rzernike_ann: Radial Zernike Annular polynomials

In mlpeck/zernike: Zernike Polynomials

Radial Zernike Annular polynomials

Description

Create a matrix of Zernike Annular polynomial values in extended Fringe sequence for a set of polar coordinates.

Usage

rzernike_ann(rho, eps, n, m, xq, qwts)

Arguments

rho	a vector of radial coordinates.
eps	the obstruction fraction 0 <= eps < 1.
n	the maximum radial order required
m	azimuthal order
xq	nodes for Gauss-Legendre quadrature
qwts	weights for Gauss-Legendre quadrature

Details

To the author's knowledge no recurrence relations for radial Zernike annular polynomials have been published, even though several are well known for the closely related Zernike circle polynomials. However the m=0 polynomials representing axially symmetric aberrations are just shifted Legendre polynomials with an easily derived recurrence relation. This routine makes use of that fact to generate recurrence relations for arbitrary polynomial indexes using chebyshev's algorithm with modified moments. The modified moments are calculated using Gauss-Legendre quadrature. If enough quadrature nodes were chosen the quadrature is nominally exact, as are the resulting annular Zernike values.

Value

A length(rho) x (n-m)/2+1 column matrix of radial Zernike Annular polynomial values evaluated at the input radial coordinates. The radial indexes are in increasing order from m, m+2, ..., n.

See Also

This function is called by zapm() and zapm_iso().

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