部分相干照明下的相位恢复方法及应用研究进展

卢兴园; 赵承良; 蔡阳健

doi:doi:10.3788/CJL202047.0500016

中国激光, 2020, 47 (5): 0500016, 网络出版: 2020-05-12

部分相干照明下的相位恢复方法及应用研究进展下载： 2615次特邀综述

Research Progress on Methods and Applications for Phase Reconstruction Under Partially Coherent Illumination

卢兴园 ¹赵承良 ^1,*蔡阳健 ^1,2,3,**

作者单位

¹ 苏州大学物理科学与技术学院, 江苏苏州 215006

² 山东师范大学物理与电子学院, 山东济南 250014

³ 山东省光场调控工程技术中心, 山东省光学与光子器件技术重点实验室, 山东济南 250014

图 & 表

图 1. 强度传输方程相位恢复的基本实验装置图^[9]。(a)基于4f系统的含透镜成像光路;(b)无透镜成像光路

Fig. 1. Schemes for transport of intensity equation phase imaging^[9].(a) 4f system-based system; (b) lens-less system

下载图片查看原文

图 2. 改变照明光源的空间相干性,利用强度传输方程恢复的相位(数值孔径NA越大,对应系统照明光源的空间相干度越低)^[26]。(a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

Fig. 2. Reconstructed phases with transport of intensity equation method under illumination with different degrees of coherence (the larger the numerical aperture, the lower the spatial coherence of the illumination)^[26]. (a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

下载图片查看原文

图 3. 相干衍射成像示意图^[1]

Fig. 3. Scheme for coherent diffraction imaging^[1]

下载图片查看原文

图 4. 部分相干照明下,直接恢复和利用模式分解法恢复的相位^[36]

Fig. 4. Reconstructed phases with and without mode decomposition methods under partially coherent illumination^[36]

下载图片查看原文

图 5. 部分相干照明的数字全息显微装置示意图^[17]

Fig. 5. Optical setup of digital holographic microscope with partially coherent illumination^[17]

下载图片查看原文

图 6. 重聚焦情况下采用数字全息法恢复的相位(左列为高相干照明,右列为低相干照明,从上至下重聚焦距离逐渐增大)^[17]

Fig. 6. Reconstructed phases with digital holographic microscopy in refocused cases (the left column is high-coherent illumination, the right column is low-coherent illumination, and the refocusing distance gradually increases from top to bottom)^[17]

下载图片查看原文

图 7. 微扰法恢复相位的实验装置图^[48]

Fig. 7. Scheme for self-referencing holography phase imaging^[48]

下载图片查看原文

图 8. 对光强进行傅里叶逆变换所得三项结果的分布与扰动点r₀位置的关系^[48]。(a) 扰动点位于物体信息覆盖范围内;(b) 扰动点位于物体信息覆盖范围外;(c) 扰动点位于物体信息覆盖范围外且足够远

Fig. 8. Three terms in the inverse Fourier transform of the diffraction pattern versus the location of the perturbation point $\begin{matrix} {r_{0}}^{[48]} \end{matrix}$
下载图片  查看原文

图 9. 部分相干照明下,利用微扰法获得的相位恢复结果^[48],其中,(c1)和(c2)对应图8(c),(b1)和(b2)对应图8(b),(a1)和(a2)对应图8(a)

Fig. 9. Reconstructed phases obtained by self-reference holography under partially coherent illumination, herein, (c1) and (c2) corresponds to Fig. 8(c); (b1) and (b2) corresponds to Fig. 8(b); (a1) and (a2) corresponds to Fig. 8(a)

下载图片查看原文

图 10. 当照明光源为具有特殊关联结构的部分相干光时,用微扰法获得的相位恢复结果^[48]。(a1)(a3)(b1)(b3)直接恢复的振幅及相位分布;(a2)(a4)(b2)(b4)光源的振幅及相位分布;(a5)(b5)利用直接恢复的相位除以光源的相位所得的物体真实的相位分布

Fig. 10. Reconstructed phases obtained by self-reference holography under specially partially coherent illumination. (a1)(a3)(b1)(b3) Amplitude and phase distribution of the direct reconstruction; (a2)(a4)(b2)(b4) amplitude and phase distribution of the illumination; (a5)(b5) actual phase distribution of the object obtained by the phase of the direct reconstruction divided by the illumination

下载图片查看原文

图 11. 多孔阵列法实现相位恢复的示意图^[49]。(a)实验装置原理图;(b) 多孔阵列包含一个位于中心位置的参考孔(灰色)和略微偏离中心的阵列孔(白色);(c) 相机采集的衍射图案的傅里叶逆变换中,自相关项(灰色阵列)和另外两个干涉项(蓝色和红色阵列)发生分离

Fig. 11. Schematic of phase reconstruction with pinhole array mask^[49]. (a) Experimental setup; (b) PAM consists of a reference pinhole at the origin (gray square) and a periodic array of the measurement pinholes with certain offset (white squares);(c) in the inverse Fourier transform of the diffraction pattern, the autocorrelation terms (gray squares) and the two interference terms (red and blue squares) are separated by the offset

下载图片查看原文

图 12. 在空间相干度较低光源的照射下,不同扰动点位置对应的相位恢复结果及整合后重构的完整视场^[49]。(a-f)相位恢复结果;(g)完整视场

Fig. 12. Reconstructed phases of different perturbation points and the final complete field of view under illumination with low degree of spatial coherence^[49]. (a-f) Reconstructed phases; (g) final complete filed of view

下载图片查看原文

图 13. 焦移法使用的星形掩模板^[50]

Fig. 13. Star-shaped mask for non-iterative focus variation phase reconstruction method^[50]

下载图片查看原文

图 14. 在空间相干度较低光源的照射下,使用焦移法仍能获得正确且完整的相位恢复^[50](第1行与第2行分别为振幅和相位恢复结果,每一列的差别在于P的选取,分别对应星形掩模板的4个顶点;第3行为最终合成的物体的振幅及相位分布,以及光源的相位及振幅分布)

Fig. 14. Correct and complete phase reconstructions obtained with focus variation method under illumination with low degree of coherence^[50] (the first and second rows are the amplitude and phase reconstructions, respectively. The difference in each column is the selection of P, which corresponds to the four vertices of the star mask. The third row is the synthesized amplitude and phase distribution of the object, and the phase and amplitude distri

下载图片查看原文

图 15. 不同传输距离(z)处的具有不同拓扑荷l的涡旋光束的强度和相位图^[51]

Fig. 15. Intensity and phase patterns of vortex beams with different topological charges at different distances (z)^[51]

下载图片查看原文

图 16. 具有不同拓扑荷数的完美拉盖尔高斯光束在焦场处的关联结构分布^[53](第1行为实验结果,第2行为理论模拟结果)

Fig. 16. Experimental results of complex degree of coherence for partially coherent elegant Laguerre-Gaussian beam with different topological charges^[53](row 1: experimental results; row 2: simulation results)

下载图片查看原文

图 17. 厄米高斯关联的拉盖尔高斯光束在焦平面前的关联结构振幅分布^[54]

Fig. 17. Modulus of degree of coherence of Hermite-Gaussian correlated Schell-model LG₀_l beam before the focal plane^[54]

下载图片查看原文

图 18. 测量部分相干涡旋光束焦场处关联结构的实验光路图^[55]。(a)BS2处的光路细节图;(b)SLM2加载扰动的实例

Fig. 18. Experimental setup for measuring the degree of coherence of partially coherent vortex beams at the focal plane^[55]. (a) Light path detail at BS2; (b) an example for the design of aperture and perturbation function

下载图片查看原文

图 19. 选取离轴参考点时,具有不同拓扑荷数的部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布^[55]

Fig. 19. Theoretical simulations and experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for the focused partially coherent vortex beams^[55]

下载图片查看原文

图 20. 选取离轴参考点时,不同拓扑荷数及径向模式数下部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布^[56]

Fig. 20. Experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for focused partially coherent vortex beams^[56]

下载图片查看原文

卢兴园, 赵承良, 蔡阳健. 部分相干照明下的相位恢复方法及应用研究进展[J]. 中国激光, 2020, 47(5): 0500016. Xingyuan Lu, Chengliang Zhao, Yangjian Cai. Research Progress on Methods and Applications for Phase Reconstruction Under Partially Coherent Illumination[J]. Chinese Journal of Lasers, 2020, 47(5): 0500016.

部分相干照明下的相位恢复方法及应用研究进展下载： 2615次特邀综述

图 1. 强度传输方程相位恢复的基本实验装置图^[9]。(a)基于4f系统的含透镜成像光路;(b)无透镜成像光路

Fig. 1. Schemes for transport of intensity equation phase imaging^[9].(a) 4f system-based system; (b) lens-less system

图 2. 改变照明光源的空间相干性,利用强度传输方程恢复的相位(数值孔径NA越大,对应系统照明光源的空间相干度越低)^[26]。(a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

Fig. 2. Reconstructed phases with transport of intensity equation method under illumination with different degrees of coherence (the larger the numerical aperture, the lower the spatial coherence of the illumination)^[26]. (a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

图 3. 相干衍射成像示意图^[1]

Fig. 3. Scheme for coherent diffraction imaging^[1]

图 4. 部分相干照明下,直接恢复和利用模式分解法恢复的相位^[36]

Fig. 4. Reconstructed phases with and without mode decomposition methods under partially coherent illumination^[36]

图 5. 部分相干照明的数字全息显微装置示意图^[17]

Fig. 5. Optical setup of digital holographic microscope with partially coherent illumination^[17]

图 6. 重聚焦情况下采用数字全息法恢复的相位(左列为高相干照明,右列为低相干照明,从上至下重聚焦距离逐渐增大)^[17]

Fig. 6. Reconstructed phases with digital holographic microscopy in refocused cases (the left column is high-coherent illumination, the right column is low-coherent illumination, and the refocusing distance gradually increases from top to bottom)^[17]

图 7. 微扰法恢复相位的实验装置图^[48]

Fig. 7. Scheme for self-referencing holography phase imaging^[48]

图 8. 对光强进行傅里叶逆变换所得三项结果的分布与扰动点r₀位置的关系^[48]。(a) 扰动点位于物体信息覆盖范围内;(b) 扰动点位于物体信息覆盖范围外;(c) 扰动点位于物体信息覆盖范围外且足够远

Fig. 8. Three terms in the inverse Fourier transform of the diffraction pattern versus the location of the perturbation point $\begin{matrix} {r_{0}}^{[48]} \end{matrix}$
下载图片  查看原文

图 9. 部分相干照明下,利用微扰法获得的相位恢复结果^[48],其中,(c1)和(c2)对应图8(c),(b1)和(b2)对应图8(b),(a1)和(a2)对应图8(a)

Fig. 9. Reconstructed phases obtained by self-reference holography under partially coherent illumination, herein, (c1) and (c2) corresponds to Fig. 8(c); (b1) and (b2) corresponds to Fig. 8(b); (a1) and (a2) corresponds to Fig. 8(a)

图 12. 在空间相干度较低光源的照射下,不同扰动点位置对应的相位恢复结果及整合后重构的完整视场^[49]。(a-f)相位恢复结果;(g)完整视场

Fig. 12. Reconstructed phases of different perturbation points and the final complete field of view under illumination with low degree of spatial coherence^[49]. (a-f) Reconstructed phases; (g) final complete filed of view

图 13. 焦移法使用的星形掩模板^[50]

Fig. 13. Star-shaped mask for non-iterative focus variation phase reconstruction method^[50]

图 15. 不同传输距离(z)处的具有不同拓扑荷l的涡旋光束的强度和相位图^[51]

Fig. 15. Intensity and phase patterns of vortex beams with different topological charges at different distances (z)^[51]

图 16. 具有不同拓扑荷数的完美拉盖尔高斯光束在焦场处的关联结构分布^[53](第1行为实验结果,第2行为理论模拟结果)

Fig. 16. Experimental results of complex degree of coherence for partially coherent elegant Laguerre-Gaussian beam with different topological charges^[53](row 1: experimental results; row 2: simulation results)

图 17. 厄米高斯关联的拉盖尔高斯光束在焦平面前的关联结构振幅分布^[54]

Fig. 17. Modulus of degree of coherence of Hermite-Gaussian correlated Schell-model LG₀_l beam before the focal plane^[54]

图 18. 测量部分相干涡旋光束焦场处关联结构的实验光路图^[55]。(a)BS2处的光路细节图;(b)SLM2加载扰动的实例

Fig. 18. Experimental setup for measuring the degree of coherence of partially coherent vortex beams at the focal plane^[55]. (a) Light path detail at BS2; (b) an example for the design of aperture and perturbation function

图 19. 选取离轴参考点时,具有不同拓扑荷数的部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布^[55]

Fig. 19. Theoretical simulations and experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for the focused partially coherent vortex beams^[55]

图 20. 选取离轴参考点时,不同拓扑荷数及径向模式数下部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布^[56]

Fig. 20. Experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for focused partially coherent vortex beams^[56]

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部分相干照明下的相位恢复方法及应用研究进展 下载： 2615次特邀综述

图 1. 强度传输方程相位恢复的基本实验装置图[9]。(a)基于4f系统的含透镜成像光路;(b)无透镜成像光路

Fig. 1. Schemes for transport of intensity equation phase imaging[9].(a) 4f system-based system; (b) lens-less system

图 2. 改变照明光源的空间相干性,利用强度传输方程恢复的相位(数值孔径NA越大,对应系统照明光源的空间相干度越低)[26]。(a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

Fig. 2. Reconstructed phases with transport of intensity equation method under illumination with different degrees of coherence (the larger the numerical aperture, the lower the spatial coherence of the illumination)[26]. (a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

图 3. 相干衍射成像示意图[1]

Fig. 3. Scheme for coherent diffraction imaging[1]

图 4. 部分相干照明下,直接恢复和利用模式分解法恢复的相位[36]

Fig. 4. Reconstructed phases with and without mode decomposition methods under partially coherent illumination[36]

图 5. 部分相干照明的数字全息显微装置示意图[17]

Fig. 5. Optical setup of digital holographic microscope with partially coherent illumination[17]

图 6. 重聚焦情况下采用数字全息法恢复的相位(左列为高相干照明,右列为低相干照明,从上至下重聚焦距离逐渐增大)[17]

Fig. 6. Reconstructed phases with digital holographic microscopy in refocused cases (the left column is high-coherent illumination, the right column is low-coherent illumination, and the refocusing distance gradually increases from top to bottom)[17]

图 7. 微扰法恢复相位的实验装置图[48]

Fig. 7. Scheme for self-referencing holography phase imaging[48]

图 8. 对光强进行傅里叶逆变换所得三项结果的分布与扰动点r0位置的关系[48]。(a) 扰动点位于物体信息覆盖范围内;(b) 扰动点位于物体信息覆盖范围外;(c) 扰动点位于物体信息覆盖范围外且足够远

Fig. 8. Three terms in the inverse Fourier transform of the diffraction pattern versus the location of the perturbation point r048 下载图片 查看原文

图 9. 部分相干照明下,利用微扰法获得的相位恢复结果[48],其中,(c1)和(c2)对应图8(c),(b1)和(b2)对应图8(b),(a1)和(a2)对应图8(a)

Fig. 9. Reconstructed phases obtained by self-reference holography under partially coherent illumination, herein, (c1) and (c2) corresponds to Fig. 8(c); (b1) and (b2) corresponds to Fig. 8(b); (a1) and (a2) corresponds to Fig. 8(a)

图 12. 在空间相干度较低光源的照射下,不同扰动点位置对应的相位恢复结果及整合后重构的完整视场[49]。(a-f)相位恢复结果;(g)完整视场

Fig. 12. Reconstructed phases of different perturbation points and the final complete field of view under illumination with low degree of spatial coherence[49]. (a-f) Reconstructed phases; (g) final complete filed of view

图 13. 焦移法使用的星形掩模板[50]

Fig. 13. Star-shaped mask for non-iterative focus variation phase reconstruction method[50]

图 15. 不同传输距离(z)处的具有不同拓扑荷l的涡旋光束的强度和相位图[51]

Fig. 15. Intensity and phase patterns of vortex beams with different topological charges at different distances (z)[51]

图 16. 具有不同拓扑荷数的完美拉盖尔高斯光束在焦场处的关联结构分布[53](第1行为实验结果,第2行为理论模拟结果)

Fig. 16. Experimental results of complex degree of coherence for partially coherent elegant Laguerre-Gaussian beam with different topological charges[53](row 1: experimental results; row 2: simulation results)

图 17. 厄米高斯关联的拉盖尔高斯光束在焦平面前的关联结构振幅分布[54]

Fig. 17. Modulus of degree of coherence of Hermite-Gaussian correlated Schell-model LG0l beam before the focal plane[54]

图 18. 测量部分相干涡旋光束焦场处关联结构的实验光路图[55]。(a)BS2处的光路细节图;(b)SLM2加载扰动的实例

Fig. 18. Experimental setup for measuring the degree of coherence of partially coherent vortex beams at the focal plane[55]. (a) Light path detail at BS2; (b) an example for the design of aperture and perturbation function

图 19. 选取离轴参考点时,具有不同拓扑荷数的部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布[55]

Fig. 19. Theoretical simulations and experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for the focused partially coherent vortex beams[55]

图 20. 选取离轴参考点时,不同拓扑荷数及径向模式数下部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布[56]

Fig. 20. Experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for focused partially coherent vortex beams[56]

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部分相干照明下的相位恢复方法及应用研究进展下载： 2615次特邀综述

图 1. 强度传输方程相位恢复的基本实验装置图^[9]。(a)基于4f系统的含透镜成像光路;(b)无透镜成像光路

Fig. 1. Schemes for transport of intensity equation phase imaging^[9].(a) 4f system-based system; (b) lens-less system

图 2. 改变照明光源的空间相干性,利用强度传输方程恢复的相位(数值孔径NA越大,对应系统照明光源的空间相干度越低)^[26]。(a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

Fig. 2. Reconstructed phases with transport of intensity equation method under illumination with different degrees of coherence (the larger the numerical aperture, the lower the spatial coherence of the illumination)^[26]. (a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

图 3. 相干衍射成像示意图^[1]

Fig. 3. Scheme for coherent diffraction imaging^[1]

图 4. 部分相干照明下,直接恢复和利用模式分解法恢复的相位^[36]

Fig. 4. Reconstructed phases with and without mode decomposition methods under partially coherent illumination^[36]

图 5. 部分相干照明的数字全息显微装置示意图^[17]

Fig. 5. Optical setup of digital holographic microscope with partially coherent illumination^[17]

图 6. 重聚焦情况下采用数字全息法恢复的相位(左列为高相干照明,右列为低相干照明,从上至下重聚焦距离逐渐增大)^[17]

Fig. 6. Reconstructed phases with digital holographic microscopy in refocused cases (the left column is high-coherent illumination, the right column is low-coherent illumination, and the refocusing distance gradually increases from top to bottom)^[17]

图 7. 微扰法恢复相位的实验装置图^[48]

Fig. 7. Scheme for self-referencing holography phase imaging^[48]

图 8. 对光强进行傅里叶逆变换所得三项结果的分布与扰动点r₀位置的关系^[48]。(a) 扰动点位于物体信息覆盖范围内;(b) 扰动点位于物体信息覆盖范围外;(c) 扰动点位于物体信息覆盖范围外且足够远

Fig. 8. Three terms in the inverse Fourier transform of the diffraction pattern versus the location of the perturbation point $\begin{matrix} {r_{0}}^{[48]} \end{matrix}$
下载图片查看原文

图 9. 部分相干照明下,利用微扰法获得的相位恢复结果^[48],其中,(c1)和(c2)对应图8(c),(b1)和(b2)对应图8(b),(a1)和(a2)对应图8(a)

图 12. 在空间相干度较低光源的照射下,不同扰动点位置对应的相位恢复结果及整合后重构的完整视场^[49]。(a-f)相位恢复结果;(g)完整视场

Fig. 12. Reconstructed phases of different perturbation points and the final complete field of view under illumination with low degree of spatial coherence^[49]. (a-f) Reconstructed phases; (g) final complete filed of view

图 13. 焦移法使用的星形掩模板^[50]

Fig. 13. Star-shaped mask for non-iterative focus variation phase reconstruction method^[50]

图 15. 不同传输距离(z)处的具有不同拓扑荷l的涡旋光束的强度和相位图^[51]

Fig. 15. Intensity and phase patterns of vortex beams with different topological charges at different distances (z)^[51]

图 16. 具有不同拓扑荷数的完美拉盖尔高斯光束在焦场处的关联结构分布^[53](第1行为实验结果,第2行为理论模拟结果)

Fig. 16. Experimental results of complex degree of coherence for partially coherent elegant Laguerre-Gaussian beam with different topological charges^[53](row 1: experimental results; row 2: simulation results)

图 17. 厄米高斯关联的拉盖尔高斯光束在焦平面前的关联结构振幅分布^[54]

Fig. 17. Modulus of degree of coherence of Hermite-Gaussian correlated Schell-model LG₀_l beam before the focal plane^[54]

图 18. 测量部分相干涡旋光束焦场处关联结构的实验光路图^[55]。(a)BS2处的光路细节图;(b)SLM2加载扰动的实例

Fig. 18. Experimental setup for measuring the degree of coherence of partially coherent vortex beams at the focal plane^[55]. (a) Light path detail at BS2; (b) an example for the design of aperture and perturbation function

图 19. 选取离轴参考点时,具有不同拓扑荷数的部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布^[55]

Fig. 19. Theoretical simulations and experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for the focused partially coherent vortex beams^[55]

图 20. 选取离轴参考点时,不同拓扑荷数及径向模式数下部分相干涡旋光束在焦平面上的关联结构的振幅及相位分布^[56]

Fig. 20. Experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for focused partially coherent vortex beams^[56]