Efficient super-resolution of phase images encoded with random phase mask by machine learning techniques

In the field of optics, a random phase mask (RPM) is used to efficiently encode and decode spatial complex amplitude distribution information of measurement targets into phase information. By encoding spatial complex amplitude distribution into a phase using an RPM, this distribution can be processed by modulating only the phase, which is efficient in computational terms. However, when encoding and decoding spatial complex amplitude distribution using an RPM, the resolution of optical devices such as a spatial light modulator (SLM) and charge-coupled device (CCD) becomes a bottleneck, resulting in decreased encoding and decoding accuracy. To address this issue, we propose a super-resolution method for phase images encoded with spatial complex amplitude distribution. This method uses a convolutional neural network (CNN) and a vision transformer (ViT), which are machine learning techniques widely used in computer vision. Through this super-resolution processing, we demonstrated that complex amplitude information can be encoded and decoded into phase images beyond the resolution of optical devices such as an SLM and CCD. Evaluation of the test images using peak signal-to-noise ratio (PSNR) showed improvements of 2.37 dB with the CNN and 1.86 dB with the ViT. Furthermore, we applied the proposed method to virtual phase conjugation based optical tomography (VPC-OT). The simulation results of measuring a microscopic target with a four-layer structure showed noise reduction at all depth positions and an improvement in the measurement accuracy of approximately 6-13 dB. (Details are shown in Fig. 7 and Table 2.) By applying the proposed method, measurement accuracy is improved with minimal computational operations, and without requiring additional optical systems or increasing the number of measurements. In addition, we examined the appropriate size of the machine learning model by observing the input image size (number of parameters) and loss progression.