Slide 7 of 19

Notes:

• This pyramid diagram is a visual catalog of the Zernike functions rendered as thumbnail images. The defining equations in polar form are given in terms of the radius parameter r raised to the n-th power, where n is called the radial order, and the angular parameter theta which has an angular frequency (or harmonic number) f.

  In this pictorial catalog, the rows correspond to different orders and the columns are for different frequencies. For any given row, the Zernike functions are analogous to a Fourier series in which positive harmonic frequencies have sine phase and negative harmonics are in cosine phase.

  So, despite the fact that almost nobody else is using this double-index naming scheme, I think it is the natural convention for the vision community to adopt.