Each profile is generated form the following script: - the script is and adapter version for python3 of the original found for Hemite-Gaussian modes: https://en.wikipedia.org/wiki/File:Hermite-gaussian.png

import sys from PIL import Image from math import * from scipy.special import genlaguerre

size = 320 I_0 = 1. w = size/4.

l = int(sys.argv[1]) m = int(sys.argv[2])

def linear_to_sRGB(l):

 # Formula from http://www.w3.org/Graphics/Color/sRGB
 if l <= 0.00304:
   l = 12.92*l
 else:
   l = 1.055*pow(l,1.0/2.4) - 0.055
 return 255.0*l

1. First, let's make a floating-point image of the raw intensities.

raw = Image.new('F', (size,size))

high = 0

for x in range(1, size, 2):

 for y in range(1, size, 2):
   I = I_0 *  (genlaguerre(m,l)(2*(x**2+y**2)/w**2) \
           *  (sqrt(2*(x**2+y**2))/w)**l \
           *  exp(-x**2/w**2) *exp(-y**2/w**2))**2
   if I > high: high = I
   raw.putpixel((int(size//2+(x-1)//2),int(size/2+(y-1)//2)), I)
   raw.putpixel((int(size//2+(x-1)//2),int(size/2-(y+1)//2)), I)
   raw.putpixel((int(size//2-(x+1)//2),int(size/2+(y-1)//2)), I)
   raw.putpixel((int(size//2-(x+1)//2),int(size/2-(y+1)//2)), I)
 #print('row ' + str((x+1)/2) + ' of ' + str(size/2) + ' complete')

1. Now, let's normalize them and export them as sRGB.
2. im_rgb_raw = raw.convert('RGB')
3. im_rgb_raw.save("raw.png")

cooked = Image.new('L', (size,size))

for x in range(size):

 for y in range(size):
   l = raw.getpixel((x,y))/high
   cooked.putpixel((x,y), int(linear_to_sRGB(l)))
 print( 'row ' + str(x+1) + ' of ' + str(size) + ' complete')

im_rgb_cooked = cooked.convert('RGB')