# Wavefront Analysis

A review of a new book on wavefront analysis. Bonus web-only content.

30 June 2014
Daniel Malacara-Hernández

SPIE Fellow Virendra N. Mahajan has published three books on Optical Imaging and Aberrations. Part 1, subtitled Ray Geometrical Optics was published in 1998, Part 2 Wave Diffraction Optics in 2001 and the third book Wavefront Analysis in 2013. These books cover an important part of classical and engineering optics and are important tools for teaching these subjects.

The last book, Optical Imaging and Aberrations, Part III Wavefront Analysis, has a wonderful description of orthonormal polynomials, quite useful in the analysis of optical systems having an entrance pupil with any shape. This book contains 14 chapters and an appendix.

The first chapter covers the fundamentals of image formation and the second describes the wave aberrations. It mainly covers aberration free systems and the concepts of point spread function (PSF) and optical transfer function (OTF).

Chapters 3 to 11 study the orthonormal polynomials to describe the wave aberrations of systems with many different pupil shapes. The chapters contain information useful to people interested in optical systems with non-circular, annular or apodized circular pupils.

Chapter 12 describes the circle Zernike polynomials and their relation to the orthonormal polynomials for circular as well as for annular apertures. Many practical numerical examples illustrate the main concepts.

Anyone planning to use Zernike polynomials for wavefront representation should read chapter 12, where the common pitfalls when used for non-circular pupils are clearly explained.

Chapter 13 studies the wave aberrations of anamorphic systems and chapter 14 the numerical wavefront analysis.

The material in this book is not easy to find in any other book. The summaries at the end of each chapter are quite useful to review its contents.

This is a book that should be in the library or bookshelf of anyone working in optical design, optical testing, or in general, studying wave aberrations.

Reviewed by SPIE Fellow Daniel Malacara-Hernández, Centro de Investigaciones en Optica, Leon, Mexico

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