THEORY OF THE F-RADIUS SPHERE MODEL
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© 2018 Univelt Inc. All rights reserved. This paper continues the research initiated in Ref.  by proposing the f-radius sphere model for pin-hole calibrated cameras as a mathematical tool to remove radial distortion in CCD or CMOS camera receivers. Since the pin-hole model performs sphere-to-plane projection (gnomonic), it creates a radial distortion that increases with the dimension of the imager and/or when using a smaller focal length. The f-radius sphere model avoids this radial distortion by projecting the observed spherical 3-dimensional world onto a fictitious spherical imager. Thus, performing sphere-to-sphere projection, and no radial distortion is generated. The f-radius sphere models for continuous (infinitesimal pixel size) and discrete (pixels with finite dimensions) imagers are summarized. The main result of the f-radius sphere is: the geometric center of a pixel is not necessarily coincident with the “barycenter” of photon flux over the pixel. This model provides the correct location of a pixel’s barycenter. The value of this correction for cameras with various fields-of-view (FOVs) is analyzed. The conclusion is that this correction is extremely small for existing imagers.
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