Details

<p>Acknowledgements ix</p> <p><b>1 Introduction 1</b></p> <p>1.1 Motivation for Revisiting Aero-Optics 2</p> <p><b>2 Fundamentals 7</b></p> <p>2.1 Wavefronts and Index of Refraction 7</p> <p>2.2 Huygens’ Principle 8</p> <p>2.3 Basic Equations and Optical Path Difference 11</p> <p>2.4 Linking Equation 15</p> <p>2.5 Image at a Focal Plane (Far-field Propagation) 17</p> <p>2.6 Far-field Intensity in the Presence of Near-field Distortions 20</p> <p>2.6.1 Temporal Intensity Variation 25</p> <p>2.7 Wavefront Components 26</p> <p><b>3 Measuring Wavefronts 31</b></p> <p>3.1 Interferometry Methods 31</p> <p>3.2 Wavefront Curvature Methods 33</p> <p>3.3 Gradient-based Wavefront Sensors 35</p> <p>3.3.1 Shack-Hartmann Wavefront Sensor 37</p> <p>3.3.1.1 Wavefront Reconstruction Algorithm 41</p> <p>3.3.2 Malley Probe 43</p> <p>3.3.3 SABT Sensor 46</p> <p>3.4 Typical Optical Set-Ups 47</p> <p><b>4 Data Reduction and Interpretation 55</b></p> <p>4.1 Statistical Analysis 56</p> <p>4.1.1 Temporal and Spatial OPD rms 56</p> <p>4.1.2 Histograms and Higher-Moment Statistics 58</p> <p>4.2 Spectral Analysis 60</p> <p>4.2.1 Relation between the Deflection Angle Spectrum and the Wavefront Statistics 62</p> <p>4.2.2 Dispersion Analysis 63</p> <p>4.3 Modal Analysis 65</p> <p>4.3.1 Zernike Functions 66</p> <p>4.3.2 Proper Orthogonal Decomposition (POD) 70</p> <p>4.3.2.1 Direct Method 73</p> <p>4.3.2.2 Snapshot Method 74</p> <p>4.3.3 Dynamic Mode Decomposition (DMD) 82</p> <p>4.4 Cross-correlation-based Techniques 85</p> <p>4.4.1 Local Convective Speeds 85</p> <p>4.4.2 Multi-point Malley Probe Analysis 89</p> <p>4.4.3 Spatially Varying 2-D Convective Velocity 92</p> <p><b>5 Aperture Effects 97</b></p> <p><b>6 Typical Aero-Optical Flows 105</b></p> <p>6.1 Scaling Arguments 105</p> <p>6.2 Free Shear Layers 106</p> <p>6.2.1 Shear-Layer Physics 106</p> <p>6.2.2 Aero-Optical Effects 109</p> <p>6.2.3 Historical Shear Layer Measurements in AEDC 110</p> <p>6.2.4 Weakly Compressible Model 114</p> <p>6.3 Boundary Layers 118</p> <p>6.3.1 Model of Aero-optical Distortions for Boundary Layers with Adiabatic Walls 122</p> <p>6.3.2 Angular Dependence 130</p> <p>6.3.3 Finite Aperture Effects 132</p> <p>6.3.4 Nonadiabatic Wall Boundary Layers 133</p> <p>6.3.5 Instantaneous Far-Field Intensity Drop-Outs 142</p> <p>6.3.5.1 Absolute SR Threshold 147</p> <p>6.3.5.2 Relative Intensity Variation 150</p> <p>6.4 Turrets 152</p> <p>6.4.1 AAOL 154</p> <p>6.4.2 Flow Topology and Dynamics 159</p> <p>6.4.3 Steady-lensing Effects at Forward-looking Angles 167</p> <p>6.4.4 Aero-optical Environment at Back-looking Angles 169</p> <p>6.4.5 Shock-effects at Transonic Speeds 172</p> <p><b>7 Aero-Optical Jitter 179</b></p> <p>7.1 Local and Global Jitter 180</p> <p>7.1.1 Local Jitter 180</p> <p>7.1.2 Global Jitter 180</p> <p>7.2 Subaperture Effects 183</p> <p>7.3 Techniques to Remove the Mechanically Induced Jitter 183</p> <p>7.3.1 Cross-correlation Techniques 184</p> <p>7.3.2 Large-Aperture Experiments 186</p> <p>7.3.3 Stitching Method 187</p> <p><b>8 Applications to Adaptive Optics 195</b></p> <p>8.1 Beam-Control Components 195</p> <p>8.2 How Much Correction Is Needed 198</p> <p>8.3 Flow-Control Mitigation 198</p> <p>8.3.1 Non-Flow-Control Mitigation 199</p> <p>8.3.2 Some Qualities of Separated Shear Layers 200</p> <p>8.3.3 Using the POD Analysis to Develop Requirements 204</p> <p>8.4 Proper Number of Wavefront Sensor Subapertures to Actuator Ratio 208</p> <p>8.4.1 Numerical Simulation 209</p> <p>8.4.2 Simulation Results 211</p> <p>8.4.3 Conclusion from the Simulation Results 213</p> <p><b>9 Adaptive Optics for Aero-Optical Compensation 217</b></p> <p>9.1 Analogies from Free-Stream Turbulence Compensation 217</p> <p>9.1.1 Statistical Optics Theoretical Considerations 217</p> <p>9.1.2 Power-Law Observations from Aero-Optical Wavefront Data 219</p> <p>9.2 Compensation Scaling Laws for Aero-Optics 222</p> <p>9.2.1 Adaptive Optics Control Law and Error Rejection Transfer Function 222</p> <p>9.2.2 Asymptotic Results for Aero-Optics Compensation 223</p> <p>9.2.3 Aero-Optics Compensation Frequency 225</p> <p>9.2.4 Relation of Aero-Optics Scaling Laws to Free-Stream Turbulence 227</p> <p>9.3 Spatial and Temporal Limitations of Adaptive Optics 228</p> <p>9.3.1 Framework for Analysis of Aero-Optical Compensation 228</p> <p>9.3.2 Deformable Mirror Fitting Error for Aero-Optical POD Modes 229</p> <p>9.3.3 Decomposition of Correctable and Uncorrectable Power Spectrum 233</p> <p>9.3.3.1 DM Sensitivity Transfer Function 233</p> <p>9.3.4 Closed-Loop Residual Wavefront Error 234</p> <p>9.3.5 Effect of Latency in Aero-Optics Compensation 236</p> <p>9.4 Application to System Performance Modeling 238</p> <p>9.4.1 Scaling of Aero-Optical Statistics to Flight Conditions 239</p> <p>9.4.2 Joint Variations in Adaptive Optics Bandwidth and Actuator Density 239</p> <p>9.4.3 Relative Impact of Aero-Optics with Other Propagation and System Effects 244</p> <p>9.4.3.1 Comparing Aero-Optics to Free-Stream Turbulence Propagation 245</p> <p>9.4.3.2 Comparing Aero-Optics to System Optical Jitter 246</p> <p>9.4.4 Tracker Performance Degradations Related to Aero-Optics 248</p> <p>9.4.4.1 Track Sensor Aero-Optical Imaging Resolution Degradation 249</p> <p>9.4.4.2 Illuminator Propagation and Active Imaging through Aero-Optics 250</p> <p><b>10 Concluding Remarks 255</b></p> <p>References 259</p> <p>Index 271</p>

<p><b>Stanislav Gordeyev</b> is an Associate Professor at the Department of Aerospace and Mechanical Engineering at the University of Notre Dame. His expertise includes the investigation of aero-optical distortions caused by compressible turbulent flows around airborne systems. <p><b>Eric J. Jumper</b> is the Roth-Gibson Professor of Aerospace and Mechanical Engineering at the University of Notre Dame. Although he has performed research in a wide range of topics, his present principal research focus is on the understanding of aero-optical phenomena. <p><b>Matthew R. Whiteley, PhD, </b>is Vice President and Senior Scientist at MZA Associates Corporation in Dayton, Ohio. His research includes aero-optical beam control and sensing of atmospheric turbulence for laser propagation.

<p><b>Explore the newest techniques and technologies used to mitigate the effects of air flow over airborne laser platforms</b> <p><i>Aero-Optical Effects: Physics, Analysis and Mitigation</i> delivers a detailed and insightful introduction to aero-optics and fully describes the current understanding of the physical causes of aero-optical effects from turbulent flows at different speeds. In addition to presenting a thorough discussion of instrumentation, data reduction, and data analysis, the authors examine various approaches to aero-optical effect mitigation using both flow control and adaptive optics approaches. <p>The book explores the sources, characteristics, measurement approaches, and mitigation means to reduce aero-optics wavefront error. It also examines the precise measurements of aero-optical effects and the instrumentation of aero-optics. Flow control for aero-optical applications is discussed, as are approaches like passive flow control, active and hybrid flow control, and closed-loop flow control. <p>Readers will benefit from discussions of the applications of aero-optics in relation to fields like directed energy and high-speed communications. Readers will also enjoy a wide variety of useful features and topics, including: <ul><li> Comprehensive discussions of both aero-effects, which include the effects that air flow has over a beam director mounted on an aircraft, and aero-optics, which include atmospheric effects that degrade the ability of an airborne laser to focus a beam</li> <li> A treatment of air buffeting and its effects on beam stabilization and jitter</li> <li> An analysis of mitigating impediments to the use of high-quality laser beams from aircraft as weapons or communications systems</li> <li> Adaptive optics compensation for aero-optical disturbances</li></ul> <p>Perfect for researchers, engineers, and scientists involved with laser weapon and beam control systems, <i>Aero-Optical Effects: Physics, Analysis and Mitigation</i> will also earn a place in the libraries of principal investigators in defense contract work and independent research and development.

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