Fourier Optics An Introduction (Second Edition),9780486435046

Fourier Optics An Introduction (Second Edition)

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Edition: 2nd
ISBN13: 9780486435046
ISBN10: 0486435040
Format: Paperback
Pub. Date: 2011-11-02
Publisher(s): Dover Publications
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Summary

A straightforward introduction to the Fourier principles behind modern optics, this text is appropriate for advanced undergraduate and graduate students. Topics include the Fraunhofer diffraction, Fourier series and periodic structures, Fourier transforms, optical imaging and processing, image reconstruction from projections (medical imaging), and interferometry and radiation sources. Solutions. 1989 edition.

Author Biography

E. G. Steward: Professor Emeritus of Physics and Molecular Medicine City University, London

Table of Contents

Preface to the Dover edition 5(2)
Preface 7(4)
Preface to the first edition 11(2)
J.B.J. Fourier 1768-1830 13(2)
1 PRELIMINARIES
1.1 Introduction
15(5)
1.2 Coherence and light sources
20(3)
1.2.1 Temporal coherence
21(1)
1.2.2 Spatial coherence
21(2)
1.3 Optical image formation
23(7)
1.3.1 Fraunhofer diffraction
25(3)
1.3.2 Lens aperture
28(2)
1.4 Interference by division of amplitude
30(2)
Problems
32(2)
2 FRAUNHOFER DIFFRACTION
2.1 Introduction
34(1)
2.2 Single-slit pattern
34(4)
2.3 Circular aperture
38(5)
2.4 Double aperture
43(3)
2.4.1 Two slits
43(3)
2.4.2 Two circular apertures
46(1)
2.5 N-slit grating
46(4)
2.6 2-dimensional gratings
50(1)
2.7 Crystals as 3-dimensional gratings
51(4)
Problems
55(2)
3 FOURIER SERIES AND PERIODIC STRUCTURES
3.1 Introduction
57(1)
3.2 Fourier series
58(2)
3.3 Determining Fourier coefficients: even functions
60(3)
3.4 Optical and crystal diffraction gratings: physical interpretation of Fourier terms
63(2)
3.4.1 Optical diffraction
63(1)
3.4.2 Crystal diffraction
64(1)
3.5 Fourier series: general formulations
65(5)
3.5.1 The sine and cosine series
65(1)
3.5.2 Exponential notation
66(3)
3.5.3 Space and time
69(1)
Problems
70(1)
4 FOURIER TRANSFORMS, CONVOLUTION AND CORRELATION
4.1 Introduction
71(1)
4.2 The Fourier transform and single-slit diffraction
72(7)
4.3 The grating pattern as a product of transforms
79(3)
4.4 Convolution
82(4)
4.4.1 Introduction
82(3)
4.4.2 The grating as a convolution
85(1)
4.5 The convolution theorem and diffraction
86(2)
4.6 Fourier transforms and light waves
88(3)
4.7 Correlation
91(6)
4.7.1 Autocorrelation theorem (Wiener-Khintchine theorem)
95(2)
Problems
97(2)
5 OPTICAL IMAGING AND PROCESSING
5.1 Introduction
99(3)
5.2 Incoherent optical imaging
102(4)
5.2.1 Determination of transfer functions
104(2)
5.3 Coherent optical imaging
106(12)
5.3.1 Periodic objects
107(3)
5.3.2 Non-periodic objects
110(1)
5.3.3 Illustrations: optical transforms
110(8)
5.4 Holography
118(4)
5.5 Optical processing
122(14)
5.5.1 Coherent processing
122(9)
5.5.2 Incoherent processing
131(5)
Problems
136(1)
6 IMAGE RECONSTRUCTION FROM PROJECTIONS (MEDICAL IMAGING)
6.1 introduction
137(2)
6.2 X-ray computed tomography
139(13)
6.2.1 Introduction
139(4)
6.2.2 Reconstruction by simple back-projection
143(2)
6.2.3 Iterative reconstruction
145(1)
6.2.4 Analytical methods of reconstruction
146(6)
6.3 Other modalities
152(9)
6.3.1 Emission computed tomography
152(1)
6.3.2 Magnetic resonance imaging (I.S. Mackenzie)
153(5)
6.3.3 Ultrasonic computed tomography (J.P. Weight)
158(3)
7 INTERFEROMETRY AND RADIATION SOURCES
7.1 Introduction
161(1)
7.2 Michelson's stellar interferometer
162(7)
7.2.1 Introduction
162(3)
7.2.2 Fringe visibility aspects
165(4)
7.3 Michelson's spectral interferometer
169(7)
7.3.1 Introduction
169(5)
7.3.2 Fringe visibility and spectral distribution
174(2)
7.4 Partial coherence, correlation, and visibility
176(7)
7.4.1 Spatial coherence
180(1)
7.4.2 Temporal coherence
181(2)
7.5 Fourier transform spectroscopy
183(6)
7.6 Applications in astronomy
189(11)
7.6.1 Aperture synthesis
189(9)
7.6.2 The intensity interferometer
198(2)
Problems
200(1)
APPENDICES
A The scalar-wave description of electromagnetic waves
201(8)
B The Stokes treatment of reflection and refraction
209(2)
C Circular-aperture Fraunhofer diffraction pattern
211(3)
D The Fourier transform of a linear array of N equally spaced δ-functions
214(2)
E Diffraction of X-rays by crystals. The equivalence of the Laue conditions and the Bragg reflection concept
216(5)
F Summary notes on Chapters 1-5
221(5)
G The length of wavetrains and their spectral width
226(3)
H Maximum entropy data processing (S.F. Gull)
229(2)
I Applications in Communications (J.D. Weaver)
231(6)
J The impulse response of the eye: a diffraction analogy (Janet E. Wolf)
237(6)
K The electromagnetic spectrum. Approximate range of principal, named regions
243(1)
L Useful formulae
244(1)
References 245(6)
Bibliography 251(4)
Solutions to problems 255(6)
Index 261

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