Diffraction and Resolving Power*

The existence of an ultimate absolute limit for resolving power is investigated utilizing the ambiguous image concept, viz., different objects cannot be distinguished if they have identical images. Any absolute limit to the resolving power of an optical system must be based upon the existence of ambiguous images rather than on an arbitrary specification of the precision of image measurement, since precision can always be improved, even at the photon-counting limit. It is shown that for all objects of finite angular size, the image spectrum within the passband of the optical system contains the information necessary to determine the object spectrum throughout the entire frequency domain. Knowledge of the object spectrum implies knowledge of the object. It is shown that two distinctly different objects of finite size cannot have identical images, so that no ambiguous image exists for such objects. Therefore, diffraction limits resolving power in the sense of only the lack of precision of image measurement imposed by the system noise. Equations are derived which describe processing procedures by means of which object detail can be extracted from diffraction images. An illustrative example shows the successful processing of the image of two monochromatic point sources separated by 0.2 of the Rayleigh criterion distance.