Forward imaging neural network with correction of positional misalignment for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a computational imaging technology used to achieve high-resolution imaging with a wide field-of-view. The existing methods of FPM suffer from the positional misalignment in the system, by which the quality of the recovered high-resolution image is determined. In this paper, a forward neural network method with correction of the positional misalignment (FNN-CP) is proposed based on TensorFlow, which consists of two models. Both the spectrum of the sample and four global position factors, which are introduced to describe the positions of the LED elements, are treated as the learnable weights in layers in the first model. By minimizing the loss function in the training process, the positional error can be corrected based on the trained position factors. In order to fit the wavefront aberrations caused by optical components in the FPM system for better recovery results, the second model is designed, in which the spectrum of the sample and coefficients of different Zernike modes are treated as the learnable weights in layers. After the training process of the second model, the wavefront aberration can be fit according to the coefficients of different Zernike modes and the high-resolution complex image can be obtained based on the trained spectrum of the sample. Both the simulation and experiment have been performed to verify the effectiveness of our proposed method. Compared with the state-of-art FPM methods based on forward neural network, FNN-CP can achieve the best reconstruction results.