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Use spherical trigonometry in PSF formulae

Open jknodlseder opened this issue 8 years ago • 1 comments

The formula

.. math:: \int_{0}^{\infty} 2 \pi r dP/dr(r) dr = 1, where dP/dr = 2 \pi r dP/d\Omega

on the PSF page is only true for small angles, the correct formula is

.. math:: \int_{0}^{\infty} 2 \pi sin(r) dP/dr(r) dr = 1, where dP/dr = 2 \pi sin(r) dP/d\Omega

Also in the description above the small angle approximation is used. The exact formulae should be given as for some instruments, the maximum PSF radius can become quite large, and the difference will be perceptible.

jknodlseder avatar Jun 08 '16 13:06 jknodlseder