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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 5, Iss. 14 — Nov. 16, 2010
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An insight into statistical refractive index properties of cell internal structure via low-coherence statistical amplitude microscopy

Pin Wang, Rajan K. Bista, Wei Qiu, Walid E. Khalbuss, Lin Zhang, Randall E. Brand, and Yang Liu  »View Author Affiliations


Optics Express, Vol. 18, Issue 21, pp. 21950-21958 (2010)
http://dx.doi.org/10.1364/OE.18.021950


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Abstract

Refractive index properties, especially at the nanoscale, have shown great potential in cancer diagnosis and screening. Due to the intrinsic complexity and weak refractive index fluctuation, the reconstruction of internal structures of a biological cell has been challenging. In this paper, we propose a simple and practical approach to derive the statistical properties of internal refractive index fluctuations within a biological cell with a new optical microscopy method – Low-coherence Statistical Amplitude Microscopy (SAM). We validated the capability of SAM to characterize the statistical properties of cell internal structures, which is described by numerical models of one-dimensional Gaussian random field. We demonstrated the potential of SAM in cancer detection with an animal model of intestinal carcinogenesis – multiple intestinal neoplasia mouse model. We showed that SAM-derived statistical properties of cell nuclear structures could detect the subtle changes that are otherwise undetectable by conventional cytopathology.

© 2010 OSA

1. Introduction

A biological cell is a complex system in which the spatial variation of its refractive index (i.e., refractive index variation) arises from the presence of heterogeneous internal structures consisting of numerous macromolecules such as double-stranded DNAs, RNAs, aggregated chromatin and bound proteins. It is now recognized that structural characterization of a biological cell, particularly sensitive determination of subtle alterations of these internal structural properties, is of primary importance for many biomedical applications, particularly for early cancer diagnosis and screening [1

1. H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. 69(13), 5357–5363 (2009). [CrossRef] [PubMed]

,2

2. P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. 35(17), 2840–2842 (2010). [CrossRef] [PubMed]

]. Interferometric imaging techniques are among the most powerful modalities to detect subtle changes of refractive index structural properties, as sensitive as sub-nanometer scale [3

3. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004). [CrossRef] [PubMed]

,4

4. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009). [CrossRef] [PubMed]

]. Low-coherence interferometric imaging microscopes, digital holographic microscopy and quantitative phase microscopy have also shown great promise in studying sub-nanometer dynamic structural properties of a biological cell [3

3. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004). [CrossRef] [PubMed]

,5

5. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]

,6

6. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006). [CrossRef] [PubMed]

].

The ideal representation of the structural properties of a biological system is a three-dimensional map detailing the refractive index of its internal structure with nanoscale accuracy. However, the accurate reconstruction of refractive index map of a biological system has been challenging. Thanks to several investigators, there has been significant progress in the reconstruction of the refractive index distribution of biological system. Bruno et al have demonstrated the feasibility of reconstructing the refractive index profile of a multi-layered sample by solving an inverse problem of the interference fringes obtained from backscattered low-coherence interferometry [7

7. O. P. Bruno and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28(21), 2049–2051 (2003). [CrossRef] [PubMed]

]. Choi et al have developed tomographic phase microscopy to quantitatively map the three-dimensional (3D) refractive index in live cells and tissues using a phase-shifting laser interferometric microscope [8

8. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007). [CrossRef] [PubMed]

]. Charriere et al have constructed three-dimensional refractive index distribution of a pollen grain with digital holographic microscopy [9

9. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006). [CrossRef] [PubMed]

]. Despite the significant advancement, due to the intrinsic complexity and extremely weak refractive index variation (i.e., nearly continuous medium) of sub-cellular structures, the reconstruction of three dimensional refractive index distribution is still challenging and complicated. Moreover, the significance of the complex three-dimensional refractive index distribution of cell internal structures in medicine and biological research has not been extensively addressed.

Here we present a simple approach to characterize the statistical properties of axial refractive index from internal sub-cellular structures of a single biological cell, which is more suitable for clinical applications. We do not focus on the accurate reconstruction of detailed three-dimensional refractive index distribution of the biological cell; instead, we aim to derive the simplified structural parameters to represent the statistical properties of cell internal sub-cellular structures. Our approach is based on the statistical analysis of Fourier-transformed amplitude of low spatiotemporal-coherence backscattering interferometric signals from an instrument that simultaneously obtains a speckle-free backscattering microscopic image in which the individual pixel contains the backscattering spectrum. This technique is therefore referred to as Low-coherence Statistical Amplitude Microscopy (SAM). We first construct a theoretical model of a biological cell whose refractive index profile is represented by one-dimensional Gaussian random field model. Then the numerical analysis of SAM is presented based on simulated one-dimensional interferometric signals from a series model of biological cells with various known statistical properties of refractive index. We further demonstrate the potential of SAM in cancer detection with an animal model of intestinal carcinogenesis – multiple intestinal neoplasia (Min) mouse model. Our results show that SAM-derived statistical properties of cell nuclear structure could detect the subtle changes that are otherwise undetectable by conventional cytopathology.

2. Materials and methods

2.1 Statistical model of refractive index profile of a single biological cell

If we describe the three-dimensional refractive index distribution of a biological cell asn(x,y,z), the spatial profile of refractive index of cell internal structures at a given pixel (x,y)within a single biological cell or a sub-cellular component can be described as a sum of the average axial refractive index n0and a spatially-varying component n(z): n(z)=n0+Δn(z), as shown in Fig. 1
Fig. 1 Illustrative refractive index profile of internal structures of a biological cell.
. The thickness of the cell at a given pixel is L(x, y). The average axial refractive index n0of the single cell can be determined by Fourier transformation of backscattered interferometric signals [2

2. P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. 35(17), 2840–2842 (2010). [CrossRef] [PubMed]

,10

10. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30(16), 2131–2133 (2005). [CrossRef] [PubMed]

,11

11. M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. 31(10), 1462–1464 (2006). [CrossRef] [PubMed]

].

To characterize the complex, inhomogeneous spatially-varying component of refractive index distribution of cell internal structures within a single biological cell, we adopted a stochastic model, one-dimensional Gaussian random field (GRF) model in the statistical software package R-project. The model has been used previously to characterize the morphology of randomly inhomogeneous materials and characterizing complex microstructures [12

12. R. J. Adler, The geometry of random fields (J. Wiley, Chichester Eng., New York, 1981).

]. Here we consider the longitudinal refractive index at a given pixel (x,y)within a single biological cell (n(z)) as a one-dimensional stochastic process having a Gaussian probability density function. Each value of n(z)is a Gaussian random variable with the mean n0=<n(z)> and its standard deviation (i.e., the average magnitude of refractive index variation) Δn=<[n(z)n0]2>. The two-point correlation function Cn(z)is defined as

Cn(z)=<[n(z=0)n0][n(z)n0]>
(1)

The Gaussian function is used as the correlation model: Cn(z)=exp(z2/(Lc/2)2), where Lc is the spatial correlation length of refractive index representing the length scale over which the spatial correlation decreases to a negligible level. Therefore, a larger n0represents the denser internal structural components of a biological cell, higher <Δn> is associated with the increased spatial variation of the density of intracellular material in the axial direction of the three-dimensional cell and a longer Lccorresponds to a slowly-changing axial refractive index profile due to the presence of large macromolecules. Figure 2
Fig. 2 The representative refractive index profiles n(z)modeled with GRF (a) with fixed n0=1.4and <Δn>=0.02, but different correlation length Lc, and (b) with fixedn0=1.4and Lc=140nm and different average magnitude of refractive index variation <Δn>.
shows the representative refractive index profiles modeled with GRF with a fixed n0=1.4, and various correlation length Lcand the standard deviation of refractive index <Δn>.

Assuming that there are 5000 pixels inside the cell which have common statistical properties of refractive index –n0and<Δn>, GRF model generates a refractive index profile for each pixel. To emulate the configuration of the cytology specimens in the experiment, we added the glass slide (refractive index n = 1.52) as the top and bottom medium that sandwich the cell. For each GRF-modeled axial refractive index profile, a one-dimensional multilayer dielectric slab model that implements Fresnel reflection [13

13. U. S. Inan, and A. S. Inan, Electromagnetic waves (Prentice Hall, Upper Saddle River, N.J., 2000).

] is used to generate its backscattering spectrum. The backscattering spectrum from each pixel was numerically resampled to evenly spaced wavenumbers and multiplied by a Hanning window before applying a fast Fourier transform. The Fourier transformed data at the prominent peak corresponding to the optical path length of interest depth z were selected for amplitude processing. After taking the discrete Fourier transform, a complex-valued F is obtained, and the amplitude can be extracted by taking the absolute value of F(z):

A(z)|(x,y)=|F(z)||(x,y)
(2)

The amplitude map is obtained by plotting the amplitude value at a certain depth plane for each pixel (5000 pixels in total). Based on the amplitude maps, three statistical parameters were quantified: the average amplitude <A>over the two-dimensional spatial distribution of A(x,y); the standard deviation of the amplitude σA, and the ratio of σAto <A>, referred to as fluctuation ratioR=σA/<A>.

2.2 Instrument

A(z)|(x,y)=|F(z)||(x,y)=S(RrRs(z))
(5)

2.3 Animal experiments

All animal studies were performed in accordance with the institutional Animal Care and Use Committee of University of Pittsburgh. All mice were housed in micro isolator cages in a room illuminated from 12-hr light-dark cycle, with access to water and ad libitum. Three 4.5 month-old C57BL wild-type mice and three age-matched C57BL Min mice were sacrificed. Their small intestines were removed, longitudinally opened and washed with phosphate buffered saline. Epithelial cells were obtained from brushing the visually normal mucosa of small intestine. The cytology brush was then quickly immersed into the Cytolyt® solution (Cytec Corporation). The slides were prepared by a standard Thin Prep processor (Cytec Corporation). Cells were then Papanicolaou-stained with a computer-controlled automated slide stainer and sealed with a mounting media (Cytoseal) and coverslip, following the standard clinical staining protocol. Cells were examined by an expert cytopathologist and non-cancerous looking cells were analyzed by SAM. For each mouse, about 20-30 cells are randomly selected for SAM analysis.

3. Results

3.1 Numerical experiments with gaussian random field model

To explore how the SAM-derived amplitude parameters are affected by the statistical properties of inhomogeneous refractive index distribution of cell internal structures, we performed numerical simulation with a series of biological cell models whose refractive index profilen(z)is modeled by one-dimensional Gaussian random field (GRF), which is described by three physical quantities: the average axial refractive index n0, the standard deviation of axial refractive index (i.e., the average magnitude of refractive index variation) <Δn>and the spatial correlation length of refractive index Lc, as defined in Section 2.1. Additionally, due to the intrinsic variations of cell thickness L, it is considered as another important variable in our numerical model. All values of these physical parameters were chosen to be within the cytologically relevant range, which is determined from our experimental data of cytological specimens from animal models and human patients.

Based on the Fourier analysis of one-dimensional interferometric signals, three simple amplitude parameters were derived from SAM including the average amplitude <A>, the standard deviation of the amplitude σA, and the fluctuation ratio R (R=σA/<A>). Figures 3(a)
Fig. 3 The dependence of statistical amplitude parameters –<A>, σAand Ron the (a) average refractive index n0, (b) standard deviation of refractive index <Δn> and (c) thickness L.
-3(c) demonstrate the dependence of these three parameters on the statistical properties of refractive index including average axial refractive index n0, the average magnitude of axial refractive index variation <Δn>and the cell thickness L with different spatial correlation length Lcof the refractive index. Assuming the biological cell has a weakly varying refractive index system, Lcis chosen from a range of 100nm to 600nm. Figure 3(a) shows the effect of n0on these three amplitude parameters with fixed <Δn>=0.02and thicknessL=4μm. It is evident that with increased n0, <A>shows a significant decrease. On the other hand, σA is slightly decreased and R is moderately increased with the increase of n0. Figure 3(b) shows the dependence of the three SAM-derived parameters on <Δn>with fixed n0=1.4and thicknessL=4μm. Increasing <Δn>leads to a significant increase in both σA and R, but it only weakly increase <A>. Figure 3(c) reveals the contribution of cell thickness L to the three SAM-derived parameters with fixed n0=1.4and <Δn>=0.02. Apparently, the variation of cell thickness in the biologically relevant range has very little effect on any of the three parameters.

3.2 Experiments with animal model of intestinal carcinogenesis

In order to demonstrate the capability of SAM to detect the subtle changes in cell refractive index and its potential in improving the diagnosis of early stage cancer, we used a well-established animal model of intestinal carcinogenesis – multiple intestinal neoplasia (Min) mouse model. It is a genetically modified animal model carrying the adenomatous polyposis coli (APC) gene mutation that spontaneously develops multiple intestinal adenomas. We analyzed the normal-appearing epithelial cells from small intestine from wild-type and Min mice at four and a half months. At this time point, the Min mice have developed macroscopically visible multiple adenomatous polyps. We analyzed the histologically normal-appearing intestinal epithelial cells from Min mice and those from wild-type mice (control group). Figure 4
Fig. 4 Representative (A) cytological images and (B) the corresponding amplitude maps of cell nuclei (as shown in circles) of intestinal epithelial cells from the wild-type and the Min mice. Scale bars in the image indicate 5μm.
shows their representative Papanicolaou-stained cytological images obtained from a conventional bright-field microscope and the corresponding amplitude maps from the cell nuclei. Although the microscopic cytological images look similar (as confirmed by an expert cytopathologist), the amplitude maps that characterize the refractive index variation of cell internal structures exhibit distinct differences. The three statistical parameters from the cell nuclei were calculated from the amplitude maps: the average amplitude <A>; the standard deviation of the amplitude σA over the entire nucleus, and the fluctuation ratio R.

Figure 5
Fig. 5 Statistical analysis of (a) A, (b) σAand (c) Rin cytologically normal-appearing cell nuclei from wild-type and Min mice. The error bar represents the standard errors.
shows the statistical analysis of these three SAM-derived amplitude parameters from all epithelial cell nuclei in six mice (approximately 20-30 cells from each mouse and three mice in each group). Apparently, <A> is significantly decreased in the cell nuclei of Min mice compared with those from wild-type mice (P=0.05) as shown in Fig. 5.(a), indicating that the average axial refractive index of cell nuclei from Min mice is higher compared to those from the wild-type mice. Figure 5(b) shows that σA is significantly increased from the cell nuclei of Min mice compared to those of wild-type mice with high statistical significance (P<0.0001), revealing a higher axial refractive index fluctuation <Δn> in the cell nuclei from Min mice. Similarly, Fig. 5(c) shows that R is also substantially increased in the epithelial cell nuclei of Min mice (P<0.0001), which reveals the higher ratio of axial refractive index fluctuation to the average axial refractive index (<Δn>/n0). The value R falls within the range from 0.1 to 0.2. Based on the lookup table created by the numerical simulation with a wide range of biologically relevant statistical properties of refractive index (n0,<Δn>,Lcand L), the correlation length Lc is estimated to be larger than 100 nm.

4. Discussion

We presented a simple approach to derive the statistical properties of complex and inhomogeneous refractive index properties of internal structures within a biological cell, based on Fourier analysis of interferometric signals from a microscopic image, referred to as Statistical Amplitude Microscopy (SAM). Although SAM does not give a detailed picture of complex refractive index distribution of cell internal structures, it provides quantitative parameters that are associated with the statistical properties of the spatial variation of refractive index within the biological cell. These statistical properties of refractive index are very sensitive to subtle sub-cellular structural alterations of carcinogenesis-associated cells that are not easily detectable with conventional microscopy techniques.

SAM derives three quantitative amplitude parameters –<A>,σAand R that are closely associated with the statistical properties of sub-cellular refractive index, characterized byn0, <Δn>, Lc and L. The results from the numerical simulation show that although the correlation between amplitude parameters and cell refractive index properties is rather complex, each of the amplitude parameter has a dominating contributor under the configuration emulating the cytology specimens. The average amplitude <A>is predominantly affected by the average axial refractive index n0, and increasing n0will decrease <A>. The standard deviation of the amplitude σA is most affected by the average magnitude of axial refractive index variation <Δn>, and increasing <Δn>will increase σA. The alterations in fluctuation ratio R mainly arise from the changes in <Δn>, with a minor contribution from n0, and is associated with the changes of <Δn>/n0. All three amplitude parameters are not affected by the correlation length of refractive index Lc when Lcis larger than 200 nm. The fact that the small changes in cell thickness do not alter the amplitude parameters is beneficial for many biomedical applications due to the intrinsic variation of cell thickness.

In order to demonstrate the ability of SAM for sensitive detection of carcinogenesis, a well-established animal model of intestinal carcinogenesis – Min mouse model was studied. We analyzed the intestinal epithelial cells that appear normal to the cytopathologist with a conventional microscopy. We found that the normal-appearing cells from Min mice resulted in a decreased<A>and increasedσA, when compared with those from wild-type mice. This result suggests that intestinal carcinogenesis is associated with increasing average refractive index and refractive index fluctuations in the cell nuclei. A higher average axial refractive index n0may indicate the higher density of nuclear components (e.g., chromatin), and a higher axial refractive index fluctuation <Δn>may be associated with increased spatial variation of the concentration of intra-nuclear solids (e.g., DNA, RNA, protein). Notably, the fact that the standard deviation of the amplitude σA (p-value < 0.0001) has a much smaller p-value than the average amplitude <A> (p-value = 0.05) implying that the refractive index variation may be more sensitive than the average refractive index in detecting the carcinogenesis-associated structural changes. It is worth pointing out that both <A>and σA could be affected by the absorption of the stains that are commonly used in the biological cell, especially for the clinical specimens. Due to the well-controlled standardized automated staining protocol, the systemic variation of staining is small. The fluctuation ratio R of axial refractive index can be used as a more experimentally robust parameter to minimize the effect of stain absorption. Such SAM-derived quantitative statistical information about the subtle alterations in nuclear architecture is otherwise undetectable with conventional optical microscopy. To confirm that these cells are truly indistinguishable with conventional microscopy, we performed the quantitative analysis on conventional bright-field cytology images and found that the intensity parameters (i.e., average intensity and standard deviation of intensity) cannot distinguish cytologically normal-appearing epithelial cell nuclei from the wild-type and Min mice (p-value = 0.10 and 0.26, respectively).

5. Conclusions

In summary, statistical amplitude microscopy is presented as a simple method to gain insights into the statistical properties of refractive index variation within a single biological cell nucleus. Our results demonstrate the potential of SAM in the clinical application of optical microscopy for early cancer detection. It could be used to enhance the detection of cancer in cells that would otherwise be diagnosed as “normal” by conventional cytopathology. This technique could also be useful to detect the field carcinogenesis [1

1. H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. 69(13), 5357–5363 (2009). [CrossRef] [PubMed]

] by analyzing the normal-appearing cells from easily accessible location to predict the presence of neoplasia anywhere in the entire organ. Due to the simplicity of this approach, it has the potential to be disseminated into the clinical diagnostic laboratories.

Acknowledgements

References and links

1.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. 69(13), 5357–5363 (2009). [CrossRef] [PubMed]

2.

P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. 35(17), 2840–2842 (2010). [CrossRef] [PubMed]

3.

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004). [CrossRef] [PubMed]

4.

N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009). [CrossRef] [PubMed]

5.

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]

6.

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006). [CrossRef] [PubMed]

7.

O. P. Bruno and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28(21), 2049–2051 (2003). [CrossRef] [PubMed]

8.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007). [CrossRef] [PubMed]

9.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006). [CrossRef] [PubMed]

10.

C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30(16), 2131–2133 (2005). [CrossRef] [PubMed]

11.

M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. 31(10), 1462–1464 (2006). [CrossRef] [PubMed]

12.

R. J. Adler, The geometry of random fields (J. Wiley, Chichester Eng., New York, 1981).

13.

U. S. Inan, and A. S. Inan, Electromagnetic waves (Prentice Hall, Upper Saddle River, N.J., 2000).

14.

Y. Liu, X. Li, Y. L. Kim, and V. Backman, “Elastic backscattering spectroscopic microscopy,” Opt. Lett. 30(18), 2445–2447 (2005). [CrossRef] [PubMed]

OCIS Codes
(110.0180) Imaging systems : Microscopy
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(290.1350) Scattering : Backscattering

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: August 30, 2010
Revised Manuscript: September 24, 2010
Manuscript Accepted: September 26, 2010
Published: September 30, 2010

Virtual Issues
Vol. 5, Iss. 14 Virtual Journal for Biomedical Optics

Citation
Pin Wang, Rajan K. Bista, Wei Qiu, Walid E. Khalbuss, Lin Zhang, Randall E. Brand, and Yang Liu, "An insight into statistical refractive index properties of cell internal structure via low-coherence statistical amplitude microscopy," Opt. Express 18, 21950-21958 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-21-21950


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References

  1. H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. S. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. 69(13), 5357–5363 (2009). [CrossRef] [PubMed]
  2. P. Wang, R. Bista, R. Bhargava, R. E. Brand, and Y. Liu, “Spatial-domain low-coherence quantitative phase microscopy for cancer diagnosis,” Opt. Lett. 35(17), 2840–2842 (2010). [CrossRef] [PubMed]
  3. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004). [CrossRef] [PubMed]
  4. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009). [CrossRef] [PubMed]
  5. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]
  6. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006). [CrossRef] [PubMed]
  7. O. P. Bruno and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28(21), 2049–2051 (2003). [CrossRef] [PubMed]
  8. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007). [CrossRef] [PubMed]
  9. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006). [CrossRef] [PubMed]
  10. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30(16), 2131–2133 (2005). [CrossRef] [PubMed]
  11. M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. 31(10), 1462–1464 (2006). [CrossRef] [PubMed]
  12. R. J. Adler, The geometry of random fields (J. Wiley, Chichester Eng., New York, 1981).
  13. U. S. Inan, and A. S. Inan, Electromagnetic waves (Prentice Hall, Upper Saddle River, N.J., 2000).
  14. Y. Liu, X. Li, Y. L. Kim, and V. Backman, “Elastic backscattering spectroscopic microscopy,” Opt. Lett. 30(18), 2445–2447 (2005). [CrossRef] [PubMed]

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