| Preface to the Dover edition | p. 5 |
| Preface | p. 7 |
| Preface to the first edition | p. 11 |
| J. B. J. Fourier 1768-1830 | p. 13 |
| Preliminaries | |
| Introduction | p. 15 |
| Coherence and light sources | p. 20 |
| Temporal coherence | p. 21 |
| Spatial coherence | p. 21 |
| Optical image formation | p. 23 |
| Fraunhofer diffraction | p. 25 |
| Lens aperture | p. 28 |
| Interference by division of amplitude | p. 30 |
| Problems | p. 32 |
| Fraunhofer Diffraction | |
| Introduction | p. 34 |
| Single-slit pattern | p. 34 |
| Circular aperture | p. 38 |
| Double aperture | p. 43 |
| Two slits | p. 43 |
| Two circular apertures | p. 46 |
| N-slit grating | p. 46 |
| 2-dimensional gratings | p. 50 |
| Crystals as 3-dimensional gratings | p. 51 |
| Problems | p. 55 |
| Fourier Series and Periodic Structures | |
| Introduction | p. 57 |
| Fourier series | p. 58 |
| Determining Fourier coefficients: even functions | p. 60 |
| Optical and crystal diffraction gratings: physical interpretation of Fourier terms | p. 63 |
| Optical diffraction | p. 63 |
| Crystal diffraction | p. 64 |
| Fourier series: general formulations | p. 65 |
| The sine and cosine series | p. 65 |
| Exponential notation | p. 66 |
| Space and time | p. 69 |
| Problems | p. 70 |
| Fourier Transforms, Convolution and Correlation | |
| Introduction | p. 71 |
| The Fourier transform and single-slit diffraction | p. 72 |
| The grating pattern as a product of transforms | p. 79 |
| Convolution | p. 82 |
| Introduction | p. 82 |
| The grating as a convolution | p. 85 |
| The convolution theorem and diffraction | p. 86 |
| Fourier transforms and light waves | p. 88 |
| Correlation | p. 91 |
| Autocorrelation theorem (Wiener-Khintchine theorem) | p. 95 |
| Problems | p. 97 |
| Optical Imaging and Processing | |
| Introduction | p. 99 |
| Incoherent optical imaging | p. 102 |
| Determination of transfer functions | p. 104 |
| Coherent optical imaging | p. 106 |
| Periodic objects | p. 107 |
| Non-periodic objects | p. 110 |
| Illustrations: optical transforms | p. 110 |
| Holography | p. 118 |
| Optical processing | p. 122 |
| Coherent processing | p. 122 |
| Incoherent processing | p. 131 |
| Problems | p. 136 |
| Image Reconstruction from Projections (Medical Imaging) | |
| Introduction | p. 137 |
| X-ray computed tomography | p. 139 |
| Introduction | p. 139 |
| Reconstruction by simple back-projection | p. 143 |
| Iterative reconstruction | p. 145 |
| Analytical methods of reconstruction | p. 146 |
| Other modalities | p. 152 |
| Emission computed tomography | p. 152 |
| Magnetic resonance imaging | p. 153 |
| Ultrasonic computed tomography | p. 158 |
| Interferometry and Radiation Sources | |
| Introduction | p. 161 |
| Michelson's stellar interferometer | p. 162 |
| Introduction | p. 162 |
| Fringe visibility aspects | p. 165 |
| Michelson's spectral interferometer | p. 169 |
| Introduction | p. 169 |
| Fringe visibility and spectral distribution | p. 174 |
| Partial coherence, correlation, and visibility | p. 176 |
| Spatial coherence | p. 180 |
| Temporal coherence | p. 181 |
| Fourier transform spectroscopy | p. 183 |
| Applications in astronomy | p. 189 |
| Aperture synthesis | p. 189 |
| The intensity interferometer | p. 198 |
| Problems | p. 200 |
| Appendices | |
| The scalar-wave description of electromagnetic waves | p. 201 |
| The Stokes treatment of reflection and refraction | p. 209 |
| Circular-aperture Fraunhofer diffraction pattern | p. 211 |
| The Fourier transform of a linear array of N equally spaced [delta]-functions | p. 214 |
| Diffraction of X-rays by crystals. The equivalence of the Laue conditions and the Bragg reflection concept | p. 216 |
| Summary notes on Chapters 1-5 | p. 221 |
| The length of wavetrains and their spectral width | p. 226 |
| Maximum entropy data processing | p. 229 |
| Applications in Communications | p. 231 |
| The impulse response of the eye: a diffraction analogy | p. 237 |
| The electromagnetic spectrum. Approximate range of principal, named regions | p. 243 |
| Useful formulae | p. 244 |
| References | p. 245 |
| Bibliography | p. 251 |
| Solutions to problems | p. 255 |
| Index | p. 261 |
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