Opposed-view digital holographic microscopy (OV-DHM) with autofocusing and out-of-focus background suppression was demonstrated and applied to measure the refractive index (RI) of suspended HeLa cells. In OV-DHM, a specimen is illuminated from two sides in a 4π-like configuration. The generated two opposite-view object waves, which have orthogonal polarization orientations, interfere with a common reference wave, and the generated holograms are recorded by a CMOS camera. The image plane of the sample was determined by finding the minimal variation between the two object waves. The out-of-focus background was suppressed by averaging the two object waves. Simultaneous determination of both the cell thickness and the phase retardation was avoided by using a spheroidal model for the detached cell obtained from confocal microscopy. Thus, the RI of suspended HeLa cells was measured from phase images of OV-DHM, with the thickness of the cells estimated by using a constant axial-to-lateral ratio. This measurement strategy reveals the RI with an accuracy of of the RI difference between cells and surrounding medium.
© 2017 Optical Society of America
Digital holographic microscopy (DHM) is a non-invasive, high-resolution, whole-field imaging technique for microscopic specimens, particularly translucent samples [1–6]. The phase imaging capability of DHM provides intrinsic contrast for transparent biological samples and also permits quantitative analyses of their 3D structures and refractive index (RI). DHM usually uses a monochromatic plane wave for illumination; consequently, both lateral resolution and axial sectioning are worse in comparison to a conventional microscope employing Koehler illumination. DHM also suffers from speckle noise due to the employed coherent illumination. Off-axis illumination [7–10], structured illumination [6,11], and speckle illumination [12–16] were introduced to improve the lateral and axial sectioning capability and to suppress speckle noise in DHM or, more generally, phase imaging. Low-coherence and incoherent illuminations were also used to reduce speckle noise of DHM [17,18]. Another variant, dark-field opposed-view digital holographic microscopy (OV-DHM), collects scattered light concurrently from both opposite views and, therefore, improves the contrast of internal structures, as well as the signal-to-noise ratio [19,20]. Recently, OV-DHM was shown not only to reduce out-of-focus background and speckle noise, but also to provide autofocusing and field-of-view (FOV) extension . Similar to other non-conventional illumination-based autofocusing methods [19,20], the image plane of a sample is identified in OV-DHM by finding the minimal variation between the two object waves propagating in opposite directions. Consequently, the sample can be refocused by propagating the object waves to their image planes in the computer. The FOV can be extended by combining two object waves propagating at an angle () with respect to each other.
DHM, which is based on interferometry and thus has optical path length measurement accuracy on the nanometer scale, is often employed to investigate the thickness or the RI of biological samples. Of note, the RI of cells is of great significance because it provides fundamental information about the composition and organizational structure of cells . For a cell with refractive index , suspended in a medium with refractive index , the phase shift of light of wavelength passing through the cell with respect to the medium is23]. The RI of a cell was also measured in comparison to an air bubble by holding both between two cover slips and assuming identical thicknesses [24,25]. A combination of confocal microscopy with transport-of-intensity (TIE)-based phase retrieval was utilized to separately measure the cell thickness and phase difference . Finally, dual-wavelength DHM was employed to measure the RI of cells, utilizing dispersion of the surrounding medium of the cells .
In this paper, we determine the RI of suspended HeLa cells by using OV-DHM. The analysis is based on a description of the cells by a spheroidal model with constant cross-sectional aspect ratio (axial/lateral), which we derived from laser scanning confocal microscopy measurements. The proposed strategy is an easy-to-use approach that—unlike other RI determination methods—avoids the difficulty of imaging the same cell in confocal and DHM modes by employing the spheroidal model. Furthermore, we demonstrate that OV-DHM has the ability to efficiently suppress out-of-focus background. This background suppression as well as the autofocusing ability of OV-DHM contribute to minimizing errors of the RI determination due to defocusing and speckle noise.
2. OV-DHM TECHNIQUE
A schematic diagram of our home-built OV-DHM setup is shown in Fig. 1. It is based on a common-path Sagnac interferometer, comprised of a polarization-maintaining beam splitter (PBS) and two mirrors, and . A 561-nm continuous-wave (CW) laser is coupled into a fiber splitter, the two outputs of which are used as the reference wave and the light irradiating the object from opposite sides. The laser output from the object-wave end of the fiber splitter is split by the PBS into two components with orthogonal (horizontal and vertical) polarizations, respectively. The horizontally (vertically) polarized component passes through the Sagnac configuration in a clockwise (counterclockwise) fashion. Two telescope systems with magnification, and , are inserted between mirrors and to image the sample in opposite views. The distance between the objectives and is about twice their working distance. The sample is placed close to the middle plane between and (Plan , Nanjing Yingxing Optical Instrument Company, Nanjing, China). The two object waves and arising from light passing through the sample in opposite directions are further magnified by the two telescopes by a factor of 1.5 and superimposed with a common reference wave via a non-polarizing BS. The reference wave is linearly polarized at an angle of 45° with respect to the polarizations of (horizontal) and (vertical). Two holograms, and , are measured sequentially, by rotating polarizer to the horizontal and vertical directions, respectively, with a complementary metal–oxide–semiconductor (CMOS) camera (, , 54 fps, DMK 23UX174, Imaging Source, Bremen, Germany). The CMOS camera is aligned so as to collect in-focus images of the middle plane between and for both clockwise and anti-clockwise directions. A small angle of the reference wave of with respect to the object waves allows separation of the real image, twin image, and terms of the generated carrier frequency hologram in the Fourier domain, while maintaining the highest spectral components of the object waves with diffraction-limited resolution . An exemplary hologram of OV-DHM and its spectrum are shown in Figs. 2(a) and 2(b), respectively. We mention in passing that this OV-DHM configuration can be further upgraded with two CCD cameras to record both holograms and simultaneously.
Due to the symmetry of the OV-DHM configuration, a sample at a defocus distance in hologram (clockwise) will have an opposite defocus distance in hologram (counterclockwise). Without loss of generality, two object waves, and , can be reconstructed and refocused to a plane at an arbitrary distance from the hologram by using the angular spectrum method :2(b). is a window function that selects the real images of and in the frequency domain and removes terms and twin images. Of note, ideally, the CMOS camera ought to be aligned so as to collect in-focus images of the middle plane between and for both clockwise and anti-clockwise directions. However, if the image/conjugate plane of has defocusing distances and to the CMOS camera along the clockwise and anti-clockwise directions, respectively, such misalignment can be compensated digitally by replacing with (for ) and (for ) in Eq. (1).
A key issue in refocusing an image from the out-of-focus hologram plane is to find the distance between the hologram plane and the image plane, since a slight out-of-focus displacement will reduce the accuracy of the phase measurement. Hitherto, there have been many reports on image plane detection, based on amplitude analysis , spectral norms , non-conventional illumination [6,7,31], and other approaches [32,33]. In OV-DHM, focus determination follows the following strategy: Because holograms and have opposite defocus, the difference between the intensity of the two object waves is minimal for the correct distance employed in the reconstruction, with being the defocus in the sample domain and the effective magnification factor of the OV-DHM system. Accordingly, the focus criterion can be defined as3). Generally, for cells located in different axial planes, the focus criterion can be applied to different regions and, consequently, enables us to refocus laterally separate regions of a hologram to different focal planes, providing 3D information of the sample . Compared with conventional image plane determination methods, this method does not rely on the type of a sample, i.e., it can be used for samples with both amplitude and phase modulations.
For a specific refocused plane, only in-focus cells will have the same images in and , whereas out-of-focus components are different [see Fig. 2(d)]. Thus, out-of-focus components as well as speckle noise can be suppressed by averaging and . Of note, out-of-focus background suppression can be further enhanced if the two object waves are not coaxial but propagate at a slight angle (). In this case, only in-focus cells appear at the same locations and are enhanced upon averaging, whereas out-of-focus cells are shifted laterally and are averaged out.
3. OUT-OF-FOCUS BACKGROUND SUPPRESSION OF OV-DHM
The auto-focusing and out-of-focus background suppression of OV-DHM were demonstrated with phase imaging of human cervical cancer (HeLa) cells. HeLa cells (LGC Standards GmbH, Wesel, Germany) were maintained at 37°C and 5% in Dulbecco’s modified Eagle’s medium (DMEM), containing 10% fetal bovine serum (FBS) and antibiotics ( penicillin and streptomycin, both from Invitrogen, Carlsbad, CA). After 24 h incubation, the cells were detached by using 500 μL trypsin and mixed with an agarose-phosphate buffered saline solution (3%, weight/weight) at 37°C. After cooling to room temperature (24°C), a transparent gel formed with cells entrapped. Figures 3(a) and 3(b) show amplitude and phase images of (left) and (right) after refocusing to the focal plane, with , obtained by the focus criterion in Fig. 3(e) for selected region 1, indicated by the white rectangle in Fig. 3(b). For comparison, Fig. 3(c) shows phase images of (left) and (right) refocused to the focal plane with , obtained by the focus criterion in Fig. 3(f) for region 2 [green rectangle in Fig. 3(c)].
Figures 3(a)–3(c) show clearly that only in-focus cells have identical images in and . Out-of-focus cells are different in and images and thus can be suppressed by averaging and . To quantify the ability of OV-DHM to suppress out-of-focus background, an area [red rectangle in Fig. 3(b)] was selected in and , and and compared in Fig. 3(d). The visibility of the out-of-focus background in the images of , , and was quantified by the standard deviation, calculated from the three rectangular regions () in Fig. 3(d), yielding 0.49, 0.40, and 0.21, respectively. Accordingly, OV-DHM has the capability of reducing out-of-focus background by averaging the two object waves.
4. REFRACTIVE INDEX MEASUREMENT ON CELLS BY OV-DHM
Live HeLa cells adhere to the bottom of cell containers and thus have a flat, carpet-like appearance . If they die or are detached from surfaces by using trypsin, they round up and become ellipsoids , shaped by the tension of cell membrane and gravity. A triaxial ellipsoid is described by the equation , with , , and being the lengths of the principal half axes along , , and , respectively. In the agarose preparation, the cells are compressed along the principal axis , chosen to be perpendicular to the glass slide supporting the cells, whereas the two other extensions are nearly equal, giving the cells an almost spheroidal shape . For the OV-DHM experiment, the sample is introduced into the setup such that the axis is along the axial direction of the microscope. Depending on the tension of the cell membrane and the density of the cells with respect to the surrounding medium, the cellular extensions may vary [36,37], but the ratio , with and being the axial and lateral extensions, is essentially fixed for a given cell type.
The 3D ellipsoid model of suspended HeLa cells was studied by using our home-built laser-scanning confocal fluorescence microscope [38,39]. In the experiment, HeLa cells were seeded on eight-well Lab-Tek II chambered cover glass (Thermo Fischer Scientific, Waltham, MA) and cultured in DMEM for 24 h. Afterwards, the cell membranes were stained with CellMask Green (Invitrogen, Darmstadt, Germany) in DMEM for 5 min. The cells were thoroughly washed twice with phosphate-buffered saline, and then embedded into agarose-water gel with the protocol described above. Then, the cells were imaged under the confocal microscope using a bandpass filter (600/37 nm) for fluorescence detection. A series of 3D images was obtained by scanning different regions () of the sample, each with voxels. Exemplarily, Figs. 4(a) and 4(b) show orthogonal views and a 3D view of cells from a selected region. The suspended cells are approximately round in view, while they are elliptical in the and views. For quantitative analysis, the cross-sectional intensities along two lines through the center of a cell along and [red and blue lines in Fig. 4(a)] are shown in Fig. 4(c). From these data, the overall axial (lateral) extension of the cell is () μm. The axial-to-lateral aspect ratio of the cell is thus . This procedure was performed for 50 cells; the statistics of axial/lateral () and lateral/lateral () ratios are shown in Fig. 4(d), yielding averages of and , respectively. Here is the average lateral extension, and the error bars indicate standard deviations of all measurements. The data show that a spheroidal model (i.e., an ellipsoid with ) is a good approximation for the suspended HeLa cells, with an almost constant aspect ratio between the axial and lateral extensions. In general, the spheroidal model can be further simplified to a 3D spherical model () if cells or tissues are prepared in a rotatory cell culture system . More generally, 3D bioprinting  allows one to produce a designed shape for live cells or tissues and thus give more freedom to extend the model.
With the spheroidal model of the suspended HeLa cells, the cell thickness along the axial direction can be computed from the lateral extension and the aspect ratio . By using Eq. (1) together with the thickness of the cell along the axial direction for a point in the lateral plane, , we obtain4), so the RI of the cell equals .
The same HeLa cell sample used for fluorescence imaging was also employed for the RI measurement. Figure 5(a) shows the wrapped phase image of cells reconstructed from the object wave in OV-DHM, after refocusing by a distance . The correct refocusing distance, determined by finding the minimal variation between and for the selected cell, helps to minimize the phase error due to image defocus. Even a slight defocus will introduce a moderate error on the phase measurement . The phase distributions of , and along the red dashed line across the cell in Fig. 5(a) were extracted and are shown in Fig. 5(b). It is apparent that the green curve is less noisy due to the averaging operation on and . Fitting this curve with Eq. (4) and setting yields and . The RI of the agarose-water gel (3%, weight/weight) was , measured by using a refractometer (PAL-RI, ATAGO, Tokyo, Japan) at 24°C. Therefore, the RI of the cell was at 24°C. Ten cells were analyzed by the same procedure, yielding , with the error denoting the standard deviation within the ensemble. The obtained agrees with the result measured by dual-wavelength DHM , implying that the OV-DHM approach provides a precise RI determination for the HeLa cells.
This paper presents a unique technique for RI determination of cells by using OV-DHM. Simultaneous determination of both and is circumvented by using a spheroidal model for detached cells, which was obtained by confocal microscopy. The proposed strategy is not entirely stand-alone because it needs a confocal microscope to quantify the parameters of the spheroidal model. However, the difficulty of imaging the same cell in confocal and DHM modes is avoided by using the spheroidal model. OV-DHM was employed to determine the phase of a light passing through a cell. The image plane within the sample was identified by finding the minimal variation between the two object waves; consequently, refocusing was performed by propagating the waves to the common image plane. Out-of-focus background can be suppressed by averaging the two object waves and because in-focus contributions are enhanced by the averaging operation, whereas out-of-focus contributions have different defocus distances and thus are at least partially cancelled, as are noise contributions (e.g., coherent noise). The autofocusing and out-of-focus light-suppressing ability of OV-DHM contributes to improving the accuracy of RI determination.
3D profiles of suspended HeLa cells in agarose gel were measured by laser-scanning confocal microscopy, revealing a spheroidal cell model with a constant axial-to-lateral aspect ratio. Based on this model, the RI can be determined by using a stand-alone phase-imaging approach (including, but not limited to, OV-DHM), since the thickness of the cell can be calculated from the phase image for all lateral positions. The RI depends on the composition of the cell, and the surrounding medium and will be maintained under constant conditions, no matter whether the cell is detached or not.
Our RI measurement strategy based on an ellipsoid model is not limited to HeLa cells studied here but also suitable for many other cell types. Different model shapes, e.g., spheres, can also be imposed by using the newly developed 3D bioprinting techniques .
Helmholtz Program Science and Technology of Nanosystems (STN); Deutsche Forschungsgemeinschaft (DFG) (GRK 2039); National Natural Science Foundation of China (NSFC) (61605150, 61475187, 61575154, 61107003, U1304617); 863 Program (2013AA014402); Fundamental Research Funds for the Central Universities (JB160511, XJS16005, JBG160502).
We thank Prof. Wolfgang Osten and Dr. Giancarlo Pedrini from University Stuttgart for discussions of opposed-view digital holographic microscopy.
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