Linear Systems, Fourier Transforms, and Optics

Written by Jack D. Gaskill
First Edition
ISBN-10: 0471292885
ISBN-13: 978-0471292883

This college-level book on optics offers a good introduction in to Fourier Transforms and their application to optics and image forming systems. The topics covered help a reader gain a greater understanding of many of Thorlabs' products. Please see theTable of Contents tab for a list of topics covered and theThorlabs Book Review tab for additional commentary about the book. If you have used this book, feel free to submit a revew using the Feedback tab.

Chapter	Chapter Title	Pages
1	Introduction	1 - 4
2	Presentation of Physical Quantities by Mathematical Functions	5 - 39
3	Special Functions	40 - 96
4	Harmonic Analysis	99 - 134
5	Mathematical Operators and Physical Systems	135 - 148
6	Convolution	150 - 176
7	The Fourier Transform	179 - 217
8	Characteristics and Application of Linear Filters	223 - 285
9	Two-Dimensional Convolution and Fourier Transformation	290 - 346
10	The Propagation and Diffraction of Optical Wave Fields	349 - 443
11	Image-Forming Systems	449 - 515
Appendix 1	Special Functions	521 - 524
Appendix 2	Elementary Geometrical Optics	526 - 544
Index		545

The following book review is intended to provide some insite as to how various topics are treated in this book. We welcome the submission of customer book reviews, which we will be happy to add to our website.

This textbook is primarily mathematical and not a theoretical book on optics. It presents to the reader the mathematical tools needed to understand concepts behind imaging and finally brings it all together in the final chapter on imaging.

The textbook is broken down into 11 chapters. The first chapter is a short introduction to the book and describes how the book is laid out. Chapters 2 through 6 describe the mathematical tools need to understand the rest of the chapters. Chapter 2 is a basic introduction to a number of special functions that will be used through out the book. Chapter 4 covers harmonic analysis and how basic equations can be combined to form more complex functions. The topics of linearity and shift invariance, impulse response function, the transfer function, and the eigenfunctions are covered in chapter 5. Finally, in chapter 6, the concepts of convolution, cross correlation, and autocorrelation operations are discuss and the mathematical tools needed are presented. In chapter 7, the textbook presents the Fourier transformation and is used in the analysis of linear shift-invariant systems. Linear filters and signal processing is covered in chapter 8. Up to this point, only one-dimensional systems have been discussed, now in chapter 9, two-dimensional systems are introduced, including the Hankel transform. Chapter 10 covers the propagation and diffraction of optical waves. In chapter 11, the last chapter of the book, the ideas of linear systems, Fourier transforms, and diffraction are all combined to examine the process of coherent and incoherent image formation.

The Author does a good job of presenting the information in the textbook in an organized manner. He starts with a good foundation and builds upon what he has just discussed. There are plenty of diagrams and exampled through out each discussion. At the end of each section there are problems, although the answers are not provided in this book.

Written by Mark at Thorlabs