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Subsurface imaging by dual-medium quantitative phase measurement
Optik 124 (2013) 4729–4733
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Subsurface imaging by dual-medium quantitative phase measurement Naifei Ren a , Weifeng Jin a,∗ , Yawei Wang a,b a b
School of Mechanical Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China
a r t i c l e
i n f o
Article history: Received 9 September 2012 Accepted 24 January 2013
Keywords: Digital holography Phase measurement Subsurface imaging Cell analysis
a b s t r a c t Quantitative phase imaging by itself allows for direct surface imaging of the transparent homogeneous sample, but it is very difficult or impossible for the inhomogeneous sample by itself due to the surface morphology and subsurface information are coupled. We hereby propose a simple method which obtains quantitative phase data and the physical thickness of sample by dual-medium quantitative phase measurement (DMQ) to extract subsurface sample information without the need of any exogenous dyes and any scan process. By using simulation technology, the feasibility of this method is demonstrated with subsurface imaging of a two-sphere model and a simulated monocyte. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Translucent specimens such as biological cells lack of contrast inherent, and thus are difficult to image using conventional optical microscopy techniques. Although using staining techniques can solve this problem, the exogenous contrast agents such as fluorescent dyes used in these techniques often have a deleterious effect on the specimen sample. By using phase microscopy such as Zernike phase contrast microscopy and Nomarski differential interference contrast microscopy, which converts the phase shift of light passing through the cells to intensity variation, can also solve the contrast problem when imaging the cells, but they do not allow extracting the quantitative optical phase shift, which include the sample thickness and refractive index. Recently, various quantitative phase microscopy techniques (QPM) have been proposed for quantitative phase imaging of transparent biological specimens [1–16]. Due to that mature red blood cells (RBCs) have no nucleus, they can be assumed as homogenous biological specimens and thus their thickness profile can be obtained directly from their phase profile. Therefore many QPM techniques have been successfully applied to the study of the surface morphology and dynamic parameters of RBCs [8–16]. However, most biological cells are nucleated and contain several other subsurface organelles, and only their certain information such as cell area, dry mass can be gotten directly from the phase information [17,18]. Their
∗ Corresponding author. E-mail address: [email protected] (W. Jin). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.01.118
intracellular information such as the size, shape, volume and surface roughness of organelles are often ignored, which provides critical information for diagnostic purposes. Thus by using QPM, one of the crucial issues of studies on such cells is to separate the valuable subsurface information from the phase data, which contains the coupling surface information. In recent research, decoupling the thickness and integrated refractive index of heterogeneous cells has been demonstrated by many methods such as combining QPM with other microscopy techniques [13,19–22], utilizing different molecular contents dispersion [23–25] and by using two different surrounding liquid mediums with slightly different refractive indices [26,27]. However, decoupling the valuable subsurface information from the phase data has scarcely mentioned in each method. Kert Edward et al proposed a procedure in which both quantitative phase and shear-force feedback topography data are simultaneous obtained to extract subsurface sample information [28]. Through this method they have successfully extracted the subsurface information of the nucleated fish red blood cells, but their method is complicated and time-consuming due to the need of a custom built near field scanning optical microscope. In this paper, we present a simple method to extract subsurface sample information by using single QPM technique. Unlike Kert Edward’s method, in which the cell’s thickness is obtained by using near field scanning optical microscope, the physical thickness of cells in our method is extracted by employing the dual-medium quantitative phase measurement (DMQ), which has been demonstrated to be an effective method for simultaneously extracting the physical thickness and integrated refractive index of cells in our previous works [29,30]. Thus our method is a simple method
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Fig. 1. (a) A nucleated cell in a perfusion chamber. (b) The typical characteristic of a relatively simple cell with a single major intracellular component in its axially averaged refractive index map.
without the need for any exogenous dyes and any scanning processes, and is very suitable for subsurface imaging of individual cells. Through computer simulation, this method was initially applied to the subsurface imaging of a relatively simple twosphere model. The shape and height of the inside small sphere were extracted with highly accuracy. The subsurface of a simulated monocyte was also imaged by this method without knowing the refractive indices of its cytoplasm or nucleus. In addition, the size of its nucleus was determined by assuming refractive index of the nucleus was known. 2. Theory Consider a simple nucleated biological cell with physical thickness of h1 and nucleus thickness of h2 , as shown in Fig. 1(a). The biological cell is in a perfusion chamber with height of h0 , which is filled with the medium. The refractive indices of the cytoplasm, the nucleus and the surrounding medium are given by n1 , n2 and nm , respectively. The phase (ı) induced by the specimen can be expressed by ı=
2 [nm h0 + h1 (n1 − nm ) + h2 (n2 − n1 )],
(1)
where is the wavelength of the laser. Removing the reference value 2nm h0 /, which can be measured anywhere outside the cell, we obtain the phase shifting induced by the biological cell as: =
2 [h1 (n1 − nm ) + h2 (n2 − n1 )].
(2)
Therefore the subsurface feature height h2 is given by h2 =
2 h1 (n1 − nm ) . − 2(n2 − n1 )
(3)
As we all know, if n1 , n2 and nm were known in Eq. (3), the crucial issue of solving h2 turns into solving h1 . To obtain the physical thickness h1 of translucent samples, DMQ was utilized in this research. The details of its theory are published elsewhere [30]. Using DMQ, the physical thickness h2 and the axially averaged refractive index can be determined by the formulas h1 =
/2(1 − 2 ) , nm2 − nm1
(4)
nc =
1 nm2 − 2 nm1 , 1 − 2
(5)
where ϕ1 and ϕ2 are the phase shifts induced by the biological cell in the surrounding medium with refractive indices of nm1 and nm2 , respectively. For relatively simple cells with a single major intracellular component such as monocyte, the characteristic of the axially averaged refractive index map is shown in Fig. 1(b). It can be seen that the axially averaged refractive indices in some areas equal n1 , and those in others are between n1 and n2 . Thus the refractive indices of the
Fig. 2. The sketch maps of three models. (a) Two-sphere model. (b) One-sphere model with a protuberance. (c) A simulated monocyte.
cytoplasm n1 can be gotten from the extracted the axially averaged refractive index map. Therefore, for relatively simple cells, as long as the refractive index of surrounding medium is known, the morphology of its subsurface, which is proportional to optical thickness of the nucleus, can be gotten by using DMQ. If the refractive index of nucleus is also known, the subsurface feature height can be obtained by Eq. (3). 3. Numerical simulations To verify this method for subsurface imaging, the numerical simulation for a phase shift digital holography system was carried out. The flow chart of the numerical simulation for obtaining the physical thickness and the axially averaged refractive index of the cell by DMQ is detailed in Ref. [30]. The followings are the mainly steps of the numerical simulation for subsurface imaging of the sample. The first step of simulation is to build the model of translucent specimen. In our simulation, as shown in Fig. 2(a)–(c), a two-sphere model, a one-sphere model with a protuberance and a simulated monocyte were used as the imaged objects. The diameter and the refractive index of the large sphere and the small sphere in the twosphere model were set to 12 m, 1.37, 6 m and 1.39, respectively. The one-sphere model with a protuberance was considered to be homogeneous with the refractive index 1.37 and its sphere of diameter 12 m. The mainly morphology parameters of the monocyte model were obtained from Kert Edward’s work [31]. The refractive indices of its cytoplasm and nucleus were given by 1.37 and 1.39, respectively. The next step is to set parameters for simulating a phase shift digital holography system to get the quantitative phase information of the sample. In our simulation, the incident wave is a plate wave with the wavelength 632.8 nm. The reference wave has the same wavelength as the incident wave with the initial phase of zero. The other values of the fundamental parameters involved in the simulation are: nm1 = 1.34, nm2 = 1.345 and h0 = 30 m. To simplify the calculation, the amplitude of the incident wave and reference wave are assumed to be 1. Then the physical thickness h1 and the axially averaged refractive index nc can be calculated by Eq. (4) and Eq. (5) using DMQ. The simulation process of DMQ is detailed in elsewhere [30]. For the relatively simple sample with a single major internal component, when the axially averaged refractive index map has been gotten, the refractive index of the outer layer can be obtained. Thus the optical thickness of the internal component, which refracts the morphology of subsurface when the internal component is homogeneous, can be calculated through computer simulation. Assuming the refractive index of internal component is known, its physical thickness also can be obtained by computing. 4. Results and discussion With the medium of refractive index nm1 = 1.34, we obtained the unwrapped phase images of the two-sphere model and one-sphere model with a protuberance as shown in Fig. 3(a) and
N. Ren et al. / Optik 124 (2013) 4729–4733
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Fig. 3. The results of two-sphere model, (a) the unwrapped phase, (c) the thickness, (f) the axially averaged refractive index. The results of one-sphere model with a protuberance, (b) the unwrapped phase, (d) the thickness, (g) the axially averaged refractive index. (e) The central horizontal sections of the phase maps (a) and (b).
(b), respectively. From these two figures, we can see that the phase shifting induced by the two-sphere model is similar to that induced by the one-sphere model with a protuberance. Through intercepting the profiles, which is shown in Fig. 3(e), we find that the phase profiles of the two models are the same. That is to say we cannot determine the structure of a sample from its phase map due to that the phase maps of different structure samples may be the same. It indicates that it is necessary to image subsurface of a sample to distinguish samples. For subsurface imaging of the two models, their physical thicknesses and the axially averaged refractive indices were obtained by using DMQ, as shown in Fig. 3(c), (d), (f) and (g). The surface structures of the two models are well reproduced in Fig. 3(c) and (g). Compared Fig. 3(a) and (b) with Fig. 3(c) and (d), we found that the surface structure of two-sphere model is distinct from the profile of phase map, while that of one-sphere model with a protuberance agrees well with the profile of its phase map. It confirms that the phase profile of the homogeneous object reflects its morphology, which is widely applied in the research on RBCs [8–16]. However, whether the translucent specimen is homogeneous or not is not known in advance in most cases. To address this issue, the axially averaged refractive index map can be a good helper. As shown in Fig. 3(f) and (g), the axially averaged refractive index of two-sphere model is different in different areas and that of onesphere model with a protuberance is the same value everywhere. It indicates that the two-sphere model is inhomogeneous and onesphere model with a protuberance is homogeneous, which consists with our settings. Since the two-sphere model is inhomogeneous, subsurface imaging is necessary for understanding its structure. It is important to note that its axially averaged refractive indices are the same in the outer layer. Thus we treat the value 1.37 at point A in the outer layer in Fig. 3(f) as the refractive index of the large sphere, which is set to be the same value. It indicates that using this method, the refractive index of the outer layer of the sample can be obtained for such relatively simple sample with a single major internal component. When the refractive index of the large sphere has been gotten, the optical thickness of the internal small sphere can be calculated by H0 = [˚1 − 2h1 (n1 − nm1 )/]/2 as shown in Fig. 4(a). Assuming that the internal component is homogeneous and the refractive index of internal small sphere is 1.39, the physical thickness of the internal small sphere, which also called subsurface feature height of the two-sphere model, can be calculated by Eq. (3), as shown in Fig. 4(b). From Fig. 4(b), it can be seen that the subsurface feature of the two-sphere model is well reproduced. By comparing Fig. 4(a) and (b), the profile of the optical thickness of internal component is similar to that of its physical thickness, which well expresses the
morphology of internal component. That is to say the optical thickness of internal component can be used to express the morphology of internal component when the internal component is homogeneous, which also can be confirmed by H0 = h2 (n2 − n1 ) when n1 and n2 are the constant values. To verify the ability of this method for getting subsurface feature height, the horizontal sections of the original and calculated physical thickness of internal sphere are given in Fig. 3(c). Clearly, the calculated physical thickness curve (circle line) agrees well with the original physical thickness curve (solid line). Fig. 5(a) is the unwrapped phase image of the simulated monocyte with the medium of refractive index nm1 = 1.34. From this figure, we can see that there is an elliptical area with higher phase in the cell area. Fig. 5(b) shows the experimental phase map of a monocyte in air [31], which also has an elliptical area with higher phase. From these two images, it can be seen that our simulated phase image of the monocyte is similar to that of the experiment, which confirms the reliability of our simulation in phase imaging. For subsurface imaging, the physical thickness and the axially averaged refractive index of the monocyte are obtained by using DMQ, as shown in Fig. 5(c) and (d). In Fig. 5(c), the surface morphology of
Fig. 4. The simulated results of the substructure of the two-sphere model. (a) The optical thickness. (b) The physical thickness. (c) The central horizontal sections of the original and calculated physical thickness.
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a simulated monocyte depicted a bean-shaped nucleus, implying that this subsurface imaging method is a useful one allowing for the identification of white blood cells. Therefore, our work will take a significant role in the experimental research on the cells, including guiding the experimental design, saving the experimental time and costs, and verifying the experiment data. Acknowledgements The authors gratefully acknowledge the support from the Natural Science Fund for Colleges and Universities in Jiangsu Province (No. 09KJA140001), the Research Innovation Program for College Graduates of Jiangsu Province (No. CXLX11 0564), and PAPD (A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions). References
Fig. 5. (a) The unwrapped phase map of the simulated monocyte in the surrounding medium of the refractive index 1.34. (b) The experimental phase image of a monocyte in the air [31]. The other simulated results of the monocyte are in (c)–(f). (c) The physical thickness. (d) The extracted axially averaged refractive index. (e) The optical thickness and (f) the physical thickness of its nucleus.
the monocyte can be seen clearly. From Fig. 5(d), we can note that the axially averaged refractive indices are the same in the outer layer of cell. Based on this characteristic of the axially averaged refractive index map, we treat the value 1.37 at point B in the outer layer in Fig. 5(d) as the refractive index of the cytoplasm, which is the same as the original value 1.37. After the physical thickness and the refractive index of the cytoplasm have been gotten, the optical thickness of nucleus can be calculated and the subsurface feature height of nucleus also can be obtained assuming that the refractive index of nucleus is 1.39, as shown in Fig. 5(e) and (f). In both Fig. 5(e) and (f), the nucleus of the monocyte has a bean-shaped appearance as is typical for these cells. And the size of the nucleus can be easily gotten from the Fig. 5(f). Therefore this subsurface imaging method is a useful one allowing for the identification of white blood cells without the need for any exogenous dyes and any scanning processes. 5. Conclusions We have proposed a simple method which allows for examining the subsurface specimen/sample features. To get the physical thickness of sample, this method is based on DMQ and thus does not need any exogenous dyes and any scanning processes. For the relatively simple sample with a single major internal component, the refractive index of the outer layer of sample could be gotten from the axially averaged refractive index map, indicating that the current method can be used for subsurface imaging sample with unknown refractive index. By simulating phase shift induced by a two-sphere model and a homogeneous one-sphere model with a protuberance, we found that it is necessary to image subsurface for nucleated samples due to the same phase induced by the different substructure samples. And the extracted shape and size of substructure of two-sphere model agree well with the original ones, which confirms the feasibility of our method. The resultant subsurface of
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[27] B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, P. Marquet, Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer, Cytom. Part A 73A (2008) 895–903. [28] K. Edward1, F. Farahi, R. Hocken, Hybrid shear force feedback/scanning quantitative phase microscopy applied to subsurface imaging, Opt. Express 17 (2009) 18408–18418. [29] W.F. Jin, Y.W. Wang, N.F. Ren, M. Bu, X.F. Shang, Y.Y. Xu, Y.J. Chen, Simulation of simultaneous measurement for red blood cell thickness and refractive index, Opt. Laser. Eng. 50 (2012) 154–158. [30] Y.W. Wang, W.F. Jin, N.F. Ren, Dual-medium quantitative measurement simulation on cells, Appl. Opt. 50 (2011) 6440–6445. [31] K. Edward, Intracellular subsurface imaging using a hybrid shear force feedback/scanning quantitative phase microscopy technique, The University of North Carolina at Charlotte, 2009 (Ph.D. dissertation).
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Subsurface imaging by dual-medium quantitative phase measurement Naifei Ren a , Weifeng Jin a,∗ , Yawei Wang a,b a b
School of Mechanical Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China
a r t i c l e
i n f o
Article history: Received 9 September 2012 Accepted 24 January 2013
Keywords: Digital holography Phase measurement Subsurface imaging Cell analysis
a b s t r a c t Quantitative phase imaging by itself allows for direct surface imaging of the transparent homogeneous sample, but it is very difficult or impossible for the inhomogeneous sample by itself due to the surface morphology and subsurface information are coupled. We hereby propose a simple method which obtains quantitative phase data and the physical thickness of sample by dual-medium quantitative phase measurement (DMQ) to extract subsurface sample information without the need of any exogenous dyes and any scan process. By using simulation technology, the feasibility of this method is demonstrated with subsurface imaging of a two-sphere model and a simulated monocyte. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Translucent specimens such as biological cells lack of contrast inherent, and thus are difficult to image using conventional optical microscopy techniques. Although using staining techniques can solve this problem, the exogenous contrast agents such as fluorescent dyes used in these techniques often have a deleterious effect on the specimen sample. By using phase microscopy such as Zernike phase contrast microscopy and Nomarski differential interference contrast microscopy, which converts the phase shift of light passing through the cells to intensity variation, can also solve the contrast problem when imaging the cells, but they do not allow extracting the quantitative optical phase shift, which include the sample thickness and refractive index. Recently, various quantitative phase microscopy techniques (QPM) have been proposed for quantitative phase imaging of transparent biological specimens [1–16]. Due to that mature red blood cells (RBCs) have no nucleus, they can be assumed as homogenous biological specimens and thus their thickness profile can be obtained directly from their phase profile. Therefore many QPM techniques have been successfully applied to the study of the surface morphology and dynamic parameters of RBCs [8–16]. However, most biological cells are nucleated and contain several other subsurface organelles, and only their certain information such as cell area, dry mass can be gotten directly from the phase information [17,18]. Their
∗ Corresponding author. E-mail address: [email protected] (W. Jin). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.01.118
intracellular information such as the size, shape, volume and surface roughness of organelles are often ignored, which provides critical information for diagnostic purposes. Thus by using QPM, one of the crucial issues of studies on such cells is to separate the valuable subsurface information from the phase data, which contains the coupling surface information. In recent research, decoupling the thickness and integrated refractive index of heterogeneous cells has been demonstrated by many methods such as combining QPM with other microscopy techniques [13,19–22], utilizing different molecular contents dispersion [23–25] and by using two different surrounding liquid mediums with slightly different refractive indices [26,27]. However, decoupling the valuable subsurface information from the phase data has scarcely mentioned in each method. Kert Edward et al proposed a procedure in which both quantitative phase and shear-force feedback topography data are simultaneous obtained to extract subsurface sample information [28]. Through this method they have successfully extracted the subsurface information of the nucleated fish red blood cells, but their method is complicated and time-consuming due to the need of a custom built near field scanning optical microscope. In this paper, we present a simple method to extract subsurface sample information by using single QPM technique. Unlike Kert Edward’s method, in which the cell’s thickness is obtained by using near field scanning optical microscope, the physical thickness of cells in our method is extracted by employing the dual-medium quantitative phase measurement (DMQ), which has been demonstrated to be an effective method for simultaneously extracting the physical thickness and integrated refractive index of cells in our previous works [29,30]. Thus our method is a simple method
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Fig. 1. (a) A nucleated cell in a perfusion chamber. (b) The typical characteristic of a relatively simple cell with a single major intracellular component in its axially averaged refractive index map.
without the need for any exogenous dyes and any scanning processes, and is very suitable for subsurface imaging of individual cells. Through computer simulation, this method was initially applied to the subsurface imaging of a relatively simple twosphere model. The shape and height of the inside small sphere were extracted with highly accuracy. The subsurface of a simulated monocyte was also imaged by this method without knowing the refractive indices of its cytoplasm or nucleus. In addition, the size of its nucleus was determined by assuming refractive index of the nucleus was known. 2. Theory Consider a simple nucleated biological cell with physical thickness of h1 and nucleus thickness of h2 , as shown in Fig. 1(a). The biological cell is in a perfusion chamber with height of h0 , which is filled with the medium. The refractive indices of the cytoplasm, the nucleus and the surrounding medium are given by n1 , n2 and nm , respectively. The phase (ı) induced by the specimen can be expressed by ı=
2 [nm h0 + h1 (n1 − nm ) + h2 (n2 − n1 )],
(1)
where is the wavelength of the laser. Removing the reference value 2nm h0 /, which can be measured anywhere outside the cell, we obtain the phase shifting induced by the biological cell as: =
2 [h1 (n1 − nm ) + h2 (n2 − n1 )].
(2)
Therefore the subsurface feature height h2 is given by h2 =
2 h1 (n1 − nm ) . − 2(n2 − n1 )
(3)
As we all know, if n1 , n2 and nm were known in Eq. (3), the crucial issue of solving h2 turns into solving h1 . To obtain the physical thickness h1 of translucent samples, DMQ was utilized in this research. The details of its theory are published elsewhere [30]. Using DMQ, the physical thickness h2 and the axially averaged refractive index can be determined by the formulas h1 =
/2(1 − 2 ) , nm2 − nm1
(4)
nc =
1 nm2 − 2 nm1 , 1 − 2
(5)
where ϕ1 and ϕ2 are the phase shifts induced by the biological cell in the surrounding medium with refractive indices of nm1 and nm2 , respectively. For relatively simple cells with a single major intracellular component such as monocyte, the characteristic of the axially averaged refractive index map is shown in Fig. 1(b). It can be seen that the axially averaged refractive indices in some areas equal n1 , and those in others are between n1 and n2 . Thus the refractive indices of the
Fig. 2. The sketch maps of three models. (a) Two-sphere model. (b) One-sphere model with a protuberance. (c) A simulated monocyte.
cytoplasm n1 can be gotten from the extracted the axially averaged refractive index map. Therefore, for relatively simple cells, as long as the refractive index of surrounding medium is known, the morphology of its subsurface, which is proportional to optical thickness of the nucleus, can be gotten by using DMQ. If the refractive index of nucleus is also known, the subsurface feature height can be obtained by Eq. (3). 3. Numerical simulations To verify this method for subsurface imaging, the numerical simulation for a phase shift digital holography system was carried out. The flow chart of the numerical simulation for obtaining the physical thickness and the axially averaged refractive index of the cell by DMQ is detailed in Ref. [30]. The followings are the mainly steps of the numerical simulation for subsurface imaging of the sample. The first step of simulation is to build the model of translucent specimen. In our simulation, as shown in Fig. 2(a)–(c), a two-sphere model, a one-sphere model with a protuberance and a simulated monocyte were used as the imaged objects. The diameter and the refractive index of the large sphere and the small sphere in the twosphere model were set to 12 m, 1.37, 6 m and 1.39, respectively. The one-sphere model with a protuberance was considered to be homogeneous with the refractive index 1.37 and its sphere of diameter 12 m. The mainly morphology parameters of the monocyte model were obtained from Kert Edward’s work [31]. The refractive indices of its cytoplasm and nucleus were given by 1.37 and 1.39, respectively. The next step is to set parameters for simulating a phase shift digital holography system to get the quantitative phase information of the sample. In our simulation, the incident wave is a plate wave with the wavelength 632.8 nm. The reference wave has the same wavelength as the incident wave with the initial phase of zero. The other values of the fundamental parameters involved in the simulation are: nm1 = 1.34, nm2 = 1.345 and h0 = 30 m. To simplify the calculation, the amplitude of the incident wave and reference wave are assumed to be 1. Then the physical thickness h1 and the axially averaged refractive index nc can be calculated by Eq. (4) and Eq. (5) using DMQ. The simulation process of DMQ is detailed in elsewhere [30]. For the relatively simple sample with a single major internal component, when the axially averaged refractive index map has been gotten, the refractive index of the outer layer can be obtained. Thus the optical thickness of the internal component, which refracts the morphology of subsurface when the internal component is homogeneous, can be calculated through computer simulation. Assuming the refractive index of internal component is known, its physical thickness also can be obtained by computing. 4. Results and discussion With the medium of refractive index nm1 = 1.34, we obtained the unwrapped phase images of the two-sphere model and one-sphere model with a protuberance as shown in Fig. 3(a) and
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Fig. 3. The results of two-sphere model, (a) the unwrapped phase, (c) the thickness, (f) the axially averaged refractive index. The results of one-sphere model with a protuberance, (b) the unwrapped phase, (d) the thickness, (g) the axially averaged refractive index. (e) The central horizontal sections of the phase maps (a) and (b).
(b), respectively. From these two figures, we can see that the phase shifting induced by the two-sphere model is similar to that induced by the one-sphere model with a protuberance. Through intercepting the profiles, which is shown in Fig. 3(e), we find that the phase profiles of the two models are the same. That is to say we cannot determine the structure of a sample from its phase map due to that the phase maps of different structure samples may be the same. It indicates that it is necessary to image subsurface of a sample to distinguish samples. For subsurface imaging of the two models, their physical thicknesses and the axially averaged refractive indices were obtained by using DMQ, as shown in Fig. 3(c), (d), (f) and (g). The surface structures of the two models are well reproduced in Fig. 3(c) and (g). Compared Fig. 3(a) and (b) with Fig. 3(c) and (d), we found that the surface structure of two-sphere model is distinct from the profile of phase map, while that of one-sphere model with a protuberance agrees well with the profile of its phase map. It confirms that the phase profile of the homogeneous object reflects its morphology, which is widely applied in the research on RBCs [8–16]. However, whether the translucent specimen is homogeneous or not is not known in advance in most cases. To address this issue, the axially averaged refractive index map can be a good helper. As shown in Fig. 3(f) and (g), the axially averaged refractive index of two-sphere model is different in different areas and that of onesphere model with a protuberance is the same value everywhere. It indicates that the two-sphere model is inhomogeneous and onesphere model with a protuberance is homogeneous, which consists with our settings. Since the two-sphere model is inhomogeneous, subsurface imaging is necessary for understanding its structure. It is important to note that its axially averaged refractive indices are the same in the outer layer. Thus we treat the value 1.37 at point A in the outer layer in Fig. 3(f) as the refractive index of the large sphere, which is set to be the same value. It indicates that using this method, the refractive index of the outer layer of the sample can be obtained for such relatively simple sample with a single major internal component. When the refractive index of the large sphere has been gotten, the optical thickness of the internal small sphere can be calculated by H0 = [˚1 − 2h1 (n1 − nm1 )/]/2 as shown in Fig. 4(a). Assuming that the internal component is homogeneous and the refractive index of internal small sphere is 1.39, the physical thickness of the internal small sphere, which also called subsurface feature height of the two-sphere model, can be calculated by Eq. (3), as shown in Fig. 4(b). From Fig. 4(b), it can be seen that the subsurface feature of the two-sphere model is well reproduced. By comparing Fig. 4(a) and (b), the profile of the optical thickness of internal component is similar to that of its physical thickness, which well expresses the
morphology of internal component. That is to say the optical thickness of internal component can be used to express the morphology of internal component when the internal component is homogeneous, which also can be confirmed by H0 = h2 (n2 − n1 ) when n1 and n2 are the constant values. To verify the ability of this method for getting subsurface feature height, the horizontal sections of the original and calculated physical thickness of internal sphere are given in Fig. 3(c). Clearly, the calculated physical thickness curve (circle line) agrees well with the original physical thickness curve (solid line). Fig. 5(a) is the unwrapped phase image of the simulated monocyte with the medium of refractive index nm1 = 1.34. From this figure, we can see that there is an elliptical area with higher phase in the cell area. Fig. 5(b) shows the experimental phase map of a monocyte in air [31], which also has an elliptical area with higher phase. From these two images, it can be seen that our simulated phase image of the monocyte is similar to that of the experiment, which confirms the reliability of our simulation in phase imaging. For subsurface imaging, the physical thickness and the axially averaged refractive index of the monocyte are obtained by using DMQ, as shown in Fig. 5(c) and (d). In Fig. 5(c), the surface morphology of
Fig. 4. The simulated results of the substructure of the two-sphere model. (a) The optical thickness. (b) The physical thickness. (c) The central horizontal sections of the original and calculated physical thickness.
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a simulated monocyte depicted a bean-shaped nucleus, implying that this subsurface imaging method is a useful one allowing for the identification of white blood cells. Therefore, our work will take a significant role in the experimental research on the cells, including guiding the experimental design, saving the experimental time and costs, and verifying the experiment data. Acknowledgements The authors gratefully acknowledge the support from the Natural Science Fund for Colleges and Universities in Jiangsu Province (No. 09KJA140001), the Research Innovation Program for College Graduates of Jiangsu Province (No. CXLX11 0564), and PAPD (A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions). References
Fig. 5. (a) The unwrapped phase map of the simulated monocyte in the surrounding medium of the refractive index 1.34. (b) The experimental phase image of a monocyte in the air [31]. The other simulated results of the monocyte are in (c)–(f). (c) The physical thickness. (d) The extracted axially averaged refractive index. (e) The optical thickness and (f) the physical thickness of its nucleus.
the monocyte can be seen clearly. From Fig. 5(d), we can note that the axially averaged refractive indices are the same in the outer layer of cell. Based on this characteristic of the axially averaged refractive index map, we treat the value 1.37 at point B in the outer layer in Fig. 5(d) as the refractive index of the cytoplasm, which is the same as the original value 1.37. After the physical thickness and the refractive index of the cytoplasm have been gotten, the optical thickness of nucleus can be calculated and the subsurface feature height of nucleus also can be obtained assuming that the refractive index of nucleus is 1.39, as shown in Fig. 5(e) and (f). In both Fig. 5(e) and (f), the nucleus of the monocyte has a bean-shaped appearance as is typical for these cells. And the size of the nucleus can be easily gotten from the Fig. 5(f). Therefore this subsurface imaging method is a useful one allowing for the identification of white blood cells without the need for any exogenous dyes and any scanning processes. 5. Conclusions We have proposed a simple method which allows for examining the subsurface specimen/sample features. To get the physical thickness of sample, this method is based on DMQ and thus does not need any exogenous dyes and any scanning processes. For the relatively simple sample with a single major internal component, the refractive index of the outer layer of sample could be gotten from the axially averaged refractive index map, indicating that the current method can be used for subsurface imaging sample with unknown refractive index. By simulating phase shift induced by a two-sphere model and a homogeneous one-sphere model with a protuberance, we found that it is necessary to image subsurface for nucleated samples due to the same phase induced by the different substructure samples. And the extracted shape and size of substructure of two-sphere model agree well with the original ones, which confirms the feasibility of our method. The resultant subsurface of
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