# Fourier Methods in Imaging

John Wiley & Sons, Nov 18, 2010 - Technology & Engineering - 954 pages
Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography.

• Provides a unified mathematical description of imaging systems.
• Develops a consistent mathematical formalism for characterizing imaging systems.
• Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions.
• Offers parallel descriptions of continuous and discrete cases.
• Includes many graphical and pictorial examples to illustrate the concepts.

This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists

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I was taught by the author himself in my core course for Fourier Methods in Imaging in PhD (Imaging Science) at Rochester Institute of Technology. The book is excellent in the sense that it begins from very fundamental questions of complex numbers and argand diagram to finally Fourier Optics. The book is really not meant to teach you Fourier Optics per se but the Mathematics which will be helpful in dealing with Fourier Optics with special emphasis to Imaging (there are few things which can be taught in a different manner, the Pure Maths way, however you're taught in this book to see those topics in terms of Imaging systems). A great book before you wanna pick up Fourier Optics by Goodman.
Warning : Don't get intimidated by the volume of the book. Just open the chapter you are interested in.
Fun Fact : Roger L. Easton Sr. (who is the father of the author Roger L. Easton Jr.) was the inventor of GPS. And he is also the same guy who designed the oldest satellite still in orbit Vanguard 2.

### Contents

 Copyright Series Editors Preface Operators and Functions Vectors with RealValued Components Complex Numbers and Functions ComplexValued Matrices and Systems 1D Special Functions 2D Special Functions
 Approximations to Fourier Transforms Discrete Systems Sampling Discrete Fourier Transforms Magnitude Filtering Allpass Phase Filters MagnitudePhase Filters Applications of Linear Filters Filtering in Discrete Systems

 Linear Operators Fourier Transforms of 1D Functions Multidimensional Fourier Transforms Spectra of Circular Functions The Radon Transform
 Optical Imaging in Monochromatic Light Incoherent Optical Imaging Systems Holography References Index