makezlist: Lists of Zernike polynomial indexes

In mlpeck/zernike: Zernike Polynomials

Lists of Zernike polynomial indexes

Description

Ordered lists of Zernike polynomial indexes.

Usage

makezlist(minorder = 2, maxorder = 14)
zlist.fr
zmult(zlist = makezlist())

Arguments

minorder	minimum value of n+m
maxorder	maximum value of n+m
zlist	a list of the form returned by makezlist

Details

Zernike polynomials are indexed by a radial index n, an azimuthal index m, and include cosine, sine, and radial terms. These routines return lists of indexes using a popular ordering scheme for Zernike polynomials.

Value

makezlist and zlist.fr return lists with the following components:

n	radial order
m	azimuthal order
t	one of c("c", "s", "n")

zmult returns a vector the same length as the components of zlist.

Note

zlist.fr is an augmented “Fringe” set of Zernike polynomials equivalent to makezlist(2,12).

makezlist returns a complete list of indexes for all orders from minorder through maxorder, where “order” is the value of n+m.

Author(s)

M.L. Peck [e-mail]

See Also

Virtually all high level functions that work with Zernike polynomials use these lists. See for example pupil, psifit, fftfit.

Examples

zlist <- makezlist(2,12)
zcoef <- rnorm(length(zlist))
zcoef		# a vector of normalized Zernike coefficients
zcoef*zmult(zlist)   # Coefficients in conventional representation
sqrt(crossprod(zcoef)) # This is the RMS error of the wavefront 
			# constructed from these Zernikes

mlpeck/zernike documentation built on April 19, 2024, 3:16 p.m.