zapm_iso_direct: Zernike Annular polynomials from formulas

In mlpeck/zernike: Zernike Polynomials

Zernike Annular polynomials from formulas

Description

Create a matrix of Zernike Annular polynomial values complete through radial and azimuthal orders 6 in ISO/ANSI sequence.

Usage

zapm_iso_direct(rho, theta, eps)

Arguments

rho	a vector of radial coordinates with eps <= rho <= 1.
theta	a vector of angular coordinates, in radians.
eps	the obstruction fraction 0 <= eps < 1.

Details

The values are from published formulas. This function is included for testing and reference only.

Value

a ⁠length(rho) x 28⁠ matrix of Zernike annular polynomial values.

See Also

Calls rzernike_ann_direct() for radial Zernike annular values. Use zapm_iso() or zapm_iso_128() for complete sequences of values to arbitrary order.

Examples

sample_az_iso_direct <- function(eps=0.33, col=rev(zernike::rygcb(400)), addContours=TRUE, cscale=TRUE) {

 ## get coordinates for obstructed aperture
 cp <- cp.default
 cp$obstruct <- eps
 prt <- pupil.rhotheta(nrow.default,ncol.default,cp=cp)
 rho <- prt$rho[!is.na(prt$rho)]
 theta <- prt$theta[!is.na(prt$theta)]
 
 ## fill up matrixes of Annular Zernikes using direct and recursive formulas
 
 zam_dir <- zapm_iso_direct(rho, theta, eps=eps)
 zam_iso <- zapm_iso(rho, theta, eps=eps, maxorder=6)
 
 ## pick a column at random and look up its index pair
 
 zlist <- makezlist.iso(6)
 i <- sample(2:ncol(zam_iso), 1)
 n <- zlist$n[i]
 m <- zlist$m[i]
 
 ## fill up the wavefront representations and plot them
 
 wf_dir <- prt$rho
 wf_dir[!is.na(wf_dir)] <- zam_dir[,i]
 class(wf_dir) <- "pupil"
 
 wf_zapm <- wf_dir
 wf_zapm[!is.na(wf_zapm)] <- zam_iso[,i]
 class(wf_zapm) <- "pupil"
 
 plot(wf_dir, cp=cp, col=col, addContours=addContours, cscale=cscale)
 mtext(paste("Annular Zernike from formula, n =", n, " m =", m))
 
 x11()
 plot(wf_zapm, cp=cp, col=col, addContours=addContours, cscale=cscale)
 mtext(paste("Annular Zernike from `zapm_iso`, n =", n, " m =", m))
 
 cat(paste("Sample wavefronts: SD of diffs", format(sd(wf_dir-wf_zapm, na.rm=TRUE), digits=6), "; range of diffs", 
     format(min(wf_zapm-wf_dir, na.rm=TRUE), digits=6),":",
     format(max(wf_zapm-wf_dir, na.rm=TRUE), digits=6),"\n\n"))
 
 cat(paste("Zernike matrixes: SD of diffs", format(sd(zam_dir-zam_iso), digits=6), "; range of diffs", 
 format(min(zam_dir-zam_iso), digits=6),":",
 format(max(zam_dir-zam_iso), digits=6),"\n"))
 
 ## return Zernike matrices and wavefronts invisibly
 ## just in case user wants to do something with them
 
 invisible(list(zam_dir=zam_dir, zam_iso=zam_iso, wf_dir=wf_dir, wf_zapm=wf_zapm))
}

sample_az_iso_direct()

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