Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function

Low-frequency mechanical vibrations are a significant problem in robotics, machine vision, and practical reconnaissance where primary image vibrations involve random process blur radii. They cannot be described by an analytical MTF. A method of numerical calculation of MTF, relevant in principle to any type of image motion, is presented. It is demonstrated here for linear, high, and low vibration frequencies. The method yields the expected closed form solutions for linear and high-frequency motion. The low-vibration-frequency situation involves random process blur radii and MTFs that can only be handled statistically since no closed form solution is possible. This is illustrated here. Comparisons are made to a closed form approximate MTF solution suggested previously for low-frequency motion. Agreement between that analytical approximation and exact MTF calculated numerically is generally good, especially for relatively large and linear motion blur radius situations. For nonlinear short exposure motion, MTF levels off at relatively high nonzero values and never approaches zero. Such situations yield a two-fold benefit: (1) larger spatial frequency bandwidth and (2) higher MTF values at all spatial frequencies since MTF does not approach zero.