#!/usr/bin/env python
# -*- coding: utf8 -*-

'''
Copyright (C) 2008 Wikimedia Foundation

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
'''

from math import *
import scipy
import scipy.special
import scipy.optimize
from PIL import Image

w = 400
h = 400
image = scipy.zeros((h, w))

# Sparrow's resolution limit
def ddf(r):
    # second derivative of airy disk intensity (j1/r)**2
    j = scipy.special.jvp(1, r, n=0)
    dj = scipy.special.jvp(1, r, n=1)
    ddj = scipy.special.jvp(1, r, n=2)
    return (2*r**2 * (dj**2+j*ddj) - 8*r * j*dj + 6 * j**2) / r**4
    
r0 = 2*scipy.optimize.brentq(ddf, 0.1, 4.)

scalex = scipy.special.jn_zeros(1, 2)[-1] + scipy.special.jn_zeros(1, 1) / 2.
scaley = h * scalex / w

# make dark areas better visible
color_func = sqrt

for y in range(h):
	for x in range(w):
		xx = ((x + .5) / w - .5) * 2. * scalex
		yy = ((y + .5) / h - .5) * 2. * scaley
		r1 = hypot(xx+r0/2., yy)
		r2 = hypot(xx-r0/2., yy)
		v1 = v2 = .5
		if r1 != 0.: v1 = (scipy.special.j1(r1) / r1) ** 2
		if r2 != 0.: v2 = (scipy.special.j1(r2) / r2) ** 2
		image[y, x] = color_func(v1 + v2)

max_val = image.max()

image_file = Image.new('L', (w, h))
for y in range(h):
	for x in range(w):
		c = int(2**8 * image[y, x] / max_val)
		image_file.putpixel((x, y), c)
image_file.save('Airydisks_sparrow_sqrt.png', 'PNG')