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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Camera distortion of sky images. was Re: NG's "Midnight Fun"
From: George Huxtable
Date: 2010 Jun 15, 13:45 +0100
From: George Huxtable
Date: 2010 Jun 15, 13:45 +0100
I've changed the threadname to make it more relevant. Earlier, I had suggested- "It would indeed be possible to calibrate the transfer function of a lens system and remap images on a corrected grid, though this would call for a lot of work if a zoom lens is being used." and Marcel answered- "The "lot of work" may really depend on what you aim at." Well, all I was thinking of, really, was that if a zoom lens was being used, that has a whole range of possible expansion factors, and presumably, a somewhat different lens-distortion for each one, so the "lot of work" was just to measure calibration curves at all these zoom settings. But I'm aware that it's difficult, if not impossible, to return to exactly the same known zoom factor as before, in the absence of a precisely marked scale-of-zoom. So I expect that the only way to use a zoom lens for such a purpose in practice is probably to use it at either maximum or minimum zoom, not in-between, and hope it returns to exactly the same value when doing so. I see now that Marcel's approach to calibration is very different from mine. He measures altitudes on a central axis crossing the frame vertically, presumably in portrait mode, up from a horizon point placed near the frame's centre, and compares those altitudes with predictions.. My suggested method (which hasn't been tried by me) calls for precisely-timed shots of the Sun as it crosses the frame, preferably corner-to-corner diagonally, in such a way as to pass close to its centre. A star might be better still. The method needs no horizon, just a very firmly-clamped camera. It presumes (as Marcel's method doesn't) that any distortion is centred on the mid-point of the frame, and is uniform in all directions from that point. It results in a radial distortion factor that can be used to correct the position of any point in the frame. Any motion of the camera over the period of observation (max: 2.5 hours or so) would damage accuracy, so it might be worthwhile to position the camera in such a way that a neighbour's chimney-pot (say) appeared in a corner of the frame as a check. It employs the fact that the Sun's motion in its path is always very close to 1 degree in every 4 minutes of time, varying very slightly but predictably as a result of the same factors as give rise to the equation of time, and being slightly affected by refraction, so requiring a rough knowledge of observer's position. For Marcel's biggest-angle observations, presumably made with a "50mm" lens, I would be very interested in the relationship between object altitude above the horizon, in degrees, and image separation, in pixels, to see how well it corresponds to the Tan A relationship that I've predicted. Marcel went on- "When you wrote a "lot of work" you may have thought to calibrate for being able to measure any (oblique) distance within the x/y-plane. Would this really be necessary for CN applications? " Well, I'm thinking about it mainly in polar coordinates, not (x, y), and presuming only a radial variation, in which case it becomes reasonably simple. and concluded- "I could however imagine that there exist somewhere professional programs which would help to do also this sort of calibration and analysis of the measurements." I can only agree. I'm pretty sure that he and I must be retracing well-trodden ground, if only we knew where to look. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.