We have developed a Linnik-type interference microscope provided with a low-coherent light source to obtain topographic images of an intact cellular membrane on a nanometer scale. Our technique is based on measurement of the interference between light reflected from the cell surface and a reference beam. The results show full field surface topography of cultured cells and reveal an intrinsic membrane motion of tens of nanometers.
©2008 Optical Society of America
Cell morphology and deformability are widely studied biophysical phenomena that have been used to examine voltage-induced motion of cell membrane [1, 2], assess red blood cells according to their membrane tension , and diagnose cancerous/non-cancerous cells by their stiffness . In this regard, one of the most clinically valuable applications of these phenomena is the study of cancer cells, since the deformability of cancer cells appears to be strongly related to their metastatic potential. Many studies have revealed that cancerous and normal cells differ in morphology and deformability [4–6]. Lekka et al. examined the stiffness of both types of cells by scanning force microscopy and showed that cancerous cells were significantly less stiff than normal ones . Scanning force microscopy is commonly used to measure cellular membrane fluctuation, which is related to cellular viscoelasticity, because the fluctuation is as small as tens of nanometers or less, i.e., hardly measurable by conventional optical microscopy [8, 9]. However, scanning force microscopy inevitably applies force on the cells and requires transversal scanning to obtain a three-dimensional image.
We have developed a technique to investigate cellular morphology. The technique, called quantitative phase microscopy (QPM), uses an interferometric microscope, which provides a full-field distribution of the optical path length on a nanometer scale using quarter-wavelength phase shifting [10, 11]. QPM works in a “transmission mode” (TM) in which the imaging light goes through the sample and reveals its optical thickness, and in a “reflection mode” (RM) in which the imaging light is reflected back from the sample surface and reveals the geometrical height of the sample surface [2, 12].
Although in the RM the surface fluctuation can be measured in a nanometer scale , previous researchers could not measure the fluctuation of the full field surface of a living cell. Since this difficulty is due to small reflectivity of the cell surface in culture medium, a low-coherence light source and high NA illumination are needed to acquire the scant light reflected from the cell surface.
In this paper, we demonstrate the usefulness of low-coherent QPM for measuring the full field surface topography of living cells. We show that by combining high NA illumination in Linnik configuration with a low-coherent light source, feedback control of the optical path difference (OPD), and control of the focal position in coordination with the OPD shift, it is possible to assess the surface topography of living cells in RM.
The experimental setup of low-coherence QPM based on a Linnik configuration is shown in Fig. 1. Light emitted from a halogen lamp passes through a Linnik interferometer provided 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 are projected onto the CCD camera (Hamamatsu, C9300-201), and an interference image is obtained.
Since the target is the surface topography of cultured cells, the sample cells are cultured on glass slides. The main problem in this configuration is the specular reflection from the glass overlapping the cellular surface reflection. The effect of specular reflection is avoided by adopting a low-coherent light source, or by using an anti-reflection (AR) coating on the glass surface beneath the cells. The wide spectral bandwidth of the light source makes the coherence length narrow; however, it also makes it difficult to achieve an effective AR coating. Considering this trade-off, we selected an AR-coating bandwidth of 550-950 nm and spectrally filtered the halogen light by a long-pass glass color filter RG695 (cutoff wavelength = 695 nm). The resultant spectral bandwidth and the center wavelength λc of the imaging light were 150 nm (FWHM) and 780 nm, respectively. Figure 2 shows the one-point interferogram I(z) seen by a single pixel of the CCD during the z-scan, where the coherence length is estimated to be 2 μm and the maximum fringe contrast is estimated to be 0.60.
A series of interferograms is obtained by periodically acquiring interference images while changing the OPD by λc/4, and a phase image is calculated by a quarter-wavelength phase-shifting algorithm. To achieve a precise quarter-wavelength phase shifting, we used a feedback control system comprising an infrared superluminescent diode (SLD) (DenseLight, DL-CS3102A), an infrared photodetector (PD) (New Focus, MODEL 2053), and a piezoelectric transducer (PZT1) (NEC TOKIN, AE0505D08F) that moved the reference mirror. This feedback system is based on the one described by Iwai et al. . The emission light of the infrared SLD (center wavelength and coherence length of 1.30 and 20 μm, respectively) is used to probe the disturbance in OPD between the sample and the reference arms. The control circuit that processes the signal from the infrared PD, monitors the disturbance with nanometer accuracy and controls PZT1 to cancel it. Reflection-enhancement coating for 1.3 μm was applied to the glass slide beneath the cells to set the reference plane for the feedback control. This glass surface is also AR coated for imaging spectral bandwidth (550-950 nm). The SLD’s luminescent spot on the sample is carefully adjusted so that a region where the cells are not attached is hit.
The major improvement from the previous feedback system is focal control by adopting an additional PZT beneath the sample dish. PZT1 on the reference arm is operated for small (<440 nm), fast (~500 Hz), and high-resolution (<1 nm) adjustment of the OPD. The large (maximum stroke: 100 μm) and relatively slow (~10 Hz) and rough (30-nm step) scanning of OPD is carried out by PZT2 (Physik Instrumente, P-611.ZS) beneath the sample dish. Therefore, during the measurements, PZT1 swings at a maximum of only 440 nm, while PZT2 moves about several μm to 10 μm to cover the whole height of the cell sample [See Figs. 3(a) and 3(b)]. Details of the image acquisition to build the full field surface topography are explained in the Results section.
3.1 Sample Preparation
Sample preparation was as follows. The sample cell type was MCF-7, which is the designation of a commonly used cell line derived from human breast cancer. We obtained a clone of MCF-7 cells from the American Type Culture Collection (cat# HTB-22). The culture medium was Dulbecco’s Modified Eagle Medium supplemented with 10% fetal bovine serum. A few days before measurement, the cells were subcultured on AR coated glass slides. The samples were immersed in the culture medium during the measurement as well as during culture.
3.2 Phase estimation algorithm and estimation error
Since the imaging light is a low-coherence light whose coherence function has an amplitude modulation in its envelope, the well-known four-point phase shifting algorithm (φ=tan-1((I 3π/2-I π/2)/(I π-I 0))) causes an error in demodulating the phase. To reduce this error, we used seven consecutive interference images to derive one phase image by
where I Φ represents the intensity of the interference image with phase shift Φ .
The phase estimation error was calculated by substituting the CCD count I(z) shown in Figs. 2 for I Φ in Eq. (1). Using I(z -3λc/8), I(z -λc/4), I(z -λc/8) , I (z), I(Z+λc/8),I(z +λc/4), and I(z +3λc/8)as interference intensities, phase value φ as the function of zoffset,can be estimated. After unwrapping φ and converting φ to z-estimated by Z estimated = λc∙φ/4π, we obtained the z-estimated as the function of z-offset. Ideally z-estimated should be equal to z-offset, but in fact, z-estimated deviates from the ideal line as the absolute value of z-offset increases. Figure 4 shows the z-estimation error (difference between z-estimated and z-offset) as a function of z-offset. 19.8 nm of the z-estimation error was expected in a measurement range of 2000 nm.
3.3 TM imaging
The optical thickness of the cell was obtained by TM phase imaging. The objective lens on the sample arm was adjusted to focus on the surface of the glass slide. The equal-path-length position was also adjusted there to achieve the highest degree of coherence [See Fig. 3(a)]. By shifting the OPD by a quarter wavelength using PZT1, a series of interference images [shown in Figs. 5(a)–5(d)] originating from the reflected light from the glass surface was sequentially obtained.
A phase image derived from the seven interference images, including those in Figs. 5(a)–5(d), is shown in Fig. 6. This phase image is a TM image where the imaging light goes through the cell and reveals its optical thickness (OT), which is related to the differential phase φ by
where Δn(z) is the relative refractive index along the beam. Using the mean refractive indexδn̄ , and cell height H, we rewrote Eq. (2) as
After removing phase wrapping and correcting tilting of the substrate, we obtained the distribution of optical thickness of the sample, as shown in Fig. 7.
3.4 RM imaging
To obtain an image of the cell surface topography, the focal plane and the equal-path-length plane should be simultaneously scanned during the measurement. We call this plane the “plane of interest”. The control of the plane of interest is carried out by moving PZT1 on the reference arm and PZT2 on the sample arm synchronously. The detail of the routine is as follows. When we measure the whole surface of a cell starting from the bottom of the cell, the control circuit increases the targeted OPD gradually by λc/4 increments; that is, the reference mirror is moved upward. Using PZT1 only would result in a discrepancy between the positions of the equal-path-length plane and the focal plane. This discrepancy would degrade fringe contrast and increase the phase estimation error.
To avoid this problem, we control PZT2 to cancel the extension/retraction of PZT1 by moving the sample downwards/upwards. The control circuit always monitors the extension of PZT1, and when it exceeds the assigned range (±120 nm), it makes PZT2 move to cancel the extension/retraction of PZT1. In this manner, PZT2 moves along the whole scanning range (the height of the sample cell; several μm to 10 μm) while PZT1 swings at a maximum of only 240nm. Therefore, the focal plane at the sample is always set to almost the same position as the equal-path-length plane; that is “the plane of interest”. By repeating this routine while gradually increasing the OPD, the glass slide surface moves downwards as shown in Fig. 3(b).In other words the height of the plane of interest measured from the glass slide surface shifts upwards.
Figure 8 shows a schematic diagram of the image processing, where I N represents the Nth interference image with an OPD shift of (N-1)×λc /4, and PN represents the Nth vertically sectioned phase image. PN is built by seven consecutive interference images I 4N-3 to I 4N+3. The maximum interference image number N1 is related to the maximum phase image number N2 by N1 = 4× N2 + 3 . We obtained forty-three interference images from which ten phase images were derived. In Figs 9(a)–9(d), we show examples of four consecutive interference images. An example of the vertically sectioned phase image is shown in Fig. 10(a), which derived from seven interference images including those in Figs 9(a)–9(d). In Fig. 10(a), the wrapped phase is properly obtained only around the plane of interest.
A full-field phase image was obtained by merging ten consecutive phase images. Figure 10(b) shows the resultant full field phase image. It should be noted that the linear tilting of the image was corrected in reference to the substrate. After processing Goldstein’s phase unwrapping algorithm , the cellular height profile was finally obtained as shown in Fig. 11, where the differential phase φ was converted to the geometrical height (H) by
As the refractive index of the medium, 1.335 was used and measured with an Abbe refractometer beforehand.
In the gray-colored area in Fig. 11, the reflection phase images were not successfully obtained because phase unwrapping was not successful. Since there were data-lost areas on the cell boundary, offset phase Δφ had to be added to the measured unwrapped phase φ measured in cell area as follows:
The number of fringes shown in the data-lost areas were counted and 6π (corresponding to three fringes) was adopted as Δφ.
There were two possible reasons for data loss. One was the sharpness of the gradient of the cellular surface. In the area where the surface is sharp, the interference fringe becomes too dense to be sufficiently unwrapped. The other was the interference fringes originating from the glass surface. These two conditions disturb the interference fringes from the cell surface in the vicinity of the cell boundary.
3.5 Estimation of the mean refractive index
The distribution of the mean refractive index of a cell was obtained as follows:
where OT is the optical thickness [Fig. 7] and H is the geometrical height [Fig. 11]. We estimated the mean refractive index as shown in Fig. 12. The measured value was mostly around 1.36 ~ 1.37 and varied in response to the intracellular organelles beneath the membrane. This result is consistent with the results of other studies [15–18].
3.6 Dynamic surface topography
Dynamic surface topography was obtained by repeating the RM phase imaging. In the dynamic measurement, only PZT1 was moved. OPD shifting was limited in a range going from -3λc /4 to 3λc /4 (seven points, swing of the PZT1 was 440 nm), so that the surface topography around the fixed plane of interest was obtained (approximately up/down to 1μm). Although this limitation reduces the horizontal regions of interest, this scheme is useful for measuring a particular region of the cell membrane at a high image-acquisition rate.
We obtained a series of local surface topographies for 500 sec at 2.4-sec intervals. Figure 13 shows the first frame of the movie of a living MCF7 cell’s RM topography. The area of the region of interest was 5.1 × 7.0 μm which corresponded to 41 × 56 pixels. To clearly visualize the surface fluctuation, linear tilting of the membrane was subtracted from the topography. The figures for the peak-to-peak amplitude of the cellular surface fluctuation on each pixel were tabulated. The resultant histogram is shown in Fig. 14. The peak-to-peak amplitude of the cellular surface fluctuation ranged from 61 to 297 nm and the average was 128 nm.
Figure 15 shows a representative time-series fluctuation observed at the center pixel in the region of interest. At this pixel, the cell showed a surface fluctuation of 120 nm peak-to-peak (27-nm standard deviation). To estimate the repeatability of the measurement, the dynamic surface fluctuation of the top surface of a 10-μm polystyrene bead (RI = 1.59 ~ 1.60) was also measured under the same conditions as the cellular surface fluctuation. The bead surface fluctuation was within a few nanometers (6.1 nm peak-to-peak, 1.2-nm standard deviation) and is shown in black line in Fig. 15.
4.1 Reliability of the absolute height and the refractive index measurements
To obtain the absolute height, offset phase Δφ had to be added to the measured unwrapped phase, as shown in Eq. (5). However, there could be, at worst, an offset phase estimation error of ±π. Because the substrate is an AR-coated glass slide, the plane where the optical field is effectively reflected is not equal to the physical surface of the glass to which the cells adhere. Therefore, the offset height ΔH = 292 nm might be ambiguous due to the phase estimation error ±π.
This ambiguity of the offset height affects the estimation of the refractive index. As the refractive index contrast Δn̄ is obtained as follows,
the error of the refractive index estimation is calculated using the following equation:
This error is proportional to the refractive index contrast and inversely proportional to the absolute height. In the worst case, that is if 0.04 and 1000 nm are substituted for Δn̄ and H, the refractive index estimation error would be 0.012. This error may be considered big compared to that found with an industrial refractometer. However, we think that our technique, which allows measurement of intact cells, is potentially applicable for biological studies, because the refractive index differs among intracellular organelles by the order of 0.01 [15, 18].
The ambiguity of the absolute height and the refractive index constitute a systematic error that originates from the estimation of the constant phase offset. If the offset phase of a particular AR-coated glass substrate could be determined, only the error of optical path length estimation, which was shown to be 1% in subsection 3.2, would ultimately remain. Thus, if the error of optical thickness estimation and that of absolute height estimation were 1% each, it would be possible to expect a 2% error of Δn̄ estimation; for example, 0.0008 for Δn̄ = 0.04.
4.2 Sensitivity of the surface topographic analysis
Concerning measurement of cellular surface fluctuation, RM phase imaging has two advantages compared to TM phase imaging. One is its high sensitivity and the other is its independence from the intracellular refractive index. Our RM phase imaging technique has nanometer-scale sensitivity; actually, repeatability with a margin of a few nanometers was demonstrated by measuring the surface of a bead. This sensitivity is hardly achievable by conventional TM phase imaging. This can be clearly seen if we want to know the surface fluctuation of a completely homogeneous, 4-μm-high cell whose refractive index is larger than its surrounding medium by 0.04. Even if the phase microscope has a 1-nm sensitivity for optical thickness, the reduced sensitivity to the geometrical fluctuation becomes 25 nm. This is because the optical thickness is given by the multiplication of the geometrical height by the refractive index contrast between the content of the sample and the medium. On the other hand, the RM phase imaging described here measures the dynamic morphology of the cells based on reflection signals directly originating from the cellular surface morphology. Consequently, nanometer-scale sensitivity to the optical path length leads to nanometer-scale sensitivity of the cellular height fluctuation.
In the case of actual cells, there are changes in the refractive index distribution mainly because of the movement of intracellular organelles. Conventional TM phase imaging cannot distinguish the fluctuation in height from the change in refractive index without any supposition or additive solutions [16, 17]. For example, if the 4 μm-high cell were not homogeneous and the intracellular refractive index at a certain position increased by 0.01, the TM phase image would not distinguish this refractive index change from a height change of 1 μm. This error is critical for cell assessment because within several minutes cellular surface fluctuation is only hundreds of nanometers at the most [8, 9]. From this viewpoint, RM phase imaging which does not depend on the intracellular refractive index is appropriate to assess cellular surface fluctuation.
In conclusion, the RM image reveals quantitatively and on a nanometer-scale the surface topography of cultured living cells, independent of the intracellular refractive index. Our technique also reveals the dynamic displacement of the cellular membrane without using a staining dye or reflection enhancement agent. A study that compares cellular membrane fluctuation among many types of cells is underway in our laboratory. The possibility to discriminate cancerous from non-cancerous cells is one of the most appealing applications. Since it has been shown that cancerous cells have a lower Young’s modulus than normal ones [6, 7], cancerous cells are expected to show an intrinsic vibration different from that found in normal ones. We believe that low-coherence QPM in RM will become a novel method for analyzing the physical properties of cells in biological studies and in clinical diagnosis.
This study was based on a collaborative research between Hamamatsu Photonics K.K. and MIT G. R. Harrison Spectroscopy Laboratory. The authors thank Dr. Michael S. Feld, Dr. Christopher Fang-Yen and Dr. Wonshik Choi at MIT, for their valuable 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 technical support.
References and links
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