Surpassing the differential synthetic wavelength of dual-wavelength digital holography by optimizing the search for an unwrapping coefficient

The measurement range of dual-wavelength digital holography (DWDH) is always limited by differential synthetic wavelength (DSW) with low signal-to-noise ratio (SNR), which limits the application of DWDH. In this paper, we propose a novel, to the best of our knowledge, algorithm to surpass DSW of DWDH by optimizing the search for an unwrapping coefficient. The measured phase of the 1st wavelength can be unwrapped by its unwrapping coefficient and used to induce a wrapped phase of the 2nd wavelength. Owing to the explicit relationship between two measured phase maps of the same sample in DWDH, the induced wrapped phase from the 1st wavelength should be equal to the measured phase of the 2nd wavelength. Therefore, by minimizing the difference between the measured and the induced phase maps of the 2nd wavelength, the unwrapping coefficient of the 1st wavelength can be retrieved, and the unwrapped phase with an extended measurement range can be reconstructed correctly. This approach aims to overcome the limitations of measurement range and low SNR by DSW, to enable high-efficiency and broad-range measurement. This advancement significantly enhances the prospect of the practical application of DWDH. The feasibility and efficiency of this approach would be validated through numerical simulations and practical experiments.