Correction of axial distance error in ptychography based on image information entropy
Authors: Dou Jian-Tai  , Gao Zhi-Shan  , Ma Jun  , Yuan Cao-Jin  , Yang Zhong-Ming  ,   School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;,   Department of Physics, Nanjing Normal University, Nanjing 210097, China
Published: December 2020

Ptychography provides an extremely robust and highly convergent algorithm to reconstruct the specimen phase with a wide field of view. The resolution and accuracy of ptychography are severely restricted by the uncertainty of the position error that includes the scanning position and axial distance error. In fact, it is difficult to accurately measure the distance between the target plane and entrance pupil of charge-coupled device (CCD) or complementary metal oxide semiconductor, which results in the axial distance error. The axial distance error can blur the reconstructed image, degrade the reconstruction quality and reduce the resolution. In order to analyze the effect of the axial distance error, the model for axial distance error is derived based on the amplitude constraint in CCD and Fresnel diffraction integral. This model indicates that the axial distance error can cause a stretching deformation of the retrieved image, which is similar to the defocusing effect caused by different axial distances in holography. In this paper, we propose a method of correcting the axial distance error by using the image information entropy in an iterative way to obtain the accurate axial distance and retrieve the distinct image. The correction method based on the image information entropy is composed of four parts:the initial calculation, the determination of the direction search, the axial error correction and the reconstruction of the distinct image. The initial calculation part is to ensure that the intensity of the reconstructed object tends to be stable before entering into the other processing parts. The search direction portion is to indicate that the initial axial distance is greater than the actual axial distance, or less than the actual axial distance. The axial error correction section is to calculate the sharpness values of the image at different axial distance, and find the peak position of the sharpness distribution that corresponds to the position of the clearest image. The axial distance can be taken from the peak position. The obtained axial distance is again taken into account in the ptychography algorithm to eliminate the axial distance error and obtain the distinct reconstructed image. In this paper, some simulations are conducted to verify the feasibility of the proposed method. The effect of the axial distance error is analyzed. The image energy variation, the Tamura coefficient and the image information entropy are selected as the image definition evaluation functions in our paper. We compare the distributions of three image definition evaluation functions in the correction process of the axial distance error. It is found that the image information entropy has higher sensitivity than the other image definition evaluation functions. Finally, both simulation and experiment have proved the feasibility of axial distance error correction based on image information entropy.