#!/usr/bin/env Rscript # Diffraction pattern for two airy disks, illustrating the Rayleigh criterion # Released to Public Domain by Spencer Bliven x = seq(-5,5,.01) y = seq(-5,5,.01)  airy <- function(xx,yy,x1,y1) {     r<-sqrt((xx-x1)**2+(yy-y1)**2)*1.22*pi     z = (2*besselJ(r,1)/r)**2     z } diffractionPlot = function(spacing=1,useRaster=F) {     z1 = outer(x, y, FUN=function(xx,yy){airy(xx,yy,-spacing/2,0)})     z2 = outer(x, y, FUN=function(xx,yy){airy(xx,yy,spacing/2,0)})     z1[is.na(z1)]=1.0     z2[is.na(z2)]=1.0     z = z1+z2     grad = grey((0:(2**16)/2**16))     par(pty="s")     # Non-linear z scale to increase contrast     image(x,y,z**(1/4),zlim=c(0,1),col=grad,axes=F,useRaster=useRaster) }  png("airy_0.5.png",bg="#FFFFFF00") diffractionPlot(.5) dev.off() png("airy_1.0.png",bg="#FFFFFF00") diffractionPlot(1) dev.off() png("airy_2.0.png",bg="#FFFFFF00") diffractionPlot(2) dev.off()