File:Airydisks sparrow sqrt.png
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Airydisks_sparrow_sqrt.png (400 × 400 pixels, file size: 15 KB, MIME type: image/png)
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Summary[edit]
DescriptionAirydisks sparrow sqrt.png |
English: Airy disks of two point light-sources seen through a round aperture. The distance of the two sources matches Sparrow's resolution limit
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Date | |
Source | Own work |
Author | Geek3 |
Source Code[edit]
The image was generated by the following python script using scipy and PIL
Python source code - click on the right to view |
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airydisks_rayleigh_sqrt.py: |
#!/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')
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Licensing[edit]
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. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:35, 5 June 2010 | 400 × 400 (15 KB) | Geek3 (talk | contribs) | Airydisks_sparrow_sqrt |
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