The Coltman series for obtaining the optical transfer function from measurements of the bar transfer function is mathematically derived. The bar transfer function rather than the contrast transfer function is defined so that the relation remains valid when an image exhibits phase reversal.
© 1998 Optical Society of America
Robert L. Lucke, "Deriving the Coltman Correction for Transforming the Bar Transfer Function to the Optical Transfer Function (or the Contrast Transfer Function to the Modulation Transfer Function)," Appl. Opt. 37, 7248-7252 (1998)