Fast phase unwrapping using digital differentiation-integration method

Abstract

Digital holography is one of the most widely used quantitative phase imaging technologies at present, owing to its non-contact, high-accuracy and full-filed measurement. However, when the optical path difference induced by the measurement sample is larger than the used wavelength, a phase unwrapping algorithm has to be utilized to unwrap the phase and retrieve the actual phase. And the existing phase unwrapping algorithms suffer huge computational burden and slow retrieval speed. Although they have been greatly improved, their retrieval speed is limited by the phase unwrapping. In order to solve the above-mentioned problems, a digital differentiation-integration based phase unwrapping is proposed in this paper. This algorithm is based on the fact that the actual phase information is contained in the complex-valued function after Fourier transform, band-pass filter and inverse Fourier transform. After Fourier transform, band-pass filter and inverse Fourier transform, a complex-valued function containing the actual phase is retrieved, and two sub complex-valued functions can be extracted with just one-pixel shift digitally. Then, two functions are divided pixel by pixel, and another complex-valued function containing the differentiation of the actual phase is obtained. So the differential phase can be retrieved easily by the phase extraction. Finally, the retrieved differential phase is integrated along the inverse direction of shifting, and the unwrapped phase can be obtained directly. This algorithm can work effectively when the variation of the measurement phase is in a range of (–π, π]. This algorithm is just based on the Fourier transform and the complex-valued division. Unlike the existing unwrapping algorithms, this algorithm is much easier to conduct and has light computation burden. Therefore, this algorithm can realize fast and accurate phase reconstruction directly. Several simulation and experimental results can verify the effectiveness of this algorithm.