Visibility-dependent depth of focus for incoherent sources

Abstract

The criterion for depth of focus is expressed solely in terms of the f/number of the lens and the wavelength of light. Perceived image quality can generally be expected to depend not only on these parameters but also on the spectral content of the object. Assuming that the optical designer knows in advance the highest frequency to be resolved in the image, with a minimum allowed visibility, a more precise criterion can be formulated. The performance of an incoherent imaging system can be specified in terms of its optical transfer function (OTF). Pieper et al.1 studied the resolution dependence of depth of focus in an incoherent imaging system, wherein the system response to spatially periodic impulses was studied and the expression for the impulse response involving arbitrary pupils was derived. The resulting analytical expression was posed in a normalized form, obviating the need for specification of actual physical lengths. The Rayleigh criterion adopted for impulse objects is not valid when the analysis is extended to nonimpulse objects, such as sinusoidal inputs. In our presentation we study the imaging properties of circularly symmetric apertures with sinusoidal sources under defocused conditions. Visibility is used as a criterion to evaluate the imaging properties. For sinusoidal inputs, the relationship between visibility and OTF follows directly from the definition of the former. Deterioration of visibility with the deviation from focus is then related to the spatial frequency through the OTF. The deviation from focus is expressed in terms of a normalized out-of-focus parameter.