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11 October 2012 Digital optical microscope as a sampled imaging system: mathematical description, camera selection, and focusing
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The paper presents the mathematical description of an optical microscope with a digital camera and an image processing as an analog-digital-analog imaging system. This description considers a channel of the microscope as a sequence of the linear spatial filters of two dimensional signals. The channel contains an optical system as a low frequency analog filter, a digital camera as a low frequency analog filter with spatial and amplitude discretization and noise generation, a digital linear filter which has to amplify the high frequency harmonics and a restoration unit that plays a role of a two dimensional interpolator. This mathematical apparatus is useful for proper selection of a digital camera which guarantees the maximal field of view with absence of image distortions. The terms like optimal, nonsufficient and non-useful (void) linear magnification of a microscope optical system are expanded from a visual microscopy to a digital one. This mathematical description is also applied for selection of a digital filter for focusing and digital focus extension. The modulation transfer function of this filter should match for the spatial spectrum of observed objects in the zone of spatial harmonics that is most sensitive to defocusing. In this case the maximal sensitivity to defocusing with minimization of influence of noise can be reached.
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Volodymyr N. Borovytsky "Digital optical microscope as a sampled imaging system: mathematical description, camera selection, and focusing", Proc. SPIE 8486, Current Developments in Lens Design and Optical Engineering XIII, 84860D (11 October 2012);


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