# 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