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Quantitative phase imaging (QPI), which combines phase imaging with optical microscopy technology, provides a marker-free, fast, non-destructive, and high-resolution imaging method for observing transparent biological samples. It is widely used in life science, biomedicine, etc. As an emerging QPI technology, spiral phase contrast microscopy (SPCM) uses a spiral phase filter to achieve edge enhancement of amplitude or phase objects. Using the multi-step phase-shifting technology, a complex sample can be measured quantitatively, which has the advantages of high stability, high sensitivity and high precision. However, the SPCM requires at least three-step phase-shifted spiral phase filtered images to achieve the quantitative reconstruction of the amplitude and phase of a sample, and the image acquisition process and the reconstruction process are relatively complicated, which require high stability of system, and the SPCM has low temporal resolution. In order to further improve the performance of SPCM and increase the system stability, sensitivity and temporal resolution, in this paper a quantitative phase imaging method and system based on a fractional spiral phase plate is proposed. Through a sample intensity image filtered by a fractional spiral phase plate, the modified Gerchberg-Saxton iterative phase retrieval algorithm is used to quantitatively reconstruct the phase of a pure phase sample, which simplifies the experimental process and phase reconstruction steps of spiral phase contrast microsocopy. In the computer simulation experiments, the phase imaging process and the reconstruction process of spiral phase plates based on different topological charges are studied, the feasibility of which is analyzed. Finally, through imaging and phase reconstruction of the phase grating and biological cell sample, it is verified that the phase contrast microscopy method based on the fractional spiral phase plate can effectively improve the contrast of spiral phase contrast microscopy and can obtain a quantitative reconstruciton of a weak phase object. The phase information of a sample has significance in research and application for developing the spiral phase contrast microscopy.
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Keywords:
- quantitative phase imaging /
- spiral phase contrast microscopy /
- spiral phase plate /
- phase retrieval
[1] Park Y, Depeursinge C, Popescu G 2018 Nat. Photonics 12 578
Google Scholar
[2] Ikeda T, Popescu G, Dasari R R, Feld M S 2005 Opt. Lett. 30 1165
Google Scholar
[3] Marquet P, Rappaz B, Magistretti P J, Cuche E, Emery Y, Colomb T, Depeursinge C 2005 Opt. Lett. 30 468
Google Scholar
[4] Warger W C, DiMarzio C A 2009 Opt. Express 17 2400
Google Scholar
[5] Zicha D, Dunn G A 1995 J. Microsc.-Oxford 179 11
Google Scholar
[6] Popescu G, Deflores L P, Vaughan J C, Badizadegan K, Iwai H, Dasari R R, Feld M S 2004 Opt. Lett. 29 2503
Google Scholar
[7] Popescu G, Ikeda T, Dasari R R, Feld M S 2006 Opt. Lett. 31 775
Google Scholar
[8] Barty A, Nugent K A, Paganin D, Roberts A 1998 Opt. Lett. 23 817
Google Scholar
[9] Wang Z, Millet L, Mir M, Ding H F, Unarunotai S, Rogers J, Gillette M U, Popescu G 2011 Opt. Express 19 1016
Google Scholar
[10] Ding H F, Wang Z, Nguyen F, Boppart S A, Popescu G 2008 Phys. Rev. Lett. 101 238102
Google Scholar
[11] Davis J A, McNamara D E, Cottrell D M, Campos J 2000 Opt. Lett. 25 99
Google Scholar
[12] Crabtree K, Davis J A, Moreno I 2004 Appl. Opt. 43 1360
Google Scholar
[13] Swartzlander G A 2001 Opt. Lett. 26 497
Google Scholar
[14] 刘婷婷, 洪正平, 国承山 2008 光电子·激光 19 96
Google Scholar
Liu T T, Hong Z P, Guo C S 2008 J. Optoelectron.·Laser 19 96
Google Scholar
[15] Furhapter S, Jesacher A, Bernet S, Ritsch-Marte M 2005 Opt. Lett. 30 1953
Google Scholar
[16] Wang J, Zhang W, Qi Q, Zheng S, Chen L 2015 Sci. Rep. 5 15826
Google Scholar
[17] 顾忠政, 殷达, 聂守平, 冯少彤, 邢芳俭, 马骏, 袁操今 2019 红外与激光工程 48 0603015
Google Scholar
Gu Z Z, Yin D, Nie S P, Feng S T, Xing F J, Ma J, Yuan C J 2019 Infrared Laser Eng. 48 0603015
Google Scholar
[18] Situ G, Pedrini G, Osten W 2009 J. Opt. Soc. Am. A: 26 1788
Google Scholar
[19] Hai N, Rosen J 2020 Opt. Lett. 45 5812
Google Scholar
[20] Fienup J R 1982 Appl. Opt. 21 2758
Google Scholar
[21] 周意 2017 硕士学位论文 (南京: 南京师范大学)
Zhou Y 2017 M. S. Thesis (Nanjing: Nanjing Normal University) (in Chinese)
[22] 黄妙娜, 黄佐华 2009 大学物理 28 6
Google Scholar
Huang M N, Huang Z H 2009 Coll. Phys. 28 6
Google Scholar
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图 1 基于4f系统的螺旋相衬成像系统示意图
Figure 1. Schematic diagram of 4f system-based spiral phase contrast imaging system.
图 2 SGSA框图
Figure 2. Block diagram of the SGSA.
图 3 分数阶拓扑荷取0.1时, SSE随迭代次数的变化曲线
Figure 3. SSE error vs. the number of iterations when the fractional topological charge is 0.1.
图 4 恢复相位与真实相位之间的MSE随迭代次数的变化曲线
Figure 4. MSE error between the recovered phase image and ground truth phase image vs. the number of iterations.
图 5 螺旋相位滤波成像及恢复结果对比 (a) 相位型样品原图; (b) 传统整数阶螺旋相位片滤波图像; (c) 对图(b)用SGSA恢复的样品相位图; (d) 分数阶螺旋相位片滤波图像; (e) 对图(d)用SGSA恢复的样品相位图
Figure 5. Comparisons of the recorded images and the recovered results: (a) The ground truth phase sample image; (b) the recorded image via traditional integer order spiral phase plate filtering; (c) the recovered phase sample image using SGSA for panel (b); (d) the recorded image via fractional spiral phase plate filtering; (e) the recovered phase sample image using SGSA for panel (d).
图 6 分数拓扑荷l取不同值时的直接相位成像结果
$\left( {\rm{a}} \right)\;l = 1$ ;$\left( {\rm{b}} \right)\;l = {\rm{0}}.{\rm{8}}$ ;$\left( {\rm{c}} \right)\;l = {\rm{0}}.{\rm{6}}$ ;$\left( {\rm{d}} \right)\;l = {\rm{0}}.{\rm{5}}$ ;$\left( {\rm{e}} \right)\;l = {\rm{0}}.{\rm{4}}$ ;$\left( {\rm{f}} \right)\;l = {\rm{0}}.{\rm{2}}$ ;$\left( {\rm{g}} \right)\;l = {\rm{0}}.1$ ;$\left( {\rm{h}} \right)\;l = {\rm{0}}.{\rm{08}}$ Figure 6. Direct phase imaging results for different fractional topological charge l :
$\left( {\rm{a}} \right)\;l = 1{{ ;}}$ $\left( {\rm{b}} \right)\;l = {\rm{0}}.{{8 ;}}$ $\left( {\rm{c}} \right)\;l = {\rm{0}}.{{6 ;}}$ $\left( {\rm{d}} \right)\;l = {\rm{0}}.{{5 ;}}$ $\left( {\rm{e}} \right)\;l = {\rm{0}}.{\rm{4}}$ ;$\left( {\rm{f}} \right)\;l = {\rm{0}}.{\rm{2}}$ ;$\left( {\rm{g}} \right)\;l = {\rm{0}}.1$ ;$\left( {\rm{h}} \right)\;l = {\rm{0}}.{\rm{08}}$ .
图 7 不同拓扑荷值恢复结果对比 (a) 拓扑荷取0.1时经SGSA恢复出的相位图; (b) 拓扑荷取0.08时经SGSA恢复出的相位图
Figure 7. Comparisons of the recovered results for different topologies: (a) The reovered phase image using SGSA when the topology is 0.1; (b) the revoverd phase image using SGSA when the topology is 0.08.
图 8 (a) 相位型闪耀光栅; (b) 螺旋相位片; (c) 复合螺旋相位图
Figure 8. (a) Phase-type blazed grating; (b) spiral phase plate; (c) composite spiral phase plate.
图 9 (a) 基于螺旋相位片滤波的定量相位成像系统光路图; (b) SLM上加载的整数阶叉形光栅; (c) SLM上加载的分数阶叉形光栅
Figure 9. (a) Optical setup of quantitative phase imaging system based on a spiral phase filter; (b) the integer order fork grating loaded on SLM; (c) the fractional fork grating loaded on SLM.
图 10 定制相位型光栅的成像 (a) 相位型光栅未滤波明场强度图; (b) 整数阶螺旋相位片滤波成像边缘增强图; (c) 恢复相位图; (d) 恢复深度图, 横纵坐标数值为像素值, 每个像素代表0.325 μm, 总长度为332.8 μm
Figure 10. Imaging of a custom phase gratinig: (a) The unfiltered bright field image of the phase grating; (b) the recorded integer-order spiral phase filtered edge enhancement image; (c) the recovered phase image; (d) the recovered depth image, the abscissa and ordinate values are pixel values, each pixel represents 0.325 μm, and the total length is 332.8 μm.
图 11 经整数阶螺旋相位片滤波后再由SGSA重构的相位型光栅SSE随迭代次数的变化
Figure 11. SSE error vs. the number of iterations for the grating phase reconstruction problem of phase retrieval from a integer-order spiral phase filtering intensity measurement using the SGSA.
图 12 定制相位型光栅的成像 (a) 相位型光栅未滤波明场强度图; (b) 拓扑荷l取0.1时分数阶螺旋相位片滤波成像强度图; (c) 恢复相位图; (d) 恢复深度图(坐标同图10(d))
Figure 12. Imaging of a custom phase grating: (a) The unfiltered phase grating bright field image; (b) the fractional spiral phase plate filtered image when the topological charge l is 0.1; (c) the recovered phase image; (d) the recovered depth image (the coordinates are the same as Fig. 10. (d)).
图 13 经分数阶螺旋相位片滤波后再由SGSA重构的相位光栅SSE随迭代次数的变化
Figure 13. SSE error vs. the number of iterations for the grating phase reconstruction problem of phase retrieval from a fractional spiral phase filtering intensity measurement using the SGSA.
图 14 SH-SY5Y细胞成像 (a) SH-SY5Y细胞未滤波明场强度图; (b) 拓扑荷l取0.1时分数阶螺旋相位片滤波神经元细胞成像强度图; (c) 恢复相位图; (d) 定量相移图(坐标同图10(d))
Figure 14. SH-SY5Y cell imaging: (a) The unfiltered SH-SY5Y cell bright field image; (b) the intensity image of the neuron cell using the fractional spiral phase filter when the topological charge l is 0.1; (c) the recoverd phase image; (d) the quantitative phase image (the coordinates are the same as Fig. 10. (d)).
图 15 SH-SY5Y细胞经分数阶螺旋相位滤波后再由SGSA重建的SSE随迭代次数的变化
Figure 15. SSE error vs. the number of iterations for the SH-SY5Y cells reconstruction problem of phase retrieval from a fractional spiral phase filtering intensity measurement using the SGSA.
表 1 三种分数拓扑荷下恢复相位图与原图的SSIM值
Table 1. The SSIM between the recovered phase image and the ground truth phase image for three fractional topological values.
拓扑荷取值 SSIM 1.0 0.1918 0.1 0.4394 0.08 0.2034 
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[1] Park Y, Depeursinge C, Popescu G 2018 Nat. Photonics 12 578
Google Scholar
[2] Ikeda T, Popescu G, Dasari R R, Feld M S 2005 Opt. Lett. 30 1165
Google Scholar
[3] Marquet P, Rappaz B, Magistretti P J, Cuche E, Emery Y, Colomb T, Depeursinge C 2005 Opt. Lett. 30 468
Google Scholar
[4] Warger W C, DiMarzio C A 2009 Opt. Express 17 2400
Google Scholar
[5] Zicha D, Dunn G A 1995 J. Microsc.-Oxford 179 11
Google Scholar
[6] Popescu G, Deflores L P, Vaughan J C, Badizadegan K, Iwai H, Dasari R R, Feld M S 2004 Opt. Lett. 29 2503
Google Scholar
[7] Popescu G, Ikeda T, Dasari R R, Feld M S 2006 Opt. Lett. 31 775
Google Scholar
[8] Barty A, Nugent K A, Paganin D, Roberts A 1998 Opt. Lett. 23 817
Google Scholar
[9] Wang Z, Millet L, Mir M, Ding H F, Unarunotai S, Rogers J, Gillette M U, Popescu G 2011 Opt. Express 19 1016
Google Scholar
[10] Ding H F, Wang Z, Nguyen F, Boppart S A, Popescu G 2008 Phys. Rev. Lett. 101 238102
Google Scholar
[11] Davis J A, McNamara D E, Cottrell D M, Campos J 2000 Opt. Lett. 25 99
Google Scholar
[12] Crabtree K, Davis J A, Moreno I 2004 Appl. Opt. 43 1360
Google Scholar
[13] Swartzlander G A 2001 Opt. Lett. 26 497
Google Scholar
[14] 刘婷婷, 洪正平, 国承山 2008 光电子·激光 19 96
Google Scholar
Liu T T, Hong Z P, Guo C S 2008 J. Optoelectron.·Laser 19 96
Google Scholar
[15] Furhapter S, Jesacher A, Bernet S, Ritsch-Marte M 2005 Opt. Lett. 30 1953
Google Scholar
[16] Wang J, Zhang W, Qi Q, Zheng S, Chen L 2015 Sci. Rep. 5 15826
Google Scholar
[17] 顾忠政, 殷达, 聂守平, 冯少彤, 邢芳俭, 马骏, 袁操今 2019 红外与激光工程 48 0603015
Google Scholar
Gu Z Z, Yin D, Nie S P, Feng S T, Xing F J, Ma J, Yuan C J 2019 Infrared Laser Eng. 48 0603015
Google Scholar
[18] Situ G, Pedrini G, Osten W 2009 J. Opt. Soc. Am. A: 26 1788
Google Scholar
[19] Hai N, Rosen J 2020 Opt. Lett. 45 5812
Google Scholar
[20] Fienup J R 1982 Appl. Opt. 21 2758
Google Scholar
[21] 周意 2017 硕士学位论文 (南京: 南京师范大学)
Zhou Y 2017 M. S. Thesis (Nanjing: Nanjing Normal University) (in Chinese)
[22] 黄妙娜, 黄佐华 2009 大学物理 28 6
Google Scholar
Huang M N, Huang Z H 2009 Coll. Phys. 28 6
Google Scholar
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