A Stochastic Analysis of Performance Limits for Optical Microscopes Open Access
Received: 28 April 2005 Revised: 22 September 2005 Accepted: 29 September 2005 DOI:
10.1007/s11045-005-6237-2 Cite this article as: Ram, S., Sally Ward, E. & Ober, R.J. Multidim Syst Sign Process (2006) 17: 27. doi:10.1007/s11045-005-6237-2 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.
Keywords Spatio-temporal stochastic processes Fisher information matrix Cramer-Rao lower bound Parameter estimation Fluorescence microscopy Optical imaging Single Molecule Microscopy Localization accuracy Download to read the full article text References Bobroff, N. 1986 Position measurement with a resolution and noise limited instrument Review of Scientific Instruments. 57 1152 1157 CrossRef Google Scholar Born, M., Wolf, E. 1999Principles of optics Cambridge University Press Cambridge, UK Google Scholar Bowman, F. 1968Introduction to Bessel functions Dover New York Google Scholar Coleman, T., Branch, M.A., Grace, A. 1999MATLAB Optimization Toolbox user manual The Mathworks, Inc. ver. 2 Natick Google Scholar Coleman, T., Branch, M.A., Grace, A. 2000MATLAB programming reference manual, Version 6 The Mathworks Inc. MA Google Scholar Goodman, J.W. 1996Introduction to Fourier optics2 Mc Graw Hill USA Google Scholar Kay, S.M. 1993Fundamentals of statistical signal processing Prentice Hall PTR New Jersey Google Scholar Kubitscheck, U., Kückmann, O., Kues, T., Peters, R. 2000 Imaging and tracking single GFP molecules in solution Biophysical Journal 78 2170 2179 Google Scholar Michalet, X., Kapanidis, A.N., Laurence, T., Pinaud, F., Doose, S., Pflughoefft, M., Weiss, S. 2003 The power and prospects of fluorescence microscopies and spectroscopies Annual Review of Biophysics and Biomolecular Structure 32 161 182 CrossRef Google Scholar Moerner, W.E., Fromm, D.P. 2003 Methods of single-molecule fluorescence spectroscopy and microscopy Review of Scientific Instruments 74 3597 3619 CrossRef Google Scholar Ober, R.J., Ram, S., Ward, E.S. 2004 Localization accuracy in single molecule microscopy Biophysical Journal 86 1185 1200 Google Scholar Ober, R.J., Martinez, C., Lai, X., Zhou, J., Ward, E. S. 2004 Exocytosis of IgG as mediated by the receptor, FcRn: An analysis at the single molecule level Proceeding of the National Academy of Sciences 101 11076 11081 Google Scholar Papoulis, A., Pillai, S.U. 2002Probability, random variables and stochastic processes4 McGraw Hill New York Google Scholar
Ram, S. (in preparation). Ph.D. Dissertation, University of Texas at Arlington/University of Texas Southwestern Medical Center at Dallas
Ram, S., Ward, E.S., Ober, R.J. 2005 How accurately can a single molecule be localized in three dimensions using a fluorescence microscope? Proceeding of SPIE 5699 426 435 Google Scholar Rudin, W. 1987Real and complex analysis Mc Graw Hill New York Google Scholar Saleh, B. 1978Photoelectron statistics Springer Verlag Berlin, Germany Google Scholar Santos, A., Young, I.T. 2000 Model-based resolution: Applying the theory in quantitative microscopy Applied Optics 39 2948 2958 Google Scholar Saxton, M.J., Jacobson, K. 1997 Single particle tracking: Applications to membrane dynamics Annual Review of Biophysics and Biomolecular Structure 26 373 399 CrossRef Google Scholar Snyder, D.L., Miller, M.I. 1999Random point processes in time and space2 Springer Verlag New York Google Scholar Snyder, D.L., Helstrom, C.W., Lanterman, A.D., White, R.L. 1995 Compensation for read out noise in charge coupled device images Journal of the Optical Society of America A- Optics Image Science and Vision 12 272 283 Google Scholar Thompson, R.E., Larson, D.R., Webb, W.W. 2002 Precise nanometer localization analysis for individual fluorescent probes Biophysical Journal 82 2775 2783 Google Scholar Watson, G.N. 1958A treatise on the theory of Bessel functions Cambridge University Press Cambridge, UK Google Scholar Weiss, S. 1999 Fluorescence spectroscopy of single biomolecules Science 283 1676 1683 CrossRef Google Scholar Winick, K. A. 1986 Cramer-Rao lower bounds on the performance of charge coupled device optical position estimators Jornal of the Optical Society America A-Optics Image Science and Vision 3 1809 1815 Google Scholar Zacks, S. 1971The theory of statistical inference John Wiley and Sons New York Google Scholar Zhang, F. 1999Matrix theory Springer Verlag New York Google Scholar Copyright information
© Springer Science + Business Media, Inc. 2006