Image:Hermite-gaussian.png

From Wikipedia, the free encyclopedia

• Image
• File history
• File links

Size of this preview: 800 × 600 pixels
Full resolution‎ (1,280 × 960 pixels, file size: 120 KB, MIME type: image/png)

Hermite-Gaussian transverse mode patterns.

Bigger and better version created with the help of this Python script:

#!/usr/bin/env python

import sys
import Image
from math import *
from scipy.special.orthogonal import hermite

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

m = int(sys.argv[1])
n = 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

# 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 * (hermite(m)(sqrt(2)*x/w)*exp(-x**2/w**2))**2 \
            * (hermite(n)(sqrt(2)*y/w)*exp(-y**2/w**2))**2
    if I > high: high = I
    raw.putpixel((size/2+(x-1)/2,size/2+(y-1)/2), I)
    raw.putpixel((size/2+(x-1)/2,size/2-(y+1)/2), I)
    raw.putpixel((size/2-(x+1)/2,size/2+(y-1)/2), I)
    raw.putpixel((size/2-(x+1)/2,size/2-(y+1)/2), I)
  print 'row ' + str((x+1)/2) + ' of ' + str(size/2) + ' complete'

# Now, let's normalize them and export them as sRGB.

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), linear_to_sRGB(l))
  print 'row ' + str(x+1) + ' of ' + str(size) + ' complete'

cooked.save('plot-' + str(m) + '-' + str(n) + '.png')

I, the copyright holder of this work, hereby publish it under the following licenses: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. This file is licensed under the Creative Commons Attribution-ShareAlike license versions 3.0, 2.5, 2.0, and 1.0. You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

• Search for duplicate files
• Edit this file using an external application

  See the setup instructions for more information.

File links