I own a copy of Klinger's book "Polarized Light in Optics and Spectroscopy." It's a very useful reference, and I find myself going back to it on an almost daily basis. I've been pretty satisfied with the information in Klinger's book, but phenomena relating to polarization are very important in my field (fiber optics) and so I decided it made good sense to get a copy of Collett's book, as well. I've not been disappointed.
Collett's book has two parts. The first part is what I was mostly interested in, and it deals with polarization in the classic optical field. The second part of the book is less relevant for me, and deals with the classical and quantum theory of radiation by accelerating charges.
The prerequisites for reading and understanding this book are pretty basic. For the first book, you'll want a strong basis in algebra, linear algebra, and trigonometry. For the second half of the book you'll also want to be versed in things like vector calculus (div, grad, curl, etc.) as well as some integral optics and concepts essential in quantum theory. Both the mathematics and physics should be easily within the grasp of anyone with a BS in physics or mathematics. This is not what I'd call a book for the armchair scientists. It is a specialist's book, with all the detail and mathematics to allow the specialist to do quantitative engineering and science.
Collett offers one of the best all-around descriptions of the Mueller matrix that I've found. The book starts with some background information describing the wave equation, various interference experiments, and reflection and transmission at a dielectric interface. With this foundational information, he moves on to describe the polarization ellipse, leading naturally to a description of the Stokes polarization parameters. In all of this, Collett does a nice job of helping the reader understand the basis of the Stokes vector in actual measurements associated with the Stokes parameters, and their fundamental utility and practicality.
With the concept of the Stokes parameters established, Collett proceeds to introduce the Muller matrix, and he derives the matrix form for several different optical components such as polarizers, phase plates, and the rotation matrix. He also has a useful chapter for the experimentalist, describing various techniques for measuring the Stokes parameters of optical components.
There is an entire chapter on the derivation of the Mueller matrix of tilted dielectric surfaces. This discussion carries over into the next chapter where Collett derives the Mueller matrices of plates, and stacks of plates. [These derivations ignore multiple reflections, though Collett is careful to make this clear, and he provides chapter references where the student can look up the completely correct treatment.] This chapter has some interesting mathematics that can be quite useful in other polarization work, since it describes the process for linearizing the Mueller matrix in terms of its eigenvectors and eigenvalues (something that makes the analysis of stacks of plates much easier to do).
Reading this book, one gets the distinct impression that Collett favors the Muller matrix calculus over the Jones calculus. Still, he has included a very nice chapter on the Jones matrix calculus that is both relatively complete, as well as written in the same easy-to-understand fashion as the rest of the book.
The chapter on the Poincare sphere was not quite what I'd expected, but was still very helpful and interesting. Be prepared to brush up on your spherical trigonometry when you read this chapter. I'd hoped for more information from a practical point of view (and a few better illustrations), so this was a bit of a disappointment. However, there are bits of practical information here, and the beauty of the spherical trigonometry is enough to make the chapter worthwhile on its own.
The first book ends with a chapter on the interference laws of Fresnel and Arago, which seems a little strange. The chapter seems somewhat out of place, and, perhaps, better suited near the front of the book, though it does provide the opportunity to illustrate some of the principles learned in earlier chapters.
Space does not permit a detailed description of the second half of the book (the first half is about 280 pages, and the entire book is roughly 580 pages).
This is a first-rate book, and if you are involved in optics and polarization, in particular, you really owe it to yourself to have this one in your personal library. The book is well written, for the most part, pretty easy to follow (not a small task, given the subject matter), and nicely referenced with additional reading material listed at the end of each chapter. There is also an adequate index, which is a good thing, since this book will find widespread use as a reference text.
I really have only two complaints: First, the book needs an appendix (like that found in Klinger) listing the different Matrix forms for various optical components. It would be nice, in addition, to have an appendix listing the definitions of variables used in the equations. Instead, I have little sticky tape all over the book so I can find my way back to important equations. There are a few blank pages at the end of the book, so perhaps I'll write my own appendix with these equations. Secondly, the book has too many typographical errors, some of which can be disastrous if you just copy the equations out of the book without looking at their derivations to check for dropped/misplaced variables. A second edition with these mistakes corrected, or at least a published erratum would be a good idea.
Other than that, this is a great book. I highly recommend getting it and reading it, if polarized light is something for which you have a quantitative interest.