Optical Imaging and Aberrations, Part II. Wave Diffraction Optics

Optical Imaging and Aberrations, Part II. Wave Diffraction Optics

by Virendra N. N. Mahajan

Part II of Virendra Mahajan's Optical Imaging and Aberrations discusses methods for determining the characteristics of an object image formed by the diffraction of the object wave at the aperture stop or exit pupil of an aberrated imaging system. Numerical results of these effects are emphasized, increasing the book's usefulness. The book describes diffractionSee more details below


Part II of Virendra Mahajan's Optical Imaging and Aberrations discusses methods for determining the characteristics of an object image formed by the diffraction of the object wave at the aperture stop or exit pupil of an aberrated imaging system. Numerical results of these effects are emphasized, increasing the book's usefulness. The book describes diffraction theory of image formation of incoherent objects and examines both aberrated and aberration-free optical systems with circular, annular, and Gaussian pupils. Random aberrations are considered, including the effects of unpredictable image motion and propagation through atmospheric turbulence. As in Part I, each chapter ends with a set of problems that provides readers with practical examples.

Product Details

SPIE Press
Publication date:
Press Monographs
Product dimensions:
7.20(w) x 10.30(h) x 1.30(d)

Table of Contents

Symbols and Notationxix
Chapter 1Image Formation1
1.2Rayleigh-Sommerfeld Theory of Diffraction and Huygens-Fresnel Principle5
1.2.1Rayleigh-Sommerfeld Formula5
1.2.2Fresnel and Fraunhofer Approximations9
1.2.3Transfer Function of Free Space12
1.3Gaussian Image12
1.4Diffraction Image14
1.4.1Pupil Function14
1.4.2Diffracted Wave17
1.4.3Incoherent PSF and Shift-Invariant Imaging of an Incoherent Object22
1.5Physical Significance of PSF24
1.6Optical Transfer Function (OTF)27
1.6.1General Relations27
1.6.2Physical Significance of OTF31
1.6.3Properties of OTF33
1.6.4OTF Slope at the Origin35
1.6.5OTF in the Limit of Zero Wavelength40
1.6.6Geometrical OTF41
1.6.7Comparison of Diffraction and Geometrical OTFs44
1.6.8Determination of OTF45
1.6.9Significance of PTF45
1.7Asymptotic Behavior of PSF45
1.7.1Point-Spread Function46
1.7.2Encircled Power47
1.8PSF Centroid50
1.8.1Centroid in Terms of OTF Slope50
1.8.2Centroid Related to Wavefront Slope51
1.8.3Centroid Related to Wavefront Perimeter52
1.9Strehl Ratio53
1.9.1General Relations53
1.9.2Approximate Expressions for Strehl Ratio56
1.9.3Determination of Strehl Ratio58
1.10Hopkins Ratio59
1.11Line-and Edge-Spread Functions (LSF and ESF)61
1.11.1Line-Spread Function61
1.11.2Edge-Spread Function64
1.11.3LSF and ESF in Terms of OTF64
1.12Shift-Invariant Imaging of a Coherent Object67
1.12.1Coherent Point-Spread Function67
1.12.2Coherent Transfer Function69
1.13Summary of Theorems71
AppendixFourier Transform Definitions74
Chapter 2Optical Systems with Circular Pupils79
2.2Aberration-Free System82
2.2.1Point-Spread Function82
2.2.2Encircled Power87
2.2.3Ensquared Power88
2.2.4Excluded Power90
2.2.5Optical Transfer Function93
2.2.6PSF and Encircled Power From OTF96
2.3Strehl Ratio and Aberration Tolerance97
2.3.1Strehl Ratio97
2.3.2Primary Aberrations98
2.3.3Balanced Primary Aberrations99
2.3.4Comparison of Approximate and Exact Results101
2.3.5Rayleigh's [lambda]/4 Rule102
2.3.6Strehl Ratio for Nonoptimally Balanced Aberrations103
2.4Balanced Aberrations and Zernike Circle Polynomials105
2.5Defocused System110
2.5.1Point-Spread Function111
2.5.2Focused Beam113
2.5.3Collimated Beam119
2.6PSFs for Rotationally Symmetric Aberrations121
2.6.2Numerical Results124
2.6.3Gaussian Approximation134
2.6.4Summary of Results135
2.7Symmetry Properties of an Aberrated PSF136
2.7.1General Theory137
2.7.2Symmetry About the Gaussian Image Plane138
2.7.3Symmetry of Axial Irradiance141
2.8PSFs for Primary Aberrations142
2.8.2Spherical Aberration Combined With Defocus142
2.8.3Astigmatism Combined With Defocus144
2.8.52-D PSFs150
2.8.6Comparison With Ray-Geometrical PSFs157
2.9Line of Sight of an Aberrated System159
2.9.1PSF Centroid159
2.9.2PSF and Numerical Results161 Tilt162 Coma162 Coma164
2.10OTFs for Primary Aberrations169
2.10.1General Relations169
2.10.3Spherical Aberration173
2.11Hopkins Ratio182
2.11.1Tolerance for Primary Aberrations182
2.11.3Hopkins Ratio in Terms of Variance of Aberration Difference Function185
2.11.4Variance of Aberration Difference Function for Primary Aberrations186
2.12Geometrical OTF187
2.12.1General Relations188
2.12.2Radially Symmetric Aberrations189
2.12.4Spherical Aberration Combined with Defocus190
2.12.5Astigmatism Combined with Defocus190
2.13Incoherent Line- and Edge-Spread Functions191
2.13.1Theory192 From PSF192 From Pupil Function192 Ratio and Aberration Tolerances193 From OTF196 From OTF198
2.13.2Numerical Results199
2.14Miscellaneous Topics205
2.14.1Polychromatic PSF205
2.14.2Polychromatic OTF208
2.14.3Image of a Disc209
2.14.4Pinhole Camera218
2.15Coherent Imaging222
2.15.1Coherent Spread Function222
2.15.2Coherent Transfer Function223
2.15.3Coherent LSF224
2.15.4Coherent ESF229
2.15.5Image of a Coherent Disc234
2.15.6Use of a Lens for Obtaining Fourier Transforms238
2.15.7Comparison of Coherent and Incoherent Imaging241
Chapter 3Optical Systems With Annular Pupils259
3.2Aberration-Free System261
3.2.1Point-Spread Function261
3.2.2Encircled Power265
3.2.3Ensquared Power265
3.2.4Excluded Power266
3.2.5Numerical Results267
3.2.6Optical Transfer Function272
3.3Strehl Ratio and Aberration Tolerance281
3.3.1Strehl Ratio282
3.3.2Primary Aberrations283
3.3.3Balanced Primary Aberrations283
3.3.4Comparison of Approximate and Exact Results284
3.4Balanced Aberrations and Zernike Annular Polynomials291
3.5Defocused System298
3.5.1Point-Spread Function298
3.5.2Focused Beam299
3.5.3Collimated Beam303
3.6Symmetry Properties of an Aberrated PSF305
3.7PSFs and Axial Irradiance for Primary Aberrations308
3.82-D PSFs311
3.9Line of Sight of an Aberrated System322
3.9.1PSF Centroid322
3.9.2PSF and Numerical Results323 Tilt323 Coma324 Coma327
Chapter 4Optical Systems With Gaussian Pupils333
4.2General Theory336
4.3Systems with Circular Pupils337
4.3.2Aberration-Free System338
4.3.3Strehl Ratio and Aberration Tolerance343
4.3.4Balanced Aberrations and Zernike-Gauss Circle Polynomials344
4.3.5Defocused System348 Irradiance349 Distribution350 Beam352
4.3.6Weakly Truncated Gaussian Circular Beams353 Distribution and Beam Radius354 of Lenses on Gaussian Beam Propagation359 Balancing362
4.3.7Symmetry Properties of an Aberrated PSF365
4.4Systems with Annular Pupils366
4.4.2Aberration-Free System368
4.4.3Strehl Ratio and Aberration Tolerance370
4.4.4Balanced Aberrations and Zernike-Gauss Annular Polynomials371
4.4.5Defocused System374 Irradiance374 Distribution376 Beam376
4.4.6Symmetry Properties of an Aberrated PSF378
4.4.7PSF Centroid379 Tilt380 Coma381 Coma382
Chapter 5Random Aberrations387
5.2Random Motion389
5.2.1General Theory390
5.2.2Circular Pupils391 Approximation392 Results393
5.2.3Annual Pupils393 results397
5.3Imaging Through Atmospheric Turbulence401
5.3.1Long-Exposure Image402
5.3.2Kolmogrov Turbulence407
5.3.3Circular Pupils412
5.3.4Annular Pupils415
5.3.5Phase Aberration in Terms of Zernike Polynomials419
5.3.6Short Exposure Image425
AppendixFourier Transform of Zernike Polynomials433
References for Additional Reading439

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