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Contents
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Contents
Preface .................................................................................................. xiii
Chapter 1 Analytic Fourier Theory Review .......................................... 1
1.1 A Little History and Purpose .................................................................... 1
1.2 The Realm of Computational Fourier Optics ............................................ 2
1.3 Fourier Transform Definitions and Existence ........................................... 3
1.4 Theorems and Separability ....................................................................... 3
1.5 Basic Functions and Transforms ............................................................... 5
1.6 Linear and Space-Invariant Systems ......................................................... 7
1.7 Exercises ................................................................................................. 10
1.8 References ............................................................................................... 12
Chapter 2 Sampled Functions and the Discrete Fourier Transform 13
2.1 Sampling and the Shannon¨CNyquist Sampling Theorem ....................... 13
2.2 Effective Bandwidth ............................................................................... 15
2.3 Discrete Fourier Transform from the Continuous Transform ................. 18
2.4 Coordinates, Indexing, Centering, and Shifting ...................................... 20
2.5 Periodic Extension .................................................................................. 21
2.6 Periodic Convolution .............................................................................. 24
2.7 Exercises ................................................................................................. 26
2.8 References ............................................................................................... 27
Chapter 3 MATLAB Programming of Functions, Vectors, Arrays,
and Fourier Transforms ................................................................... 29
3.1 Defining Functions ................................................................................. 29
3.2 Creating Vectors ..................................................................................... 32
3.3 Shift for FFT ........................................................................................... 34
3.4 Computing the FFT and Displaying Results ........................................... 36
3.5 Comparison with Analytic Results ......................................................... 38
3.6 Convolution Example ............................................................................. 39
3.7 Two Dimensions ..................................................................................... 41
3.8 Miscellaneous Hints ................................................................................ 43
3.9 Exercises ................................................................................................. 45
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