Fourier optics and computational imaging / Kedar Khare.

Format:

Book

Author/Creator:

Khare, Kedar, author.

Series:

Ane/Athena Bks

Language:

English

Subjects (All):

Fourier transform optics.

Image processing--Mathematics.

Image processing.

Physical Description:

1 online resource (249 pages)

Edition:

1st ed.

Place of Publication:

Chichester, West Sussex, England : John Wiley & Sons, Ltd., 2016.

Summary:

This book covers both the mathematics of inverse problems and optical systems design, and includes a review of the mathematical methods and Fourier optics. The first part of the book deals with the mathematical tools in detail with minimal assumption about prior knowledge on the part of the reader. The second part of the book discusses concepts in optics, particularly propagation of optical waves and coherence properties of optical fields that form the basis of the computational models used for image recovery. The third part provides a discussion of specific imaging systems that illustrate the power of the hybrid computational imaging model in enhancing imaging performance. A number of exercises are provided for readers to develop further understanding of computational imaging. While the focus of the book is largely on optical imaging systems, the key concepts are discussed in a fairly general manner so as to provide useful background for understanding the mechanisms of a diverse range of imaging modalities.

Contents:

Intro

Table of Contents

Title

Copyright

Preface

1. Introduction

1.1 Organization of the book

Part 1: Mathematical preliminaries

2. Fourier series and transform

2.1 Fourier Series

2.2 Gibbs phenomenon

2.3 Fourier transform as a limiting case of Fourier series

2.4 Sampling by averaging, distributions and delta function

2.5 Properties of delta function

2.6 Fourier transform of unit step and sign functions

2.7 Fourier transform of a train of delta functions

2.8 Fourier transform of a Gaussian

2.9 Fourier transform of chirp phase

2.10 Properties of Fourier transform

2.11 Fourier transform of the 2D circ function

2.12 Fourier slice theorem

2.13 Wigner distribution

3. Sampling Theorem

3.1 Poisson summation formula

3.2 Sampling theorem as a special case

3.3 Additional notes on the sampling formula

3.4 Sampling of carrier-frequency signals

3.5 Degrees of freedom in a signal: space bandwidth product

3.6 Slepian (prolate spheroidal) functions

3.7 Extrapolation of bandlimited functions

4. Operational introduction to Fast Fourier Transform

4.1 Definition

4.2 Usage of 2D Fast Fourier Transform for problems in Optics

5. Linear systems formalism and introduction to inverse problems in imaging

5.1 Space-invariant impulse response

5.2 Ill-posedness of inverse problems

5.3 Inverse filter

5.4 Wiener filter

6. Constrained optimization methods for image recovery

6.1 Image denoising

6.2 Image de-convolution by optimization

6.3 Blind image deconvolution

6.4 Compressive Imaging

6.5 Topics for further study

7. Random processes

7.1 Probability and random variables

7.2 Random Processes

Part 2: Concepts in optics

8. Geometrical Optics Essentials

8.1 Ray transfer matrix

8.2 Stops and pupils.

9. Wave equation and introduction to diffraction of light

9.1 Introduction

9.2 Review of Maxwell equations

9.3 Integral theorem of Helmholtz and Kirchhoff

9.4 Diffraction from a planar screen

10. The angular spectrum method

10.1 Angular spectrum method

11. Fresnel and Fraunhoffer diffraction

11.1 Fresnel diffraction

12. Coherence of light fields

12.1 Spatial and temporal coherence

12.2 van Cittert and Zernike theorem

12.3 Space-frequency representation of the coherence function

12.4 Intensity interferometry: Hanbury Brown and Twiss effect

12.5 Photon counting formula

12.6 Speckle phenomenon

13. Polarization of light

13.1 The Jones matrix formalism

13.2 The QHQ geometric phase shifter

13.3 Degree of polarization

14. Analysis of optical systems

14.1 Transmission function for a thin lens

14.2 Fourier transforming property of thin lens

14.3 Canonical optical processor

14.4 Fourier plane filter examples

14.5 Frequency response of optical imaging systems: coherent and incoherent illumination

15. Imaging from information point of view

15.1 Eigenmodes of a canonical imaging system

Part 3: Selected computational imaging systems

16. Digital Holography

16.1 Sampling considerations for recording of digital holograms

16.2 Complex field retrieval in hologram plane

16.3 Digital holographic microscopy

16.4 Summary

17. Phase retrieval from intensity measurements

17.1 Gerchberg Saxton algorithm

17.2 Fienup's hybrid input-output algorithm

17.3 Phase retrieval with multiple intensity measurements

17.4 Gerchberg-Papoulis method for bandlimited extrapolation

18. Compact multi-lens imaging systems

18.1 Compact form factor computational camera

18.2 Lightfield cameras

19. PSF Engineering

19.1 Cubic phase mask

19.2 Log-asphere lens.

19.3 Rotating point spread functions

20. Structural illumination imaging

20.1 Forward model and image reconstruction

21. Image reconstruction from projection data

21.1 X-ray projection data

21.2 Image reconstruction from projection data

22. Ghost Imaging

22.1 Schematic of a ghost imaging system

22.2 A signal processing viewpoint of ghost imaging

23. Appendix: Suggested Excercises

Index

End User License Agreement.

Notes:

Includes index.

Description based on online resource; title from PDF title page (ebrary, viewed December 15, 2016).

ISBN:

1-118-90036-7

1-118-90037-5

1-118-90035-9

OCLC:

923137984