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The APEX Method and Real-Time Blind Deconvolution of Scanning Electron Microscope Imagery



Alfred S. Carasso, D S. Bright, Andras Vladar


Loss of resolution due to image blurring is a major concern in electron microscopy. The point spread function describing that blur is generally unknown. This paper discusses the use of a recently developed FFT-based direct blind deconvolution procedure, the APEX method, that can process 512 x 512 images in less than a minute on current desktop platforms. The method is predicated on a restricted but significant class of shift-invariant blurs, consisting of finite convolution products of Levy probability density functions. Such blurs considerably generalize Gaussian and Lorentzian point spread functions. In this paper, the method is successfully applied to a wide variety of original SEM micrographs. Quantitative sharpness analysis of ¿ideal sample¿ micrographs, shows that APEX processing can produce sharper imagery than is achievable with optimal microscope settings.
NIST Interagency/Internal Report (NISTIR) - 6835
Report Number


Carasso, A. , Bright, D. and Vladar, A. (2001), The APEX Method and Real-Time Blind Deconvolution of Scanning Electron Microscope Imagery, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online],, (Accessed February 22, 2024)
Created October 31, 2001, Updated October 12, 2021