Fourier Optics An Introduction (Second Edition)

by Steward, E. G.

• ISBN13: 9780486435046
• ISBN10: 0486435040
• Edition: 2nd
• Format: Paperback
• Copyright: 2011-11-02
• Publisher: Dover Publications
• More Book Details

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