NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Px vs. MOA/Px Graph for 50mm Prime Lens
From: Marcel Tschudin
Date: 2010 Jun 27, 20:43 +0300
From: Marcel Tschudin
Date: 2010 Jun 27, 20:43 +0300
Greg's 50mm lens has been calibrated on the basis of calculated sun heights above the horizon. This type of calibration doesn't require to know the differential scales in moa/pixels as Greg showed in his graph. This graph however shows the amount of non-linearity. For this type of calibration one can directly look at the calculated height in moa as a function of pixel heights. It already has been mentioned that the 2nd order polynomial fit (3 parameters) or the arc-tan fit (2 parameters) resulted in a standard deviations which are slightly less than half of the linear fit which Greg's figure shows. The favoured calibration consists however in using e.g. the sun's diameter to measure the differential scales in moa/pixels along the centre line, approximate these data with a fitted function and then integrate this function over the pixel range. This procedure avoids the errors which might be introduced in the calibration from abnormal dip/refraction. I have prepared a little tool on Google docs for those of you who would like to calibrate their camera-lens-system with the first version (measured pixels and calculated sun heights) and who are not familiar with "function-fitting". You find this tool here: http://spreadsheets.google.com/ccc?key=0AkSe4XuaHqY1dHcwc2dicHRVdmNPZ0NIcUpFV3kxdUE&hl=en&authkey=COS7l84G Enter in the yellow cells your data and look then in the sheet "Linear" the results in the grey-coloured cells. The input data which you find there are those which Greg posted me for his 50mm lens. Before you use the tool copy it please in your preferred format on your computer, or - for Mac users - copy it on your own Google doc account which you may possibly first have to set up. Note: Since Google docs has a similar tool like "Solver", I tried also to add the fit to the arc-tan function or the 2nd order polynomial. Unfortunately I couldn't make this work, it always complains to be a non-linear problem. To my understanding this shouldn't be the case for the coefficients of a polynomial. However, for a good quality lens the less accurate linear fit allows still measurements with accuracies around 1 moa. Marcel
