We describe an approach for arbitrarily adjusting the focal positions in quantitative phase imaging (QPI) based on a Linnik interferometer. Our setup employs a unique sample configuration in which transparent objects are imaged by a Linnik interferometer. By introducing a focus-tunable lens on top of the Linnik interferometer, we successfully decoupled the spatio-temporal coherence gating from the focal positioning and achieved dynamic focusing without disturbing the optical path length. Depth-sectioned quantitative phase images of polystyrene beads and live cultured cells were obtained without mechanical scanning.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Quantitative phase imaging (QPI) in cell biology is a group of imaging techniques for quantitatively obtaining spatially resolved mapping of optical path difference, and QPI can visualize the structure and dynamics of living cells in a label-free, non-invasive, and preprocessing-free manner . Biological applications of QPI include measurement of volumetric changes in live cells, visualization of the heterogeneity of refractive index in cells and tissues, apoptotic shrinkage of cells, membrane fluctuations of live cell’s plasma membrane and nuclear membrane, and so on [2–9]. Compared to optical coherence tomography (OCT), QPI is more applicable to the study of intracellular heterogeneity and sub-wavelength scale fluctuations in cell morphology.
Phase reconstruction methods in QPI are roughly classified into two categories, namely, interferometric methods and propagation-based non-interferometric methods, and various phase acquisition methods are under research and development. These methods involve trade-offs in terms of the image acquisition speed, horizontal resolution, temporal sensitivity, and spatial sensitivity [5,10–14]. Compared to non-interferometric methods, classical interferometric methods require relatively large set-ups and high cost, but their results are not affected by the reconstruction algorithms attributed to propagation-based methods and can be applied to slowly-varying phase objects such as confluently cultured cells. In interferometric methods, the use of spatially and/or temporally incoherent light sources allows the spatial resolution of QPI to be as high as that of bright-field imaging and also eliminates speckle noise [4,15–18].
When the light source has spatial and temporal incoherence, to perform a focus scan on cells or living organisms beyond the depth of focus (DOF), the optical path lengths (OPLs) and geometric focusing need to be adjusted simultaneously. In previous publications on time-domain OCT (TD-OCT), these adjustments were performed by relatively elaborated mechanical actuators which adjust the path length and the focal condition respectively . In recent studies on spectral-domain OCT (SD-OCT) and swept-source OCT (SS-OCT), a focus tunable lens (FTL) is introduced into solely the sample arm to achieve both fast focus movement and high lateral resolution [20–22], but this configuration is not applicable for the system with spatially incoherent illumination.
In the field of QPI, one of the successful implementations of focal scanning with incoherent light source is a common-path technique called Spatial Light Interference Tomography (SLIT) . In the SLIT system, a focus scan of the sample was successfully performed by using the axial movement of the objective lens. Because the sample wavefront and the reference wavefront are always matched in common-path QPI methods, the SLIT technique did not suffer from the mismatch of the sample and the reference wavefronts while Z-scanning. Implementation of FTL for the Z-scanning of SLIT system should work though this configuration has not been reported yet. On the other hand, in the full-field two-beam interference system with spatially incoherent light source, the wavefront matching of the sample light and the reference light is critical.
In this study, we propose an optical system that decouples the coherence gating from the geometric focusing by introducing a cost-effective FTL on top of a Linnik interferometer-based QPI setup with a compact single-ended configuration, to achieve fast dynamic focusing. Different from previously reported configuration in TD-OCT , our unique sample configuration with a mirror below the sample dish enabled the focus scanning done solely by the FTL. Because our setup is based on a two-beam interferometer, spatially low-frequency component of the image was preserved, and the image was inherently halo-free. In the experiment, we demonstrated focus adjustment of the QPI with the FTL in measurements of polystyrene beads and live cells.
2. Experimental setup
2.1 Setup of dynamic-focus low-coherence Linnik interferometer
In order to construct a compact QPI system, we adopted a Linnik interferometer employing single-ended illumination. Figures 1(a) and 1(b) show a schematic illustration and a photograph of the optical system and the sample configuration, where a mirror that we call a “sample mirror” was placed under the sample chamber.
In Fig. 1(a), when the path lengths of the sample arm and reference arm are equal and the reference mirror and the sample mirror are optically conjugate, we can obtain interference fringes with high visibility. This condition can be fulfilled by means of two degrees of freedom in the optical setup: the axial positioning of the reference mirror and the reference objective lens. In order to adjust the focal position, which is the conjugate plane of the CMOS camera, we adopt a third degree of freedom: an FTL (Optotune, EL-16-40-TC-VIS-5D) placed between the tube lens and the beam splitter. By changing the focal power of the FTL, the plane conjugate to the CMOS camera moves back and forth along the optical axis, while keeping the optical path lengths of the sample and the reference arms constant. In other words, the coherence gating and the geometric focusing are decoupled. Therefore, the contrast of the interference fringes does not change even after a focused scan by the FTL (see Visualization 1). For the illumination part, we constructed a Köhler illumination system using a low-coherence light source (Cree, XQ-E LED, center wavelength = 528 nm), in order to acquire images without speckle noise. In addition, a band-pass filter (Thorlabs, FL532-3, FWHM = 3 nm) was inserted into the illumination part to make the adjustment of the OPL easier. The temporal coherence length calculated from the spectral bandwidth was 42 μm in the air.
Identical objective lenses (Olympus, LUCPLFLN 20X, NA = 0.45) were used for the sample and reference arms to balance the optical path lengths. A compensation plate was bonded to the sample mirror in order to match the aberration between the sample arm (sample chamber) and the reference arm. The light emitted from the Köhler illumination system was split by a beam splitter, reflected from the sample and the reference mirrors, combined again to pass through the FTL, and then formed interference fringes on the imaging surface of a CMOS camera (IDS Imaging Development Systems, UI-3080CP-M-GL Rev.2) by a tube lens (OptoSigma, DLB-25.4-200PM, f = 200 mm).
The details of the optical paths of the sample beam and the reference beam are shown in Figs. 1(c) and 1(d). The samples were immersed in an immersion liquid (gelatin solution or culture medium) on a glass-bottom dish, and a coverslip was placed on top. Additionally, a sample mirror was placed under the glass-bottom dish. On the sample beam side, the illumination light passed through the coverslip, sample, and glass slide and was reflected from the mirror. Since the sample was illuminated by the light reflected from the mirror, this was a single-ended configuration. On the other hand, on the reference arm side, the illumination light passes through the compensation plane and is reflected by the mirror. The advantage of this method is that the transparent sample could be observed in the same way as with a transmission microscope by simply placing the mirror under the chamber.
As described in previous publications, coherence gating in two-beam interferometers works both temporally and spatially , and with spatially incoherent light sources such as halogen lamps and LEDs, the effect of spatial coherence, which is also called “longitudinal coherence”, is more dominant than that of temporal coherence [24–26]. Figure 2(a) shows the plot of the interference fringe visibility measured by translating the reference objective lens along the optical axis while keeping the path length constant. The measured FWHM of the spatial coherence gating was 32 μm with the band-pass filter and 25 μm without the band-pass filter. On the other hand, the interference fringe visibility as a function of the path length difference measured by translating the reference arm along the optical axis is shown in Fig. 2(b). The measured FWHM of the temporal coherence gating was 46 μm with the band-pass filter and 16 μm without the band-pass filter. As expected, the spectral filtering affects less on the spatial coherence gating width than on the temporal one. This result explains why implementing the FTL only in the sample arm does not work in a full-field interferometer with spatially incoherent light source.
2.2 Image acquisition method
In our setup, the phase change of the light transmitted once through the sample was measured. In contrast to the double-pass configuration in conventional Linnik/Michaelson interferometers, our setup is still a single-ended configuration. Though the illumination light incident on the sample mirror also passed through the sample, while the light coming back from the sample mirror passed through the sample, the wavefront modulation undergone by the incident light occurred far away from the focus and did not affect the resultant interference images. Therefore, the phase delay attributed to the wavefront modulation by the sample is related to the optical thickness (OT) by:
The phase images were acquired by temporal phase shifting by means of nanometer scale translational motion of the piezoelectric transducer, and we adopted the well-known four-step phase shifting algorithm  which is described by:
Figure 4 shows the timing charts of the focal changes given by the FTL, the phase shifting given by the PZT, and the exposure of the camera. In our experiments, the exposure time was 10 milliseconds, and the time interval between each phase shifting was 50 milliseconds. The focal shift was performed 50 milliseconds after the fourth phase shifting (3π/2). This means that the measurement time required for one slice in QPI at one focal plane was 250 milliseconds. The incremental focal changes were always upward motions, and the FTL was returned to the original position after one cycle of the focal scanning.
On the phase map calculated with Eq. (2), we processed the phase unwrapping and the background correction. The background distortion was corrected by subtracting the weighted sum of Zernike polynomials up to the sixth component . The coefficients for the background correction were determined by the least-squares method to minimize the mean-squared error of the corrected phase of the roughly estimated background pixels.
3.1 QPI slices of bead suspension
Polystyrene beads were observed in order to confirm how the focus adjustment implemented by the FTL works. The beads (Polysciences, Catalog No. 17154-10) were 1 µm in diameter and were prepared by dispersing them in a 10 wt% gelatin solution. Scanning of the focal plane was performed at a pitch of 0.88 µm, and we acquired 36 slices in total (Z = 0 –30.8 µm).
Figures 5(a) and 5(b) show OT images of the beads at two different focal planes (Z = 7.92 and 15.84 µm, respectively) in the same Z-scan. At each focal plane, only beads that were in focus were observed without speckle noise, which could be caused by digital refocusing using lasers. The measured image of the best-focused bead at Z = 15.84 µm and the OT distribution are shown in Figs. 5(c) and 5(d), respectively. The expected OT from the bead is given by30], ns is the refractive index of the gelatin solution (n = 1.35), and d is the known diameter of the bead (1 μm). The experimental result was almost in agreement with the expected OT profile of the bead, as displayed in Fig. 5(d). The OT measurements showed a gradual broadening at the periphery of the beads. Since the lateral resolution of the optical system is 0.72 µm, which is not enough for the bead diameter of 1 µm, the measured values were affected by the diffraction limit.
3.2 Time-lapse QPI of MCF-7
To demonstrate depth resolved quantitative phase imaging of living cells, we imaged MCF-7 cells (derived from human breast cancer cells) with our setup. Two days before the measurement, the cells were passively cultured on a glass-bottom dish (Matsunami glass industry, D11130H) and the cells were almost confluent at the time of the measurement. During the measurement, the samples were immersed in culture medium, and the temperature was kept at 37°C. Focus scanning was performed at a pitch of 1.76 μm, and a total of 8 slices were acquired. The acquisition of these 8 slices took 2.0 seconds (250 milliseconds Ö 8). In the time-lapse imaging, this focal scanning cycle was repeated at 5-second intervals (the waiting time between the completion of one Z-scan and the beginning of the next Z-scan was 3 seconds).
Figure 6(a), (b), and (c) are OT images at different focal positions (Z = 1.76 µm, 7.04 µm, and 12.32 µm, respectively) in the same Z-scan. Figure 6(b) is an in-focus image, while Figs. 6(a) and (c) are slightly out of focus. The cross-sectional profiles of the OT along the white lines in Figs. 6(a), 6(b), and 6(c) are shown in Fig. 6(d) to confirm that the best focus was achieved in Fig. 6(b). The cross-sectional profile of the OT at Z = 7.04 µm had the highest contrast in the modulation of the intracellular particles.
Figure 6(e) shows the OT image from the time-lapse video (see Visualization 4) of the in-focus images at Z = 7.04 µm. As the video shows, the positions of the intracellular particles and the boundaries of the plasma membranes were dynamically changing all the time, indicating that the observation environment was not damaging the cells.
4. Discussion and conclusions
In this paper, we have introduced a compact single-ended QPI setup that enables non-mechanical focal scanning combined with a low-coherence Linnik interferometer, and we have shown examples of measurements on static and dynamic samples. Due to the decoupling of the coherence gating and the geometric focusing, the focal position could be arbitrarily adjusted without disturbing the optical path length. Compared to digital refocusing, our method employing a low-coherence light source does not cause speckle noise in the image, although our method requires a longer acquisition time.
In the current optical system, the FTL is placed between the objective lens and the imaging lens, so the magnification changes slightly as the focus moves. Therefore, in future research, the FTL will be placed in a telecentric arrangement to suppress changes in observation magnification.
Dynamic focusing in QPI by ETL can be applied not only to adherent cells but also to the observation of floating cells distributed at different heights. In addition, this approach eliminates the need for mechanical motorized stages or expensive piezo stages, thus contributing to the construction of a compact and inexpensive QPI system. Our future work will include the application of our setup to an automated cell imager for mass screening of floating cells.
We would like to thank Ms. Masumi Suzuki for generously providing us with live cells.
The authors declare no conflicts of interest.
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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