In vitro imaging of living single cells with light microscopy is crucial for many research fields in biology and medicine. Live-cell imaging provides important insights into various cellular properties, such as motility or biomechanics related to cell structure changes. In particular, the cellular dry mass, which accurately reflects the accumulation of cellular contents, is relevant to cell growth research and is of great significance. This requires measurements must be performed at the single cell level with high precision and high throughput, thus bringing challenges to microscopy. Quantitative Phase Imaging (QPI) techniques are rapidly gaining momentum and popularity as new imaging tools in cellular biology (Zuo et al., 2017; Fan et al., 2019; Li et al., 2019; Zuo et al., 2020; Lu et al., 2022; Zhou et al., 2022), where Digital holographic microscopy (DHM) (Cuche et al., 1999; Mann et al., 2005; Huang et al., 2022) combines interferometric technique, modern CCD sensor and image processing systems, opening up a new perspective for the accurate characterization of physical properties of living cells.

Different from conventional microscopic imaging techniques that require exogenous contrast agents for visualization and detection of samples (Giloh and Sedat, 1982; Betzig et al., 2006), DHM is optical, enabling high contrast imaging of all cells in the entire field-of-view (FoV) without being limited to fluorescent or stained samples. DHM is also a non-invasive technique since the radiation used does not damage the cells. Therefore, non-destructive long-term time-lapse investigations for quantitative monitoring of dynamic changes of cell morphology, motility, and proliferation are accessible. Moreover, DHM converts the invisible sample thickness into a detectable intensity variation and provides quantitative measurements, a capability that Zernike phase contrast (PC) (Nomarski, 1955) and differential interference contrast (DIC) (Zernike, 1942) lack. The reconstruction of quantitative phase images allows for the acquisition of samples’ three-dimensional morphological information, thereby permitting the extraction of integral biophysical parameters globally quantifying the intracellular content, dynamic morphology, and volume changes as well as cell motility. In addition, it has been proved that an optical path can be used to measure the mass of a total substance other than water in a living cell or in any of its parts, i.e., cellular dry mass (Davies and Wilkins, 1952). DHM uses the laser with high coherence as the physical medium for optical modulation to reconstruct phase information by measuring the optical path difference induced by a micro-sample. This direct observation recovers the phase results more accurately to benefit the analysis of morphological characteristics like dry mass, which becomes a unique advantage of DHM. Consequently, DHM is a desirable tool for live-cell imaging that efficiently serves physical features analysis (Kemper and Von Bally, 2008; Rappaz et al., 2009).

Since the spectral aliasing degree of the object information and background intensity directly affects the accuracy of phase demodulation through linear Fourier domain filtering, conventional digital holographic microscopy suffers from the problem of incompatibility between high-quality reconstruction and high-throughput imaging. To avoid the introduction of zero-order information to degrade the fidelity of the reconstructed wavefront, quasi-off-axis DHM sacrifices substantial imaging throughput (Takeda et al., 1982). This leads to a considerable reduction in image resolution, which renders the reconstructed cell phases lose in detail to a great extent and is not conducive to cell structure analysis. The enhancement of space-bandwidth product by the slightly off-axis DHM is necessarily accompanied by the zero-order suppression; otherwise, artifacts will be formed on the phase image due to the residual background intensity information (Pavillon et al., 2009; Pavillon et al. 2010; Baek et al., 2019). In our previous work (Shen et al., 2022), we innovatively proposed a slightly off-axis holographic imaging system (FPDH) based on Fourier ptychographic reconstruction (Zheng et al., 2013; Sun et al., 2017; Shu et al., 2022). FPDH effectively breaks through the spatial bandwidth limitation of quasi-off-axis holography and reconstructs high-quality artifact-free phase images while reaching the theoretical resolution, laying the foundation for high-precision measurement of the physical properties of living cells.

Over the years, light microscopy has achieved many breakthroughs in improving resolution and imaging quality, but the biological interpretation of its imaging results (e.g., cell fusion, morphology, and dry mass) still requires additional processing analysis software. The combination of the two and its application to the observation of living cells is more valuable to the life science field. In this paper, we further present a systematic analysis framework for live-cell imaging and morphological characterization based on FPDH, named LAF. Since the phase information reconstructed by FPDH is not interfered by the background intensity, the accuracy of LAF is guaranteed. More importantly, the high-throughput imaging and achievement of theoretical resolution can preserve the high-frequency details of cell edges, solving the problem of difficulty in identifying cell contours due to unclear boundaries. The evaluation of the recorded quantitative phase contrast images allows the extraction of data for simplified object tracking and image segmentation, thus realizing single cell observations. Based on this, LAF is equipped with a set of automated cell segmentation method to extract the valid cellular region, which improves the existing methods to make the framework more robust and accurate. Various physical properties of each individual living cell can be measured and analyzed using phase information and segmentation data. According to parameters such as medium refractive index, LAF provides calculations of the area, perimeter, irregularity and volume of each single cell and translates the surface integral of the optical phase shift through a cell layer into an estimation of the cellular dry mass (Barer, 1952; Popescu et al., 2014). The measurement of these physical properties reflects the cellular nature, which is beneficial for quantitative studies of cell growth and biochemical status. In other words, LAF is a complete live-cell systematic analysis framework that covers the entire process from quantitative phase imaging to the acquisition of individual cell morphological structure data. Experiments on HeLa live-cells demonstrate the validity and effectiveness of the proposed framework for physical and morphological analysis of cells.

The proposed systematic analysis framework (Figure 1) begins with the application of FPDH imaging system to obtain quantitative phase images of cells. This chapter reviews the reconstruction principle of FPDH.

Based on the off-axis architecture, FPDH adjusts the system parameters such as the source wavelength and the numerical aperture of the objective lens so that the autocorrelation and intercorrelation terms are distributed diagonally and partially overlapped in the frequency domain. When the tilt angle between the object beam and the reference beam is at a certain angle, the spectrum of ±1-order is tangent at the origin with a complete and continuous display, which forms a slightly off-axis spectrum configuration with maximum spectrum utilization. However, since the extreme spectral configuration mentioned above makes full use of the spatial bandwidth, aliasing of spectral information will lead to the inability of the Fourier method to reconstruct the phase correctly. Therefore, FPDH solves the problem by the non-linear optimization algorithm (Khare et al., 2013), which is solved by a Gechberg-Saxton (GS) (Gerchberg, 1971; Gerchberg, 1972) algorithm-like method.

Build a forward physical model of the imaging process of off-axis digital holography and the complex amplitude distribution of the hologram is expressed as U(x, y) = O(x, y) + R(x, y), where O(x, y) and R(x, y) are respectively the complex amplitudes of the object and reference beams, and the reference beam is considered as a quasi-plane wave. With the recorded intensity images of the hologram and the reference beam, the complex amplitude distribution of the reference beam is reconstructed from the offset of ±1-order of the hologram in the frequency domain and the amplitude information of the reference beam.

Define the cost function with the purpose of minimizing the amplitude error ε O = ∑ x , y I x , y − F − 1 O u , v P u , v + R x , y 2 , (1) and derive the updated equation of the hologram as U u , v = U u , v + α P u , v 2 P u , v max 2 P * u , v P u , v 2 + δ U u u , v − U e u , v (2) where U ^e (u, v) = O(u, v)P(u, v) + R(u, v) represents the subspectrum before the update and U u ( x , y ) = I ( x , y ) U e ( x , y ) U e ( x , y ) represents the subspectrum updated by the captured hologram intensity I(x, y). P(u, v) is a mask function for spectrum selection of the numerical reconstruction in the actual phase recovery process (The ideal state is the above-mentioned pupil function determined by NA). α is the updated step-size, which usually ranges from 0.5 to 1. And δ is a regularization parameter (a minimal value near 0) to prevent the denominator from going to zero. The cost function converges to a minimum value that tends to zero by updating functions back and forth between the real and Fourier spaces.

During the iteration, the square root of the recorded digital hologram intensity is always employed to update the reconstructed complex amplitude, as shown in Figure 2, where the structural similarity index of both the reconstructed amplitude and phase images is 1. With the non-linear optimization algorithm, FPDH constructs a high-resolution, high-throughput, artifact-free slightly off-axis holographic imaging system, which is a solid foundation for subsequent cell morphology analysis algorithms of LAF to operate with high robustness and accuracy.

In the paragraphs below we provide a detailed summary of each image processing step in LAF for live-cell imaging and morphological characterization (Figure 1), followed by a description of the methods involved.

At this point, we have achieved the extraction of the valid cellular region. Finally, LAF performs cell morphology analysis with the reconstructed phase information and segmentation data. The framework allows for quantitative measurements of the area, circumference and volume of individual living cells as well as the definition of cell irregularity. In addition, in view of the fact that cellular dry mass has long been considered an important physical property, LAF completes its estimation using cellular phase, i.e., optical path difference. The calculations of these cellular morphological features are described below.

To demonstrate the capability of the above systematic analysis framework for live-cell imaging and morphological characterization, we performed experiments on HeLa live-cells. The Digital Holographic Smart Computational Light Microscope (DH-SCLM) (Figure 1) developed by SCILab (Fan et al., 2021) was used to acquire holograms. Its central wavelength of illumination is 532 nm, and the pixel size of the CCD camera (The Imaging Source DMK 23U274, 1600 × 1200) is 4.4 μm. We selected a specific objective (UPLanSAPO ×10/0.4NA, Olympus, Japan) to maximize spectral utilization and combined it with the FPDH non-linear optimization algorithm to achieve artifact-free high-resolution imaging. LAF performed cell segmentation on quantitative phase images reconstructed by the FPDH imaging system.

Figure 3 illustrates the ability of LAF to automatically segment individual cell in the phase maps. Figures 3A1, B1 are segmentation results of the reconstructed high-quality phase images of HeLa cells in the full FoV, respectively. The blue lines indicate the contours of the cell edges and the red points represent the locations of the cell centroids. The EGT method preserves the main structure and edge details of single or multiple aggregated cells, which further improves the accuracy and robustness of the segmentation in combination with thresholding. Similarly, the cell centroids are also correctly identified by the DT method and thresholding. Based on the overall cell contours and centroid locations, single cell segmentation is performed on the cells connected to the edge of their neighbors by the Marker-controlled watershed segmentation. Figures 3C1, G1 shows the boundary subregions of dense cells in the phase images. It can be seen that the edge contours and centroids of cells in these regions are identified with high precision.

To illustrate the better performance of LAF on cell segmentation, we performed comparison experiments using only the EGT method and the DT method on the same FoV. As shown in Figures 3A2, B2, the accuracy of foreground-background segmentation is considerably reduced. More importantly, the under-recognition of cell centroid can directly lead to the failure of the watershed algorithm, thereby resulting in the inability to separate several neighboring cells, as shown in Figure 3C2. In addition, we also conducted segmentation experiments on cell phase images reconstructed by the conventional Fourier method, as shown in Figures 3A3, B3. It can be obviously seen that there is much background intensity information remaining on the reconstructed phase images due to the lack of zero-order suppression, which has a negative impact on the cell segmentation. In contrast, LAF images HeLa cells with FPDH system to obtain high-quality quantitative phase images, which eliminates the background artifacts while preserving the high-frequency detail information of cells, thus further guaranteeing the measurement precision.

Depending on the cell segmentation results and quantitative phase information, LAF allows for provision of the physical features measurements of single HeLa live-cells for analysis. We respectively selected a cell-dense FoV (Figure 4A) and a cell-sparse FoV (Figure 4D) as the analysis samples. Figures 4B, E are the segmentation results of the selected cell regions of interest from the original phase images. To conveniently demonstrate the cell analysis results, Figures 4C, F mark the numbers of the cells for morphological analysis on the binary images obtained after cell segmentation. Tables 1, 2 show the analysis results of the physical properties calculated with the reconstructed Hela cell phase and the segmentation data previously obtained. We evaluated the morphological characteristics of HeLa live-cells by Eqs 4–10, involving area, circumference, irregularity, volume and dry mass. The experimental results confirm that the systematic analysis framework has a highly efficient practicality for both sparse and dense cell analysis.

Based on this, LAF can utilize the real-time imaging capability of digital holography to provide dynamic observation of important physiological processes in living cells. By tracking the physical properties mentioned above, we can measure the growth rate of individual cells and thereby obtain their growth characteristics. Moreover, the observation process of growth trends is beneficial for understanding the link between cell cycle progression and mass. Therefore, the LAF systematic analysis framework holds considerable potential for biomedical applications.

In this paper, we present a systematic analysis framework, which employs FPDH imaging to study the physical properties of HeLa live-cells at the single cell level in a non-invasive manner. The application of FPDH slightly off-axis holography system realizes high-throughput artifact-free imaging, further improving the resolution and reconstruction quality of quantitative phase images and laying the foundation for high-precision cell segmentation and analysis. LAF also equips a set of highly robust algorithms for automated cell segmentation and morphological analysis, allowing the analysis of individual cells in culture or the statistical measurement of large populations of cells. Furthermore, the cellular dry mass has long been recognized as an important physical property, but its biological applications as an experimental tool have been limited due to the lack of readily accessible methods. With the methods mentioned here, the quantitative measurement of cellular dry mass is placed on a solid physical background and made available as a practical microscopic assay.

LAF has a FoV of 2.32323 mm² (10×), permitting dynamic and full-field topography analysis. It should be mentioned that LAF is mainly applicable to adherent cells. Since the thickness of suspended cells is large, the significance of the phase measured by QPI techniques is not clear. It is better to use three-dimensional tomography to measure suspended cells. Moreover, if the reconstructed phase image is slightly defocused, digital holography allows fine-tuning by auto-focusing methods, thus enhancing the accuracy of cell segmentation and measurement of physical properties. With image processing, LAF can measure the growth rates of individual cells among confluent population with cell-to-cell contacts and achieve high measurement throughput. LAF is also completely non-invasive as it uses the cellular refractive index as the source of microscopic contrast. In addition, a combination of synthetic aperture technology (Zheng et al., 2020; Gao and Yuan, 2022) can be considered to further improve the spatial resolution of the framework. Thus, the systematic analysis framework has the potential to form versatile tools to generate quantitative phase data in a very simple way in life sciences, etc., which may be evaluated to quantify the physical properties of various morphological living cells.