Readjusting image sharpness by numerical parametric lenses in Forbes - representation and Halton sampling for selective refocusing in digital holographic microscopy

Digital holographic microscopy (DHM) is utilized for quantitative phase contrast microscopy in optical testing of reflective or transparent specimens and allows altering the focus numerically by propagating the complex wave. Especially for compensation of deformations or displacements and for long-term investigations of living cells, a reliable region selective numerical readjustment of the focus is of particular interest in digital holographic microscopy. Since this method is time consuming, a Halton point set with low discrepancy has been chosen. By this, the effective axial resolution can be enhanced numerically by post processing of complex wave fronts without narrowing the field of view leading to a loss of information around the focus plane by blurring. The concept of numerical parametric lenses is another key feature in DHM and used to correct aberrations in the reconstructed wave front caused by the setup. To reduce the number of parameters for parametric lenses, the polynomial basis by Forbes is applied for the needs of DHM. Both numerical approaches have been characterized and adapted to the requirements of DHM. The applicability is demonstrated by results of investigations of engineered surfaces and biological cells.