Slide 6 of 19

Notes:

• To demonstrate the kinds of traps that await the beginner, let me illustrate just 3 examples of how I became confused when attempting to understand the art and science of aberration measurements.

  First, the Zernike polynomials have a reputation for being good to work with because they have the nice mathematical property of orthogonality. Now you might have thought that any polynomial that has been around as long as Zernike's polynomials would have a well known naming scheme.

  Not true! Although there is an ISO standard scheme, it seems that almost nobody follows it. Of this list of reputable books and papers in the field, only one - a short paper by Love on adaptive optics - follows the standard convention. Everybody else follows some other convention, and almost nobody agrees on which convention is best. Furhtermore, there at least two different schemes for normalizing the Zernike functions to achieve convenient properties such as unit variance or unit amplitude.

  In my opinion, the scheme advocated by Schwiegerling, Greivenkamp and Miller is the most sensible. It is a double- index description that fits naturally with the Zernike functions as shown on the next slide.