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El. knyga: Integrated Modeling of Telescopes

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Ground- or space-based telescopes are becoming increasingly more complex and construction budgets are typically in the billion dollar range. Facing costs of this magnitude, availability of engineering tools for prediction of performance and design optimization is imperative. Establishment of simulation models combining different technical disciplines such as Structural Dynamics, Control Engineering, Optics and Thermal Engineering is indispensable. Such models are normally called Integrated Models because they involve many different disciplines. The models will play an increasingly larger role for design of future interdisciplinary optical systems in space or on ground. The book concentrates on integrated modeling of optical and radio telescopes but the techniques presented will be applicable to a large variety of systems. Hence, the book will be of interest to optical and radio telescope designers, designers of spacecrafts that include optical systems, and to designers of various complex defense systems. The book may also find use as a textbook for undergraduate and graduate courses within the field. "Adaptive Optics" is an exciting and relatively new field, originally dedicated to correction for blurring when imaging through the atmosphere. Although this objective is still of high importance, the concept of Adaptive Optics has recently evolved further. Today, the objective is not only to correct for atmospheric turbulence effects but also for a range of static and dynamical telescope aberrations. The notion of adaptive optics has expanded to the field of "Wavefront Control", correcting for a variety of system aberrations. Wavefront control systems maintain form and position of optical elements with high precision under static and dynamical load. In many ways, such systems replace the steel structures of traditional optical systems, thereby providing much lighter systems with a performance not possible before. Integrated Modeling is the foremost tool for studies of Wavefront Control for telescopes and complex optics and is therefore now of high importance. Springer has recently published two books on telescopes, "Reflecting Telescope Optics" by R. Wilson, and "The Design and Construction of Large Optical Telescopes" by P. Bely. Noting that a new (and expensive) generation of Extremely Large Telescopes with apertures in the 30-100 m range is on the way, the present book on integrated modeling is a good match to the existing books and an appropriate specialization and continuation of some subjects dealt with in those books.

This book presents tools of integrated modeling together with concepts of ground-based telescopes. It also describes modeling of optical systems, structures, wavefront control systems with emphasis on segmented mirror control and active and adaptive optics.
1 Introduction
1(6)
2 Integrated Models
7(8)
2.1 Systems Engineering and Integrated Modeling
7(2)
2.2 Integrated Modeling Objectives
9(2)
2.3 Modeling Concepts
11(4)
3 Basic Modeling Tools
15(30)
3.1 Brief Introduction to Linear Algebra
15(4)
3.2 Eigenvalues and Eigenmodes
19(1)
3.3 Singular Value Decomposition
20(2)
3.4 Coordinate Transformations
22(1)
3.5 Least-Squares Fitting
23(3)
3.6 Orthogonal Polynomials
26(5)
3.6.1 Zernike Expansion
26(3)
3.6.2 Karhunen-Loeve Expansion
29(2)
3.7 Change of Basis
31(3)
3.8 State-Space Models
34(11)
3.8.1 General Form
34(2)
3.8.2 Controllability and Observability
36(1)
3.8.3 Transfer Functions from State-Space Models
37(2)
3.8.4 State-space Models from Transfer Functions
39(6)
4 Fourier Transforms and Interpolation
45(32)
4.1 Fourier Transforms
45(20)
4.1.1 Continuous Fourier Transforms
45(4)
4.1.1.1 Linear Shift Invariant Systems
49(2)
4.1.1.2 Sampling and Truncation
51(7)
4.1.2 Discrete Fourier Transform
58(7)
4.2 Interpolation
65(12)
4.2.1 Properties
66(2)
4.2.2 Interpolation Kernels
68(3)
4.2.3 Discrete Convolution
71(3)
4.2.4 Frequency Domain Operations
74(3)
5 Telescopes and Interferometers
77(88)
5.1 Typical Telescopes
77(15)
5.1.1 General Telescope Concepts
77(4)
5.1.2 A Large Optical Telescope: Grantecan
81(4)
5.1.3 A Large Radio Telescope: LMT
85(2)
5.1.4 Combining Telescopes into Interferometers
87(2)
5.1.5 Trends in Telescope Design
89(1)
5.1.5.1 Optical Domain
89(2)
5.1.5.2 Radio Domain
91(1)
5.2 Optics
92(12)
5.2.1 Optical Design Parameters
92(5)
5.2.2 Aberrations
97(7)
5.3 Mechanics
104(11)
5.3.1 Telescope Mounts
104(3)
5.3.2 Mirror Supports
107(4)
5.3.3 Bearings
111(2)
5.3.4 Materials
113(2)
5.4 Main Telescope Servos
115(13)
5.4.1 Main Axes Servomechanisms
115(3)
5.4.2 Locked Rotor Resonance Frequency
118(10)
5.5 Wavefront Control Concepts
128(27)
5.5.1 Active Optics
129(2)
5.5.2 Segmented Mirrors
131(2)
5.5.3 Adaptive Optics
133(5)
5.5.4 Wavefront Sensors
138(1)
5.5.4.1 Shack-Hartmann Wavefront Sensor
139(4)
5.5.4.2 Pyramid Wavefront Sensor
143(1)
5.5.4.3 Curvature Wavefront Sensor
144(3)
5.5.5 Deformable Mirrors
147(2)
5.5.6 Tip/tilt Mirrors
149(1)
5.5.7 Focal Plane Arrays
150(3)
5.5.8 Reconstructors and Filters
153(2)
5.6 Performance Metrics
155(10)
6 Optics Modeling
165(62)
6.1 Electromagnetic Field Model
166(2)
6.2 Geometrical Optics Modeling
168(17)
6.2.1 Eikonal Equation and Optical Pathlength
168(1)
6.2.2 Ray Equation and Optical Pathlength
169(5)
6.2.3 Optical Path Difference
174(1)
6.2.4 Transport Equation and Amplitude
175(1)
6.2.5 Matrix Methods
175(2)
6.2.6 General Ray Tracing
177(6)
6.2.7 Sensitivity Matrices
183(2)
6.3 Physical Optics Modeling
185(20)
6.3.1 Diffraction and Interference
186(1)
6.3.2 Rayleigh-Sommerfeldt Diffraction Integral
187(1)
6.3.3 Fresnel Diffraction
188(2)
6.3.4 Fraunhofer Diffraction
190(1)
6.3.5 Numerical Implementation
191(10)
6.3.6 Coherence and Incoherence
201(1)
6.3.7 Point Spread Function and Optical Transfer Function
202(3)
6.4 Building a Model: Optics
205(8)
6.4.1 Summary of Optical Propagation Models
206(2)
6.4.2 Modeling an Optical Telescope
208(1)
6.4.2.1 Point Sources
208(3)
6.4.2.2 Extended Objects
211(2)
6.5 Radio Telescopes
213(14)
6.5.1 Radio Telescope Optics
213(6)
6.5.2 Modeling of Radio Telescope Optics
219(8)
7 Radiometric Modeling
227(26)
7.1 Radiometry
228(1)
7.2 Sources
228(9)
7.2.1 Blackbody Radiation
228(2)
7.2.2 Stellar Magnitude
230(5)
7.2.3 Sky Distribution
235(2)
7.3 Atmosphere
237(6)
7.3.1 Extinction
238(3)
7.3.2 Atmospheric Refraction
241(2)
7.4 Sky Background
243(4)
7.5 Telescope Optics
247(2)
7.6 Building a Model: Radiometry
249(4)
8 Modeling of Structures
253(56)
8.1 Finite Element Modeling
253(22)
8.1.1 Modeling Principles
254(2)
8.1.2 Elements
256(3)
8.1.3 Static Analysis
259(3)
8.1.1 Modal Analysis
262(1)
8.1.4.1 Boundary Conditions
263(1)
8.1.4.2 Eigenfrequencies and Eigenmodes
263(2)
8.1.4.3 Orthogonality
265(1)
8.1.4.4 Modal Representation
266(1)
8.1.4.5 Generalized Coordinates
267(1)
8.1.5 Structural Damping
268(7)
8.2 State-space Models of Structures
275(4)
8.3 Model Reduction
279(23)
8.3.1 Static Condensation
281(3)
8.3.2 Guyan Reduction
284(1)
8.3.3 Dynamic Condensation
285(1)
8.3.4 Modal Truncation
286(6)
8.3.5 Balanced Model Reduction
292(2)
8.3.6 Krylov Subspace Technique
294(3)
8.3.7 Component Mode Synthesis
297(5)
8.4 Stitching Models Together
302(3)
8.5 SISO Structure Models
305(2)
8.6 Thermoelastic Modeling of Structures
307(2)
9 Modeling of Servomechanisms
309(8)
9.1 Model of a Generic Servomechanism
311(3)
9.2 State-Space Models of Generic Servomechanisms
314(3)
10 Modeling of Wavefront Control Systems
317(70)
10.1 Wavefront Sensors
317(9)
10.1.1 Shack-Hartmann Wavefront Sensors
318(1)
10.1.1.1 Wavefront Grid, Subaperture Grid and Pixel Grid
318(1)
10.1.1.2 Subaperture Models
319(4)
10.1.2 Pyramid Wavefront Sensors
323(1)
10.1.3 Curvature Wavefront Sensors
324(2)
10.2 Active Optics
326(7)
10.2.1 Mirror structure
327(1)
10.2.2 Wavefront sensor
328(1)
10.2.3 Controller
329(4)
10.3 Segmented Mirrors
333(22)
10.3.1 Principles and Control Algorithms
333(9)
10.3.2 Rigid-Body Motion of Stiff Segments
342(6)
10.3.3 Optical Performance
348(1)
10.3.3.1 Analytical Model
349(3)
10.3.3.2 Numerical Model
352(3)
10.4 Deformable Mirrors
355(8)
10.5 Tip/Tilt Mirrors
363(1)
10.6 Focal Plane Arrays
363(5)
10.6.1 Conversion to Photon Rate
363(1)
10.6.2 Dynamics Model
364(1)
10.6.2.1 Charge Collection
365(1)
10.6.2.2 Delays
366(1)
10.6.3 Noise Model
366(1)
10.6.3.1 Photon Noise
366(1)
10.6.3.2 Dark Current
366(1)
10.6.3.3 Readout Noise
367(1)
10.6.3.4 Quantization Noise
367(1)
10.6.4 Building a Model: Detector Noise
367(1)
10.7 Reconstructor and Controller for Adaptive Optics
368(13)
10.7.1 Reconstructor
369(1)
10.7.1.1 Forward Model
369(2)
10.7.1.2 Reconstructor algorithms
371(5)
10.7.2 Controller
376(5)
10.8 Building a Model: Adaptive Optics
381(6)
11 Disturbance and Noise
387(90)
11.1 Noise Characterization
387(7)
11.1.1 White Noise
389(5)
11.2 Wind
394(28)
11.2.1 Mean Wind Velocity
395(1)
11.2.2 Spectral Models
396(4)
11.2.3 Time Histories
400(1)
11.2.3.1 Pre-calculated Wind Time Series
400(4)
11.2.3.2 Two-Dimensional Wind Screen
404(3)
11.2.3.3 Autoregressive Filters
407(3)
11.2.4 Loads on Structures
410(6)
11.2.5 Building a Model: Wind Effects
416(6)
11.3 Gravity
422(1)
11.4 Thermal Disturbance
423(6)
11.5 Earthquakes
429(8)
11.6 Atmosphere
437(40)
11.6.1 Atmospheric Turbulence
437(1)
11.6.1.1 Refractive Index Structure Function
438(2)
11.6.1.2 Atmospheric Layers
440(2)
11.6.1.3 Wind Speed Profile
442(1)
11.6.2 Optical Effects and Characteristic Parameters
443(1)
11.6.2.1 Phase Structure Function and Power Spectrum
444(1)
11.6.2.2 Optical Transfer Function
445(4)
11.6.2.3 Characteristic Parameters
449(2)
11.6.2.4 Scintillation
451(2)
11.6.3 Numerical Models
453(2)
11.6.3.1 Phase Screen Generation
455(14)
11.6.3.2 Propagation Through the Atmosphere
469(2)
11.6.3.3 Wind
471(2)
11.6.3.4 Checking the Implementation
473(4)
12 Model Implementation and Analysis
477(32)
12.1 Building a Model: Global System
477(4)
12.2 Simulation
481(2)
12.3 Eigensolvers
483(2)
12.4 Ordinary Differential Equation Solvers
485(8)
12.4.1 ODE solver basics
486(3)
12.4.2 Multirate Solvers
489(4)
12.5 Sparse Matrix Methods
493(1)
12.6 Model Verification and Validation
494(15)
12.6.1 Comparison with Discipline Models
495(1)
12.6.2 Modal Testing of Structures
495(9)
12.6.3 Model Uncertainty
504(3)
12.6.4 Models of Models
507(2)
References 509(24)
Index 533