Modelling a Microscope as Low Dimensional Subspace of Operators

Abstract

We propose a novel approach to calibrate a microscope. Instead of seeking a single linear integral operator (e.g. a convolution with a point spread function) that describes its action, we propose to describe it as a low-dimensional linear subspace of operators. By doing so, we are able to capture its variations with respect to multiple factors such as changes of temperatures and refraction indexes, tilts of optical elements or different states of spatial light modulator. While richer than usual, this description however suffers from a serious limitation: it cannot be used directly to solve the typical inverse problems arising in computational imaging. As a second contribution, we therefore design an original algorithm to identify the operator from the image of a few isolated spikes. This can be achieved experimentally by adding fluorescent micro-beads around the sample. We demonstrate the potential of the approach on a challenging deblurring problem.Important note: this paper is an abridged version of a preprint [3] by the same authors, submitted for a journal publication.