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Digital holographic microscopy (DHM) is a cutting-edge interferometric technique to recover the complex wavefield scattered by microscopic samples from digitally recorded intensity patterns. In off-axis DHM, the challenge is digitally generating the reference wavefront replica to compensate for the tilt between the interfering waves. Current methods to estimate the reference wavefront's parameters rely on brute-force grid searches or heuristics algorithms. Whereas brute-forced searches are time-consuming and impractical for video-rate quantitative phase imaging and analysis, applying heuristics methods in holographic videos is limited since the phase background level occasionally changes between frames. A semi-heuristic phase compensation (SHPC) algorithm is proposed to address these challenges to reconstruct phase images with minimum distortion in the full field-of-view (FOV) from holograms recorded by a telecentric off-axis digital holographic microscope. The method is tested with a USAF test target, smearing red blood cells and alive human sperm. The SHPC method provides accurate phase maps as the reference brute-force method but with a 92-fold reduction in processing time. Furthermore, this method was tested for reconstructing experimental holographic videos of dynamic specimens, obtaining stable phase values and minimal differences in the background between frames. This proposed method provides state-of-the-art phase reconstructions with high accuracy and stability in holographic videos, allowing the successful XYZ tracking of single-moving sperm cells. 

Six different methods for phase compensation in Digital Holographic Microscopy are compared using a calibrated test target and aToxocara canislarva sample regarding processing time, measurement accuracy, and usefulness in biological imaging. 

We propose two Match-Zehnder interferometers coupled to create a structured illumination digital holographic microscope with tunable modulation frequency capability, expanding the system's numerical aperture regardless of the microscope objective lens used. 

A rapid computational algorithm is presented for Structured Illumination in Digital Holographic Microscopy. The proposed algorithm is based on the minimization of two cost functions to reconstruct improved resolution images with minimum user input automatically.