Non-interferometric phase retrieval is a fundamental technique for phase-modulated holographic data storage due to its advantages of easy implementation, simple system setup, and robust noise tolerance. Usually, the iterative algorithm of non-interferometry needs hundreds of iteration numbers to retrieve phase accurately, which decreased the data transfer rate severely. Strong constraint conditions, such as embedded data, can be used on the phase data page to reduce the iteration numbers. However, introducing embedded data will reduce the code rate of the system. We proposed a method that combined the single-shot interferometric method with the non-interferometric iterative Fourier transform algorithm method. We used the phase decoding result by single-shot interferometry as the embedded data in the process of non-interferometry. Therefore, no extra embedded data are needed in the signal code. We realized the code rate improvement as well as keeping fast data transfer rate. In the demonstration, we recorded a four-level phase pattern and retrieved the phase correctly. The bit error rate of phase retrieval is less than 1% within 20 iterations, which proves our approach is practical. In our case, the code rate is increased by two times.
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