The first textbook on mathematical methods focusing on techniques for optical science and engineering, this text is ideal for upper division undergraduate and graduate students in optical physics. Containing detailed sections on the basic theory, the textbook places strong emphasis on connecting the abstract mathematical concepts to the optical systems to which they are applied. It covers many topics which usually only appear in more specialized books, such as Zernike polynomials, wavelet and fractional Fourier transforms, vector spherical harmonics, the z-transform, and the angular spectrum representation. Most chapters end by showing how the techniques covered can be used to solve an optical problem. Essay problems based on research publications and numerous exercises help to further strengthen the connection between the theory and its applications.
Gregory J. Gbur is professor of physics and optical science at the University of North Carolina at Charlotte. He contributed to the book Science Blogging: The Essential Guide and writes two blogs about horror and the history of science.
I would recommend it for anyone studying optics, photonics or optical engineering. I wish I had this book when I started. It covers all the important areas of mathematics which are otherwise buried in many different maths courses, and links them to their application in optics through the "Focus" sections. Good for self study, additional exercises for a course and for checking your understanding. It would also be a good textbook for a course dealing specifically with the mathematics needed in optics, photonics and optical engineering.