Hopkins Variance Formula Extended to Low Relative Modulations

Publisher Website
Google Scholar
Abstract
A simple exponential modification of the known Hopkins variance formula, which is analogous to the exponential reformulation of the Marechal result for the Strehl ratio, has been tested for primary aberrations over a range of frequencies. It appears that the modified formula may be applied even when the true value of relative modulation is less than half the value admitted by the original Hopkins' approach. Our approach is also very useful for fast and fairly accurate evaluation of the modulus of the optical transfer function, provided that the relative modulation a 0·4 over the whole frequency range. Some details concerning the analytic evaluation of the Hopkins integrals Hk,l (s) and the variance of the wavefront difference function are also given.