THEORY OF THE F-RADIUS SPHERE MODEL - Texas A&M University (TAMU) Scholar

2018 Univelt Inc. All rights reserved. This paper continues the research initiated in Ref. [1] 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 pixels 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.

THEORY OF THE F-RADIUS SPHERE MODEL Conference Paper