Phase retrieval method based on the transport of intensity equation and the threshold duty ratio

Abstract

When cells are observed with a microscope, the phase information for the sample is usually obtained from the acquired intensity images using the transport of intensity equation (TIE). However, to solve the TIE, it is necessary to obtain an in-focus image. The accuracy and speed of focus positioning affect the accuracy and time of phase retrieval. We propose a fast phase retrieval method based on the TIE and the threshold duty ratio. We first perform pixel reduction on a series of acquired intensity images, and these images are segmented using the optimal threshold to calculate the threshold duty ratios. The original image corresponding to the minimum threshold duty ratio is the optimal focus image. Finally, the optimal in-focus image and related defocused images are used to solve for the phase of the sample using the TIE under the boundary conditions. The correlation coefficient for the results of the simulation experiment reached 0.9317. In a microlens array experiment, the relative error between the results from our algorithm and the actual value was only 7.1%, thus, proving the correctness and effectiveness of the proposed method.