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Introduction to Aberrations in Optical Imaging Systems

Book Description

The competent and intelligent optical design of today's state-of-the-art products requires an understanding of optical aberrations. This accessible book provides an excellent introduction to the wave theory of aberrations and will be valuable to graduate students in optical engineering, as well as to researchers and technicians in academia and industry interested in optical imaging systems. Using a logical structure, uniform mathematical notation and high quality figures, the author helps readers to learn the theory of optical aberrations in a modern and efficient manner. In addition to essential topics such as the aberration function, wave aberrations, ray caustics and aberration coefficients, this text covers pupil aberrations, the irradiance function, aberration fields and polarization aberrations. It also provides a historical perspective by explaining the discovery of aberrations and two chapters provide insight into classical image formation; these topics of discussion are often missing in comparable books.

Table of Contents

  1. Coverpage
  2. Introduction to Aberrations in Optical Imaging Systems
  3. Title page
  4. Copyright page
  5. Epigraph
  6. Epigraph
  7. Contents
  8. Preface
  9. Acknowledgements
  10. Harold H. Hopkins
  11. Roland V. Shack
  12. Symbols
  13. 1 Introduction
    1. 1.1 Optical systems and imaging aberrations
    2. 1.2 Historical highlights
    3. References
  14. 2 Basic concepts in geometrical optics
    1. 2.1 Rays and wavefronts
    2. 2.2 Symmetry in optical imaging systems
    3. 2.3 The object and the image spaces
    4. 2.4 The aperture stop, the pupils, and the field stop
    5. 2.5 Significant planes and rays
    6. 2.6 The field and aperture vectors
    7. 2.7 Real, first-order, and paraxial rays
    8. 2.8 First-order ray invariants
    9. 2.9 Conventions for first-order ray tracing
    10. 2.10 First-order ray-trace example
    11. 2.11 Transverse ray errors
    12. 2.12 Stop shifting
    13. Exercises
    14. Further reading
  15. 3 Imaging with light rays
    1. 3.1 Collinear transformation
    2. 3.2 Gaussian imaging equations
    3. 3.3 Newtonian imaging equations
    4. 3.4 Derivation of the collinear transformation equations
    5. 3.5 Cardinal points and planes
    6. 3.6 First-order rays’ congruence with the collinear transformation
    7. 3.7 The camera obscura
    8. 3.8 Review of linear shift-invariant systems theory
    9. 3.9 Imaging with a camera obscura
    10. 3.10 Optical transfer function of the camera obscura
    11. 3.11 The modulation transfer function and image contrast
    12. 3.12 Summary
    13. Exercises
    14. Further reading
  16. 4 Imaging with light waves
    1. 4.1 Spherical, oblique, and plane waves
    2. 4.2 Light diffraction by an aperture
    3. 4.3 Far-field diffraction
    4. 4.4 Diffraction by a circular aperture
    5. 4.5 Action of an aplanatic lens system on a plane wave
    6. 4.6 Fourier transforming properties of a lens system
    7. 4.7 4f optical relay system
    8. 4.8 Imaging with an 8f optical projection system
    9. 4.9 Imaging with coherent illumination
    10. 4.10 Imaging with incoherent illumination
    11. 4.11 Imaging with partially coherent illumination
    12. 4.12 The Weyl–Lalor relationship
    13. 4.13 Summary
    14. Exercises
    15. References
    16. Further reading
  17. 5 The wave aberration function
    1. 5.1 Theory of aberrations
    2. 5.2 Learning aberration theory
    3. 5.3 Heuristic approach to aberrations according to symmetry
    4. 5.4 The aberration function
    5. 5.5 Determination of the wavefront deformation
    6. 5.6 Parity of the aberrations
    7. 5.7 Note on the choice of coordinates
    8. 5.8 Summary
    9. Exercises
    10. References
  18. 6 The location and size of an image
    1. 6.1 Change of focus and change of magnification
    2. 6.2 Piston terms
    3. 6.3 Change of reference sphere radius
    4. 6.4 Images in the presence of defocus
    5. 6.5 Chromatic aberrations
    6. 6.6 Surface contributions to the chromatic aberrations
    7. 6.7 Cases of zero surface contribution
    8. 6.8 Chromatic coefficients for a system of thin lenses
    9. 6.9 Cases of zero thin lens contribution
    10. 6.10 The achromatic doublet lens
    11. Exercises
    12. Further reading
  19. 7 Wavefront aberrations
    1. 7.1 Wavefront deformation
    2. 7.2 Wave aberration fans
    3. 7.3 Physical images in the presence of aberrations
    4. 7.4 Wavefront variance
    5. 7.5 Aberration balancing
    6. 7.6 The Rayleigh–Strehl ratio
    7. Exercises
    8. Further reading
  20. 8 Ray aberrations
    1. 8.1 Relationship between the wavefront deformation and the transverse ray error
    2. 8.2 Components of the transverse ray aberrations
    3. 8.3 Spot diagrams
    4. 8.4 Through focus spot diagrams
    5. 8.5 Images of extended objects
    6. 8.6 Discussion of transverse ray aberrations
    7. 8.7 Meridional and sagittal ray paths
    8. 8.8 Summary
    9. Exercises
    10. Further reading
  21. 9 Ray caustics
    1. 9.1 Principal curvatures and caustic
    2. 9.2 Spherical aberration
    3. 9.3 Coma aberration
    4. 9.4 Astigmatism aberration
    5. 9.5 Curvature of the wavefront deformation
    6. 9.6 Astigmatic field curves
    7. 9.7 Coddington equations
    8. 9.8 Physical images along the optical axis
    9. Exercises
    10. Further reading
  22. 10 Aberration coefficients
    1. 10.1 Spherical aberration
    2. 10.2 Petzval field curvature
    3. 10.3 Aberration function when the stop is at the center of curvature
    4. 10.4 Aberration function when the aperture stop shifts
    5. 10.5 Aberration function of a combination of two spherical surfaces
    6. 10.6 Cases of zero aberration
    7. 10.7 Contributions from an aspheric surface
    8. 10.8 Contributions from stop shifting
    9. 10.9 Aberration coefficients of a Cooke triplet lens
    10. Exercises
    11. Further reading
  23. 11 Structural aberration coefficients
    1. 11.1 Coefficient definition
    2. 11.2 Vertex curvature of the field curves
    3. 11.3 Structural aberration coefficients of a refracting surface
    4. 11.4 Structural aberration coefficients of a reflecting surface
    5. 11.5 Structural aberration coefficients of a thin lens
    6. 11.6 Contrbutions to the structural aberration coefficients from a parallel plate
    7. 11.7 Structural aberration coefficients of an optical system
    8. 11.8 Application to the achromatic doublet
    9. 11.9 Application to the two-mirror Mersenne telescope
    10. 11.10 Application to a diffractive lens
    11. Exercises
    12. Further reading
  24. 12 Pupil aberrations
    1. 12.1 Definitions
    2. 12.2 Beam deformation at the entrance pupil
    3. 12.3 Pupil effects
    4. 12.4 Object shift equations
    5. 12.5 Invariance of aberrations
    6. 12.6 Chromatic pupil aberrations
    7. 12.7 The Bow–Sutton conditions
    8. 12.8 Second-order chromatic coefficients revisited
    9. Exercises
    10. Further reading
  25. 13 Irradiance function
    1. 13.1 Construction of the irradiance function
    2. 13.2 Irradiance transport
    3. 13.3 The element of throughput
    4. 13.4 The radiance theorem
    5. 13.5 Image and pupil aberrations relationships
    6. 13.6 The sine condition
    7. 13.7 The Herschel condition
    8. Exercises
    9. Further reading
  26. 14 Sixth-order aberration coefficients
    1. 14.1 Extrinsic aberrations
    2. 14.2 Intrinsic aberrations
    3. 14.3 Contributions from an aspheric surface
    4. 14.4 Contributions from the sixth-order coefficients of asphericity
    5. 14.5 Connections between pupil and image coefficients
    6. 14.6 Fifth-order transverse ray aberrations
    7. 14.7 Change of aberration coefficients with aperture vector location
    8. 14.8 The Buchdahl–Rimmer coefficients
    9. 14.9 Summary
    10. Exercises
    11. Further reading
  27. 15 Aberrations of non-axially symmetric systems
    1. 15.1 Tilted component systems
    2. 15.2 The Shack–Thompson aberration fields
    3. 15.3 Plane symmetric optical systems
    4. 15.4 Optical system tolerancing
    5. Exercises
    6. Further reading
  28. 16 Polarization aberrations
    1. 16.1 Polarization fields
    2. 16.2 Amplitude transmittance and optical phase coefficients
    3. 16.3 Amplitude and phase changes in the optical field
    4. 16.4 Chipman's polarization aberrations
    5. 16.5 Polarization fields’ nodal characteristics
    6. 16.6 Elliptical polarization
    7. Exercises
    8. Further reading
  29. 17 Conclusion
  30. Appendix Wave coefficients
  31. Index