Resolution, focus depth in the Fresnel-Fraunhofer domains

Abstract

Defocused imaging can be analyzed as Fresnel diffraction. The defocus parameter, that characterizes this imaging, is related to an effective Fresnel number, which is induced by the geometry of the imaging set-up. From this point of view, perfectly focused images result from Fraunhofer diffraction. Therefore, the same criteria for distinguishing between Fraunhofer and Fresnel diffraction can be applied to determine if the image is or not focused. As a consequence, new definitions of the focus depth can be deduced. In addition, resolution of two point-objects under different states of spatial coherence and focus conditions is discussed and some resolution criteria are deduced. Then, they are compared to the classical resolution criteria, which are considered as applicable to the extreme cases of fully spatial coherence and fully spatial incoherence. Some classical examples, such as, imaging of one point object and two near point objects, are discussed to illustrate the analysis.