The role of Poisson's binomial distribution in the analysis of TEM images.

Frank's observation that a TEM bright-field image acquired under non-stationary conditions can be modeled by the time integral of the standard TEM image model [J. Frank, Nachweis von objektbewegungen im lichtoptis- chen diffraktogramm von elektronenmikroskopischen auf- nahmen, Optik 30 (2) (1969) 171-180.] is re-derived here using counting statistics based on Poisson's binomial distribution. The approach yields a statistical image model that is suitable for image analysis and simulation.

[1]  F. A.,et al.  Ultimate resolution and information in electron microscopy II . The information limit of transmission electron microscopes , 2002 .

[2]  K. W. Cattermole.  The Fourier Transform and its Applications , 1965 .

[3]  D. Van Dyck,et al.  Ultimate resolution and information in electron microscopy II. The information limit of transmission electron microscopes , 1993 .

[4]  Jun S. Liu,et al.  STATISTICAL APPLICATIONS OF THE POISSON-BINOMIAL AND CONDITIONAL BERNOULLI DISTRIBUTIONS , 1997 .

[5]  K. M. Zinn,et al.  Transmission electron microscopy. , 1973, International ophthalmology clinics.

[6]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[7]  S. V. Aert,et al.  Statistiscal Experimental Design for Quantitative Atomic Resolution Transmission Electron Microscopy , 2003 .

[8]  D Van Dyck,et al.  Does a monochromator improve the precision in quantitative HRTEM? , 2001, Ultramicroscopy.

[9]  L. Reimer.  Transmission Electron Microscopy: Physics of Image Formation and Microanalysis , 1989 .

[10]  M. Fernandez,et al.  Closed-Form Expression for the Poisson-Binomial Probability Density Function , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[11]  Jan Sijbers,et al.  How to optimize the design of a quantitative HREM experiment so as to attain the highest precision. , 1999 .

[12]  David B. Williams,et al.  Transmission Electron Microscopy , 1996 .

[13]  S. M. Samuels.  On the Number of Successes in Independent Trials , 1965 .

[14]  A. Kirkland,et al.  Characterisation of the signal and noise transfer of CCD cameras for electron detection , 2000, Microscopy research and technique.

[15]  Arturo Tejada,et al.  Introducing measure-by-wire, the systematic use of systems and control theory in transmission electron microscopy. , 2011, Ultramicroscopy.

[16]  J. L. Hodges,et al.  The Poisson Approximation to the Poisson Binomial Distribution , 1960 .

[17]  D. Van dyck,et al.  How to optimize the design of a quantitative HREM experiment so as to attain the highest precision , 1999, Journal of microscopy.

[18]  L. L. Cam,et al.  An approximation theorem for the Poisson binomial distribution. , 1960 .

[19]  Athanasios Papoulis,et al.  Probability, random variables, and stochastic processes , 2002 .

[20]  Z. Wang.  Introduction to Conventional Transmission Electron Microscopy , 2003 .

[21]  B. Roos.  Sharp constants in the Poisson approximation , 2001 .