Abstract

In a series of recent papers [1-4] we have proposed an approach to achieving superresolution in confocal scanning microscopy based on a singular system approach to the inverse problem. In this approach the Fredholm equation of the first kind which describes the imaging system is solved by finding its singular-value spectrum and its "object" and "image" singular functions. These functions provide complete orthonormal basis sets for the description of object and image which have the desirable feature of minimum "representational entropy". The inversion is performed by finding the coefficients of the singular function expansion up to an index determined by the level of noise in the image and the singular value spectrum. We have recently described an all optical technique to perform these operations which involves designing an optical mask to place in the image plane of the system (apodisation in the pupil plane is not suitable for incoherent light imaging). The mask function for five terms in the series is shown in Fig 1 [3]. The transfer function for this mask is shown by the heavy line in Fig 3.

© 1992 Optical Society of America