Many applications in non-destructive testing at a microscopic level and in live cell imaging require automated focusing due to unstable environmental conditions, moving specimen or the limited depth of field of the applied optical imaging systems. Digital holography permits the recording and the numerical reconstruction of optical wave fields in amplitude and phase. This enables imaging of multiple focal planes from a single recorded hologram without mechanical realignment. The combination of numerical refocusing with image sharpness quantification algorithms yields subsequent autofocusing. With calibrated optical imaging systems this feature can be used also to determine the position and axial displacements of a sample. In order to show the application potential of digital holographic autofocusing in microscopy the method and results from investigations on several amplitude and phase objects are reviewed. This includes a demonstration of the reliability of automated refocusing, multi-focus quantitative phase contrast imaging of suspended cells, refocusing of quantitative phase contrast images during the analysis of the temporal dependency of cell spreading on surfaces and the quantification of toxin mediated morphological cell alterations during long-term observations. It is also shown for the example of sedimenting red blood cells that the method can be applied for minimally-invasive tracking of multiple particles. Finally, the usage of numerical autofocus for quantitative migration analysis of arbitrary shaped cells in a three-dimensional collagen matrix is demonstrated.
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