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A Stochastic Analysis of Performance Limits for Optical Microscopes

Multidimensional Systems and Signal Processing volume 17, pages27–57(2006)Cite this article

Abstract

The optical microscope is a powerful instrument for observing cellular events. Recently, the increased use of microscopy in quantitative biological research, including single molecule microscopy, has generated significant interest in determining the performance limits of an optical microscope. Here, we formulate this problem in the context of a parameter estimation approach in which the acquired imaging data is modeled as a spatio-temporal stochastic process. We derive formulations of the Fisher information matrix for models that allow both stationary and moving objects. The effects of background signal, detector size, pixelation and noise sources are also considered. Further, formulations are given that allow the study of defocused objects. Applications are discussed for the special case of the estimation of the location of objects, especially single molecules. Specific emphasis is placed on the derivation of conditions that guarantee block diagonal or diagonal Fisher information matrices.

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Affiliations

  1. Center for Immunology, NB9.106, University of Texas Southwestern Medical Center at Dallas, 6000 Harry Hines Boulevard, Dallas, TX, 75390-8576, USA

    Sripad Ram, E. Sally Ward & Raimund J. Ober

  2. Joint Biomedical Engineering Graduate Program, University of Texas at Arlington and University of Texas Southwestern Medical Center at Dallas, Texas

    Sripad Ram

  3. Department of Electrical Engineering, University of Texas at Dallas Richardson, TX, 75083-0688, USA

    Raimund J. Ober

Authors
  1. Sripad Ram
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  2. E. Sally Ward
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  3. Raimund J. Ober
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Correspondence to Raimund J. Ober.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Ram, S., Sally Ward, E. & Ober, R.J. A Stochastic Analysis of Performance Limits for Optical Microscopes. Multidim Syst Sign Process 17, 27–57 (2006). https://doi.org/10.1007/s11045-005-6237-2

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Keywords

  • Spatio-temporal stochastic processes
  • Fisher information matrix
  • Cramer-Rao lower bound
  • Parameter estimation
  • Fluorescence microscopy
  • Optical imaging
  • Single Molecule Microscopy
  • Localization accuracy