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Spie Press Book

Basic Optics for the Astronomical Sciences
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Book Description

This text was written to provide engineers and students of astronomy an understanding of optical science—the study of the generation, propagation, control, and measurement of optical radiation—as it applies to telescopes and instruments for astronomical research in the areas of astrophysics, astrometry, exoplanet characterization, and planetary science. The book provides an overview of the elements of optical design and physical optics within the framework of the needs of the astronomical community.

Features of this text include:

    • an historical perspective on the development of telescopes and their impact on our understanding of the universe
    • a review of the optical measurements that astronomers record, and identification of the attributes for ground and space observations
    • presentation of the fundamentals of optics, such as image location and size, geometrical image quality, image brightness, scalar diffraction and image formation, interference of light, and radiometry
    • discussion of the role of partial coherence in image formation and factors that affect image quality, as well as the role of optical metrology and wavefront sensing and control in astronomical telescopes
    • presentation of the fundamentals of optics, such as image location and size, geometrical image quality, image brightness, scalar diffraction and image formation, interference of light, and radiometry
    • investigations of segmented telescopes and their applications and performance metrics, sparse-aperture telescopes, and the optical challenges of designing and building telescopes or instruments for detecting and characterizing exoplanets

Book Details

Date Published: 21 June 2012
Pages: 448
ISBN: 9780819483669
Volume: PM202

Table of Contents
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List of Acronyms

Chapter 1 Historical Perspective
1.1 Introduction
1.2 Angle Measurements
1.3 The Evolution of Optics

Chapter 2 Astronomical Measurements: Ground and Space
2.1 Introduction
2.2 Measurement
2.3 Comparison of Space- and Ground-based Astronomical Optics
      2.3.1 Introduction
      2.3.2 Wavelength coverage
      2.3.3 Scattered light
      2.3.4 Angular resolution
      2.3.5 Thermal environment
      2.3.6 Gravity
      2.3.7 Accessibility
      2.3.8 Operations
      2.3.9 Summary
2.4 Mathematical Tools for Optics
      2.4.1 Introduction
      2.4.2 Geometrical optics (first-order optics)
      2.4.3 Scalar diffraction
      2.4.4 Vector diffraction
      2.4.5 Radiometric analysis (radiometry)
      2.4.6 Statistical theory
      2.4.7 Quantum theory
      2.4.8 Summary
2.5 Analysis and Synthesis of Optical Systems

Chapter 3 First-Order Optics
3.1 Introduction
3.2 Interaction of Light and Matter
      3.2.1 Index of refraction
      3.2.2 Snell's law
   Snell's law for reflection from a mirror
   Total internal reflection
   Temperature sensitivity
      3.2.3 Glass and crystal types
   Optical materials
      3.2.4 Ray deviation and dispersion: prisms
   Achromatic prism pair
   Direct-vision spectroscope
3.3 Image Location and Sign
      3.3.1 Conventions and signs
      3.3.2 Simple single lens
      3.3.3 Object, pupil, and image plane
      3.3.4 Paraxial optics
   Collinear transformations and Gaussian image formation
   The paraxial approximation
      3.3.5 Cardinal points
      3.3.6 Thick-lens multiple elements and matrix raytracing
      3.3.7 Combining two systems
   Reflective surfaces
   Combining two optical power surfaces
      3.3.8 Matrix methods for raytracing paraxial optics
      3.3.9 Magnification
   Lateral or transverse magnification
   Longitudinal magnification
   Angular magnification
   Magnification in visual systems
      3.3.10 Chromatic aberration
   Thin-lens chromatic aberration
      3.3.11 Image orientation
   Prism devices used for shifting images
3.4 F-Number
3.5 Numerical Aperture
3.6 Summary

Chapter 4 Aberration Theory: Image Quality
4.1 Introduction
4.2 Conic Sections: Surface of Revolution
4.3 Coordinate System for Geometric Aberration Analysis
4.4 Relationship Between Rays and Geometric Waves
4.5 Geometric-Wave Aberration Theory
      4.5.1 Seidel aberrations
   Seidel terms
      4.5.2 Zernike polynomials
4.6 Ray Errors in the Vicinity of the Image Plane
      4.6.1 Spot diagrams
4.7 Chromatic Aberrations: First-Order Color
      4.7.1 Optical-path-distance error and focus error sign convention
4.8 Third-Order Monochromatic Error Terms
      4.8.1 Spherical aberration
      4.8.2 Astigmatism and field curvature
      4.8.3 Petzal curvature (field curvature)
   Sagittal focus
   Tangential focus
   Medial focus
      4.8.4 Coma
      4.8.5 Wavefront errors combined
      4.8.6 Distortion
4.9 Optical Design
4.10 Tolerancing an Optical System
4.11 Applications of Aberration Theory
      4.11.1 Introduction
      4.11.2 Plane-parallel plate aberrations
      4.11.3 Aberrations for a thin lens
      4.11.4 Thin lens, stop at the center
      4.11.5 Relationship between spherical and coma
      4.11.6 Single-lens aberration with stop shift
      4.11.7 Application of the stop-shift equations
      4.11.8 Structural aberration coefficients for a mirror
      4.11.9 Magnification factors of interest
      4.11.10 The Schmidt camera
      4.11.11 Field curvature from a spherical mirror
4.12 Telecentric Optical Systems
4.13 Summary

Chapter 5 Transmittance, Throughput, and Vignetting
5.1 Introduction
5.2 System Transmittance
5.3 System Throughput (Etendue)
      5.3.1 Invariant on refraction
      5.3.2 Invariant on transfer
      5.3.3 Conservation of the area–solid-angle product
5.4 Vignetting
5.5 Image Contrast
5.6 Unwanted Radiation and Scattered Light
      5.6.1 Baffling an optical system
      5.6.2 Ghost images
5.7 Summary

Chapter 6 Radiometry and Noise
6.1 Introduction
6.2 Nomenclature
6.3 Radiant Power from a Source
6.4 Geometric Properties of Radiation
6.5 Fundamental Equation of Radiative Transfer
6.6 Lambertian Emitters
6.7 Specular Reflection
6.8 Reflectivity, Emissivity, and Absorption
6.9 Signal and Noise Calculation
      6.9.1 Power on the detector from the source
      6.9.2 Background power
      6.9.3 Simplification
6.10 Kirchoff's Laws
6.11 Uniform Illumination
6.12 Bidirectional Emission and Reflectance
6.13 Throughput or Etendue and Power
6.14 Astronomical Magnitudes
6.15 Noise
      6.15.1 Signal-to-noise ratio
      6.15.2 Detectors

Chapter 7 Optics of the Atmosphere
7.1 Introduction
7.2 Turbulence
      7.2.1 Quantitative atmospheric optical propagation
      7.2.2 Strehl ratio
      7.2.3 Wind
7.3 Atmospheric Transmission with Wavelength
7.4 Observatory Location
7.5 Conclusion

Chapter 8 Scalar and Vector Waves: Polarization
8.1 Introduction
8.2 Vector Waves
      8.2.1 Linear polarization
      8.2.2 Circular and elliptical polarization
8.3 Methods to Describe Polarized Light
      8.3.1 Introduction
      8.3.2 The Jones calculus
      8.3.3 The Stokes vector
      8.3.4 The Mueller matrix operator
8.4 Source of Polarization in Instruments
8.5 Polarization at the Interface of Dielectrics
8.6 Polarization at the Interface of Dielectrics and Metals
8.7 Powered (Curved) Optics Introduce Polarization
      8.7.1 Mueller matrices for various devices

Chapter 9 Scalar Diffraction and Image Formation
9.1 Introduction
      9.1.1 Image formation
9.2 The Coordinate System
9.3 Introduction to Diffraction and Image Formation
      9.3.1 The Huygens–Fresnel principle
      9.3.2 The Fresnel approximation
9.4 The Fraunhofer Approximation
9.5 The Airy Diffraction Pattern
9.6 Rayleigh Criterion
9.7 Diffraction for a Cassegrain Telescope
9.8 Phase-Transforming Properties of a Lens
9.9 The Fourier Transforming Properites of Lenses
      9.9.1 Fraunhofer diffraction pattern
9.10 Fourier Transforms and Applications to Optics
      9.10.1 Shorthand notation for Fourier transform applications
   The rectangle function
   The sinc function
   The sgn function
   The triangle function
   The delta function
   The comb function
   The circ function
   The Gaus function
   Shorthand notation for Fourier transform
      9.10.2 The Fourier transforms of two-dimensional functions
      9.10.3 Fourier-transform theorems and shorthand notations
      9.10.4 Similarity theorem
      9.10.5 Shift theorem
      9.10.6 Parseval's theorem
      9.10.7 Convolution theorem
      9.10.8 Autocorrelation theorem
      9.10.9 Representation of pupil functions (apertures)
9.11 Optical Transfer Function (OTF)
      9.11.1 Introduction
      9.11.2 Summary
9.12 Digital Images
      9.12.1 Detector resolution
      9.12.2 Pixels per point spread function
      9.12.3 Astronomical applications:summary
9.13 Image Processing
      9.13.1 The inverse filter
      9.13.2 The least-mean-square error filter (Wiener filter)
9.14 Apodization
      9.14.1 Example
9.15 Encircled Energy
9.16 Strehl Ration
9.17 Image Quality and Wavefront Error
      9.17.1 Cumulative wavefront error
      9.17.2 Power spectrum of wavefront errors
      9.17.3 Root-mean-square wavefront error
9.18 Diffractive Optical Elements
      9.18.1 The Fresnel lens
      9.18.2 The photon sieve
9.19 Diffraction-Grating Spectrometers
      9.19.1 Diffraction gratings
      9.19.2 Resolving power of a diffraction grating
      9.19.3 The Littrow spectrometer
      9.19.4 The concave-grating spectrometer
      9.19.5 The convex-grating spectrometer
      9.19.6 Image-plane multiplex spectrometers
9.20 Scalar Diffraction and Image Formation: Summary

Chapter 10 Interferometry
10.1 Introduction
10.2 Historical Perspective
      10.2.1 Young's double-slit experiment
      10.2.2 High-angular-resolution astronomy: stellar diameters
      10.2.3 Spectrometers
10.3 Complex Representation of Real Polychromatic Fields
10.4 Temporal-Frequency Interferometer
      10.4.1 Polarization in interferometers
10.5 Fourier Transform Spectrometer
      10.5.1 The interferogram
      10.5.2 Recording and processing interferograms
10.6 Tilt-Compensated Fourier Transform Spectroscopy
10.7 Fabry-Perot Interferometry
10.8 Spatial Interferometry: The Rotational Shear Interferometer
10.9 Michelson Stellar Interferometry
10.10 Image Formation and Interferometry
10.11 Contrast and Coherence
10.12 Imaging Through Turbulence
      10.12.1 Astronomical speckle interferometry
      10.12.2 Tilt anisoplanatism
      10.12.3 Chromatic anisoplanatism
      10.12.4 Recording speckle patterns
      10.12.5 Applications to double stars
10.13 Coherence Interferometry Imaging
      10.13.1 Introduction
      10.13.2 Coherence interferometry
      10.13.3 Analysis
      10.13.4 Imaging through atmospheric turbulence
      10.13.5 Fringe measurements
      10.13.6 Alignment for white light
      10.13.7 Signal-to-noise ratio
10.14 Heterodyne Interferometry
      10.14.1 Introduction
      10.14.2 Heterodyne spectrometer
      10.14.3 Application to stellar interferometry
10.15 Intensity Interferometry
10.16 Interferometric Testing of Optical Systems
      10.16.1 Introduction
      10.16.2 Optical testing
10.17 Assessing System WFE: Tolerancing
10.18 Quasi-optics of Gaussian Beam Propagation
10.19 Summary

Chapter 11 Optical Metrology and Wavefront Sensing and Control
Siddarayappa Bikkannavar
11.1 Introduction
      11.1.1 Wavefront error
11.2 Optical Metrology: Mechanical Structure Alignment
      11.2.1 Introduction
      11.2.2 Athermalization
   Analyses: sensitivity and tolerance
   Mechanical structure
   Athermalization of the structure
      11.2.3 Active control for optical metrology
      11.2.4 Edge sensors
11.3 Wavefront Sensing
11.4 Hartmann Screen Test
11.5 Shack-Hartmann Sensor
      11.5.1 Introduction
      11.5.2 Lenslet model for sensing local phase gradients
      11.5.3 Shack–Hartmann OPD reconstruction
11.6 Curvature Sensing
11.7 Phase Retrieval
      11.7.1 Introduction
      11.7.2 Iterative-transform Fourier mathematics
      11.7.3 Modifications to the basic Gerchberg-Saxton phase retrieval
      11.7.4 Limitations of phase retrieval
11.8 Phase Diversity
      11.8.1 Introduction
      11.8.2 Relationship between object and phase aberrations
      11.8.3 Phase-diversity objective function (maximum-liklihood
11.9 Wavefront Control Principles
11.10 Influence Functions and Sensitivity Matrix
11.11 Deformable Mirror Technology and Configurations
11.12 Linear Wavefront Control
11.13 Nonlinear Wavefront Control
11.14 Laser Guide Star Adaptive Optics
11.15 Wavefront Sensing & Control for Ground and Space
Author Biography

Chapter 12 Segmented-Aperture Telescopes
12.1 Introduction
12.2 Two-Stage Optics Applied to Continuous Primary Mirrors
      12.2.1 Monolithic mirrors
      12.2.2 Correcting the Hubble Space Telescope
12.3 Two-Stage Optics Applied to Segmented Primary Mirrors
      12.3.1 Introduction
      12.3.2 Large deployable reflector
12.4 Alignment and Manufacturing Tolerances for Segmented Telescopes
      12.4.1 Curvature manufacturing tolerance
      12.4.2 Segmented wavefront corrector
12.5 Image Quality with a Segmented Telescope
      12.5.1 Image quality
      12.5.2 Correcting errors in a segmented telescope with two-stage optics
   Piston error
   Field-angle errors
   Tilt errors
   Lateral image displacement
   Focal shift
12.6 Effects of Gaps on Image Quality
12.7 The James Webb Space Telescope
12.8 Giant Ground-based Telescopes

Chapter 13 Sparse-Aperture Telescopes
13.1 Introduction
13.2 Pupil Topology: Filled, Segmented, Sparse, and Interferometer Apertures
      13.2.1 Redundant and nonredundant apertures
      13.2.2 Angular resolution from a sparse aperture
13.3 Sparse-Aperture Equivalent Resolution
13.4 Image Reconstruction
13.5 Partially Filled Apertures
      13.5.1 Modulation transfer function of a sparse aperture
      13.5.2 Nonredundant pupils
      13.5.3 Rotating the sparse aperture to fill the pupil plane
13.6 Methods for Recombining Beams in Sparse-Aperture Telescopes
      13.6.1 Introduction
      13.6.2 Multiple-telescope telescope
      13.6.3 The Fizeau telescope
      13.6.4 The coherence interferometer
13.7 Sparse-Aperture Advantages
13.8 Space-based Fizeau Telescope Design Considerations
      13.8.1 Mechanical connection
      13.8.2 Free-formation flying Fizeau telescopes
13.9 Signal-to-Noise Ratio in Sparse-Aperture Imaging: Theory
13.10 Performance Modeling for Sparse-Aperture Telescopes
      13.10.1 Analysis
      13.10.2 Integration time and scene contrast: CCD full well
                  limits the exposure at three contrast levels
      13.10.3 Method for determining the relative exposure times by
                   matching the RMS residual from a filled aperture with that
                   of a sparse aperture
13.11 Pupil Topographies
      13.11.1 Processing 20% contrast images
      13.11.2 Processing 10% contrast images
13.12 Signal-to-Noise Ratio for Sparse-Aperture Images
13.13 The Future of Sparse-Aperture Telescopes in Astronomy

Chapter 14 Astrometric and Imaging Interferometry
14.1 Introduction
14.2 Principles of Stellar Interferometry
14.3 Astronomical Applications of Spatial Interferometry
      14.3.1 Introduction
      14.3.2 Astrometry
14.4 Instrument Parameters: Subsystem Requirements
14.5 Technologies
      14.5.1 Polarization
14.6 Interferometer Observatories
14.7 The Center for High Angular Resolution Astronomy (CHARA) Interferometer
      14.7.1 Optical phase-delay lines
14.8 The Infrared Spatial Interferometer (ISI)
14.9 The Very Large Telescope Interferometer (VLTI)
14.10 Astrometric Interferometry
      14.10.1 Introduction
      14.10.2 Applications of interferometry to exoplanet science
      14.10.3 The Space Interferometry Mission (SIM)
14.11 Interferometric Imaging: Phase Retrieval
14.12 Summary

Chapter 15 Coronography: Control of Unwanted Radiation
15.1 Introduction
15.1 Background
15.3 Coronograph Design Concept
15.4 Using Masks to Control Unwanted Radiation: Apodization
      15.4.1 Introduction
      15.4.2 Apodization and masks
   Image-plane masks
   Pupil-plane masks
   Imaging thermal sources
      15.4.3 Inner working angle
      15.4.4 Degrees of mask freedom
15.5 Pupil-Mask Effectiveness
      15.5.1 Unapodized aperture with star and planet
   Image-plane PSF profile with different amplitude
   Results of apodization
15.6 Fresnel Diffraction
15.7 Summary



Astronomical science advances use the following research cycle: measure parts of the universe, develop theories to explain the observations, use these new theories to forecast or predict observations, build new telescopes and instruments, measure again, refine the theories if needed, and repeat the process. Critical to the success of this cycle are new observations, which often require new, more sensitive, efficient astronomical telescopes and instruments.

Currently, the field of astronomy is undergoing a revolution. Several new important optical/infrared windows into the universe are opening as a result of advances in optics technology, including systems using high angular resolution, very high dynamic range, and highly precise velocity and position measurements. High-angular-resolution systems, which incorporate adaptive optics and interferometry, promise gains of more than 104 in angular resolution on the sky above our current capabilities. Advanced coronagraphs enable very high-dynamic-range systems that enable astronomers to image an exoplanet in the presence of the blinding glare from its parent star that is more than 1012 times brighter.

Optical science is the study of the generation, propagation, control, and measurement of optical radiation. The optical region of the spectrum is considered to range across the wavelength region of ~0.3 to ~50 μm, or from the UV through the visual and into the far infrared. Different sensors or detectors are used for covering sections of this broad spectral region. However, the analysis tools required to design, build, align, test, and characterize these optical systems are common: geometrical raytracing, wavefront aberration theory, diffraction theory, polarization, partial coherence theory, radiometry, and digital image restoration. Advances in allied disciplines such as material science, thermal engineering, structures, dynamics, control theory, and modeling within the framework of the tolerances imposed by optics are essential for the next generation of telescopes.

This text provides the background in optics to give the reader insight into the way in which these new optical systems are designed, engineered, and built. The book is intended for astronomy and engineering students who want a basic understanding of optical system engineering as it is applied to telescopes and instruments for astronomical research in the areas of astrophysics, astrometry, exoplanet characterization, and planetary science. Giant ground-based optical telescopes such as the Giant Segmented Mirror Telescope, the Thirty Meter Telescope, and the Extremely Large Telescope are currently under development. The James Webb Space Telescope is under construction, and the Space Interferometer Mission has successfully completed its technology program. The astronomical sciences are, indeed, at the threshold of many new discoveries.

Chapter 1 provides an historical perspective on the development of telescopes and their impact on our understanding of the universe. Chapter 2 reviews the optical measurements astronomers record and identifies the attributes for ground and space observatories. Chapter 3 provides the tools used for obtaining image location, size, and orientation and presents the geometrical constraints that need to be followed to maximize the amount of radiation passed by the system. Chapter 4 presents geometrical aberration theory and introduces the subject of image quality. Chapter 5 provides methods to maximize the amount of radiation passing through the optical system: transmittance, throughput, scattered light, and vignetting. Chapter 6 provides a basic introduction to radiative transfer through an optical system and identifies several factors needed to maximize the signal-to-noise ratio. Chapter 7 provides an introduction to the optics of the atmosphere necessary for ground-based astronomers. Chapter 8 introduces the scalar and vector wave theories of light and identifies sources of instrumental polarization that will affect the quality of astronomical data.

Using the Fourier transform, Chapter 9 provides an in-depth analysis of the propagation of scalar waves through an optical system as the basis of a discussion on the effects of astronomical telescopes and instruments on image quality. Chapter 10 provides a discussion of interferometry within the framework of partial coherence theory. The Fourier transform spectrometer, the Michelson stellar interferometer, and the rotational shear interferometer are used as examples and are analyzed in detail. Chapter 11, coauthored with Siddarayappa Bikkannavar, discusses the important new role that optical metrology and wavefront sensing and control play in the design and construction of very large ground- and space-based telescopes.

These 11 chapters have formed the basis of the Optical System Engineering class given by the author at CALTECH. Chapter 12 provides an analysis that is fundamental to the understanding of segmented-aperture telescopes and how they enable the next-generation, very large ground- and space-based telescopes. Chapter 13 presents an analysis of sparse-aperture telescopes, describes how they are used for extremely high angular resolution, and identifies their limitations. Chapter 14 discusses astrometric and imaging interferometry within the framework of basic optics. Chapter 15 develops basic concepts for extreme-contrast systems such as coronagraphs for the characterization of exoplanet systems.

James B. Breckinridge
Pasadena, California
April 2012

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