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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, sparseaperture telescopes, and the optical challenges of designing and building telescopes or instruments for detecting and characterizing exoplanets
Pages: 448
ISBN: 9780819483669
Volume: PM202
 Preface
 Acknowledgments
 List of Acronyms
 Chapter 1 Historical Perspective
 1.1 Introduction
 1.2 Angle Measurements
 1.3 The Evolution of Optics
 References
 Bibliography
 Chapter 2 Astronomical Measurements: Ground and Space
 2.1 Introduction
 2.2 Measurement
 2.3 Comparison of Space and Groundbased 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 (firstorder 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
 References
 Chapter 3 FirstOrder Optics
 3.1 Introduction
 3.2 Interaction of Light and Matter
 3.2.1 Index of refraction
 3.2.2 Snell's law
 3.2.2.1 Snell's law for reflection from a mirror
 3.2.2.2 Total internal reflection
 3.2.2.3 Temperature sensitivity
 3.2.3 Glass and crystal types
 3.2.3.1 Optical materials
 3.2.4 Ray deviation and dispersion: prisms
 3.2.4.1 Achromatic prism pair
 3.2.4.2 Directvision 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
 3.3.4.1 Collinear transformations and Gaussian image formation
 3.3.4.2 The paraxial approximation
 3.3.5 Cardinal points
 3.3.6 Thicklens multiple elements and matrix raytracing
 3.3.7 Combining two systems
 3.3.7.1 Reflective surfaces
 3.3.7.2 Combining two optical power surfaces
 3.3.8 Matrix methods for raytracing paraxial optics
 3.3.9 Magnification
 3.3.9.1 Lateral or transverse magnification
 3.3.9.2 Longitudinal magnification
 3.3.9.3 Angular magnification
 3.3.9.4 Magnification in visual systems
 3.3.10 Chromatic aberration
 3.3.10.1 Introduction
 3.3.10.2 Thinlens chromatic aberration
 3.3.11 Image orientation
 3.3.11.1 Prism devices used for shifting images
 3.4 FNumber
 3.5 Numerical Aperture
 3.6 Summary
 References
 Bibliography
 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 GeometricWave Aberration Theory
 4.5.1 Seidel aberrations
 4.5.1.1 Tilt
 4.5.1.2 Defocus
 4.5.1.3 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: FirstOrder Color
 4.7.1 Opticalpathdistance error and focus error sign convention
 4.8 ThirdOrder Monochromatic Error Terms
 4.8.1 Spherical aberration
 4.8.2 Astigmatism and field curvature
 4.8.3 Petzal curvature (field curvature)
 4.8.3.1 Sagittal focus
 4.8.3.2 Tangential focus
 4.8.3.3 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 Planeparallel 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 Singlelens aberration with stop shift
 4.11.7 Application of the stopshift 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
 References
 Bibliography
 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–solidangle 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
 References
 Bibliography
 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 Signaltonoise ratio
 6.15.2 Detectors
 References
 Bibliography
 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
 References
 Bibliography
 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
 References
 Bibliography
 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 PhaseTransforming 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
 9.10.1.1 The rectangle function
 9.10.1.2 The sinc function
 9.10.1.3 The sgn function
 9.10.1.4 The triangle function
 9.10.1.5 The delta function
 9.10.1.6 The comb function
 9.10.1.7 The circ function
 9.10.1.8 The Gaus function
 9.10.1.9 Shorthand notation for Fourier transform
 9.10.2 The Fourier transforms of twodimensional functions
 9.10.3 Fouriertransform 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 leastmeansquare 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 Rootmeansquare wavefront error
 9.18 Diffractive Optical Elements
 9.18.1 The Fresnel lens
 9.18.2 The photon sieve
 9.19 DiffractionGrating 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 concavegrating spectrometer
 9.19.5 The convexgrating spectrometer
 9.19.6 Imageplane multiplex spectrometers
 9.20 Scalar Diffraction and Image Formation: Summary
 References
 Bibliography
 Chapter 10 Interferometry
 10.1 Introduction
 10.2 Historical Perspective
 10.2.1 Young's doubleslit experiment
 10.2.2 Highangularresolution astronomy: stellar diameters
 10.2.3 Spectrometers
 10.3 Complex Representation of Real Polychromatic Fields
 10.4 TemporalFrequency 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 TiltCompensated Fourier Transform Spectroscopy
 10.7 FabryPerot 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 Signaltonoise 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 Quasioptics of Gaussian Beam Propagation
 10.19 Summary
 References
 Bibliography
 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
 11.2.2.1 Analyses: sensitivity and tolerance
 11.2.2.2 Mechanical structure
 11.2.2.3 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 ShackHartmann 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 Iterativetransform Fourier mathematics
 11.7.3 Modifications to the basic GerchbergSaxton 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 Phasediversity objective function (maximumliklihood
 estimation)
 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
 References
 Bibliography
 Author Biography
 Chapter 12 SegmentedAperture Telescopes
 12.1 Introduction
 12.2 TwoStage Optics Applied to Continuous Primary Mirrors
 12.2.1 Monolithic mirrors
 12.2.2 Correcting the Hubble Space Telescope
 12.3 TwoStage 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 twostage optics
 12.5.2.1 Piston error
 12.5.2.2 Fieldangle errors
 12.5.2.3 Tilt errors
 12.5.2.4 Lateral image displacement
 12.5.2.5 Focal shift
 12.6 Effects of Gaps on Image Quality
 12.7 The James Webb Space Telescope
 12.8 Giant Groundbased Telescopes
 References
 Bibliography
 Chapter 13 SparseAperture 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 SparseAperture 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 SparseAperture Telescopes
 13.6.1 Introduction
 13.6.2 Multipletelescope telescope
 13.6.3 The Fizeau telescope
 13.6.4 The coherence interferometer
 13.7 SparseAperture Advantages
 13.8 Spacebased Fizeau Telescope Design Considerations
 13.8.1 Mechanical connection
 13.8.2 Freeformation flying Fizeau telescopes
 13.9 SignaltoNoise Ratio in SparseAperture Imaging: Theory
 13.10 Performance Modeling for SparseAperture 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 SignaltoNoise Ratio for SparseAperture Images
 13.13 The Future of SparseAperture Telescopes in Astronomy
 References
 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 phasedelay 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
 References
 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
 15.4.2.1 Imageplane masks
 15.4.2.2 Pupilplane masks
 15.4.2.3 Occulters
 15.4.2.4 Imaging thermal sources
 15.4.3 Inner working angle
 15.4.4 Degrees of mask freedom
 15.5 PupilMask Effectiveness
 15.5.1 Unapodized aperture with star and planet
 15.5.1.1 Imageplane PSF profile with different amplitude
 apodizations
 15.5.1.2 Results of apodization
 15.5.1.3 Comment
 15.6 Fresnel Diffraction
 15.7 Summary
 References
 Index
Preface
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. Highangularresolution 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 highdynamicrange systems that enable astronomers to image an exoplanet in the presence of the blinding glare from its parent star that is more than 10^{12} 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 groundbased 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 signaltonoise ratio. Chapter 7 provides an introduction to the optics of the atmosphere necessary for groundbased 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 indepth 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 spacebased 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 segmentedaperture telescopes and how they enable the nextgeneration, very large ground and spacebased telescopes. Chapter 13 presents an analysis of sparseaperture 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 extremecontrast systems such as coronagraphs for the characterization of exoplanet systems.
James B. Breckinridge
Pasadena, California
April 2012
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