5776
OPTICS LETTERS / Vol. 39, No. 19 / October 1, 2014
Coded aperture pair for quantitative phase imaging Jiamin Wu,1,2,† Xing Lin,1,2,† Yebin Liu,1,2 Jinli Suo,1,2 and Qionghai Dai1,2,* 1 2
Department of Automation, Tsinghua University, Beijing 100084, China
Beijing Key Laboratory of Multi-dimension & Multi-scale Computational Photography (MMCP), Tsinghua University, Beijing 100084, China *Corresponding author: [email protected] Received June 30, 2014; revised August 31, 2014; accepted September 1, 2014; posted September 2, 2014 (Doc. ID 214114); published October 1, 2014
This Letter proposes a novel quantitative phase-imaging approach by optically encoding light fields into a complementary image pair followed by computational reconstruction. We demonstrate that the axial intensity derivative for phase recovery can be well estimated by a coded-aperture image pair without z axial scanning. The experimental results demonstrate that our approach can achieve higher accuracy and robustness compared with conventional transport-of-intensity equation (TIE) based approaches under partial coherence illumination. © 2014 Optical Society of America OCIS codes: (110.0180) Microscopy; (100.5070) Phase retrieval; (110.1758) Computational imaging; (170.1630) Coded aperture imaging. http://dx.doi.org/10.1364/OL.39.005776
Quantitative phase imaging can be used for recovering the structure or refractive index of a transparent object and has been actively investigated during the past decades because of its extensive applications in various areas, such as astronomy and high-resolution microscopy. Among the large number of phase-imaging approaches, transport-of intensity equation (TIE) based phase-imaging approaches [1] attract lots of attention due to their noninterferometric property, which eliminates the coherence requirements on the illumination. This entails the applicability in bright-field microscope [2]. Moreover, the TIE-based phase-imaging approach is unique because of its quantitative, low-complexity, and noniterative characteristics [3]. Mathematically, TIE reconstructs phase information from a differential intensity measurement: 2π ∂Ix; y −∇Ix; y∇φx; y; λ ∂z
(1)
where x; y denotes the 2D spatial dimensions, z denotes the 1D optical axis, λ is the wavelength of light, I holds the intensity measurements, and φ is the phase (the phase in this Letter refers to optical path length due to the using of partial-coherence illumination). Equation (1) states that the derivative of intensity with respect to the optical axis can be used for inferring phase. Generally, the TIE calculates ∂I∕∂z from a pair of [4] or multiple defocused images [5] captured at different focal planes, and the phase can be recovered by solving a partial differential equation. In order to avoid mechanical movement of the focal plane, a spatial light modulator (SLM) is placed at the Fourier plane so that different defocus distances can be chosen by displaying different phase patterns on the SLM [6]. With an additional beam splitter, two laterally separated images can be captured within a single exposure [7]. Other snapshot approaches such as phase from chromatic aberrations [8] and volume holographic microscope [9] capture multiple defocused images by sacrificing the spatial resolution. Besides low spatial resolution, existing approaches suffer from limited reconstruction accuracy due to the approximation of the axial intensity derivatives using either the first- [7] or higher- [9] order 0146-9592/14/195776-04$15.00/0
difference. Furthermore, these approaches are highly sensitive to the defocus distances whose optimal setting is dependent on the object spatial spectrum and the intensity-measurement noise [4]. Against this backdrop, we present a method using a coded-aperture pair for quantitative phase imaging (CAPPI), which eliminates the aforementioned requirement for changing of the focal plane, and substantially improves the accuracy and robustness of phase retrieval. Our approach is inspired from recent lightfield research that showed defocused images for TIE can be synthesized by a 4D light field based on Fourier slice theory [10]. It has also been proved in [11] that the light field is equivalent to the smoothed Wigner distribution function, and it is further demonstrated in [12] that phase information can be extracted from the local first-order moment of the Wigner distribution function. In this light-field computing regime, a more accurate and robust representation of the axial intensity derivatives can be obtained without the need for optimizing the defocus distance. Acquiring the light-field distribution [13] or phasespace measurement [14] requires either multiplexing the low-resolution 4D light field onto the 2D sensor or enforcing an extensively temporal scanning process. In this Letter, we propose to optically encode the 4D light field into a 2D image pair, which alleviates the sacrifice of spatial or temporal resolution. Our two captured images are complementary to each other to obtain the accurate derivatives of intensity measurement, then the full-sensor resolution phase can be recovered without the need for complete 4D light-field capturing. Although a coded-aperture method has been reported for phase-contrast enhancement [15], the coded aperture we present aims for quantitative phase imaging by using an alternative light-field computing paradigm. We first introduce the mathematical foundations of the coded-aperture pair acquisition scheme for phase retrieval. According to light-field theory [13,16], light field Lx; y; u; v describes a mapping from rays to radiance, as a function of position x; y and direction u; v in the free space (shown on the upper-left corner of [Fig. 1(a)]). © 2014 Optical Society of America
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Fig. 1. Schematic of the CAPPI system (a) and a photograph showing the prototype system (b).
Then, the image I Z x; y captured at the sensor plane is a weighted integral of the light field Lx; y; u; v along its angular dimension u; v over the aperture area Θ: I Z x; y
1 Z2
ZZ Θ
Lx; y; u; vdudv;
(2)
where Z is the focal length of the system. Furthermore, the intensity measurement with axial shift δz from the sensor plane is I Zδz x;y
1 Z2
ZZ
Zx−u Zy−v ;v ;u;v dudv: L u Z δz Z δz Θ (3)
As such, the axial-intensity derivative can be obtained: dIx; y I x; y − I Z x; y lim Zδz δz→0 dz δz ZZ 1 ∂ ∂ uLx; y; u; v vLx; y; u; vdudv 3 ∂x ∂y Z Θ 1 ∂ 1 ∂ 3 B1 x; y 3 B2 x; y; Z ∂x Z ∂y (4) where
RR B1 x; y RRΘ uLx; y; u; vdudv B2 x; y Θ vLx; y; u; vdudv
5
are the linear intensity modulations of the light field along two angular dimensions. In CAPPI, we capture the light-field-encoded image pair B1 x; y and B2 x; y by placing two patterns called the u pattern and v pattern at the aperture plane, respectively. The axial-intensity derivatives can be calculated by taking partial derivatives along the x and y directions of the captured image pair, respectively. Then, the full-sensor resolution phase is estimated by applying a fast-Fourier-transform-based Poisson solver with Tikhonov regularization to solve the TIE in Eq. (1). In light-field microscopy, diffraction indeed places an upper limit on the product of lateral and axial resolution [13]. However, the defocused images generated by the
light field are equivalent to the defocused images generated by the ambiguity function [11], which ensures that the ray approximation of the light field will not affect our approach. Figure 1 shows the schematic of our proposed optical system and a photograph of our prototype setup. We employ a commercial inverted bright-field microscope (Olympus IX73) to produce a magnified image of the specimen at the image plane. A partial coherent whiteLED light source with a green interference filter (central wavelength λ 550 nm) is used to provide illumination for the system. The image plane is relayed by a 4f system (f 1 150 mm, f 2 50 mm) onto the sensor (Point Grey flea2-08S2C). A SLM is placed at the Fourier plane for flexible changing of the coded-aperture patterns. A liquid-crystal-on-silicon (LCoS) display (HOLOEYE LC2012) is employed as the SLM in conjunction with two polarizers, and the SLM achieves amplitude modulation (the pattern displayed on the LCoS has been precalibrated for linear intensity modulation) with a resolution of 1024 × 768 pixels. The experimental results in Fig. 2 demonstrate the accuracy and robustness of our approach for quantitative phase retrieval. We adopt a custom-made plano–convex microlens array, which is made of a plastic material (Cyclic Olefin Copolymer) with excellent optical properties, as the target sample (100 μm pitch, refractive index n 1.53). The objective lens we used in the experiments is the Olympus LUCPlanFLN 20 × 0.45 NA. As shown in Fig. 2, phase-reconstruction results are displayed as the height h of the object in the axial dimension for better visualization, where h φλΔn∕2π and Δn is the differential refractive index between the specimen and environment. Figures 2(a) and 2(b) are the results obtained by the TIE approaches [1] and [4] with different defocus distances, respectively, for a pair of defocused images. Our approach takes a light-field encoded image pair in Fig. 2(c) for full-sensor resolution phase reconstruction as shown in Fig. 2(d). For quantitative comparison, we calculate the normalized root-mean-square error (NRMSE) of the reconstructed results, with respect to the result measured by scanning confocal microscopy (Olympus FV1200). Conventional TIE approaches [1] and [4] are sensitive to the defocus distance. As shown in Figs. 2(a) and 2(b) (left), the axial-intensity derivative suffers from
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OPTICS LETTERS / Vol. 39, No. 19 / October 1, 2014
Fig. 3. Experimental results for unstained colon cancer cells (HCT116). (a) Encoded sensor-image pair. (b) Recovered phase by our approach. (c) The image captured under bright-field mode. (d) The image captured under phase-contrast mode. (e) Recovered phase by approach in [4], with optimal distance.
Fig. 2. Experimental results for a microlens array. (a), (b) Phase estimated by the TIE approach proposed in [1] and [4], with different defocus distances, respectively. (c) Encoded sensor-image pair of our approach. (d) Recovered phase by our approach. (e) Lens thickness cross-sections corresponding to the line profiles indicated in (a), (b), and (d), respectively.
sensor noise under small defocus distances, while large defocus distances deteriorate its accuracy; the reconstruction results with the optimal distance are shown in Figs. 2(a) and 2(b) (right). Our approach captures the coded-aperture image pair in focus, which eliminates the careful adjustment of the defocus distance. In addition, due to more accurate estimation of the axial-intensity derivative, our phase-reconstruction results (NRMSE 0.0312) apparently outperform previous TIE approaches in [1] (NRMSE 0.0399) and [4] (NRMSE 0.0345), with optimized defocus distances. Finally, we compare the microlens thickness cross-sections obtained by different approaches as shown in Fig. 2(e). Our results achieve more faithful reconstruction and better agreement to the confocal microscopy, and the sensitivity of the system is comparable to the confocal microscope. To further validate the proposed approach, the phasereconstruction results of the unstained colon cancer cells (HCT116) are shown in Fig. 3. Figure 3(a) shows the coded-aperture image pair captured with an Olympus UPlanFLN 40 × 0.75 NA objective and their corresponding u pattern and v pattern in the upper-right corner. The reconstructed phase by our approach is shown in Fig. 3(b). Our approach can provide higher contrast and reveal more details of transparent cells, such as nuclei, compared with the bright-field image [Fig. 3(c)], the phasecontrast image [Fig. 3(d)], and the result of the first-order TIE approach [Fig. 3(e)] proposed by [4].
Since the frame rate of the employed SLM is 60 Hz, we conduct an experiment on live cells by dynamically changing two patterns. In the experiment, we investigate the apoptosis of the unstained colon-cancer cells (HCT116) caused by oxidative damages. For this purpose, we use 10 ml DMEM (Dulbecco’s modified Eagle’s medium) high-glucose medium (HyClone SH30022.01), with 10% fetal bovine serum (HyClone) as the feeding media and add 11.33 μl hydrogen peroxide to the medium to cause the oxidative damage to the HCT116 cells. We synchronize the SLM and the camera in software and capture the process with an Olympus UPlanFLN 40 × 0.75 NA objective. Figure 4(a) shows the encoded sensor-image pair captured before the chemical treatment, and Fig. 4(b) is its reconstructed phase. Figure 4(c) is the bright-field image, which is of very low contrast. Although the phasecontrast image in Fig. 4(d) shows high contrast, it’s a nonquantitative approach. Figure 4(e) shows the reconstructed phase of the HCT116 cells’ apoptosis at different stages. Figure 4(f) is the close-up view of the highlighted regions in Fig. 4(b) at different stages. As shown in Figs. 4(e) and 4(f) and Media 1, our quantitative phase retrieval result reveals not only the morphological changing of each cell but also the movement of the cells among the cell clusters. We also demonstrate the application of our approach for fast-moving dynamic events and its flexibility for both micro- and macroscenes. As shown in Fig. 5(a), we implement our coded-aperture pair by using two cameras (Point Grey flea2-08S2C) with the same cameraparameter settings and placing the statistic mask pair at the Fourier plane. A beam splitter is used to duplicate the optical light path, and two cameras are synchronized with a hardware trigger (Trigger Mode 5 of an industrial camera) for highly accurate synchronic light-fieldencoded video-pair acquisition. The light source is a partial-coherence illumination system provided by microscope. With the proposed setup, we image a macroscopic-transparent object, which is two letters (“OL”) written with glue on a glass, and the object is moved by hand. One frame of the reconstructed video (Media 2) is shown in Fig. 5(b). The artifacts are caused by the multiple reflections of the glass sample. The “shadow” around the letters “OL” is caused by the suppression
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Fig. 4. Apoptosis process of the unstained living colon-cancer cells (HCT116). (a) Encoded sensor-image pair before chemical treatment. (b) Recovered phase by our approach. (c) Image captured under bright-field mode. (d) Image captured under phase-contrast mode. (e) The reconstructed phase of the HCT116 cells’ apoptosis process at different stages. (f) The close-up views of highlighted region in (b) at different stages. (Media 1).
coded-aperture image pair in a snapshot and facilitate a wider range of applications. This work was supported by the Project of NSFC (Nos. 61327902, 61120106003, and 61035002). The authors thank Yan Chen for providing the microlens array. †These authors contributed equally to this work.
Fig. 5. Photograph showing the binocular CAPPI system (a) and one frame of our reconstructed result for the macroscene (b) (Media 2).
of the low-frequency components of the phase, which is introduced by the Tikhonov regularization. Although there are small misalignment and color differences between the captured video pair, our approach successfully reconstructs the phase of dynamic objects, which demonstrates its robustness. CAPPI uses a light-field encoded image pair for accurate phase imaging without the capturing of full light-field distributions or requiring z axial scanning. Due to the linear intensity modulation of the aperture coding, the SLM employed in this Letter can be replaced by a low-cost printed mask pair. In addition, our approach can be easily integrated to conventional bright-field microscope with the theoretical light efficiency of 25% (due to the application of the beam splitter and masks). In the future, we would like to develop an optical system to acquire the
References 1. M. R. Teague, J. Opt. Soc. Am. 73, 1434 (1983). 2. J. C. Petruccelli, L. Tian, and G. Barbastathis, Opt. Express 21, 14430 (2013). 3. J. R. Fienup, Appl. Opt. 52, 45 (2013). 4. M. Soto, E. Acosta, and S. Ros, Opt. Express 11, 2577 (2003). 5. L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010). 6. C. Falldorf, M. Agour, and R. B. Bergmann, Appl. Opt. 49, 1826 (2010). 7. C. Zuo, Q. Chen, W. Qu, and A. Asundi, Opt. Lett. 38, 3538 (2013). 8. L. Waller, S. S. Kou, C. J. R. Sheppard, and G. Barbastathis, Opt. Express 18, 22817 (2010). 9. L. Waller, Y. Luo, S. Y. Yang, and G. Barbastathis, Opt. Lett. 35, 2961 (2010). 10. R. Ng, ACM Trans. Graph. 24, 735 (2005). 11. Z. Zhang and M. Levoy, in Proceedings of the ICCP (IEEE, 2009), pp. 1–10. 12. A. Semichaevsky and M. Testorf, J. Opt. Soc. Am. A 21, 2173 (2004). 13. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006). 14. L. Waller, G. Situ, and J. W. Fleischer, Nat. Photonics 6, 474 (2012). 15. T. Kim, S. Sridharan, and G. Popescu, Opt. Express 20, 6737 (2012). 16. M. Levoy and P. Hanrahan, in Proceedings of the ACM SIGGRAPH (ACM, 1996), pp. 31–42.
OPTICS LETTERS / Vol. 39, No. 19 / October 1, 2014
Coded aperture pair for quantitative phase imaging Jiamin Wu,1,2,† Xing Lin,1,2,† Yebin Liu,1,2 Jinli Suo,1,2 and Qionghai Dai1,2,* 1 2
Department of Automation, Tsinghua University, Beijing 100084, China
Beijing Key Laboratory of Multi-dimension & Multi-scale Computational Photography (MMCP), Tsinghua University, Beijing 100084, China *Corresponding author: [email protected] Received June 30, 2014; revised August 31, 2014; accepted September 1, 2014; posted September 2, 2014 (Doc. ID 214114); published October 1, 2014
This Letter proposes a novel quantitative phase-imaging approach by optically encoding light fields into a complementary image pair followed by computational reconstruction. We demonstrate that the axial intensity derivative for phase recovery can be well estimated by a coded-aperture image pair without z axial scanning. The experimental results demonstrate that our approach can achieve higher accuracy and robustness compared with conventional transport-of-intensity equation (TIE) based approaches under partial coherence illumination. © 2014 Optical Society of America OCIS codes: (110.0180) Microscopy; (100.5070) Phase retrieval; (110.1758) Computational imaging; (170.1630) Coded aperture imaging. http://dx.doi.org/10.1364/OL.39.005776
Quantitative phase imaging can be used for recovering the structure or refractive index of a transparent object and has been actively investigated during the past decades because of its extensive applications in various areas, such as astronomy and high-resolution microscopy. Among the large number of phase-imaging approaches, transport-of intensity equation (TIE) based phase-imaging approaches [1] attract lots of attention due to their noninterferometric property, which eliminates the coherence requirements on the illumination. This entails the applicability in bright-field microscope [2]. Moreover, the TIE-based phase-imaging approach is unique because of its quantitative, low-complexity, and noniterative characteristics [3]. Mathematically, TIE reconstructs phase information from a differential intensity measurement: 2π ∂Ix; y −∇Ix; y∇φx; y; λ ∂z
(1)
where x; y denotes the 2D spatial dimensions, z denotes the 1D optical axis, λ is the wavelength of light, I holds the intensity measurements, and φ is the phase (the phase in this Letter refers to optical path length due to the using of partial-coherence illumination). Equation (1) states that the derivative of intensity with respect to the optical axis can be used for inferring phase. Generally, the TIE calculates ∂I∕∂z from a pair of [4] or multiple defocused images [5] captured at different focal planes, and the phase can be recovered by solving a partial differential equation. In order to avoid mechanical movement of the focal plane, a spatial light modulator (SLM) is placed at the Fourier plane so that different defocus distances can be chosen by displaying different phase patterns on the SLM [6]. With an additional beam splitter, two laterally separated images can be captured within a single exposure [7]. Other snapshot approaches such as phase from chromatic aberrations [8] and volume holographic microscope [9] capture multiple defocused images by sacrificing the spatial resolution. Besides low spatial resolution, existing approaches suffer from limited reconstruction accuracy due to the approximation of the axial intensity derivatives using either the first- [7] or higher- [9] order 0146-9592/14/195776-04$15.00/0
difference. Furthermore, these approaches are highly sensitive to the defocus distances whose optimal setting is dependent on the object spatial spectrum and the intensity-measurement noise [4]. Against this backdrop, we present a method using a coded-aperture pair for quantitative phase imaging (CAPPI), which eliminates the aforementioned requirement for changing of the focal plane, and substantially improves the accuracy and robustness of phase retrieval. Our approach is inspired from recent lightfield research that showed defocused images for TIE can be synthesized by a 4D light field based on Fourier slice theory [10]. It has also been proved in [11] that the light field is equivalent to the smoothed Wigner distribution function, and it is further demonstrated in [12] that phase information can be extracted from the local first-order moment of the Wigner distribution function. In this light-field computing regime, a more accurate and robust representation of the axial intensity derivatives can be obtained without the need for optimizing the defocus distance. Acquiring the light-field distribution [13] or phasespace measurement [14] requires either multiplexing the low-resolution 4D light field onto the 2D sensor or enforcing an extensively temporal scanning process. In this Letter, we propose to optically encode the 4D light field into a 2D image pair, which alleviates the sacrifice of spatial or temporal resolution. Our two captured images are complementary to each other to obtain the accurate derivatives of intensity measurement, then the full-sensor resolution phase can be recovered without the need for complete 4D light-field capturing. Although a coded-aperture method has been reported for phase-contrast enhancement [15], the coded aperture we present aims for quantitative phase imaging by using an alternative light-field computing paradigm. We first introduce the mathematical foundations of the coded-aperture pair acquisition scheme for phase retrieval. According to light-field theory [13,16], light field Lx; y; u; v describes a mapping from rays to radiance, as a function of position x; y and direction u; v in the free space (shown on the upper-left corner of [Fig. 1(a)]). © 2014 Optical Society of America
October 1, 2014 / Vol. 39, No. 19 / OPTICS LETTERS
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Fig. 1. Schematic of the CAPPI system (a) and a photograph showing the prototype system (b).
Then, the image I Z x; y captured at the sensor plane is a weighted integral of the light field Lx; y; u; v along its angular dimension u; v over the aperture area Θ: I Z x; y
1 Z2
ZZ Θ
Lx; y; u; vdudv;
(2)
where Z is the focal length of the system. Furthermore, the intensity measurement with axial shift δz from the sensor plane is I Zδz x;y
1 Z2
ZZ
Zx−u Zy−v ;v ;u;v dudv: L u Z δz Z δz Θ (3)
As such, the axial-intensity derivative can be obtained: dIx; y I x; y − I Z x; y lim Zδz δz→0 dz δz ZZ 1 ∂ ∂ uLx; y; u; v vLx; y; u; vdudv 3 ∂x ∂y Z Θ 1 ∂ 1 ∂ 3 B1 x; y 3 B2 x; y; Z ∂x Z ∂y (4) where
RR B1 x; y RRΘ uLx; y; u; vdudv B2 x; y Θ vLx; y; u; vdudv
5
are the linear intensity modulations of the light field along two angular dimensions. In CAPPI, we capture the light-field-encoded image pair B1 x; y and B2 x; y by placing two patterns called the u pattern and v pattern at the aperture plane, respectively. The axial-intensity derivatives can be calculated by taking partial derivatives along the x and y directions of the captured image pair, respectively. Then, the full-sensor resolution phase is estimated by applying a fast-Fourier-transform-based Poisson solver with Tikhonov regularization to solve the TIE in Eq. (1). In light-field microscopy, diffraction indeed places an upper limit on the product of lateral and axial resolution [13]. However, the defocused images generated by the
light field are equivalent to the defocused images generated by the ambiguity function [11], which ensures that the ray approximation of the light field will not affect our approach. Figure 1 shows the schematic of our proposed optical system and a photograph of our prototype setup. We employ a commercial inverted bright-field microscope (Olympus IX73) to produce a magnified image of the specimen at the image plane. A partial coherent whiteLED light source with a green interference filter (central wavelength λ 550 nm) is used to provide illumination for the system. The image plane is relayed by a 4f system (f 1 150 mm, f 2 50 mm) onto the sensor (Point Grey flea2-08S2C). A SLM is placed at the Fourier plane for flexible changing of the coded-aperture patterns. A liquid-crystal-on-silicon (LCoS) display (HOLOEYE LC2012) is employed as the SLM in conjunction with two polarizers, and the SLM achieves amplitude modulation (the pattern displayed on the LCoS has been precalibrated for linear intensity modulation) with a resolution of 1024 × 768 pixels. The experimental results in Fig. 2 demonstrate the accuracy and robustness of our approach for quantitative phase retrieval. We adopt a custom-made plano–convex microlens array, which is made of a plastic material (Cyclic Olefin Copolymer) with excellent optical properties, as the target sample (100 μm pitch, refractive index n 1.53). The objective lens we used in the experiments is the Olympus LUCPlanFLN 20 × 0.45 NA. As shown in Fig. 2, phase-reconstruction results are displayed as the height h of the object in the axial dimension for better visualization, where h φλΔn∕2π and Δn is the differential refractive index between the specimen and environment. Figures 2(a) and 2(b) are the results obtained by the TIE approaches [1] and [4] with different defocus distances, respectively, for a pair of defocused images. Our approach takes a light-field encoded image pair in Fig. 2(c) for full-sensor resolution phase reconstruction as shown in Fig. 2(d). For quantitative comparison, we calculate the normalized root-mean-square error (NRMSE) of the reconstructed results, with respect to the result measured by scanning confocal microscopy (Olympus FV1200). Conventional TIE approaches [1] and [4] are sensitive to the defocus distance. As shown in Figs. 2(a) and 2(b) (left), the axial-intensity derivative suffers from
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OPTICS LETTERS / Vol. 39, No. 19 / October 1, 2014
Fig. 3. Experimental results for unstained colon cancer cells (HCT116). (a) Encoded sensor-image pair. (b) Recovered phase by our approach. (c) The image captured under bright-field mode. (d) The image captured under phase-contrast mode. (e) Recovered phase by approach in [4], with optimal distance.
Fig. 2. Experimental results for a microlens array. (a), (b) Phase estimated by the TIE approach proposed in [1] and [4], with different defocus distances, respectively. (c) Encoded sensor-image pair of our approach. (d) Recovered phase by our approach. (e) Lens thickness cross-sections corresponding to the line profiles indicated in (a), (b), and (d), respectively.
sensor noise under small defocus distances, while large defocus distances deteriorate its accuracy; the reconstruction results with the optimal distance are shown in Figs. 2(a) and 2(b) (right). Our approach captures the coded-aperture image pair in focus, which eliminates the careful adjustment of the defocus distance. In addition, due to more accurate estimation of the axial-intensity derivative, our phase-reconstruction results (NRMSE 0.0312) apparently outperform previous TIE approaches in [1] (NRMSE 0.0399) and [4] (NRMSE 0.0345), with optimized defocus distances. Finally, we compare the microlens thickness cross-sections obtained by different approaches as shown in Fig. 2(e). Our results achieve more faithful reconstruction and better agreement to the confocal microscopy, and the sensitivity of the system is comparable to the confocal microscope. To further validate the proposed approach, the phasereconstruction results of the unstained colon cancer cells (HCT116) are shown in Fig. 3. Figure 3(a) shows the coded-aperture image pair captured with an Olympus UPlanFLN 40 × 0.75 NA objective and their corresponding u pattern and v pattern in the upper-right corner. The reconstructed phase by our approach is shown in Fig. 3(b). Our approach can provide higher contrast and reveal more details of transparent cells, such as nuclei, compared with the bright-field image [Fig. 3(c)], the phasecontrast image [Fig. 3(d)], and the result of the first-order TIE approach [Fig. 3(e)] proposed by [4].
Since the frame rate of the employed SLM is 60 Hz, we conduct an experiment on live cells by dynamically changing two patterns. In the experiment, we investigate the apoptosis of the unstained colon-cancer cells (HCT116) caused by oxidative damages. For this purpose, we use 10 ml DMEM (Dulbecco’s modified Eagle’s medium) high-glucose medium (HyClone SH30022.01), with 10% fetal bovine serum (HyClone) as the feeding media and add 11.33 μl hydrogen peroxide to the medium to cause the oxidative damage to the HCT116 cells. We synchronize the SLM and the camera in software and capture the process with an Olympus UPlanFLN 40 × 0.75 NA objective. Figure 4(a) shows the encoded sensor-image pair captured before the chemical treatment, and Fig. 4(b) is its reconstructed phase. Figure 4(c) is the bright-field image, which is of very low contrast. Although the phasecontrast image in Fig. 4(d) shows high contrast, it’s a nonquantitative approach. Figure 4(e) shows the reconstructed phase of the HCT116 cells’ apoptosis at different stages. Figure 4(f) is the close-up view of the highlighted regions in Fig. 4(b) at different stages. As shown in Figs. 4(e) and 4(f) and Media 1, our quantitative phase retrieval result reveals not only the morphological changing of each cell but also the movement of the cells among the cell clusters. We also demonstrate the application of our approach for fast-moving dynamic events and its flexibility for both micro- and macroscenes. As shown in Fig. 5(a), we implement our coded-aperture pair by using two cameras (Point Grey flea2-08S2C) with the same cameraparameter settings and placing the statistic mask pair at the Fourier plane. A beam splitter is used to duplicate the optical light path, and two cameras are synchronized with a hardware trigger (Trigger Mode 5 of an industrial camera) for highly accurate synchronic light-fieldencoded video-pair acquisition. The light source is a partial-coherence illumination system provided by microscope. With the proposed setup, we image a macroscopic-transparent object, which is two letters (“OL”) written with glue on a glass, and the object is moved by hand. One frame of the reconstructed video (Media 2) is shown in Fig. 5(b). The artifacts are caused by the multiple reflections of the glass sample. The “shadow” around the letters “OL” is caused by the suppression
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Fig. 4. Apoptosis process of the unstained living colon-cancer cells (HCT116). (a) Encoded sensor-image pair before chemical treatment. (b) Recovered phase by our approach. (c) Image captured under bright-field mode. (d) Image captured under phase-contrast mode. (e) The reconstructed phase of the HCT116 cells’ apoptosis process at different stages. (f) The close-up views of highlighted region in (b) at different stages. (Media 1).
coded-aperture image pair in a snapshot and facilitate a wider range of applications. This work was supported by the Project of NSFC (Nos. 61327902, 61120106003, and 61035002). The authors thank Yan Chen for providing the microlens array. †These authors contributed equally to this work.
Fig. 5. Photograph showing the binocular CAPPI system (a) and one frame of our reconstructed result for the macroscene (b) (Media 2).
of the low-frequency components of the phase, which is introduced by the Tikhonov regularization. Although there are small misalignment and color differences between the captured video pair, our approach successfully reconstructs the phase of dynamic objects, which demonstrates its robustness. CAPPI uses a light-field encoded image pair for accurate phase imaging without the capturing of full light-field distributions or requiring z axial scanning. Due to the linear intensity modulation of the aperture coding, the SLM employed in this Letter can be replaced by a low-cost printed mask pair. In addition, our approach can be easily integrated to conventional bright-field microscope with the theoretical light efficiency of 25% (due to the application of the beam splitter and masks). In the future, we would like to develop an optical system to acquire the
References 1. M. R. Teague, J. Opt. Soc. Am. 73, 1434 (1983). 2. J. C. Petruccelli, L. Tian, and G. Barbastathis, Opt. Express 21, 14430 (2013). 3. J. R. Fienup, Appl. Opt. 52, 45 (2013). 4. M. Soto, E. Acosta, and S. Ros, Opt. Express 11, 2577 (2003). 5. L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010). 6. C. Falldorf, M. Agour, and R. B. Bergmann, Appl. Opt. 49, 1826 (2010). 7. C. Zuo, Q. Chen, W. Qu, and A. Asundi, Opt. Lett. 38, 3538 (2013). 8. L. Waller, S. S. Kou, C. J. R. Sheppard, and G. Barbastathis, Opt. Express 18, 22817 (2010). 9. L. Waller, Y. Luo, S. Y. Yang, and G. Barbastathis, Opt. Lett. 35, 2961 (2010). 10. R. Ng, ACM Trans. Graph. 24, 735 (2005). 11. Z. Zhang and M. Levoy, in Proceedings of the ICCP (IEEE, 2009), pp. 1–10. 12. A. Semichaevsky and M. Testorf, J. Opt. Soc. Am. A 21, 2173 (2004). 13. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006). 14. L. Waller, G. Situ, and J. W. Fleischer, Nat. Photonics 6, 474 (2012). 15. T. Kim, S. Sridharan, and G. Popescu, Opt. Express 20, 6737 (2012). 16. M. Levoy and P. Hanrahan, in Proceedings of the ACM SIGGRAPH (ACM, 1996), pp. 31–42.
