DIRECTED ENERGY PROFESSIONAL SOCIETY

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Beam Control for Laser Systems
Paul Merritt

Hardback Textbook
Accompanying CD
373 Pages
2011, Directed Energy Professional Society

Product Details       Table of Contents       Preface

This book, as well as other books on Directed Energy, are available from the DEPS online store.

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

 
Copyright 2012 Directed Energy Professional Society   Last updated: 14 March 2012