Super Resolution in an Optical Confocal Microscope

Steve Isakson
Department of Computer Science
University of California
Santa Barbara, CA 93106

Abstract

Researchers know that the diffraction limited image of an object of finite dimensions in a noiseless environment can be resolved to an arbitrary degree. However, the inverse problem is often so ill-conditioned that even a very small noise signal limits the resolution to only slightly better than the Rayleigh limit. Therefore the Rayleigh resolution criterion is generally accepted as a practical resolution limit.

The use of a confocal microscope allows control of the effective size of the object and the signal noise to a very large degree. In addition proper selection of the two lens systems in the microscope reduces the ill-conditioning of the inverse problem. This approach improves the user's ability to produce an accurate Bayesian image of the object.

This paper presents a Bayesian procedure using the prior information available for a confocal microscope to produce a semi-continuous image of the object. Accuracy and computational complexity are compared for maximum probability versus minimum mean squared error methodologies. It also examines similar tradeoffs for resolution, signal-to-noise ratio, and ill-conditioning.

The paper also discusses the possibility of using the acquired and the mathematical expression of image probability estimates to answer point process type questions about the image. Such questions as ``how big is this object?'' or ``how far apart are these objects?'' would fit this category. Questions such as these can then be given probabilistic ranges as answers. The difficulties in developing mathematical expressions for some of these questions will also be discussed.


MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk