In our work, red blood cells (RBCs) in microfluidic channels were imaged using a partially coherent point diffraction digital holographic microscope (PC-pDHM) (Zhuo et al., 2021). As shown in Figure 1, a partially coherent illumination (PCI) generated by combining a rotating diffuser and a multimode fiber is used.

Under the PCI, the sample is imaged by a telescope system consisting of a 10×/0.45 microscopic objective MO and a tube lens L₁ (f = 150 mm). Then, a polarization grating (G) splits the object wave into several copies along different diffraction orders of the grating. The +1st diffraction order is used as the object wave while the -1st order acts as the reference wave after being spatially filtered out (pinhole mask). Due to the polarization dependence of the grating’s diffraction orders, the object and reference waves are elliptically polarized along two orthogonal directions. Finally, the object and reference light are converted to the same polarized wave by a linear polarizer (P), and interfere with each other in the plane of the digital sensor (CCD). The relative intensity of the object and reference waves, i.e., the fringe contrast of the hologram, can be adjusted by rotating the polarizer P. The digital camera (DMK33UX174, The Imaging Source, LLC, Charlotte, NC, United States) records the hologram sequence at up to 162 frames per second (fps), limiting the temporal resolution to about 6 ms. PC-pDHM has the advantages of high accuracy, low speckle noise, and instant amplitude/phase imaging. Notably, PC-pDHM is robust against environmental disturbances due to its common-path configuration.

On the CCD plane, the interference between the object wave and the reference wave produces an intensity distribution of I r → = O ∼ 2 + R ∼ 2 + 2 O ∼ R ∼ ⋅ ⁡ cos φ r → + K → ⋅ r → , (1) For Eq. 1, O ∼ and R ∼ are the complex amplitudes of the object wave and the reference wave in the camera plane, respectively, φ ( r → ) is the phase distribution of the sample, and K → and r → = x , y denote the carrier-frequency vector of the interference fringes and the two-dimensional coordinates on the camera plane, respectively. The amplitude of K → , or the carrier-frequency of the off-axis hologram, is determined by the period of the grating G and the magnification of the telescope system L₂-L₃. The camera plane can be reconstructed as O r r → = I F T F T I r → ⋅ R D ⋅ W ∼ ξ , η , (2) where, ξ and η are the coordinates in the Fourier domain. FT ⋅ and IFT ⋅ represent the Fourier transform and inverse Fourier transform, respectively. A digital reference wave R D = ⁡ exp − i K → · r → is used to compensate for the spectral shift caused by the angle between the object wave and the reference wave. In the experiment, R D (x,y) can be determined by measuring the carrier frequency vector K → of the interference stripe. W ∼ ξ , η is the window function to select the spectrum of the real image. Then, both the amplitude and phase image can be obtained from O r r → . Compared to the amplitude image, the phase image has much higher contrast, and notably, in a quantitative manner. Therefore, it is more advantageous to use the phase image to perform the cell segmentation. Once using automatic cell identification and segmentation strategy, high throughput cell inspection can be performed.

In the conventional cell segmentation using Sobel operator, the threshold value for edge segmentation is usually identified by using the grayscale histogram of the image. This technique may result in overlooked and misidentified edges for the images with feeble edge contrast. Herein, we propose a cell segmentation method guided by the Sobel operator (Sobel and Feldman, 1968; Gao et al., 2010) and Dice coefficient (Shamir et al., 2019), of which the threshold value is identified using ground truth images to achieve automatic optimal segmentation. The specific details of the segmentation process are shown in Figure 1B.

Step 1

Cell edge detection.

At first, the background of the original phase images is removed by subtracting the mean value of the phase images.

Then, the edge contour of cells is extracted using Sobel operators, which compute the gradient of an image along four-direction (0°, 45°, 90°, and 135°). Specifically, the gradient along these directions can be calculated by convolving the phase image I (x, y) with Sobel matrix S θ (θ = 0°, 45°, 90°, and 135°). S 0 = − 1 − 1 − 1 0 0 0 1 1 1   S 45 = − 1 0 1 − 1 0 0 − 1 0 1   S 90 = 1 0 − 1 0 0 0 − 1 0 1 , S 135 = − 1 0 1 0 0 0 1 0 − 1 (3)

For Eq. 3, the squares of the gradients in the four specified directions are added, and the square root of their summation is the overall gradient magnitude G. This process the cell edges exhibit higher intensity values, making them easily distinguishable, as shown the Gradient in Figure 1B.

Step 2

Cell segmentation.

First, convert the gradient image into a binarized image using an initial threshold n.

Second, an expansion kernel of size 1 × 1 pixel² is employed to perform a dilation operation. This operation examines the surrounding pixels of a target pixel, if any of the 8 surrounding pixels has a value of 1 (foreground pixel), the value of the current pixel is set to 1. Otherwise, it is left unchanged, enabling the expansion or joining of foreground regions. The dilation operation can somehow suppress disjointed or inaccurate edge due to the presence of noise.

Third, the holes are eliminated and the edges are smoothed by morphological closing operations (dilation and erosion). The dilation operation is first repeated continuously until the foreground pixels are filled in the connected region. However, this may result in the foreground region becoming irregular or too large. In order to eliminate these problems, the erosion operation is then performed. Specifically, the dilation kernel defined above is compared to the current pixel position and its surrounding pixels. If the value of the image pixel corresponding to the dilation kernel with all the surrounding pixels is 1, the value of the current pixel is set to 1. Otherwise, it is set to 0. The erosion process modifies the shape and size of the foreground region, removing minor details and smoothing edges to create a more accurate cell mask.

Fourth, automatic threshold identification using ground truth (GT) images is applied where accurate selection of threshold value is crucial for cell segmentation. In this method, the threshold n is identified using GT images to obtain the best segmentation. The Dice coefficient, which is the most commonly used objective metric in deep learning-based segmentation (Milletari et al., 2016): D i c e = 2 M a s k ∩ G T M a s k + G T (4)

Actually, Eq. 4 assesses segmentation quality by comparing the overlap between the segmented (Mask) and GT images, and the value ranges from 0 to 1. The closer the value is to 1, the higher the overlap similarity between Mask and GT, i.e., the more accurate the segmentation result. In the implementation, the threshold n is varied so that an optimal threshold is found that maximizes the value of the Dice coefficient. For the GT images in this cellular segmentation task, manual labelling was performed with ImageJ. Firstly, the cell boundaries were precisely outlined on the phase image. And secondly, the cell regions were filled with a paintbrush to obtain the labelled image for cell regions.

Dry mass, which is the mass of a cell or an organism after all the water content has been evaporated, is often used to evaluate the morphology or the density of biological samples. The dry mass of the target as a whole can be obtained by integrating the refractive indices of the target body volume regions (Sung et al., 2012): m = 1 α ∭ v c n x , y , z − n 0 d V = 1 α ∬ S O P D d x d y = 1 2 π α σ 2 λ ∑ S Δ φ i . j (5)

Here, n x , y , z and n 0 denote the refractive indices of the cell and the background, respectively, v c and S denotes the cell region in 3D and 2D, and α = 0.19   μ m ³ / p g is a constant indicating the rate of change of refractive index per unit of change in density or concentration. In addition, σ denotes the pixel size in the image, O P D = Δ φ λ ∕ 2 π denotes the optical path difference, Δ φ i , j denotes the discrete spatial distribution of the phase difference, and λ denotes the wavelength of light. Eq. 5 allows us to relate the phase value Δ φ of a cell to its dry mass m. In the proposed technique, the dry mass of the cells can be calculated from the cell phase images acquired by PC-pDHM.

In the first experiment, we demonstrate that the proposed technique can be applied to the analysis of rat blood. Fresh blood was extract from a rat and was diluted at a volume ratio of 1:100. Then, the diluted blood was pumped through a microfluidic channel equipped in PC-pDHM and continuous recording of off-axis holograms were taken at a ratio of 30 fps. Using Eq. 2, quantitative phase images of the blood cells can be reconstructed, as shown in Figure 2A. The contours of individual cells are extracted based on the automatic segmentation methodology previously introduced, as shown in Figure 2B. The area of each individual cell can be calculated by counting the number of pixels within each cell area and multiplying a factor of 0.078 μm²/pixel². The statistics of cell areas among 43,711 cells is represented in Figure 2C. In the statistics, the area below 13.50 μm² is from speckle noise and the area above 28.0 μm² is from the cells clusters in the phase images (see the area marked with red circles in Figure 2B). The range in between (13.50–28.0 μm²) corresponds to a valid area region (containing 13,943 cells for the statistic) and this region is magnified and shown with Figure 2E where the useful cells are labeled. Often, the valid area range for individual cells can be determined by analyzing the phase image containing sparse cells, as shown in Figures 2B, E. At low density of cells, the cell contour can be easily isolated and segmented since there is a large difference between the noise points and the actual cells. The Gaussian fit on the histogram reveals that the mean area of individual cells is 21.80 ± 0.14 μm² (mean ± SD).

Considering the observation volume of the microfluidic channel falling in the field of view (FOV) of 149.76 × 84.24 × 100 μm³, we can calculate the volume concentration of blood cells in the diluted blood sample. Using the cell area distribution included in Figure 2D as a constraint for cell counting, we obtained the number of cells N = 61 cells in the observation volume of 149.76 × 84.24 × 100 μm³ for the exemplary frame (Figure 2E), which means that the cell concentration can be deduced to be 4.84 × 10⁶ μL⁻¹. In this case, we performed an automated count on 1,134 manually counted cells and assessed the accuracy of the algorithm to be approximately 97% when compared to an automated count of 1,099 cells. Once repeating this process for 1,400 images, the histogram of cell concentration can be obtained and shown in Figure 2F. The Gaussian fit of the histogram tells that RBCs concentration in the diluted solution is (4.32 ± 0.89) ×10⁴ μL⁻¹ (mean ± SD). Taking the dilution factor 1:100 into consideration, the blood cell concentration in rat blood is (4.32 ± 0.89) ×10⁶ μL⁻¹ (mean ± SD). This information is essential for deeper understanding of cellular behavior and characteristics during cell proliferation or under effect of drugs.

The dry mass of a cell is the amount of solid material, such as proteins, nucleic acids and other organic molecules, existing in the cell. Measuring the dry mass of a cell can provide information about the cell’s metabolism, growth and health states. It is useful for assessing rates of cell proliferation, comparing the biochemistry of different cell types, and studying the effects of drugs on cells. Several approaches exist for determining cell dry mass. One possibility involves the direct measurement of the dry weight of cells by collecting them, washing and centrifuging them, and subsequently drying them (Bratbak and Dundas, 1984). Another approach is to quantitatively measure the cell dry mass by phase change determination (Popescu, 2011). This method has the advantage of being non-destructive and does not require additional treatment of the sample. Therefore, it is widely used in fields such as cell biomass measurement and cell growth monitoring.

In our experiment, we acquired phase images by using the PC-pDHM for label-free measurement of RBCs’ dry mass. As shown in Figure 3A, the phase values were first integrated point-by-point over the cell region, yielding the integrated phase value ∑ s Δ φ i , j of the entire single cell. Then, the dry mass m was obtained using the linear relation described by Eq. 5. In the calculation, the following parameters, λ = 532 nm, σ = 0.078 μm/rad, were used. The histogram of the dry mass distribution among 17,452 cells are shown in Figure 3B. The Gaussian fit on the histogram tells that the average dry mass of individual cells is 26.42 ± 4.34 pg (mean ± SD). We can deduce the number of cells in a cell-cluster by dividing the dry mass of the cluster by the average dry mass of individual cells. The proposed technique provides a non-invasive means of quantifying cell properties, enabling researchers to obtain essential information about cell behavior, metabolism, and overall functionality.

Cell segmentation is crucial in high-throughput, automatic analysis of cell morphology. In this experiment, we demonstrate the proposed approach can be used for segmentation of different kinds of cells. We imaged Siha cells using the DHM setup shown in Figure 1 and segmented them using the proposed method in comparison with the following four well-established methods: 1) Cellpose (Stringer et al., 2021): A deep learning based cell segmentation method; 2) Trainable Weka Segmentation (TWS) (Arganda-Carreras et al., 2017): A machine learning based cell segmentation method; 3) Empirical Gradient Threshold (EGT) (Chalfoun et al., 2015): A feature-extracting strategies; 4) Ostu (Ostu, 1979): A thresholding based method. Cellpose based segmentation was performed using its startup web version. TWS and EGT were implemented using plugins integrated in Fiji, while Ostu was implemented using python. The phase diagram of Siha cells is shown in Figure 4A, and the GT image (Figure 4B) was obtained by manual segmentation. The segmentation results obtained by different methods are shown in Figures 4C–G. We visualize the deviation of the segmentation results against the GT images, including TP (correctly identified positive samples), FN (positive samples missed cases), FP (negative samples misreported cases), and TN (correctly identified negative samples). The segmentation results were evaluated using F1 scores and Hausdorff Distance (HD) as secondary criteria, of which F1 scores indicate consistency of the segmentation results with the actual labels and HD values indicate segmentation accuracy. The F1 scores for Figures 4C–G were 0.95, 0.87, 0.91, 0.89, and 0.87, and their HD values were 6.40, 33.11 16.28, 12.04, and 18.79, respectively. In comparison, the method proposed in this paper has better performance.

First, there is no need to obtain a large amount of labeled data since only one piece of labelled data for the same kind of samples taken by the same device is sufficient to guide the thresholding optimization in the segmentation operation. Second, the method is relatively simple and computationally efficient, and by contrast, the learning network model in a neuron network often requires a lot of computational resources and time. Just as an example, the complete segmentation of the proposed method takes only about 0.05 s for an image with 96 × 96 pixels, while the U-Net needs 17 h to be trained with 3,600 pairs of data. Considering the phase image can be acquired in real-time using off-axis DHM configuration, real-time dynamic imaging and segmentation is possible once using parallel processing techniques. Third, the proposed approach can segment different kinds of cell profiles. In particular, our method shows excellent ability to extract cell contours of COS7 cells (Figures 4H, I). We further demonstrate in Figures 4J, K that the proposed approach works also in the segmentation of both human erythrocytes and mouse embryo cells (Ljosa et al., 2012). By contrast, the network model can only predict the structures that are identical or similar to those in the training set. However, our proposed method has some shortcomings and the segmentation results of the model may be somewhat poor for images containing complex textures, significant shape changes, or no clear delineation between target and background.