Double-index Zernike polynomials

n=radial

order

0

Common names

Piston

Tip, Tilt

Astigmatism, Defocus

1

Coma, Trefoil

Spherical

2

3

4

5

6

7

f=Angular frequency

-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7

Secondary coma

Secondary spherical

Z(rn,fq)=

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View graphic version

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 angula

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 negati

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.