The digital holography has been widely employed in the microscopic imaging, which enables quantitative phase analysis. The phase image is obtained in the numerical reconstruction procedure. The in-focus reconstruction distance could be determined according to the extremum of the autofocusing criterion function, which is commonly applied to the amplitude image of the object. With regard to a pure phase sample, such as the living cell, its in-focus amplitude image should be a uniform bright field, so the minimum value needs be found. Then the in-focus reconstruction distance for the phase image is considered to be equal to the one for the amplitude image. However, in the experiment, the in-focus amplitude image is often not an ideal uniform bright field, so this method will result in some deviation. In this contribution, two derivatives-based criterion functions are applied to the phase image directly to accomplish the in-focus phase contrast imaging, which is proved to be more intuitive and precise. In our experiments, two optical configurations of the digital holography are established firstly. Then the standard phase grating and the living cervical carcinoma cells are detected. The phase aberration is corrected by two- step algorithm. The final autofocusing results verify the principle proposed in this paper.
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