1.College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China 2.Key Laboratory of Advanced Marine Communication and Information Technology, Ministry of Industry and Information Technology, Harbin Engineering University, Harbin 150001, China
Fund Project:Project supported by National Natural Science Foundation of China (Grant No. 61775046), Natural Science Foundation of Heilongjiang Province, China (Grant No. LC2018027), and Fundamental Research Funds for the Central Universities
Received Date:09 April 2021
Accepted Date:01 June 2021
Available Online:15 August 2021
Published Online:20 November 2021
Abstract:Dual-wavelength digital holography can expand the unambiguous measurement depth in phase unwrapping by using a differential synthetic wavelength which is longer than the single illumination wavelength. However, the phase noise is significantly amplified due to the magnification of the differential synthetic wavelength, resulting in a lower measurement accuracy. On the other hand, a lower noise level can be achieved by using additive synthetic-wavelength which is shorter than the single illumination wavelength. However, the corresponding unambiguous measurement depth is greatly reduced due to the phase ambiguity. In this case, combining the merits of the differential synthetic-wavelength and the additive synthetic-wavelength, different low noise phase unwrapping algorithms have been developed in recent years. However, these algorithms are complex and time consuming because they need to calculate multiple intermediate variables or search for the constrained boundary conditions in two-dimensional space. Therefore, in this paper, we develop a hierarchical phase unwrapping algorithm by using the two synthetic wavelengths for dual-wavelength digital holography to realize low noise and fast unambiguous measurement with large depth. In this algorithm, the unwrapped phase difference obtained by the differential synthetic wavelength is used to guide the wrapped phase of one single wavelength to realize phase unwrapping, and then the optical path difference obtained by the single-wavelength unwrapped phase is employed to guide the wrapped phase sum, and thus realizing phase unwrapping. As a result, the phase noise is attenuated and the depth sensitivity is preserved for dual-wavelength phase unwrapping. After theoretical analysis, a series of simulation experiments is carried out on the reconstructed quality, anti-noise characteristics and speed through comparing with state-of-the-art dual-wavelength phase unwrapping algorithms, including the conventional algorithm, the linear programming algorithm and the direct linear programming algorithm. In this case, a flipping dual-wavelength common-path digital holography with orthogonal carrier is built to acquire multiplexed off-axis hologram in one shot and illustrate the operation of the algorithm with circular step target, and stability test of the setup. Both the simulation and experimental results show that the proposed method can be simplified and deterministic, resulting in a lower noise phase unwrapping in a time of 20.5 ms for a phase map of one megapixel. We expect that the proposed method can have practical applications in measurement that requires high accuracy, fast speed, and large depth. Keywords:dual-wavelength digital holography/ phase unwrapping/ synthetic wavelength/ low noise
图 7 (a)复合全息图; (b)频谱图; (c) λ1和(d) λ2对应的包裹相位 Figure7. (a) Multiplexed hologram and its (b) power spectrum; and corresponding wrapped phase maps at (c) λ1 and (d) λ2.
图 1 分级解包裹流程图
图 2 (a)待测物体高度图; (b)离轴全息图; (c) λ1和(d) λ2对应的包裹相位
图 3 (a)算法I, (b)算法Ⅱ, (c)算法Ⅲ和(d)算法Ⅳ的恢复结果; (e)算法I, (f)算法Ⅱ, (g)算法Ⅲ和(h)算法Ⅳ恢复结果的残差图
图 4 残差图(图3(e)—3(h))中黑色虚线标注数据
图 5 残差图(图3(e)—3(h))中(a)标准差和(b)峰谷值
图 6 视场翻转双波长载波正交数字全息原理图
图 7 (a)复合全息图; (b)频谱图; (c) λ1和(d) λ2对应的包裹相位
图 8 圆柱恢复结果 (a)算法I; (b)算法Ⅱ; (c)算法Ⅲ; (d)算法Ⅳ
图 9 恢复结果的一维剖面图(图8中白色虚线)
图 10 液滴酒精恢复结果 (a)算法I; (b)算法Ⅱ; (c)算法Ⅲ; (d)算法Ⅳ;
图 11 恢复结果的一维剖面图(图10中白色虚线)
图 12 稳定性实验