I recently was asked what good resources existed for learning more about Zernike polynomials, ranging from an introduction through intermediate texts.
In my experience, I relied on Dr. Wyant’s course notes on the topic, and consider them ranging from intro to intermediate: http://wyant.optics.arizona.edu/zernikes/Zernikes.pdf
Dr. Mahajan’s texts and books on the subject qualify as intermediate to expert level resources, and cover the historical background as well as practical application: https://www.spie.org/Publications/Book/2029485 (for only one example).
Born and Wolf’s Principles of Optics was probably the first text I read that introduced Zernike polynomials to me, although I haven’t revisited it recently and can’t comment too strongly on how good of a resource it is (although the book as a whole is incredible, and is a must have if you’ve got spare money burning a hole in your pocket): Principles of Optics (Electromagnetic Theory of Propagation, Interference and Diffraction of Light): Born, Max: 9780521642224: Amazon.com: Books
Lastly, I found while searching a tutorial paper, which is a pretty great fast and to the point introduction and practical guide to using Zernike polynomials : https://www.tandfonline.com/doi/abs/10.1080/09500340.2011.554896 (seriously, its like 2 weeks of a course in 9 pages, pretty impressive stuff).
To the community at large, do you have any other recommendations for texts, videos, lectures, etc. for explaining the use and origination of Zernike polynomials to optical systems? I will specifically ask @Isaac , @bdube , and @heejoooptics and @hkang as I know all of you have great experience with optical design and Zernike polynomials.