The second moment method is proposed as a method of obtaining a one dimensional approximation to a two dimensional angularly averaged modulation transfer function for low spatial frequencies. For two orthogonal knife-edge scans of a point spread function, the second moments about the centroid of the corresponding line spread functions are determined. The two second moment values are then used to approximate the two dimensional angularly averaged modulation transfer function. Two rotationally asymmetric point spread functions were used to test the approximation, an equilateral triangle and a rectangle. The results show, for both cases, that in the 1.0 to 0.5 modulation range, there was no difference in the modulation transfer function curves determined by using the approximation and the actual angular average of the modulation transfer function. In the 0.5 to 0.1 modulation range, a difference of only 5% was calculated.
Imaging Science (BS)
Department, Program, or Center
School of Photographic Arts and Sciences (CIAS)
Curtis, Christopher, "The second moment method, a new way to test a lens" (1984). Thesis. Rochester Institute of Technology. Accessed from
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