File:Airy disk spacing near Rayleigh criterion.png
Summary
| Description |
English: Two airy disks at various spacings: (top) twice the distance to the first minimum, (middle) exactly the distance to the first minimum (the Rayleigh criterion), and (bottom) half the distance.
This image uses a nonlinear color scale (specifically, the fourth root) in order to better show the minima and maxima.
Русский: Изображение, накладывающихся друг на друга, двух дисков Эри (Эйри), расположенных на расстояниях порядка предела Эри.
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| Date | |
| Source | Own work |
| Author | Spencer Bliven |
Source Code
The three images were created in R, then cropped and assembled using GIMP.
| R source code - click on the right to view |
|---|
| airydisks_rayleigh_sqrt.py: |
#!/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()
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Licensing
 |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
