The theory of a superresolution experiment is developed. To achieve superresolution one must know in advance some properties of the objects, e.g., nonbirefringence, time independence, or wavelength independence. Assuming that the objects are nonbirefringent, it would be wasteful to use the two possible states of independent linear polarization of the light for simultaneously carrying the same information twice through the image-forming system. One can avoid this waste by inserting polarizers and certain double-refracting components into the system, so that the two states of polarization instead carry different information through the conventional image-forming system. The transfer function of such a superresolution system is derived for coherent and incoherent object illumination. It confirms qualitatively the results of previously reported experiments. A modification of the system is then proposed so that the one-dimensional restriction of the original concept is eliminated. The transfer function for the modified system is derived and numerical examples are presented. The modification imposes a further constraint on the class of allowed objects: the objects must be time-independent or only slowly time-varying.
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