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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 4 — May. 4, 2011
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Label-free imaging of intracellular motility by low-coherent quantitative phase microscopy

Toyohiko Yamauchi, Hidenao Iwai, and Yutaka Yamashita  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 5536-5550 (2011)
http://dx.doi.org/10.1364/OE.19.005536


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Abstract

The subject study demonstrates the imaging of cell activity by quantitatively assessing the motion of intracellular organelles and cell plasma membranes without any contrast agent. The low-coherent interferometric technique and phase-referenced phase shifting technique were integrated to reveal the depth-resolved distribution of intracellular motility. The transversal and vertical spatial resolutions were 0.56 μm and 0.93 μm, respectively, and the mechanical stability of the system was 1.2 nm. The motility of the cell was assessed by mean squared displacement (MSD) and we have compensated for the MSD by applying statistical noise analysis. Thus we show the significant change of intracellular motility after paraformaldehyde treatment in non-labeled cells.

© 2011 OSA

1. Introduction

The measurement of cell motility is important for the study of living cells sampled from biological tissues. For example, the motility of cancer cells correlates with their metastatic potentials [1

1. A. W. Partin, J. S. Schoeniger, J. L. Mohler, and D. S. Coffey, “Fourier analysis of cell motility: correlation of motility with metastatic potential,” Proc. Natl. Acad. Sci. U.S.A. 86(4), 1254–1258 (1989). [CrossRef] [PubMed]

]. As for nanometer-scale measurements, the voltage-induced cell membrane motion was examined by applying atomic force microscopy (AFM), and its relationship to the charge density of the cell surface was demonstrated [2

2. P. C. Zhang, A. M. Keleshian, and F. Sachs, “Voltage-induced membrane movement,” Nature 413(6854), 428–432 (2001). [CrossRef] [PubMed]

]. In recent years, the biophysical properties of cancer cells have been investigated by AFMs in nanometer scale [3

3. S. Suresh, “Biomechanics and biophysics of cancer cells,” Acta Biomater. 3(4), 413–438 (2007). [CrossRef] [PubMed]

].

Considering the intactness of the cell samples, it is desirable to use a non-invasive label-free technique to image the dynamic morphology of the cells. In this regard we expect that an optical technique that uses interferometry would be ideal. There are two optical schemes available to measure the cell morphology. One is quantitative phase microscopy (QPM), which allows the measurement of the phase of optical fields in the sub-wavelength resolution. So far, Hilbert Phase Microscopy (HPM) [4

4. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005). [CrossRef] [PubMed]

6

6. G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett. 97(21), 218101 (2006). [CrossRef] [PubMed]

], Quantitative Phase Microscopy by white-light interferometry [7

7. X. Li, T. Yamauchi, H. Iwai, Y. Yamashita, H. Zhang, and T. Hiruma, “Full-field quantitative phase imaging by white-light interferometry with active phase stabilization and its application to biological samples,” Opt. Lett. 31(12), 1830–1832 (2006). [CrossRef] [PubMed]

], and Digital Holographic Microscopy (DHM) [8

8. 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]

,9

9. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13(23), 9361–9373 (2005). [CrossRef] [PubMed]

] have been used for the imaging of living cells. The other is Optical Coherence Tomography (OCT), which allows the acquisition of weak light reflected from spatially localized regions [10

10. W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24(17), 1221–1223 (1999). [CrossRef]

12

12. A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh-resolution full-field optical coherence tomography,” Appl. Opt. 43(14), 2874–2883 (2004). [CrossRef] [PubMed]

].

The key technique of QPM is to compensate the phase drifts and phase noise associated with the measurement system by monitoring the phase-referenced signals [4

4. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005). [CrossRef] [PubMed]

,13

13. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics,” Opt. Lett. 26(16), 1271–1273 (2001). [CrossRef]

]. HPM and the DHM have the nanometer-scale resolution of the optical path [6

6. G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett. 97(21), 218101 (2006). [CrossRef] [PubMed]

,8

8. 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]

]. However, they do not allow the discrimination of multiple reflection surfaces [4

4. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005). [CrossRef] [PubMed]

,9

9. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13(23), 9361–9373 (2005). [CrossRef] [PubMed]

,14

14. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007). [CrossRef] [PubMed]

]. OCT, on the other hand, allows the discrimination of reflection signals attributed to multiple surfaces in a sample. However, many cases of conventional OCT have omitted the phase information of reflected light for obtaining the distribution of the amplitude of reflectance [10

10. W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24(17), 1221–1223 (1999). [CrossRef]

,12

12. A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh-resolution full-field optical coherence tomography,” Appl. Opt. 43(14), 2874–2883 (2004). [CrossRef] [PubMed]

].

Increasing numbers of researchers in recent years have integrated the advantages of the quantitative-phase imaging technique with OCT in order to measure the dynamic morphology of a particular surface with sub-cellular resolution. Yang et al. developed a phase-referenced interferometer with a low-coherence light source in order to observe the phase fluctuation associated with cell surface motion [13

13. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics,” Opt. Lett. 26(16), 1271–1273 (2001). [CrossRef]

]. Moreover, they employed the phase-referenced low-coherence technique to measure nerve displacement during action potential [15

15. C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, “Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer,” Opt. Lett. 29(17), 2028–2030 (2004). [CrossRef] [PubMed]

,16

16. T. Akkin, D. Davé, T. Milner, and H. Rylander Iii, “Detection of neural activity using phase-sensitive optical low-coherence reflectometry,” Opt. Express 12(11), 2377–2386 (2004). [CrossRef] [PubMed]

]. Concerning the OCT approach, Jeong et al. developed Fourier Domain Digital Holographic OCT (FD-DHOCT) to quantify the degree of cell motility by an intensity-based statistical technique [17

17. K. Jeong, J. J. Turek, and D. D. Nolte, “Fourier-domain digital holographic optical coherence imaging of living tissue,” Appl. Opt. 46(22), 4999–5008 (2007). [CrossRef] [PubMed]

,18

18. K. Jeong, J. J. Turek, and D. D. Nolte, “Volumetric motility-contrast imaging of tissue response to cytoskeletal anti-cancer drugs,” Opt. Express 15(21), 14057–14064 (2007). [CrossRef] [PubMed]

], and Ellerbee et al. were able to capture an image of the phase fluctuation of chick embryos by applying Multi-Dimensional Spectral Domain Phase Microscopy (MD-SDPM) [19

19. A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, “Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy,” Opt. Express 15(13), 8115–8124 (2007). [CrossRef] [PubMed]

]. To distinguish a particular cell surface, some researchers used nanoparticles to enhance the reflection signals of cells by OCT [20

20. D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett. 32(6), 626–628 (2007). [CrossRef] [PubMed]

22

22. J. Oh, M. D. Feldman, J. Kim, H. W. Kang, P. Sanghi, and T. E. Milner, “Magneto-motive detection of tissue-based macrophages by differential phase optical coherence tomography,” Lasers Surg. Med. 39(3), 266–272 (2007). [CrossRef] [PubMed]

]. These studies showed nanometer-scale motions of cells. However, in a label-free state the reflected light from the cell surface was not sufficiently distinguished from that of other boundaries, including the glass surface or the membrane of intracellular organelles, and when the researchers needed to take the signal from the membranes only, it was necessary to use contrast agents.

This paper shows the three-dimensional distribution of quantitatively assessed phase fluctuation caused by the motion of multiple surfaces in cultured cells. We used high-numerical-aperture (NA) illumination with a low-coherence light source while controlling the phase-referenced optical path difference at the nanometer scale [23

23. T. Yamauchi, H. Iwai, M. Miwa, and Y. Yamashita, “Low-coherent quantitative phase microscope for nanometer-scale measurement of living cells morphology,” Opt. Express 16(16), 12227–12238 (2008). [CrossRef] [PubMed]

]. The longitudinal spatial resolution (FWHM (Full Width at Half Maximum) of the interference fringe) of the imaging system was 0.93 μm, while the transversal resolution was 0.56 μm (diffraction limit). The results quantitatively revealed the depth-resolved fluctuations of the intracellular surfaces, allowing us to measure the plasma membrane, the reflecting surfaces in cytoplasmic region and the surface of the substrate independently.

2. Methods

Figure 1(a)
Fig. 1 Schematic illustration of the experimental Setup. (a): Whole setup, (b): Interference fringe observed on the CCD camera while moving the PZT2, (c): Detail of the sample arm. IR-LD: Infrared laser diode, PZT: Piezoelectric transducer, PD: Photo detector, ND: Neutral density filter, M: Mirror, L: Lenses, BS: Beam splitter, DM: Dichroic mirror (cutoff: 900nm).
depicts the experimental setup of Low-Coherent QPM based on a Linnik configuration. Light emitted from a halogen lamp (Nikon, LV-UEPI 50W) passed through a Linnik interferometer equipped with two identical water-immersion objective lenses (Nikon, CFI Fluor 60 × W, NA = 1.0). The reflected wavefronts from the sample and the reference mirror were focused onto the 12-bit CCD camera (Hamamatsu, C9300-201) in order to obtain interference images.

The cells under testing were cultured on a glass slide to which both an AR coating for the bandwidth of 550-950 nm and a reflection enhancement coating for 1.3 μm were applied. The AR coating was necessary because the light reflected from the cell membrane and intracellular membranes was so weak that the reflection from the glass surface would easily overwhelm the cell reflection even if coherence gating was used. The reflection enhancement coating caused the glass surface to work as a reference plane for the feedback control of optical path difference (OPD).

The PZT1 adjusts the OPD fast (~500 Hz) with a small stroke (<330 nm) at high resolution (<1 nm), while the PZT2 under the sample dish covers a large stroke (100 μm maximum) at coarse resolution (20-nm step). The feedback circuit continuously controls the PZT1 in the reference arm to adjust the OPD by nanometer resolution. Only when the PZT1 exceeds its assigned maximum stroke (330 nm) does the PZT2 complementally move the sample dish to cancel the PZT1 motion. Therefore, by consecutively commanding the OPD scanning at sub-wavelength increments/decrements, the focal plane and equal-path-length plane are scanned simultaneously.

The minimum number of raw images needed to make a phase image is 3 [25

25. K. Creath, “V Phase-Measurement Interferometry Techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.

]. However, in order to compensate for the non-uniformity of the interference amplitude due to the envelope of the coherence function, a more sophisticated phase-shifting algorithm is preferable. Because Hibino et al have demonstrated that their seven points phase shifting algorithm estimates the phase ϕ more accurately than the traditional four step algorithm, under the presence of the amplitude modulation of the interferogram [26

26. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12(4), 761–768 (1995). [CrossRef]

], we adopted their algorithm. Following Hibino’s algorithm, we take seven raw images I3π/2,Iπ,Iπ/2 ,I0,Iπ/2 ,Iπ,I3π/2 to construct a single-phase image. Here Iδφ represents the raw intensity image on CCD with phase shift δφ. Notice that 2π of the phase shift corresponds to the displacement of the PZT2 of Λ (327 nm). Using the optical electric field of the reference and the sample as E r and E s, the raw intensity on CCD can be expressed as
Iδφ=η(|Er|2+|Es|2+2|Er||Es|cos(φδϕ)γ(z)),
(1)
where γ(z) is the optical coherence function, z is the optical path difference, η is the proportionality factor and ϕ is the differential phase between E r and E s. The two-dimensional distribution of a complex electric field image C, having the square amplitude of R and the phase of ϕ, can be extracted as C(x,y)=A+Bi,where

A=(Iπ(x,y)+2I0(x,y)Iπ(x,y))/4,B=(I3π/2(x,y)3Iπ/2(x,y)+3Iπ/2(x,y)I3π/2(x,y))/8.
(2)

Because C(x,y)=η(2γ(z)|Er||Es|)(cosφ+isinφ), R and ϕ are thus

R(x,y)=|C(x,y)|2|Es|2γ(z)2, φ(x,y)=arg(C(x,y)).
(3)

As shown in Fig. 2
Fig. 2 Timing chart of the phase shifting and CCD exposure.
, we increased the OPD from 3π/2 to3π/2, and then decreased it from 3π/2 to 3π/2 at intervals ofπ/2, while capturing the images. In this cycle, two electric field images were obtained by scanning in the forward and reverse directions, and we averaged them in the complex plane to make one image per measurement cycle. By repeating this phase-shifting cycle a series of electric field images C n, reflectance images R n and reflection phase images ϕ n were obtained at time intervals Δt.

3. Results

3.1 Phase image and mean squared displacement

The sample is a cell line derived from human breast cancer cells labeled MCF-7. The cells were subcultured on the glass slides two days prior to measurement. The phase shifting was performed at intervals of 104 milliseconds so that phase images were obtained in the intervals of Δt = 1.25 sec. Figure 3(a)
Fig. 3 Phase images of the living cell under test, including (a) transmission phase image; (b) reflection phase image at the height 2.4 μm above the glass surface; and (c) typical temporal fluctuation of the phase of the reflection signal. The blue and black lines show the temporal fluctuation at the points A and B shown in Fig. 3(b), respectively. The green line shows the temporal fluctuation measured at the top of a 10 μm polystyrene bead immersed in pure water.
shows transmission-phase and reflection-phase images of the living cell sample under testing. The transmission phase image is obtained by using the specular reflection from the bottom glass underneath the cells. The reflection-phase image shown in Fig. 3(b) was taken at the height 2.4 μm above the cell bottom. We captured the reflection-phase image of this cell at this height for 125 seconds. The phase of the reflected light from the cell fluctuated over time, as shown in Fig. 3(c), with the trend in fluctuation being dependent on the position. The fluctuation of the phase of the light reflected from the cell membrane (point A) shows the vertical motion of the membrane. In the case of the fluctuation of the reflection signal from the first surface of the sample, the conversion factor of the phase change Δϕ to the vertical motion Δh is Δh=λcΔφ/(4πnm)=52nm/rad×Δφ, where n m is the refractive index of the medium (n m = 1.335).

Figure 3(c) also indicates the phase fluctuation of the reflected light from the top of a 10 μm polystyrene bead immersed in pure water (n = 1.333) as a means to compare the mechanical stability of the system. The stability of the phase of the light reflected from the polystyrene bead was 0.023 radian (the standard deviation), which corresponds to 1.2 nm.

In order to quantify the phase fluctuation, we used the mean squared displacement (MSD) Δφ2(τ):

Δφ2(τ)=|φ(t)φ(tτ)|2¯.
(4)

The MSD, which is the mean squared change of the displacement at times t and t-τ, characterizes the random migration of cells [27

27. M. H. Gail and C. W. Boone, “The locomotion of mouse fibroblasts in tissue culture,” Biophys. J. 10(10), 980–993 (1970). [CrossRef] [PubMed]

] or particle motion in the cells [28

28. H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991). [CrossRef] [PubMed]

]. Recently, the researchers using the quantitative phase imaging technique employed MSD to characterize the cell membrane displacement caused by cell growth of epithelial cells or beating of cardiomyocyte [29

29. G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295(2), C538–C544 (2008). [CrossRef] [PubMed]

,30

30. N. T. Shaked, L. L. Satterwhite, N. Bursac, and A. Wax, “Whole-cell-analysis of live cardiomyocytes using wide-field interferometric phase microscopy,” Biomed Opt. Express 1(2), 706–719 (2010). [CrossRef]

]. Here we also employ the MSD to characterize the z-directional motion of the membrane in order to quantify the activity in the cells. To calculate the MSDs accurately, it was necessary to compensate for the overestimation of MSD attributable to the random phase fluctuation due to the noise on the CCD. All the images of phase fluctuation in this section were compensated for random noise, and the compensation procedure is given in Section 4.

3.2 Full-field image of phase fluctuation

The MSDs were calculated at every position in the field of view. Figures 4(b)
Fig. 4 Phase fluctuation of the living MCF7 cell sample: The unit of the x axis and y axis is the micrometer. (a): Reflectance image R(x,y). The unit of color is arbitrary. (b)-(c): Distribution of the MSD: The pseudo color shows the MSD Δφ2(x,y,τ) and the unit of the color bar is the radian2. The τ is 1.25, 3.75 and 6.25 seconds in the Figs. 4(b), 4(c) and 4(d), respectively. The unit of the x axis and y axis is μm.
-4(d) show the distribution of the MSD with the τ of 1.25, 3.75 and 6.25 seconds. Figure 4(a) shows the distribution of the reflectance R(x,y) in Eq. (3). The pixels where the fringe contrasts were insufficient were masked out and shown by white color in Figs. 4(b)-4(d). The MSD increases by making the τ larger. The intracellular cytoplasmic region, such as the point B in Fig. 4(b), fluctuates more dynamically than the membrane region, such as at point A. The source of the reflection from the intracellular region such as the point B can be intracellular organelle surface reflection or the inhomogeneity of the concentration of chemicals in cytosol which behaves as a superficial surface. Though we do not have a conclusion about the source of the reflection in cytoplasm, the motion of the objects or superficial surfaces in cytoplasm should reflect the liquidity of the intracellular region. There is a space within the cell where the reflectance was smaller than the surrounding area. Based on the three-dimensional morphology, which will be shown later, we believe this area is a nucleus and the high reflectance granular objects in this space are nucleoli. The reflectance from inside the nucleus was so weak that sufficient interference signals for the phase measurement were not obtained. To see the reflection from inside the nucleus, the employment of a light source with higher power would be useful.

In order to demonstrate the validity of our method, we fixed the sample with 2% paraformaldehyde. After the treatment, the cells died and the membrane and intracellular structures were fixed chemically. Figure 5
Fig. 5 Phase fluctuation of the MCF7 cell sample after paraformaldehyde treatment. The unit of the x axis and y axis is the micrometer. (a): Reflectance image R(x,y): The unit of the color is arbitrary. (b)-(c): Distribution of the MSD: The pseudo color shows the MSD Δφ2(x,y,τ) and the unit of the color bar is the radian.2 The τ is 1.25, 3.75 and 6.25 seconds in the Figs. 5(b), 5(c) and 5(d), respectively. The unit of the x axis and y axis is μm.
shows the phase fluctuation observed in the same cells after fixation. Figure 5(a) shows the reflectance R(x,y), and Figs. 5(b)-5(d) show the distribution of the MSD with the τ of 1.25, 3.75 and 6.25 seconds, respectively. The MSD dramatically decreased, and the intracellular fluctuation, which was distinctive in the living cells, was suppressed to the same level as that of the membrane region. Figure 6
Fig. 6 MSDΔφ2(τ)at the positions A and B in Fig. 4 and C and D in Fig. 5.
summarizes the behavior of the MSD as a function of τ, where the MSD at the positions A and B in Fig. 4(b) and C and D in Fig. 5(b) are plotted as a function of τ. The right axis of Fig. 6 also indicates the MSD measured by the corresponding vertical motion of the first surface in culture medium. Because the conversion factor of the phase change Δϕ to the vertical motion Δh is Δh=52nm/rad×Δφ, the conversion factor between the MSD in phase to the MSD in vertical motion is Δh2(τ)=2704nm2/rad2×Δφ2(τ). The slope of the MSD at the point A, as measured by the nanometer scale, is 31 nm2/sec., which is in agreement with the AFM studies on cell membrane [31

31. J. A. Hessler, A. Budor, K. Putchakayala, A. Mecke, D. Rieger, M. M. Banaszak Holl, B. G. Orr, A. Bielinska, J. Beals, and J. Baker Jr., “Atomic force microscopy study of early morphological changes during apoptosis,” Langmuir 21(20), 9280–9286 (2005). [CrossRef] [PubMed]

].

3.3 Three-dimensional tomography of the phase fluctuation

To analyze the fluctuation of the cell membrane and intracellular structure in detail, we captured the phase-fluctuation image at different heights. Figure 7
Fig. 7 Timing chart of phase shift for tomographic imaging of phase fluctuation.
indicates a chart of phase-shift timing. The phase image at one sectioning height was taken for 10 times (12.5 sec.). Subsequently, the sectioning height was shifted by 327 nm, corresponding to 2π phase shift of the illumination light, and another 10 phase images were taken at this new sectioning height. By repeating this procedure, the stack of en-face phase images at every sectioning height is obtained.

By calculating the MSD at each sectioning height, we obtained the tomographic image of MSD as a function of four variables Δφ2(x,y,z,τ). Figure 8
Fig. 8 Tomographic image of phase fluctuation: The time difference τ for calculating MSD is 3.75 sec. (a): Δφ2(x,y,z=2.4μm,τ=3.75), (b): Δφ2(x,y,z=3.9μm,τ=3.75), (c): Δφ2(x,y,z=5.5μm,τ=3.75), and (d): Δφ2(x,y,z=7.4μm,τ=3.75). The unit of the x, y and z axes is μm.
shows horizontal, cross-sectional images of the tomographic phase-fluctuation data Δφ2(x,y,z,τ) where τ = 3.75 and z = 2.4, 3.9, 5.9 and 7.4 μm. Figure 9
Fig. 9 Vertical cross section of the tomographic phase-fluctuation image. Figs. (a) and (b) are images of the living cell, and the figs. (c) and (d) are images of the paraformaldehyde-treated cell. Figs. (a) and (c) are the cross sections of the reflectance, which is calculated from the amplitude component of the interference image. Figs (b) and (d) are the cross-sectional images of the mean squared displacement of phase fluctuation Δφ2 where τ = 3.75 and y = 20μm. The unit of the color bar for the figs. (b) and (d) is the radian.2 The unit of the x axis and z axis is μm.
shows the vertical cross-sectional images of the tomographic phase fluctuation, as reconstructed from the overall data Δφ2(x,y,z,τ). The sectioning line for Fig. 9 is shown in Fig. 8(a). The cross section of the reflection amplitude is shown in Figs. 9(a) and 9(c), which correspond to the so-called B-scan image of the line-field OCT. In Fig. 9(a) can be seen a spherical membrane inside the cell, which we believe is the nuclear membrane.

4. Numerical processing

4.1 Overview

The mean squared displacement (MSD) of the phase Δφ2(τ), which is the mean squared change of the phase at times t and t-τ, deviates by the fringe contrast of the interference image. When the fringe contrast is low, the measured phase has a significant degree of error due to the random intensity noise of the CCD [32

32. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7(4), 537–541 (1990). [CrossRef]

], so that the MSD is overestimated. The fringe contrast observed on the cell membrane was typically ± 100 counts over 3000 counts of the DC, and the error attributed to the random intensity noise of the CCD was not negligible. To compensate the overestimation of the MSD, we have formulated the phase errors attributed to the CCD noise and shown the manner in which the overestimation of MSD was compensated.

4.2 Estimation of random noise

The signal intensity measured with the CCD camera, at each exposure, has random noise attributable to the readout noise of the analog-to-digital converter as well as the electron counting noise (quantum noise). Figure 10(a)
Fig. 10 Noise characteristic of the CCD camera C9300-201. (a) Standard deviation σCCD of the measured CCD intensity (analog-to-digital converted value) as a function of the average intensity N CCD. (b) Example of the distribution of the intensity: Black line: measured histogram of the count on the CCD pixels. The mean value is 3261 and the standard deviation is 26.28. Green line: Gaussian curve with the mean value of 3261 and the standard deviation of 26.28. The inset shows a zoom-in of the region contained within the gray box.
shows the temporal standard deviation σCCD of the signal from the pixels of the CCD camera (C9300-201, Hamamatsu, 12-bit, gamma = 1.0) as a function of the temporal average of the count NCCD. We uniformly illuminated the CCD with the halogen lamp and took 1,200 images in order to derive the average count NCCD and the temporal standard deviation σCCD. The measurement was repeated with different (OD = 0 and OD = 0.4) light intensities and exposure times (20msec., 40msec. and 80msec.). The noise characteristic of the CCD camera was consistent with the following equation:

σ=CCD1.922+0.211×NCCD.
(5)

Notice that the electron counting noise σelectron is given by the count of the electron Nelectron: σelectron=Nelectron. Because the well depth of the CCD camera C9300-201 is 20,000 electrons (as indicated by the manufacturer’s operating manual), the electron counting noise should be 20000=141 electrons at the maximum, which is 0.7% of the mean intensity. This is consistent with our estimation (σCCD=29 at NCCD=4096).

The histogram of the counts on the CCD pixels well fits to the normal distribution with the mean value of N CCD and the variance of σ CCD 2, as shown in Fig. 10(b). We recorded the raw intensity on the CCD; I(x,y,n), for n = 1 to 1,200 frames while uniformly illuminating it, then cropped a 100 × 100 area in which the uniformity of the illumination was the best. From the 100 × 100 × 1200 samples, we made the histogram shown in Fig. 10(b). The mean value of the spatial standard deviation at every frame was 26.22, and the mean value of the temporal standard deviation at every pixel was 26.17. This result implies that the noise characteristic of the CCD is ergodic.

This uncertainty regarding the intensity of each image affects the complex interference image C written in the Eq. (2). According to the nature of normal distribution, the variance of the summation of normal distributions is the summation of the variances of the normal distributions. Therefore, the standard deviation of the real part and the imaginary part of the interference signal C in the Eq. (2) are estimated to be σRe=0.433σCCD and σIm=0.405σCCD, respectively. To make the following calculation easier, we approximated the probability density function of the interference signal to be cylindrically symmetric as,
p(X,Y)=12πσR2exp(X2+Y22σR),
(6)
where X and Y is the real and imaginary part of C and σR=σRe2+σIm2=0.419σCCD.

This uncertainty of the interference signal is schematically shown in Fig. 11(a)
Fig. 11 Interference signal shown in the complex plane: (a) Schematic illustration, (b) The experimentally measured probability density function of the interference signal C on a bead surface measured for 125 seconds.
and the uncertainty of the phase (in radian) is written as,

σφ=σR|C|.
(7)

Therefore, the uncertainty of the phase σφ will make the MSD overestimated as,
Δφ2(τ)=(Ν(φ(t),σφ2)Ν(φ(tτ),σφ2))2     =(Ν(φ(t)φ(tτ),2σφ2))2     =|φ(t)φ(tτ)|2+2σφ2     =Δφ^2(τ)+2σφ2,
(8)
, where N(μ,σ 2) is a normal distribution with the mean value of μ and the variance of σ 2, and Δφ^2(τ) is the true value of the MSD.

To show the validity of this estimation of the MSD, we measured the surface of 10 μm polystyrene beads immersed in pure water as a test target. We recorded 100 phase images with time intervals of 1.25 second. Figure 11(b) shows an example of the temporal fluctuation of the interference signal C on a position (x 0,y 0) on the bead, where the real part and imaginary part of C(x0,y0,t) are plotted. The blurring of the interference signal due to the random intensity noise σCCD can be seen.

Figure 12
Fig. 12 Raw mean squared displacement observed on a bead surface as a function of the estimated offset of the MSD. The green lines show Δφ2=2σφ2. (a) τ = 1.25, (b) τ = 12.5.
shows the relationship between the estimated overestimation of the MSD and the measured MSD. We have sampled a 30 x 30 pixel area (corresponding to 3.5 μm by 3.5 μm) on the surface of the 10 μm bead. Due to the coherence gating by the white light, the fringe contrast was not uniform on the bead surface, and such a situation was suitable for demonstrating the effect of low fringe contrast. Figure 12 plots the measured MSD as a function of estimated MSD. The result implies that the random intensity noise of the CCD is the dominant factor in the overestimation of the superficial MSD.

4.3 Compensating the overestimation of MSD

Because we estimated the overestimation of the MSD quantitatively as Eq. (8), we can compensate the overestimation by subtracting it from the superficial MSD:

Δφ^2(τ)=Δφ2(τ)2σφ2.
(9)

Figure 13
Fig. 13 Compensation of the MSD on the bead surface: (a) Interference fringe, (b) MSD before compensation, (c) MSD after compensation. The unit of the color bar is the radian2.
shows the MSD on the 10 μm bead surface (3.5 μm by 3.5 μm area). On the pixels where the fringe contrast is low (see Fig. 13(a)), the MSD will be overestimated as shown in Fig. 13(b); however, the overestimation is compensated as shown in Fig. 13(c) after the offset subtraction. We demonstrate how the overestimation of the MSD is successfully compensated also in the cell measurement by comparing the images before and after compensation. For instance, we show the compensation of MSD in the case of the fixed cell shown in Fig. 5. Figure 14(a)
Fig. 14 The MSD of the fixed cell shown in the Fig. 5 before and after the compensation. τ = 3.75 was chosen for the demonstration; (a) the raw MSD before the compensation, (b) the estimated overestimation of MSD, (c) the MSD after the compensation performed by subtracting the image (b) from the image (a). The unit of the x and y axes is μm. The unit of the color bar which is common in these three images is the radian2.
shows the raw MSD before compensation. τ = 3.75 was chosen for the demonstration. Figure 14(b) shows the estimated overestimation of the MSD. Then, Fig. 14(c) shows the MSD after compensation. Figure 14(c) is the repetition of Fig. 5(c), but the scale of the color bar is changed.

As shown in the Eq. (8), the random intensity noise offsets the MSD independent of τ. Figure 15
Fig. 15 The raw MSD Δφ2(τ) before compensation as a function of τ. (a): The raw MSD of the living MCF7 cell at the positions A and B in Fig. 4. (b): The raw MSD of the fixed MCF7 cell at the positions C and D in Fig. 5. In these figures, the estimated offset of Δφ2(τ) is also shown by dashed lines.
shows the MSD Δφ2(τ)at the positions A and B in Fig. 4 and C and D in Fig. 5 before the compensation. In the living cell sample, the estimated overestimations of the MSD at the points A and B were 0.0187 and 0.0511 radians2, respectively, while in the fixed cell sample, the estimated overestimations of the MSD at the points C and D were 0.0521 and 0.0824 radians2, respectively. Because the overestimations of MSD are inversely proportional to the intensity of the reflection signal, the overestimation of MSD tend to be larger in the intracellular region than on the cell membrane. The compensation of the MSD is important especially when we analyze the quiet cells or dead cells in order not to pick up artifact signals.

5. Conclusion

Our Low-Coherent QPM visualizes the distribution of the fluctuations of the intracellular surfaces and cell membrane. The image acquisition rate is 1.25 sec. per image, and the lateral resolution is 0.56 μm. The mechanical stability of the system is 0.023 radian (the standard deviation), corresponding to 1.2 nm. Because the uncertainty of the phase attributed to the random intensity noise of the CCD is typically 0.1 radian (the standard deviation) on the cell surface, the dominant source of the uncertainty of the reflection phase is the random intensity noise of the CCD. We estimated the phase noise attributed to the random variance of the intensity observed on the CCD at every exposure. As shown in Fig. 12, the estimated phase noise is consistent with the results of our experimentation.

By subtracting the estimated overestimation of the MSD attributed to the random phase noise, we successfully compensated the systematic error in the MSD. However, in order to reduce the random phase noise it was necessary to enhance the fringe contrast and the increase of the total electron count on the CCD. Therefore, to enhance the fringe contrast, the reduction of the stray lights from optical component and the employment of the more efficient anti-reflection coating on the glass slide would be useful. Moreover, to sufficiently increase the total electron count on the CCD, the use of a light source with higher power and the optimization of the compatibility of the light source and the sensitivity curve of the camera would be useful.

Because the MSD relates to the diffusion constant, which is one of the important characteristics in cell biology [28

28. H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991). [CrossRef] [PubMed]

], the potential application of our setup includes the three-dimensional trace of the intracellular particle’s motion to reveal the diffusion constant of the cytoplasm. Our future works also include the assessment of the cell condition in terms of the diffusion constant after drug treatment. To the best of our knowledge, our system visualized the depth-resolved intracellular motility for the first time in sub-micrometer resolution without the use of contrast agents.

Acknowledgments

This study was based on a collaborative research between Hamamatsu Photonics K.K. and MIT G. R. Harrison Spectroscopy Laboratory. The authors would like to express their sincere gratitude to Dr. Michael S. Feld at MIT and Dr. Wonshik Choi at Korea University, who gave invaluable advice. We also thank Mr. Teruo Hiruma and Dr. Kenneth J. Kaufmann for their strong encouragement, and Mr. Masaomi Takasaka and Mr. Takahiro Ikeda for their technical support.

References and links

1.

A. W. Partin, J. S. Schoeniger, J. L. Mohler, and D. S. Coffey, “Fourier analysis of cell motility: correlation of motility with metastatic potential,” Proc. Natl. Acad. Sci. U.S.A. 86(4), 1254–1258 (1989). [CrossRef] [PubMed]

2.

P. C. Zhang, A. M. Keleshian, and F. Sachs, “Voltage-induced membrane movement,” Nature 413(6854), 428–432 (2001). [CrossRef] [PubMed]

3.

S. Suresh, “Biomechanics and biophysics of cancer cells,” Acta Biomater. 3(4), 413–438 (2007). [CrossRef] [PubMed]

4.

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005). [CrossRef] [PubMed]

5.

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Erythrocyte structure and dynamics quantified by Hilbert phase microscopy,” J. Biomed. Opt. 10(6), 060503 (2005). [CrossRef]

6.

G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett. 97(21), 218101 (2006). [CrossRef] [PubMed]

7.

X. Li, T. Yamauchi, H. Iwai, Y. Yamashita, H. Zhang, and T. Hiruma, “Full-field quantitative phase imaging by white-light interferometry with active phase stabilization and its application to biological samples,” Opt. Lett. 31(12), 1830–1832 (2006). [CrossRef] [PubMed]

8.

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]

9.

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13(23), 9361–9373 (2005). [CrossRef] [PubMed]

10.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24(17), 1221–1223 (1999). [CrossRef]

11.

S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express 16(12), 8406–8420 (2008). [CrossRef] [PubMed]

12.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh-resolution full-field optical coherence tomography,” Appl. Opt. 43(14), 2874–2883 (2004). [CrossRef] [PubMed]

13.

C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics,” Opt. Lett. 26(16), 1271–1273 (2001). [CrossRef]

14.

J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007). [CrossRef] [PubMed]

15.

C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, “Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer,” Opt. Lett. 29(17), 2028–2030 (2004). [CrossRef] [PubMed]

16.

T. Akkin, D. Davé, T. Milner, and H. Rylander Iii, “Detection of neural activity using phase-sensitive optical low-coherence reflectometry,” Opt. Express 12(11), 2377–2386 (2004). [CrossRef] [PubMed]

17.

K. Jeong, J. J. Turek, and D. D. Nolte, “Fourier-domain digital holographic optical coherence imaging of living tissue,” Appl. Opt. 46(22), 4999–5008 (2007). [CrossRef] [PubMed]

18.

K. Jeong, J. J. Turek, and D. D. Nolte, “Volumetric motility-contrast imaging of tissue response to cytoskeletal anti-cancer drugs,” Opt. Express 15(21), 14057–14064 (2007). [CrossRef] [PubMed]

19.

A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, “Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy,” Opt. Express 15(13), 8115–8124 (2007). [CrossRef] [PubMed]

20.

D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett. 32(6), 626–628 (2007). [CrossRef] [PubMed]

21.

D. C. Adler, S. W. Huang, R. Huber, and J. G. Fujimoto, “Photothermal detection of gold nanoparticles using phase-sensitive optical coherence tomography,” Opt. Express 16(7), 4376–4393 (2008). [CrossRef] [PubMed]

22.

J. Oh, M. D. Feldman, J. Kim, H. W. Kang, P. Sanghi, and T. E. Milner, “Magneto-motive detection of tissue-based macrophages by differential phase optical coherence tomography,” Lasers Surg. Med. 39(3), 266–272 (2007). [CrossRef] [PubMed]

23.

T. Yamauchi, H. Iwai, M. Miwa, and Y. Yamashita, “Low-coherent quantitative phase microscope for nanometer-scale measurement of living cells morphology,” Opt. Express 16(16), 12227–12238 (2008). [CrossRef] [PubMed]

24.

A. Dubois, J. Selb, L. Vabre, and A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39(14), 2326–2331 (2000). [CrossRef]

25.

K. Creath, “V Phase-Measurement Interferometry Techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.

26.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12(4), 761–768 (1995). [CrossRef]

27.

M. H. Gail and C. W. Boone, “The locomotion of mouse fibroblasts in tissue culture,” Biophys. J. 10(10), 980–993 (1970). [CrossRef] [PubMed]

28.

H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991). [CrossRef] [PubMed]

29.

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295(2), C538–C544 (2008). [CrossRef] [PubMed]

30.

N. T. Shaked, L. L. Satterwhite, N. Bursac, and A. Wax, “Whole-cell-analysis of live cardiomyocytes using wide-field interferometric phase microscopy,” Biomed Opt. Express 1(2), 706–719 (2010). [CrossRef]

31.

J. A. Hessler, A. Budor, K. Putchakayala, A. Mecke, D. Rieger, M. M. Banaszak Holl, B. G. Orr, A. Bielinska, J. Beals, and J. Baker Jr., “Atomic force microscopy study of early morphological changes during apoptosis,” Langmuir 21(20), 9280–9286 (2005). [CrossRef] [PubMed]

32.

C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7(4), 537–541 (1990). [CrossRef]

OCIS Codes
(170.1530) Medical optics and biotechnology : Cell analysis
(180.3170) Microscopy : Interference microscopy
(240.6648) Optics at surfaces : Surface dynamics

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: January 31, 2011
Revised Manuscript: February 28, 2011
Manuscript Accepted: February 28, 2011
Published: March 9, 2011

Virtual Issues
Vol. 6, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Toyohiko Yamauchi, Hidenao Iwai, and Yutaka Yamashita, "Label-free imaging of intracellular motility by low-coherent quantitative phase microscopy," Opt. Express 19, 5536-5550 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-6-5536


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References

  1. A. W. Partin, J. S. Schoeniger, J. L. Mohler, and D. S. Coffey, “Fourier analysis of cell motility: correlation of motility with metastatic potential,” Proc. Natl. Acad. Sci. U.S.A. 86(4), 1254–1258 (1989). [CrossRef] [PubMed]
  2. P. C. Zhang, A. M. Keleshian, and F. Sachs, “Voltage-induced membrane movement,” Nature 413(6854), 428–432 (2001). [CrossRef] [PubMed]
  3. S. Suresh, “Biomechanics and biophysics of cancer cells,” Acta Biomater. 3(4), 413–438 (2007). [CrossRef] [PubMed]
  4. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005). [CrossRef] [PubMed]
  5. G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Erythrocyte structure and dynamics quantified by Hilbert phase microscopy,” J. Biomed. Opt. 10(6), 060503 (2005). [CrossRef]
  6. G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett. 97(21), 218101 (2006). [CrossRef] [PubMed]
  7. X. Li, T. Yamauchi, H. Iwai, Y. Yamashita, H. Zhang, and T. Hiruma, “Full-field quantitative phase imaging by white-light interferometry with active phase stabilization and its application to biological samples,” Opt. Lett. 31(12), 1830–1832 (2006). [CrossRef] [PubMed]
  8. 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]
  9. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13(23), 9361–9373 (2005). [CrossRef] [PubMed]
  10. W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24(17), 1221–1223 (1999). [CrossRef]
  11. S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express 16(12), 8406–8420 (2008). [CrossRef] [PubMed]
  12. A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh-resolution full-field optical coherence tomography,” Appl. Opt. 43(14), 2874–2883 (2004). [CrossRef] [PubMed]
  13. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics,” Opt. Lett. 26(16), 1271–1273 (2001). [CrossRef]
  14. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007). [CrossRef] [PubMed]
  15. C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, “Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer,” Opt. Lett. 29(17), 2028–2030 (2004). [CrossRef] [PubMed]
  16. T. Akkin, D. Davé, T. Milner, and H. Rylander Iii, “Detection of neural activity using phase-sensitive optical low-coherence reflectometry,” Opt. Express 12(11), 2377–2386 (2004). [CrossRef] [PubMed]
  17. K. Jeong, J. J. Turek, and D. D. Nolte, “Fourier-domain digital holographic optical coherence imaging of living tissue,” Appl. Opt. 46(22), 4999–5008 (2007). [CrossRef] [PubMed]
  18. K. Jeong, J. J. Turek, and D. D. Nolte, “Volumetric motility-contrast imaging of tissue response to cytoskeletal anti-cancer drugs,” Opt. Express 15(21), 14057–14064 (2007). [CrossRef] [PubMed]
  19. A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, “Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy,” Opt. Express 15(13), 8115–8124 (2007). [CrossRef] [PubMed]
  20. D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett. 32(6), 626–628 (2007). [CrossRef] [PubMed]
  21. D. C. Adler, S. W. Huang, R. Huber, and J. G. Fujimoto, “Photothermal detection of gold nanoparticles using phase-sensitive optical coherence tomography,” Opt. Express 16(7), 4376–4393 (2008). [CrossRef] [PubMed]
  22. J. Oh, M. D. Feldman, J. Kim, H. W. Kang, P. Sanghi, and T. E. Milner, “Magneto-motive detection of tissue-based macrophages by differential phase optical coherence tomography,” Lasers Surg. Med. 39(3), 266–272 (2007). [CrossRef] [PubMed]
  23. T. Yamauchi, H. Iwai, M. Miwa, and Y. Yamashita, “Low-coherent quantitative phase microscope for nanometer-scale measurement of living cells morphology,” Opt. Express 16(16), 12227–12238 (2008). [CrossRef] [PubMed]
  24. A. Dubois, J. Selb, L. Vabre, and A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39(14), 2326–2331 (2000). [CrossRef]
  25. K. Creath, “V Phase-Measurement Interferometry Techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), pp. 349–393.
  26. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12(4), 761–768 (1995). [CrossRef]
  27. M. H. Gail and C. W. Boone, “The locomotion of mouse fibroblasts in tissue culture,” Biophys. J. 10(10), 980–993 (1970). [CrossRef] [PubMed]
  28. H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991). [CrossRef] [PubMed]
  29. G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295(2), C538–C544 (2008). [CrossRef] [PubMed]
  30. N. T. Shaked, L. L. Satterwhite, N. Bursac, and A. Wax, “Whole-cell-analysis of live cardiomyocytes using wide-field interferometric phase microscopy,” Biomed Opt. Express 1(2), 706–719 (2010). [CrossRef]
  31. J. A. Hessler, A. Budor, K. Putchakayala, A. Mecke, D. Rieger, M. M. Banaszak Holl, B. G. Orr, A. Bielinska, J. Beals, and J. Baker., “Atomic force microscopy study of early morphological changes during apoptosis,” Langmuir 21(20), 9280–9286 (2005). [CrossRef] [PubMed]
  32. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7(4), 537–541 (1990). [CrossRef]

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