zlist | R Documentation |
Ordered lists of Zernike polynomial indexes.
makezlist(minorder = 2, maxorder = 14)
zlist.fr
zmult(zlist = makezlist())
minorder |
minimum value of |
maxorder |
maximum value of |
zlist |
a list of the form returned by |
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.
makezlist
and zlist.fr
return lists with the following components:
n |
radial order |
m |
azimuthal order |
t |
one of |
zmult
returns a vector the same length as the components
of zlist
.
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
.
M.L. Peck mpeck1@ix.netcom.com
Virtually all high level functions that work with Zernike polynomials
use these lists. See for example pupil
, psifit
,
fftfit
.
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
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