Robust and fast dual-wavelength phase unwrapping in quantitative phase imaging with region segmentation

Digital holographic microscopy (DHM) is used for phase imaging of micro-scale samples owing to its numerous advantages, including high resolution and non-destructive nature. Numerical phase unwrapping algorithms have been used to obtain continuous unwrapped phase maps by evaluating the fringe orders of the wrapped phase maps. However, these algorithms are usually slow and fail to unwrap the phase maps correctly for phase differences greater than 2π. This often leads to inaccurate reconstruction of the final phase map due to the difficulty in differentiating the number of 2π jumps wrapped between two adjacent pixels.

Dual-wavelength DHM has been proposed to solve such phase ambiguity issues. It acquires two wrapped phase maps at different wavelengths to produce a new synthetic phase map corresponding to the longer synthetic wavelength. A proper selection of two distinct wavelengths allows fitting of physical changes of the measured samples within the [-π,π] to achieve phase unwrapping. Unfortunately, dual-wavelength DHM suffers from increased phase noise in the synthetic phase map, which reduces its axial phase sensitivity.

Although several algorithms have been developed to suppress noise and improve phase sensitivity, they are still sensitive to increased noise, especially for large beat wavelengths. This is mainly attributed to the individual evaluation of the fringe order of each pixel, leading to inaccurate results. To this noted, Dr. Rongli Guo, Dr. Shuaidong Lu, Dr. Yinhua Wu, Dr. MiaoMiao Zhang and Dr. Fan Wang from Xi’an Technological University developed a new robust and fast dual-wavelength phase unwrapping method for dual-wavelength DHM. Their work is currently published in the journal, Optics Communication.

Briefly, the authors commenced by generating a synthetic map by subtracting two wrapped phase maps. It was then divided into multiple regions based on phase discontinuities of the wrapped phase maps. By directly determining the fringe order of each region, the final denoised phase map was calculated using one of the wrapped phase maps. All the pixels in a region were assumed to have equal fringe order and fringe order evaluation was done based on segmented regions. The method was validated by applying it to both experimental and simulative data.

The authors demonstrated the robustness and capability of the proposed method in suppressing the magnified noise associated with synthesizing the large beat wavelength to the level of a single wavelength. It worked well for both stepped and continuous objects. For continuous objectives, it achieved phase unwrapping relatively fast heavy avoiding heavy computational burden. Interestingly, the proposed method provided the only efficient solution for imaging large step height steps.

Successful implementation of this method required correct identification of the various regions from the wrapped phase map. Continuous sample measurement required setting only one threshold by evaluating the derivative map values, while the number of thresholds in step samples was equivalent to the number of steps contained. The thresholds were set by considering the values of different steps and noise magnitude. For cases with too large phase noises, other segmentation algorithms like denoising method or manual segmentation could be employed. Furthermore, this method was also applicable in quantitative imaging of microstructures with beat wavelengths up to 20.475 μm.

In summary, a robust and fast phase unwrapping method capable of suppressing phase noise in dual-wavelength DHM was successfully developed. This method worked effectively in the large beat wavelength while reducing the noise to the same level as that of single wavelength DHM. The experimental and simulation results demonstrated the superiority of the proposed method over other methods. In a joint statement to Advances in Engineering, the authors explained their new method is a powerful tool for realizing a large unambiguous measurement range in dual-wavelength interferometric techniques.