[Numpy-discussion] Coordinate Camera Optics for Astrophotography -- sin(zenith)

Wayne Watson sierra_mtnview@sbcglobal....
Thu Jun 3 10:32:58 CDT 2010

It's been quite awhile since I've dealt with spherical geometry and 
related matters.

I'm looking at a paper involving a camera and a photographic plate. The 
author is trying to determine the center of projection, (x0,y0), on the 
plate,and the rotation (or the lens, a0 (azimuth), for a lens on the 
plate. He forms a difference function to solve for these parameters for 
a0, x0, and y0. In doing so, he mentions that he needs to introduce 
sin(zi(cat)), "..., which converts differences in azimuth to the 
great-circle angular distances comparable to differences in zi." zi is 
the i-th observation in the zenith angle (measured from the zenith) and 
(cat) is the cataloged angle for a star on the plate.

My question is where does the sin(zenith) come from? Does it have 
something to do with measuring an arc on a sphere for a plane that cuts 
through the sphere perpendicular to the x-y axis? In other words, 
something like measuring an arc of latitude at 60 degrees for someone 
who lives between a longitude of say 121 and 125 degrees of longitude.

Is there a book or source that gets into such matters for various lens 
used in astronomy?  The topic is more or less trying to determine 
properties of an objective lens that may have non-linear features.

I can provide an excerpt from the paper, if the above is not clear.

            Wayne Watson (Watson Adventures, Prop., Nevada City, CA)

              (121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
               Obz Site:  39° 15' 7" N, 121° 2' 32" W, 2700 feet

                "Science and democracy are based on the rejection
                "of dogma."  -- Dick Taverne, The March of Unreason

                     Web Page: <www.speckledwithstars.net/>

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