removal process yields the true mirror shape, allowing further analysis of the DM shape.

Fig. 4. Reduction of native-tilt-corrected OPD image (left) to 12×12 actuator image (right) by sampling each actuator’s location of maximum influence (center).

3.2. Linearization of actuators

Fig. 5. Plot of displacement (top) and residuals (bottom) vs voltage for a representative DM actuator in the center of the mirror. Plot of displacement data includes second-order fit produced using polyfit.

For large displacements close to a wavelength (1.55 μm), the interferometer cannot always determine the correct OPD value. Data might be missing from steep discontinuities at the edges of the DM boundary where light reflects out of the interferometer field-of-view. Once physical displacements become greater than a quarter wavelength (λ/2 in OPD due to the double-pass configuration), the interferometer may mistake the sign and/or magnitude of a displacement. To counteract this effect, we reduce the actuator displacement along the edges to lessen the slope. This helps provide sufficient data to show a smooth, continuous slope from the mirror edges to the deflected actuator.

The edge actuators require additional treatment. Although the data was only collected up to a 2000-nm displacement, we intended for the operational boundary-layer emulator to utilize the edge actuators over their full range of 3500 nm. To extend their displacements beyond 2000 nm, MATLAB’s spline function is used to extrapolate the polynomial curve beyond the existing data points. Our testbed configuration uses a slightly over-sized DM of 4.8 mm compared to the 1/e -2 optical beam diameter of 4.4 mm. Therefore, this extrapolation technique is suitable since the edge actuators weakly impact the beam.

4. Evaluating the look-up table

4.1. Flat surfaces

To characterize performance of the linearization table, the DM is commanded flat with varying amounts of piston (displacement), and then the root-mean-square (RMS) wave-front error, the maximum peak-to-valley (PV) wave-front error, and mean height are analyzed. For high quality optics, PV performance of less than one-tenth of a wavelength (0.1 waves) and RMS error less than one-fiftieth of a wavelength (0.02 waves) are generally acceptable for diffraction-limited systems. Mean height is calculated from the average OPD over an area, and it should match the commanded displacement. The linearization table is deemed viable if the DM produces a flat surface that meets these specifications over a wide displacement range. The mirror surface is characterized in 10-V increments, corresponding to displacement increments ranging from 40 to 170 nm, dependent on the operating point. All calculations of the LUT wave-front error assume a wavelength (λ) of 1.55 μm.

The RMS, PV, and mean height criteria are calculated using a circular mask centered on the DM membrane. The “soft” mask is applied using the Fizeau’s MetroPro® software, allowing straightforward adjustment of the diameter. In order to eliminate the less important distortions near the fixed edges of the DM, we found it helpful to characterize the mirror using a mask diameter set to 75% of the distance between actuators located on opposite extremes of the membrane. The corresponding results using the LUT shown in Fig. 6 demonstrate highly linear displacement. An initial lag in the displacement results from the inherent curvature of the DM in its unenergized state. This inherent curvature of the mirror is not completely removed at low voltages, causing greater RMS and PV errors at low voltages. Since those displacements are not necessary for our application, this limitation is not a problem. At larger voltages, the slope is steady and exhibits linear characteristics. The data in Fig. 6 shows PV wave-front errors less than λ/10 and RMS wave-front errors below λ/50 over the mirror displacement range of 500 to 3000 nm. Additional mask diameters were also characterized, and Table 1 lists the PV and RMS wave-front errors using the LUT and varying circular mask diameters. The values Table 1 provides are averaged over the displacement range.

4.2. Zernike surfaces

We rely on a simple model for generating and evaluating Zernike shapes that neglects the inter-actuator coupling effects discussed in Ref. 7

7. Y. Zhou and T. Bifano, “Characterization of Contour Shapes Achievable with a MEMS Deformable Mirror,” Proc. SPIE 6113, 123–130 (2006).

. This method involves discretely evaluating the fitting error over the whole usable surface using a resolution corresponding to the actuator size. The full surface is measured on the Fizeau interferometer, then each actuator region is analyzed. We then compare the expected and commanded values for each actuator region. The fitting error is then computed over the full area by calculating an RMS error <x2>, defined as the summation 1ni=1n(xi2), where n = 100 (number of actuator regions analyzed) and xi = [(RMS error at actuator i) - (desired shape at actuator i)].

The analysis results show that the linearization LUT reproduces moderately complex Zernike shapes on the DM. In the lower-order terms (astigmatism and tilt) the RMS error is low, approximately 0.02 waves for tilt Y, and astigmatism X and Y. Based on the DM’s 12×12 actuator resolution, we expected the errors to increase with Zernike complexity. This is evident in the coma Y and primary spherical terms, which have larger errors as shown in Table 2. This is partially attributable to inter-actuator coupling and the continuous surface membrane, since these shapes require large displacements occurring in close proximity to other actuators. This effect is not corrected in the LUT method used. The large primary spherical error may be due to imperfect centering of the shape on the actuators, making it difficult for the DM to recreate this shape. With the exception of primary spherical aberration, the errors for these surfaces are within 0.055 waves RMS.

Fig. 6. Mean surface displacement (top), peak-to-valley wave-front error (bottom left), and root-mean-square (RMS) wave-front error (bottom right) using linearization look-up table method and 75% circular mask diameter. PV and RMS errors with respect to ideal, flat surface.

4.3. Boundary-layer OPD surfaces

We performed further validation of the static performance of the DM using OPD boundary-layer distortion data generated from CFD simulations. The CFD data represents the airflow distortions from a hyper-hemispherical turret designed to enclose a lasercom terminal and mounted on top of an aircraft’s fuselage. The OPD is calculated by first selecting a look angle through the turret and an aperture size. Next, a cylinder representing the beam’s path and size through the boundary layer is placed into the CFD mesh. A column integration of air density through this cylinder using a specified aperture resolution (12×12 in this case) produces the effective OPD across the aperture. The process is repeated for each time step to create a time-series of OPD maps for the selected look angle and aperture size.

Table 1. RMS and peak-to-valley wave-front error using look-up table and various circular mask diameters. Error values in waves based on λ = 1.55 μm. Characterization performed over stated displacement ranges in 10-V increments; corresponding displacement increments ranged from 40 nm to 170 nm depending on voltage bias point (c.f., quadratic voltage response in Fig. 5). Mean errors represent averages of the errors observed over the applicable displacement range.

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Table 2. RMS errors between theoretical Zernike surface and experimentally-generated Zernike surface produced by the deformable mirror and measured using the Fizeau interferometer (λ = 1.55 μm). ρ and θ define radial coordinates for the wave-front shape.

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Fig. 7. Comparison of ideal, desired surfaces (“Commanded”) and deformable mirror replicated surfaces measured on the Fizeau interferometer (“Reproduced”) for various Zernike terms. Colorbar units of OPD in waves at λ = 1.55 μm.

To verify the mirror’s ability to reproduce the boundary-layer data, the first 15 time steps of CFD OPD data for two look angles are sent to the DM, one-by-one, and measured on the Fizeau interferometer. These measurements are reduced to a 12×12 matrix for comparison to the actual CFD data. For calculation of RMS error between the two, each is normalized to its own mean. Edges are also trimmed, leading to a 10 × 10 matrix. For the aircraft look angle of 90° azimuth and 45° elevation, the mean pixel RMS error averaged over 15 frames yields 0.029 waves. For the look angle 180° azimuth and 45° elevation, the average RMS error for the 15 frames is 0.023 waves. Additional discussion of the mirror’s fidelity in reproducing the CFD data is contained in Ref. 10

10. R. A. Conrad, Impact of the Boundary Layer on Pointing and Tracking in Airborne Free-Space Laser Communication Links (Master’s Dissertation, Aeronautics & Astronautics Department, M.I.T., June 2008). [PubMed]

.

Both error values appear consistent with the Zernike shapes tested in Sec. 4.2. The likely sources of error are coupling effects between actuators and the limited, 12×12 resolution of the DM surface. Note that these errors correspond to the surface itself, and the reflection-mode configuration of the DM leads to a doubling of the errors.

5. Dynamic performance

The Fizeau interferometer can perform highly accurate wave-front measurements of static conditions, but the slow data acquisition time (approximately 1 – 10 sec) limits it from analyzing the boundary-layer emulator when framed at the intended 2-kfps rate. At speeds up to approximately 200-Hz, the Fizeau interferometer’s camera provides fringe-pattern image data in analog form, that can be collected using a separate frame-grabber board. This technique allows for low-speed BLE verification, yet faster than if exclusively using the Fizeau interferometer’s data acquisition capability. Figure 8 shows a video of the fringe pattern created from the boundary-layer emulator running at 100 frames per second (fps). The video is slowed down to 30 fps to facilitate viewing.

At higher speeds, frame shots from a 1550-nm InGaAs tracking camera running at 2.4-kfps in the focal plane of the aircraft terminal’s aperture allow us to capture the intensity pattern resulting from the boundary-layer distortions. These images of experimental data compare well to images produced by numerical simulations [11

11. S. Zheng, Tracking Algorithms Under Boundary Layer Effects for Free-Space Optical Communications (Master’s Dissertation, Department of Electrical Engineering & Computer Science, M.I.T., August 2007).

], suggesting suitable emulation at a 1.2-kHz frame rate determined by the Nyquist frequency of the camera. Figure 9 shows a video of focal-plane images using this high-speed InGaAs camera at the same three look angles as in Fig. 8. These images also indicate how a received beam could be distorted by boundary-layer turbulence. Extracting phase-plane information to verify BLE operation using only focal-plane images is not a trivial matter since it requires one to reconstruct phase in an iterative manner and since the inverse Fourier transform does not yield unique solutions. However, work is underway to develop improved algorithms that might be used here.

To more carefully validate the dynamic performance of the BLE, we use a technique to determine what frame rate the entire system including the mirror, supporting electronics, and software controller could support. The BLE is programmed with a periodic tip/tilt circular motion and the beam is measured on a quadrant-cell detector in the focal plane. The BLE periodically cycles through a tip/tilt time series of 165 frames, covering one full circular motion with a diameter of approximately one beamwidth. This trajectory requires a maximum peak-to-peak displacement on the actuators of 1550 nm, corresponding to 44% of the specified 3500-nm stroke. However, since each period of motion results from a series of 165 frames, the displacement at the frame rate consumes on average 0.3% of the full stroke, meaning the measurement operates in the small-signal regime. This approach provides the advantages that it uses an easily observable tilt, provides aggregate performance of all actuators, and more closely resembles the fast, small-amplitude changes encountered in boundary layer dynamics. In addition, the down-conversion approach also allows us to observe the framing performance without being limited by the 12.5-kHz bandwidth of the quadrant detector and its electronics, whose Nyquist frequency is below 10 kfps, the maximum rate at which we seek to characterize the BLE.

Fig. 8. Experimental results of fringe patterns on the deformable mirror’s surface using an interferometer. The boundary layer is emulated for look angles at 45° elevation, 0° azimuth (left), 90° azimuth (center), and 180° azimuth (right). Video slowed down to 30 fps for easier viewing. [video, 3.9 MB]
Fig. 9. Experimental results of beam break-up due to boundary-layer distortions. Focal plane images of beam for look angles of 45° elevation and 0° azimuth (left), 90° azimuth (center), and 180° azimuth (right). [video, 3.2 MB]

We vary the frame rate of the BLE using the software controller, and record the peak tone’s output frequency and power level on a dynamic signal analyzer (Hewlett Packard, model no. 3562A). Figure 10 shows the resulting measurements. The top graph indicates that the output frequency is down-converted by the expected factor of 165, remaining nearly constant from 100 fps to 10 kfps. The peak tone’s power level, plotted in the bottom graph, also shows modest roll-off of approximately 1 dB from 100 fps to 10 kfps, indicating that the BLE produces the same pattern for all frame rates studied. These measurements are consistent with results of similar devices [3

3. T. G. Bifano, J. A. Perreault, and P. A. Bierden “A micromachined deformable mirror for optical wavefront compensation,” Proc. SPIE 4124, 7–14 (2000). [CrossRef]

,12

12. T. Bifano, P. Bierden, and J. Perreault, “Micromachined Deformable Mirrors for Dynamic Wavefront Control,” Proc. SPIE 5553, 1–16 (2004). [CrossRef]

], and validate the BLE small-signal dynamic performance at the intended 2-kfps rate.

Fig. 10. Framing performance of boundary-layer emulator. Output frequency versus BLE frame rate (top graph) showing expected down-conversion factor of 165 consistent with input time series. Peak tone output power level versus BLE frame rate (bottom graph) shows nearly flat frequency response well beyond the intended 2-kfps frame rate.

6. Summary

Aircraft boundary-layer turbulence creates fluctuations in the index of refraction of air, causing time-varying phase shifts across an aperture. These distortions can impact communications, pointing, acquisition, and tracking performance. We show the ability to replicate these phase shifts using a MEMS DM that introduces variable optical path delay across a beam propagating in free-space. This article discusses the development of a displacement look-up table for the DM, and evaluation of its performance at emulating static and dynamic boundary-layer phase distortions. We show that the boundary-layer emulator matches the CFD data to within approximately 0.03 waves and supports frame rates of 2 kfps. The results of this work indicate that the boundary-layer emulator replicates aero-optical phase shifts expected for an airborne lasercom terminal.

Acknowledgments

The authors wish to acknowledge Frederick G. Walther and Robert J. Murphy for their guidance on this work.

References and links

1.

S. G. Lambert and W. L. Casey, Laser Communications in Space (Artech House, Norwood, MA, 1995), Chap. 3.

2.

R. Parenti, R. J. Sasiela, L. C. Andrews, and R. L. Phillips, “Modeling the PDF for the irradiance of an uplink beam in the presence of beam wander,” Proc. SPIE 6215, 621508.1–13 (2006).

3.

T. G. Bifano, J. A. Perreault, and P. A. Bierden “A micromachined deformable mirror for optical wavefront compensation,” Proc. SPIE 4124, 7–14 (2000). [CrossRef]

4.

J. M. Roth, R. J. Murphy, W. E. Wilcox, and R. A. Conrad, “Experimental Emulation of Air-to-Space Laser Communication Links,” 2008 IEEE-LEOS Annual Meeting, 13 November 2008, Paper ThAA2, 886-7.

5.

R. A. Conrad, R. J. Murphy, T. H. Williams, W. E. Wilcox, S. Michael, and J. M. Roth, “Experimental comparison of tracking algorithms in the presence of aircraft boundary-layer distortions for emulated free-space laser communication links,” Appl. Opt. 48, A98–A106 (2009). [CrossRef]

6.

J. M. Roth, R. E. Bland, and S. I. Libby, “Large-Aperture Wide Field of View Optical Circulators,” IEEE Photon. Technol. Lett. 17, 2128–2130 (2005). [CrossRef]

7.

Y. Zhou and T. Bifano, “Characterization of Contour Shapes Achievable with a MEMS Deformable Mirror,” Proc. SPIE 6113, 123–130 (2006).

8.

Y. Zhou and T. Bifano, “Adaptive optics using a MEMS deformable mirror,” Proc. SPIE 6018, 350–356 (2005).

9.

J. Wyant, “Zernike Polynomials,” http://www.optics.arizona.edu/jcwyant/Zernikes/ZernikePolynomialsForTheWeb.pdf

10.

R. A. Conrad, Impact of the Boundary Layer on Pointing and Tracking in Airborne Free-Space Laser Communication Links (Master’s Dissertation, Aeronautics & Astronautics Department, M.I.T., June 2008). [PubMed]

11.

S. Zheng, Tracking Algorithms Under Boundary Layer Effects for Free-Space Optical Communications (Master’s Dissertation, Department of Electrical Engineering & Computer Science, M.I.T., August 2007).

12.

T. Bifano, P. Bierden, and J. Perreault, “Micromachined Deformable Mirrors for Dynamic Wavefront Control,” Proc. SPIE 5553, 1–16 (2004). [CrossRef]

OCIS Codes
(010.7060) Atmospheric and oceanic optics : Turbulence
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(110.0115) Imaging systems : Imaging through turbulent media
(060.2605) Fiber optics and optical communications : Free-space optical communication
(230.4685) Optical devices : Optical microelectromechanical devices
(110.7348) Imaging systems : Wavefront encoding

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: August 26, 2008
Revised Manuscript: January 23, 2009
Manuscript Accepted: January 30, 2009
Published: February 20, 2009

Citation
Ross A. Conrad, Williams E. Wilcox, Timothy H. Williams, Steven Michael, and Jeffrey M. Roth, "Emulation of dynamic wavefront disturbances using a deformable mirror," Opt. Express 17, 3447-3460 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3447


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References

  1. S. G. Lambert and W. L. Casey, Laser Communications in Space (Artech House, Norwood, MA, 1995), Chap. 3.
  2. R. Parenti, R. J. Sasiela, L. C. Andrews, and R. L. Phillips, "Modeling the PDF for the irradiance of an uplink beam in the presence of beam wander," Proc. SPIE 6215, 621508.1-13 (2006).
  3. T. G. Bifano, J. A. Perreault, and P. A. Bierden "A micromachined deformable mirror for optical wavefront compensation," Proc. SPIE 4124, 7-14 (2000). [CrossRef]
  4. J. M. Roth, R. J. Murphy, W. E. Wilcox, and R. A. Conrad, "Experimental Emulation of Air-to-Space Laser Communication Links," 2008 IEEE-LEOS Annual Meeting, 13 November 2008, Paper ThAA2, 886-7.
  5. R. A. Conrad, R. J. Murphy, T. H. Williams, W. E. Wilcox, S. Michael, and J. M. Roth, "Experimental comparison of tracking algorithms in the presence of aircraft boundary-layer distortions for emulated free-space laser communication links," Appl. Opt. 48, A98-A106 (2009). [CrossRef]
  6. J. M. Roth, R. E. Bland, and S. I. Libby, "Large-Aperture Wide Field of View Optical Circulators," IEEE Photon. Technol. Lett. 17, 2128-2130 (2005). [CrossRef]
  7. Y. Zhou and T. Bifano, "Characterization of Contour Shapes Achievable with a MEMS Deformable Mirror," Proc. SPIE 6113, 123-130 (2006).
  8. Y. Zhou and T. Bifano, "Adaptive optics using a MEMS deformable mirror," Proc. SPIE 6018, 350-356 (2005).
  9. J. Wyant, "Zernike Polynomials," http://www.optics.arizona.edu/jcwyant/Zernikes/ZernikeP lynomialsForTheWeb.pdf
  10. R. A. Conrad, Impact of the Boundary Layer on Pointing and Tracking in Airborne Free-Space Laser Communication Links (Master’s Dissertation, Aeronautics & Astronautics Department, M.I.T., June 2008). [PubMed]
  11. S. Zheng, Tracking Algorithms Under Boundary Layer Effects for Free-Space Optical Communications (Master’s Dissertation, Department of Electrical Engineering & Computer Science, M.I.T., August 2007).
  12. T. Bifano, P. Bierden, and J. Perreault, "Micromachined Deformable Mirrors for Dynamic Wavefront Control," Proc. SPIE 5553, 1-16 (2004). [CrossRef]

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