Originally posted by AstroDave For the 50mm lens compared to the 100mm macro, the factor is not quite so close: 10.15/18.80 = 0.5399, compared to the expected 0.500 . Since the shorter the focal length, the more uncertain (at least in my mind) the actual location of the “focal point” of the lens will be compared to the sensor plane,

It appears to me that you overlook the fact that equal angular distances will not cover the same amount of pixels (= the same linear extent) near the centre and near the corners of your image.

Take any pair of stars with a given angular separation: If you place the image of the pair of stars at the corner of your sensor, then the distance between the images of the two stars - as measured on a linear scale (: say, in milimeters) - will be longer than if you place the image of the pair near the centre of your sensor. For wide field lenses this difference will be quite significant. For long FL lenses you will hardly note the effect.

Let RA0 and Dec0 be the co-ordinates of the centre point of your image (i.e.: the co-ordinates at which your telescope / lens was pointing during exposure). Then, a star with co-ordinates RA1 and Dec1 will be projected on your focal plane in an x-y co-ordinate system with origo (x=0, y=0) at the centre of your image as follows:

**x1 = FAC * (sin(RA1-RA0) * cos(Dec1)**

**y1 = FAC * (cos(RA1-RA0) * cos(Dec1 * sin (Dec0) - sin(Dec1) * cos(Dec0))**

*where FAC is a constant depending upon the focal length of your optical system and the magnification of your image on the sensor, (if applicable)*