zapm: Zernike Annular polynomials

In mlpeck/zernike: Zernike Polynomials

Zernike Annular polynomials

Description

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

Usage

zapm(rho, theta, eps, maxorder = 12L, nq = maxorder/2L + 5L)

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.
maxorder	the maximum radial polynomial order (defaults to 12).
nq	the number of quadrature points for numerical integration

Details

The radial polynomials are calculated using recurrence relations generated numerically using chebyshev's algorithm with modified moments. See the documentation for rzernike_ann(). A formal presentation is included in the package documentation.

Value

a matrix of Zernike Annular polynomial values evaluated at the input polar coordinates and all radial orders from 0 through maxorder in Fringe sequence, with orthonormal scaling.

Examples

  sample_az <- function(maxorder=12, eps=0.33, col=rev(zernike::rygcb(400)), addContours=TRUE, cscale=TRUE) {
  
    ## get coordinates for unobstructed and obstructed apertures
    cpa <- cp.default
    cpa$obstruct <- eps
    prt <- pupil.rhotheta(nrow.default,ncol.default,cp.default)
    prta <- pupil.rhotheta(nrow.default,ncol.default,cp=cpa)
    rho0 <- prt$rho[!is.na(prt$rho)]
    theta0 <- prt$theta[!is.na(prt$theta)]
    rhoa <- prta$rho[!is.na(prta$rho)]
    thetaa <- prta$theta[!is.na(prta$theta)]
    
    ## fill up matrixes of Zernikes and Annular Zernikes
    
    zm <- zpmC(rho0, theta0, maxorder=maxorder)
    zam <- zapm(rhoa, thetaa, eps=eps, maxorder=maxorder, nq=maxorder/2+5)
    
    ## pick a column at random and look up its index pair
    
    zlist <- makezlist(0, maxorder)
    i <- sample(2:ncol(zm), 1)
    n <- zlist$n[i]
    m <- zlist$m[i]
    
    ## fill up the wavefront representations and plot them
    
    wf0 <- prt$rho
    wf0[!is.na(wf0)] <- zm[,i]
    class(wf0) <- "pupil"
    
    wfa <- prta$rho
    wfa[!is.na(wfa)] <- zam[,i]
    class(wfa) <- "pupil"
    
    plot(wf0, cp=cp.default, col=col, addContours=addContours, cscale=cscale)
    mtext(paste("Zernike, n =", n, " m =", m))
    
    x11()
    plot(wfa, cp=cpa, col=col, addContours=addContours, cscale=cscale)
    mtext(paste("Annular Zernike, n =", n, " m =", m))
    
    ## return Zernike matrices and wavefronts invisibly
    ## just in case user wants to do something with them
    
    invisible(list(zm=zm, wf0=wf0, zam=zam, wfa=wfa))
  }

  sample_az()

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