We demonstrate a simple method for quantitative phase imaging of tiny transparent objects such as living cells based on the transport of intensity equation. The experiments are performed using an inverted bright field microscope upgraded with a flipping imaging module, which enables to simultaneously create two laterally separated images with unequal defocus distances. This add-on module does not include any lenses or gratings and is cost-effective and easy-to-alignment. The validity of this method is confirmed by the measurement of microlens array and human osteoblastic cells in culture, indicating its potential in the applications of dynamically measuring living cells and other transparent specimens in a quantitative, non-invasive and label-free manner.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
When light passes through a transparent object, its amplitude remains nearly unaltered. However, the phase of the transmitted light carries specific information about the sample structure. Phase contrast microscope and differential interference contrast microscope [1, 2] have proven to be powerful phase visualization platforms for biological and transparent samples, but they provide only qualitative phase information. In recent years, quantitative phase measurement techniques have been proposed and utilized for obtaining accurate phase distribution [3, 4], which presents great opportunities for studying cells and tissues quantitatively and non-invasively. Digital holographic microscopy (DHM), one of the established quantitative phase measurement techniques, has been successfully applied in the measurement of living cells [5, 6], surface profiling [7–9] and thermal lensing effect . Conventional DHM using coherent illumination is plagued by speckle noises, which ultimately limit the spatial resolution and image quality. To mitigate this problem, incoherent DHM based on white light has also been proposed [11–13]. However, there is a challenge for the practical implementation due to the extremely short coherent length of the illumination source. More recently, non-interferometric techniques using transport of intensity equation (TIE)  have gained much attention, which require only a series of through–focus intensity images [15–17]. Generally, the intensity images at multiple axially displaced planes are recorded by translating CCD manually, which slows down the data acquisition speed inevitably. To increase capturing efficiency and expand the applicability to dynamic objects, a dozen approaches have been proposed [18–27], among which the schemes based on chromatic aberrations , volume holographic microscope , flow cytometry , tunable lens , phase spatial light modulator for modulating defocus distance [23–26] have proven to be promising TIE phase imaging technologies.
In this paper, we present a method for quantitative phase imaging of live cells and other transparent specimens, which offers a simple design, high-performance, as well as suitability for operation in an existing microscopy setting. Inspired by flipping interferometry , a flipping imaging module is designed and attached to an inverted bright field microscope. This add-on module is compact, cost-effective, and easy to implement, which enables to simultaneously create two laterally separated images with unequal defocus distances. We demonstrate the capacity and validity of the method by quantitative phase imaging of microlens array and time-lapse morphological changes of living human osteoblastic cells.
2. Theory and principle
TIE states the relationship of the derivative of intensity with respect to the optical axis and the object-plane phase :
A common way for retrieving the phase from TIE is to define an auxiliary function ψ [14, 29] that meetsEqs. (1) and (2) can be transformed into a pair of Poisson equations,30, 31].
3. Experimental setup
Figure 1 shows the schematic of the inverted bright field microscope upgraded with a flipping imaging module to achieve quantitative phase imaging based on TIE. A halogen lamp is used for illumination light source. The spatial coherence of the illumination is determined by size of the condenser aperture, which can be represented by coherent parameter S, where S is the ratio of the condenser to objective numerical apertures (NA). Experimentally the condenser aperture is properly adjusted to set the coherent parameter S around 0.3 [24, 32, 33]. The beam passing through the sample (placed on a motorized sample translation platform with axial minimum step size of 50 nm) is focused by a microscope objective, and then projected through a tube lens onto the CCD (Imaging Source SVS16000MFGE, 3280 × 4892, 7.44 μm pixel size). After passing through the output port of the inverted microscope, the imaging beam enters a flipping imaging module immediately, which consists of a diaphragm, a beam splitter, a retro reflector and a mirror mounted on motorized translation stage. In this module, the imaging beam firstly passes through a diaphragm, then is split into two parts via a beam splitter BS. The transmitted beam propagates towards a mirror placed perpendicularly to optical axis and then is reflected back along the original propagation direction. The reflected beam propagates towards an orthogonal retro reflector (built with a pair of mirrors) and after being reflected twice it is laterally displaced by a certain amount. To avoid redundant free-space propagation, the retro reflector is integrated with the BS faces. As a result two images with symmetrical arrangement in lateral direction are captured by the same CCD camera in one single shot.
4. Defocus distance calibration and image registration
As demonstrated in Fig. 1, the recorded two images have different optical paths from the BS to CCD. Because the retro reflector is integrated on the BS faces, the length of the optical path marked by the red lines is fixed. While the length of the optical path marked by the blue lines can be adjusted by properly translating the Mirror axially. In order to accurately equalize the distances from BS to CCD plane along both optical paths, we use a 5 μm pinhole as object and implement proper axial translation of the Mirror until two laterally separated spots can be both focused in CCD camera. We label the plane in which the Mirror is as the reference plane when both focused. Then by translating the Mirror a certain axial distance ∆z from the reference plane, two laterally separated images with defocus distance 2∆z between them (one in-focus image and one defocus image with defocus distance 2∆z) can be created. Additionally, to simultaneously achieve over-focal and under-focal images with the same defocus distance ∆z from the in-focus image (central difference provides a more accurate estimate of the intensity derivative), a traditional positive target is used as sample and focal scanning has been done with the motorized translation platform. With properly translation the sample platform along the optical axis, both in-focal planes of images in the left- and right- side of the CCD camera can be determined, and thus through proper control of the translation platform, the sample could be precisely set at the central plane between over-focal and under-focal images with defocus distance of ± ∆z.
Prior to recovering the phase, it is necessary to perform image registration [22, 27]. The traditional positive target is still acting as object to determine the coordinate transformation. First a flipping transformation is performed in one of the camera halves, and then the affine transformation  is applied which could fix both images to the same coordinate.
5. Experiment results
To demonstrate the validity of this approach, we take a planoconvex microlens array (Opton, MLA-2R250, 250 μm pitch) as measured example and use a × 10/0.25 NA objective for imaging. Figure 2(a) shows the local regions of raw image and the raw image obtained in both halves of the camera is shown at the top right corner of Fig. 2(a). The defocus distance ∆z is chosen as 100 μm. Because the splitting ratio of BS is not exactly 1:1, the two images have different background intensity, a normalized process is needed for further process (The intensity normalized characterization has been done before introducing the sample in its place). The two normalized images are used to approximate the axial derivative of intensity according to the finite difference method. The in-focus image can be estimated as the average of the two normalized images with opposite defocus distance [22, 24]. Two standard Poisson functions using Fourier transform  are implemented under Matlab 2012(a). The phase distribution of single microlens (in the red square of Fig. 2(a)) is shown in Fig. 2(c), and the corresponding three dimensional image is illustrated in Fig. 2(d). The reconstructed phase distribution of the same microlens array using DHM (wavelength 561 nm, magnification 10 × ) is shown in Fig. 2(b). The actual height of microlens measured by TIE along the red solid line and that measured by DHM along the black solid line, are plotted together in Fig. 2(e). The height measured by TIE is 13.41 μm, which is a little underestimate compared with DHM measurement result (13.64 μm) and the manufacturer specification (13.60 μm). The small discrepancy could be attributed to the linear filtering in performing inverse Fourier transform on Poisson equations [36, 37].
We further applied our approach to image living human osteoblastic cells. The samples are maintained overnight in humidified incubator at 33.5°C and 5% CO2 in Alpha minimum essential media (αMEM, Gibco by life technologies) supplemented with 10% heat-inactivated fetal bovine serum, 1% penicillin, streptomycin mixture, and 1% L-Glutamine. Experimentally the prepared cells are placed on the stage of the microscope and magnified by a × 40/0.65 NA objective.
As shown in Visualization 1 and Figs. 3(a)-3(j), we show the dynamic division process of one selected human osteoblastic cell over the course of 30 minutes. The movie and phase images clearly reveal the cell morphological changes during different phases of mitosis. At prophase, the mother cell rounds up and this can be observed by comparing the different sizes of cells in Figs. 3(a) and 3(b). The cell in Fig. 3(c) is at metaphase, where the chromosomes are aligned at the equator of the spindle midway between the spindle poles. Figures 3(d)-3(f) display the cell phase changes at anaphase: the sister chromatids are synchronously separated and each one is pulled slowly toward the spindle pole that it faces, and the poles of the cell scale out at the same rate simultaneously. Figures 3(g)-3(j) correspond to telophase, in which the division of the cell begins with contraction of the contractile ring. As the two sets of chromosomes form two nuclei, the mitosis process comes to the end.
The temporal phase changes of three points on the cell, indicated in Fig. 3(a), are further plotted in Fig. 4. The curves A and C follow opposite trends: they grow (decrease) rapidly at prophase and reach the maximum (minimum) at metaphase, then drop (grow) abruptly first and decrease (grow) progressively, and finally at the end of telophase return to a lower (higher) level compared to the beginning. Unlike the abrupt changes during the whole course of curves A and C, curve B follows a slow change, and the difference between the final phase value and that of the beginning signal is almost negligible.
Except growth and reproduction, human osteoblastic cells, like many other cells, migrate during embryonic development. Mesenchymal migration mode used by osteoblasts is characterized by long membrane protrusions. To study more complex cellular structures, we image human osteoblastic cells in the translocation process. Figure 5(a) shows the opposite defocus images of a single human osteoblastic cell in spreading state. The estimated intensity derivative and in focus bright field image are shown in Figs. 5(b) and 5(c), respectively. Figure 5(d) shows the recovered phase distribution of Fig. 5(a). Figure 5(e) illustrates the color-coded 3D rendering of phase changes of the cell over the whole 2h in the translocation process. In the first half of the process, with head protrusions stretching out and the relatively shorter tail protrusions retracting progressively, the cell is dragged forward. In the later stage, accompanied by protrusions retracting into the body gradually, the cell contracts with obvious back movement, leading to a considerable increase in cell thickness.
With prior knowledge of refractive index (RI) of the feeding media nmedium = 1.3377 and assuming a constant and homogeneous cellular RI nspecimen = 1.375 for the entire cell contents , we estimate that the phase difference of 1 rad corresponds to a cellular thickness of 2.347 μm. Figure 6(a) shows the two-dimensional cellular phase distribution at one selected moment, where the maximum phase value position is labeled with a red asterisk. The thickness profile along the black dotted line indicated in Fig. 6(a) is plotted in Fig. 6(b). Visualization 3 illustrates the temporal dynamics of the two-dimensional cell morphometry and cellular thickness during the translocation process.
In conclusion, we have presented a quantitative phase measurement method using an inverted bright field microscope upgraded with a flipping imaging module. The setup enables to record two laterally separated images with unequal defocus distances in a single shot, which extends TIE phase imaging to monitor phase varying object dynamically. The measurement of microlens array and investigation of morphological changes of living human osteoblastic cells demonstrate its validity and capacity for quantitative phase visualization. Considering the advantages of simple-design, cost-effective and easy-to-implement features, this approach could be adopted on a large scale by most non-specialists for quantifying the morphological changes and directional motion of living cells and other transparent specimens in a non-invasive and label-free manner, which is critical for medical diagnosis in the field of biological sciences.
NSAF (U1730137); National Natural Science Foundation of China (61405164); Key Research and Development Program of Shaanxi Province (2017KW-012).
We thank Dr. Li Ren and Wanqing Wu from School of Life Sciences of Northwestern Polytechnical University for providing the specimens.
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