Chapter 1. Introduction ...........................................................................................................................1

Chapter 2. System Engineering, Performance Equations, and Error Budgets .......................5

• Basic Concepts ........................................................................................................................5
• Radiometric Units..................................................................................................................5
• Propagation through Rectangular Slit ................................................................................6
• Propagation through Circular Aperture ..............................................................................8
• Gaussian Fit to Airy Pattern ................................................................................................9
• Peak Irradiance ..................................................................................................................11
• Average Irradiance ............................................................................................................16
• Preliminary Error Budget ......................................................................................................17
• Line-of-Sight Jitter .............................................................................................................17
• Local Loop Jitter ................................................................................................................18
• Obscuration Strehl .............................................................................................................21
• Target Loop Jitter ..............................................................................................................23
• Atmospheric Jitter .............................................................................................................23
• Higher Order Aberrations .................................................................................................26
• Atmospheric Higher-Order Strehl with Tilt ......................................................................28
• Atmospheric Higher-Order Strehl without Tilt .................................................................28
• Scintillation Strehl...............................................................................................................28
• Aero-Optical Strehl ............................................................................................................31
• Thermal Blooming Strehl ...................................................................................................44
• Optics Manufacturing Strehl ..............................................................................................47
• Beam Quality Strehl ...........................................................................................................47
• Thermal Distortion of Optics .............................................................................................48
• Laser Transmission Losses .............................................................................................49
• Example Error Budget without Control Systems ............................................................50
• Beam Quality and Power in the Bucket ...............................................................................51

Chapter 3. Modeling of Components and Systems in Frequency and Time Domains ......67

• Closed-Loop Equation ..........................................................................................................76
• Open-Loop Transfer Function ...............................................................................................79
• Setting the Magnitude of a Bode Plot ..................................................................................80
• Phase Lead Network .............................................................................................................81
• Phase Margin..........................................................................................................................86
• Closed-Loop Transfer Function ............................................................................................87
• Decibel (dB) ...........................................................................................................................89
• Error Rejection Bode Plot .....................................................................................................90
• Type of Control System .........................................................................................................91
• Type 1 Added to Beam Steering Mirror Example.............................................................100
• PID Compensation...............................................................................................................102
• State Space Equations........................................................................................................103

Chapter 4. Analysis Using Random Data.....................................................................................109

• Probability Density Functions...............................................................................................112

Chapter 5. Optical Train Components and Small-Angle Control............................................153

• Device Jitter...........................................................................................................................156
• Relay Mirrors..........................................................................................................................156
• Beam Steering Mirrors..........................................................................................................157
• Optical Bench Motion............................................................................................................158
• Rectilinear Vibration Inputs...................................................................................................158
• Beam Walk Mirrors................................................................................................................159
• Inertial Reference Units..........................................................................................................161
• Vibration Inputs to the Beam Train ......................................................................................168

Chapter 6. Gimbals and Large-Angle Control...............................................................................171

• Gimbal Slew Using PTOS.....................................................................................................176
• Gimbal Disturbances.............................................................................................................177
• Control Considerations for Multiple-Gimbal Design...........................................................179
• Control System Effects on Input Angular Velocity............................................................179
• Kinematic Coupling................................................................................................................181
• Beam Tilt and Translation Transmission through a Telescope..........................................185

Chapter 7. Tracking Systems and Atmospheric Limitations.....................................................189

• Base Motion............................................................................................................................195
• Tracking Systems Radiometrics...........................................................................................196
• Tracking Algorithms................................................................................................................199
• Tracking Bandwidth................................................................................................................208

Chapter 8. Control Theory for Adaptive Optics and Fiber Optics.............................................215

• SISO control analysis...............................................................................................................218
• MIMO controls analysis............................................................................................................221
• Obtaining Models for Adaptive Models Controls..................................................................223
• Analysis of the Ideal Adaptive Optics Control Model............................................................229
• Analysis of Pertubations..........................................................................................................230
• Performance Reduction Due to Misregistration....................................................................236
• Fiber Optics..............................................................................................................................238
• Conclusion on Beam Control of Fiber Laser Systems.........................................................246

Chapter 9. Systems Analysis Using Controls Models and Error Budgets.............................247

• Loop Architectures...................................................................................................................249
• Analysis of Loop Stability........................................................................................................251
• Disturbance Input Data............................................................................................................258
• Evaluation of Jitter Disturbances............................................................................................262
• Jitter Contribution to Error Budget..........................................................................................270
• Higher-Order Wavefront Errors...............................................................................................271
• Atmospheric Higher-Order Errors...........................................................................................271
• Populating the Error Budget....................................................................................................274

Appendices.............................................................................................................................................277

• Appendix A. Combining Jittered Laser Beams....................................................................279
• Jitter on a Single Beam........................................................................................................279
• Incoherent Beam Combining...............................................................................................281
• Coherent Combining of beams...........................................................................................282
• Considering Jitter on the Combined Coherent Beam.......................................................283
• Appendix B. Examples of Atmospheric Transmission Calculations...................................284
• Absorption..............................................................................................................................284
• Scattering..............................................................................................................................288
• Appendix C. Atmospheric Parameters in Beam Control.....................................................289
• Power Spectral Density of Atmospheric Higher-Order Aberrations...............................289
• Power Spectral Density of Atmospheric Tilt......................................................................299
• Derivation of Turbulence Tilt Power Spectral Densities...................................................300
• Appendix D. MATLAB SIMULINK Tutorial Text.....................................................................309
• Appendix E. Propagation Equations for Gaussian Beams.................................................314
• Appendix F. Design of Compensation for Second-Order Systems....................................321
• Appendix G. Rigid Optical Bench Rotation...........................................................................324
• Appendix H. Derivation of Fitts Correlation Tracking Algorithm.........................................328
• Appendix I. Derivation of Final Value Theorem....................................................................332
• Appendix J. Homework Problems.........................................................................................334
• Chapter 2 Homework...........................................................................................................334
• Chapter 3 Homework...........................................................................................................337
• Chapter 4 Homework...........................................................................................................339
• Chapter 5 Homework...........................................................................................................342
• Chapter 6 Homework...........................................................................................................347
• Chapter 7 Homework...........................................................................................................351
• Chapter 8 Homework...........................................................................................................352

Index..........................................................................................................................................................355