Glossary

Introduction

Conventional Adaptive Optics System

Image Spread with Atmospheric Turbulence

The Principle of Phase Conjugation

Point Spread Function for an Astronomical Telescope

Modeling the Effect of Atmospheric Turbulence

Fried's Coherence Length

Isoplanatic Angle

Kolmogorov Model

Atmospheric Turbulence Models

Coherence Length for Various Wavelengths and Turbulence Models

Greenwood Frequency

Wind Models

Scintillation

Zernike Polynomials

Legendre Polynomials

Angle of Arrival (Tilt) Fluctuations (Image Motion)

Modulation Transfer Function

Beam Propagation

System Performance Estimation

Modal and Zonal Fitting Error

Wavefront Sensors

Partial Correction

Shack-Hartmann Wavefront Sensor and Error

Shack-Hartmann Lenslet Array Selection

Curvature Wavefront Sensor and Error

Pyramid Wavefront Sensor and Error

Deformable Mirrors

Photodiodes

Photodiode Noise

Lateral-Effect Position-Sensing Detectors

Quad Cells

Noise Equivalent Angle

The Strehl Ratio: Laser-Beam Propagation to the Far Field with Wavefront Error

Strehl Ratio

Laser "Brightness"

Laser Beam Quality

Astronomical "Brightness"

Spot Size for a Gaussian Beam

Spot Size for a Uniform Circular Aperture

Temporal Error

Focal Anisoplanatism (the "Cone Effect")

Laser Guide Stars

Subsystem Requirements: The Wavefront Sensor

Angular Isoplanatic Error

Subsystem Requirements: Tilt Mirror

Subsystem Requirements: How many actuators? Zonal or Modal Control

Subsystem Requirements: Deformable Mirror

Deformable Mirror Actuator Configurations

Ferroelectric Actuators

Electrostatic Actuators

Voice Coil Actuators

Deformable Mirror Influence Function Models

Bimorph and MEMS Mirrors

Segmented Deformable Mirrors

Control and Reconstruction

Actuator and Wavefront Sensor Layouts

Correctability and Flattening of a Deformable Mirror

Adaptive Optics System Feedback Configuration

Deformable Mirror Dynamic Model

Controller Dynamic Model

Wavefront Sensor Dynamic Model

Latency

One-Dimensional Sampling

Two-Dimensional Sampling

Temporal Sampling Rate Selection

System Stability

General Control-System Parameters

Sensitivity Functions

Bandwidth Estimation from Controller Gains

Poke Matrix

Example System Geometry

Singular-Value Decomposition of the Poke Matrix

Actuator and Subaperture Observability

Identification of Actuator Locations

Poke Matrix Smoothing

Actuator Slaving: Active Actuator Identification

Actuator Slaving: Slave Logic

Adding Slaving into the Reconstructor

Tilt Removal

Piston and Waffle Removal

Reconstructor Generation: Least Squares

Reconstructor Generation: Regularization

T-Filter

Modal Suppression

Interactuator Shear Suppression

Nullspace Suppression

Weighting Matrices

Modal Feedback

Reconstructor Generation: Procedure

Reconstructor Comparison

Slope Discrepancy

Offloads and Woofer-Tweeter Systems

Open-Loop Wavefront Estimation

Kalman Filtering

Multivariable System Performance

Disturbance Injection

Wavefront Sensor Calibration

Centroiding and Thresholding

Misregistration

Subaperture Spillover

Equation Summary

Bibliography

Index

There have been a number of books and thousands of papers published with descriptions and mathematical expressions regarding adaptive optics. The material in this Field Guide is a summary of the methods for determining the requirements of an adaptive optics system, the performance of the system, and requirements for the components of the system. This second edition has a greatly expanded presentation of adaptive optics control system design and operation. Discussions of control models are accompanied by various recommendations for implementing the algorithms in hardware.

This book is not just another book on adaptive optics. There are already many fine volumes. This volume is intended for students, researchers, and practicing engineers who want a "go to" book when the calculation was "needed yesterday" (by a customer who won't be paying for it until the next fiscal year).

Many of the expressions are in the form of integrals. When that is the case, we show the results graphically for a variety of practical values. Some of the material in this volume duplicates similar expressions found in other volumes of the Field Guide series. We have attempted to remain consistent with symbols of the other volumes. In some cases, however, we chose different symbols because they are well known within the adaptive optics literature.

Descriptions of the operation of subsystems and components and specific engineering aspects remain in the citations of the Bibliography.

This Field Guide is dedicated to the late Horace Babcock, whose pioneering ideas created the field of adaptive optics.

Robert K. Tyson
Benjamin W. Frazier
April 2012