Single-shot quantitative phase microscopy: a multi-functional tool for cell analysis

Abstract

This study showcases the multifunctionality of a single-shot quantitative phase microscopy (QPM) system for comprehensive cell analysis. The system captures four high-contrast images in one shot, enabling tasks like cell segmentation, measuring cell confluence, and estimating cell mass. We demonstrate the usability of the QPM system in routine biological workflows, showing how its integration with computational algorithms enables automated, precise analysis, achieving accuracy scores between 85% and 97% across samples with varying cell densities, even those with low signal-to-noise ratios. This cost-effective tool operates under low-intensity light and resists vibrations, making it highly versatile for researchers in both optical and biological fields.

1. Introduction

Cell confluence refers to the percentage of the culture surface covered by adherent cells, which is a critical parameter in various biological experiments, including cell proliferation, drug testing, and tissue engineering. Accurately determining cell confluence is essential for assessing cell growth and ensuring consistency across experiments. Traditionally, these tasks have relied on qualitative visual inspection techniques such as brightfield microscopy, where cell coverage on the culture surface is estimated by eye based on the contrast between cells and the background. While this method is widely used for its simplicity and non-invasive nature, it is inherently subjective and prone to variability, particularly when applied to large datasets or during long-term studies [1].

Advanced techniques like fluorescence microscopy have been employed to improve the accuracy of cell confluence measurements by enhancing cellular features through staining [2–4]. However, the toxicity of staining agents, along with the potential for photobleaching, makes this method unsuitable for long-term monitoring [5,6]. Additionally, while commercially available automated software offer enhanced precision [7,8], our technique allows for the simultaneous use of images from different modalities, which can significantly simplify the computational effort required for accurate analysis.

Quantitative Phase Microscopy (QPM) has emerged as a powerful tool to overcome these limitations, providing label-free, non-invasive imaging that can quantitatively assess transparent biological samples [9]. Techniques such as diffraction phase contrast [10], digital holography [11], ptychography [12,13], and interferometry [14] have been explored for QPM, offering various benefits in resolution and sensitivity. However, these methods often require complex setups, demanding reconstruction algorithms, or are sensitive to environmental conditions, limiting their practicality for routine use in biological laboratories.

In this study, we present a versatile QPM system that not only addresses these challenges but also enables the seamless integration of computational algorithms for automated analysis. Our system is based on a common-path configuration [15,16] that utilizes the optical non-linearity of azobenzene liquid crystal material [17,18]. A polarization-sensing camera is employed to capture four interferograms simultaneously, providing high-contrast intensity and phase images in a single shot. This high contrast is critical for accurately extracting cell confluence through automated image processing.

One of the key advantages of our setup is its ability to leverage the high contrast provided by the QPM system [19] to implement computational algorithms that can easily and reliably extract quantitative information, such as cell confluence. By integrating advanced image processing techniques [20], our system automates the confluence measurement, reducing subjectivity and improving reproducibility. Additionally, the ability to generate phase maps enables further analysis, such as cell mass estimation, enhancing the versatility of the system for various biological applications.

Moreover, the system operates under low-intensity illumination, minimizing the risk of phototoxicity, and is robust against vibrations, making it ideal for long-term monitoring of cell cultures. Our QPM system offers a highly cost-effective alternative to commercial solutions because we do not require expensive equipment [18]. This affordability, combined with its advanced capabilities, makes our system an accessible tool for researchers in the fields of optical science and biology.

In the following sections, we will discuss the methodology and experimental setup of our QPM system, including the implementation of computational algorithms for automated cell confluence measurement. We will also present the results of our system's performance, including the validation of its accuracy and reliability in various biological applications. Finally, we will offer conclusions on the versatility and cost-effectiveness of our system, highlighting its potential as a valuable tool for researchers in both the optical and biological fields.

2. Methods

The methods employed in this study provide a comprehensive evaluation of the accuracy and effectiveness of our QPM system in measuring cell confluence. To ensure a thorough assessment, we used label-free HeLa cells at varying densities, allowing us to test the system under diverse experimental conditions. Our optical setup captures high-contrast images, facilitating the application of standard image processing techniques and enabling precise phase extraction for quantitative analysis. After applying an algorithm to reduce noise, we used morphological operations in MATLAB to segment the images and calculate cell confluence. The resulting measurements were validated against manually established ground truth values. Additionally, the generation of phase maps provided further insights into the system’s capabilities, demonstrating its versatility and robustness in cell analysis.

2.1. Preparation of the biosamples

We used label-free HeLa cells to demonstrate the effectiveness of our system in estimating confluence, segmentation and phase calculation. The samples were prepared as follows: HeLa cells were grown in RPMI 1640 medium supplemented with 10% FBS and 1% pen-strep at 37°C in a 5% CO₂ environment. The cells were plated onto cover glasses in six-well plates at a density of 1 × 10⁵ cells per well and incubated for 24 hours at 37°C in a 5% CO₂ atmosphere, then fixed with a formaldehyde solution. This process was repeated for 1 × 10⁴ and 5 × 10³ cells per well to analyze three population densities, labeled as low density, medium density, and high density.

2.2. Optical experimental setup

The experimental configuration shown in Fig. 1 builds on the QPM system from our previous research [18], but has been converted into a macroscope to enable visualization and monitoring of larger fields of view, facilitating the study of cell population changes. The light source is a 10 mW Coherent StingRay Laser Diode Module (λ=640 nm), followed by a linear polarizer and a quarter-wave plate resulting in circular polarization. The beam illuminates the sample with an intensity of I = 0.198 mW/cm², providing gentle illumination that minimizes the risk of phototoxicity and makes the system suitable for long-term monitoring. For this application, the compound microscope is equipped with a 20X microscope objective and a Lens 1 with a focal distance of . Following Lens 1 is a 4-f system composed of two lenses (Lenses 2 and 3), each with a focal distance of $f_{2,3}=100mm$ . An azobenzene liquid crystal (LC) cell acts as a Zernike filter, placed in the Fourier plane, generating a phase shift between the zero-order spatial frequency component and higher frequency content [15,21] This phase shift is inherently generated by the optical anisotropy of the LC material, resulting from its response to the intensity and polarization of the incident light, inducing photoisomerization of the molecules and thus, producing phase shifted interferograms [22].The LC material, synthesized by Beam Co [23], is azobenzene 4955, and is contained in an Instec [24] LC cell with a 5 µm cell gap, a homogeneous alignment layer, and antiparallel rubbing. Importantly, we use circularly polarized light to leverage the geometric phase exhibited by the LC material and a polarized camera to capture four interferograms or phase shifted mages as reported in [18].

Fig. 1.

Quantitative phase microscopy system. LP: Linear polarizer; QWP: Quarter-wave plate. The light illuminating the object passes through a 20X microscope objective and a lens system (Lens 1, 2, and 3). The liquid crystal cell, used as the Zernike filter, has a 5 µm cell gap. The polarized camera captures four images in a single shot.

We use a BFS-U3-51S5P-C USB 3.1 Blackfly S Polarization Monochrome Camera (polarized camera) with a pixel pitch of 3.45 µm serves as the detector. The camera can capture four images at linear polarization angles of 0°, 45°, 90°, and 135°, each yielding an interferogram corresponding to a phase shift of 0, π/2, π, and 3π/2, respectively [25].

The system operates at a frame rate of approximately 1 fps [18], limited by the low-intensity illumination and the camera’s acquisition speed, but fast enough for several biological applications.

2.3. Image processing

We demonstrate the capabilities of our system by analyzing the three HeLa cell samples previously described. For each sample, 10 regions were studied, and 10 measurements were taken for each region. Each measurement yielded four interferograms (or phase-contrasted images), corresponding to the four polarization angles captured by the pixel array of the detector, as shown in Fig. 2(a)).

Fig. 2.

Image processing. a) Four interferograms obtained for one region of the high-density population sample. b) Intensity map generated by subtracting the 0° from the 90° interferogram. c) Intensity map following block-matching and 3D filtering to reduce noise. d) Segmentation and binarization of the filtered image. e) Binary mask created after applying morphological operations. f) Final binary label overlaid on the intensity map.

We first calculated the average intensity map to process the data using the 10 measurements recorded per region. Next, we selected the images with complementary contrast. The high contrast offered by our method reveals both positive and negative contrasts, simplifying the analysis process. Specifically, we chose the two interferograms with the highest positive and most negative contrast, corresponding to the 0° and 90° polarization angles, which facilitates further image analysis. The result of this calculation is shown in Fig. 2(b).

The noise in the averaged interferograms was minimized using the state-of-the-art block-matching 3D (BM3D) denoising algorithm [26,27]. The principle behind this method is similar to the wavelet shrinkage thresholding technique [28], which has been widely used for its effectiveness in differentiating between noise and signal. In general, noise corrupts the interferogram across all scales and orientations, yet it can be described as random and non-correlated with the signal. Therefore, wavelet coefficients for noise tend to be significantly smaller than those for the information part of the analyzed interferogram, allowing for simple removal via a thresholding operation. In the BM3D denoising algorithm, the first step is grouping the analyzed 2D signal into 3D blocks of similar regions before performing the transform operation. This approach enhances the differentiation between noise and signal, avoiding computationally costly wavelet coefficient thresholding in the transform domain.

The corresponding denoised interferograms were used to generate an intensity map from the operation between the selected polarization angles (90° - 0°). The result of this calculation is shown in Fig. 2(c)), where the denoising effect can be visualized by comparing this map to 2b), which represents the intensity map without denoising. The images were limited to a circle with a radius of 1024 pixels to match the calculated phase maps, ensuring proper analysis.

Following the denoising operation, the samples are segmented into 10 clusters (k = 10) using the imsegkmeans function in MATLAB. The pixel count for each cluster is calculated and normalized by the total number of pixels in the image. These normalized counts are then sorted in descending order. To distinguish between background and cell clusters, the derivative of the sorted, normalized counts is calculated and normalized. The cluster corresponding to the maximum derivative serves as the threshold; all clusters that follow are considered cells and the preceding clusters are discarded.

An additional filtering step is required to further eliminate background clusters. Some of these clusters may contain pixels that are unevenly distributed across the image. In contrast, clusters containing cell information tend to be more uniformly distributed, with mean positions closer to the center of the image. To address this, we calculate the mean position of each cluster. Clusters with mean positions that fall outside a threshold radius of 100 are filtered out, ensuring that only clusters representing cell pixels are retained.

For low signal-to-noise ratio samples, semi-automated image processing is necessary, where the selection of clusters representing cells must be done manually to ensure more accurate analysis. This approach was specifically applied to the low-density sample.

After filtering, the remaining clusters are combined to generate a binary label that distinguishes cell areas from the background -see Fig, 2(d))-.

Morphological filtering functions from MATLAB's image processing toolbox were used to clean up the labels. The bwareaopen function was applied first to remove pixel groups numbering less than 400. The imdilate function, with a disk structuring element of radius 5, was used to close gaps in cell outlines. The imfill function was then employed to fill empty spaces in the cell labels. Finally, the imerode function, using a disk structuring element of radius 5, was used to remove excess positive predictions caused by the previous dilation operation (imdilate); the result of applying these operations is shown in Fig. 2(e)). Figure 2(f)) shows the final binary label overlaid on the intensity map. The confluence of the sample was then calculated by dividing the total number of pixels corresponding to cell regions by the total number of pixels in the entire field of view (cells + background). This value was compared to the confluence determined from the ground truth.

2.4. Determination of ground truth

The ground truth was established by manually segmenting each of the 30 analyzed images using the open-source software, GNU Image Manipulation Program (GIMP). This meticulous process involved carefully delineating the cells to create binary masks, with each image requiring up to five hours of work. This rigorous approach ensured a highly reliable ground truth, which was then used to compare and validate the confluence values calculated by our method. The confluence value was based on the binary mask, where the one and zero values represented the cells and background, respectively. We divided the total number of pixels corresponding to cell regions (ones) by the total number of pixels in the entire field of view (ones + zeros).

2.5. Phase map calculations

With the four interferograms provided by the polarized camera, the wrapped phase map of the sample is retrieved through a four-step phase-shifting algorithm [29]. The phase is unwrapped [30], and the aberrations of the wavefront are corrected through Zernike polynomials [31]. The resultant map is limited to a circle of 1024 pixels of radius, due to the characteristics of the set of polynomials [32]. Then, the raw phase map is masked by the label created from the intensity images, and the areas surrounding the cells are set to zero, eliminating any background noise. This process results in a segmented phase map that is clear and easy for microbiologists to visualize, enhancing the accuracy and usability of the data.

3. Results

3.1. Cell segmentation and confluence determination

The segmentation of HeLa cells through the image processing of intensity maps enabled the calculation of the percentage of confluence for each sample. Figure 3(a)) shows the comparison between the average confluence values per population density obtained through the ground truth (GT) and those predicted using the QPM system. The confluence confusion matrices for each population density are displayed in Fig. 3(b)) showing the number of pixels classified as true positive, true negative, false positive, and false negative. This information is also included in Table 1 for a better analysis of the results.

Fig. 3.

a) Left: Confluence determined from ground truth. Right: Confluence calculated using the QPM system for low-density (LD, blue), medium-density (MD, green), and high-density (HD, orange) samples across ten regions. b) Left: Confluence of the low-density sample determined by ground truth. Right: Comparison of confluence calculated using the automated approach (auto, blue) and the semi-automated approach (semi-auto, light green). c) Confusion matrices for each sample, used to assess the system's performance.

Table 1. Metrics of the QPM system for cell confluence determination.

Metric	Low Density (semi-automated)	Medium Density (automated)	High Density (automated)
GT Confluence (%)	1.664	6.281	31.751
Measured Confluence (%)	1.461	5.684	27.172
Accuracy Score (%)	98.4	95.3	87.2
F1 Score (%)	48.8	61.1	78.3
True Positive (pixels)	62.849 × 103	3.011 × 105	1.898 × 106
True Negative (pixels)	8.04 × 106	7.550 × 106	5.281 × 106
False Positive (pixels)	57.495 × 103	1.668 × 105	3.389 × 105
False Negative (pixels)	74.171 × 103	2.160 × 105	7.160 × 105

As shown in Fig. 3(a)), the ground truth (GT) and measured confluence values exhibit similar trends across different regions. In this figure, the orange diamonds represent confluence measurements obtained from 10 regions of the high-density (HD) HeLa cell samples, while the green squares and blue circles correspond to measurements from the medium and low-density samples, respectively. Across all densities, the predicted values generally follow the GT trends, although discrepancies are more pronounced in the low and mid-density samples.

The HD samples demonstrate the most consistent measurements compared to the GT, with predicted values closely matching the actual confluence percentages. However, the low-density sample exhibited a significantly lower signal-to-noise ratio (SNR) than the medium and high-density samples. Consequently, extracting accurate information becomes more challenging when only a few cells, such as four, are present in the field of view. This lower cell confluence naturally reduces the accuracy of the analysis, and a semi-automated approach is required -Fig. 3(b))-. Despite these challenges, our system still achieved a commendable accuracy of approximately 98% for the low-density population, and 95% and 87% for the medium and high-density population, respectively.

The following table summarizes the confluence values and metrics to validate our measurements for the three populations of cells that were analyzed. The accuracy score is calculated as the ratio of true positives (TP) and true negatives (TN) to the total number of samples, which includes true positives, true negatives, false positives (FP), and false negatives (FN). The F1 score, a measure of predictive performance, is the harmonic mean of precision (TP / (TP + FP)) and recall (TP / (TP + FN)). The F1 score provides an idea of how effectively the system can identify the presence of cells. The key metrics such as accuracy and F1 scores are provided in Table 1. to evaluate the method's performance.

We achieved an accuracy score above 87% for the high-density sample and above 95% for the medium-density sample with an automated approach. The corresponding F1 scores were above 78% and 61%, respectively. The low-density sample had the lowest predictive performance; while the accuracy score was 98.4%, the F1 score was 48.8% using a semi-automated approach due to low SNR.

3.2. Phase map calculation

Figure 4 presents 3D phase map representations of one region for each population density, highlighting the system's ability to retrieve versatile information in a single shot using the polarized camera. Figures 4(a)-(c) show the phase information calculated using the four images from Fig. 2(a) and (a) four-step phase-shifting algorithm. The background noise observed in Figs. 4(a)-(c) is caused by the biological tissue or the medium used to prepare the sample. The phase information can be utilized in two keyways: first, to improve confluence measurements in low SNR scenarios, and second, by combining the phase information with binary masks generated during image processing (Fig. 2(e)) to eliminate background noise. By masking the phase maps with these labels, background noise is effectively removed, allowing for the extraction of additional sample characteristics, such as cell mass [33]. Figures 4(d)-(f) demonstrate this latter approach.

Fig. 4.

Phase Map Calculations. (a-c) Phase maps calculated using a four-step phase-shifting algorithm, each representing a different population density sample. (d-f) Phase maps after masking to remove background noise.

4. Discussion and conclusions

In this study, we presented a versatile Quantitative Phase Microscopy (QPM) system designed to address the challenges of traditional cell analysis methods, such as manual confluence measurement, which is often subjective and prone to variability. Our QPM system, utilizing a common-path configuration and azobenzene liquid crystal material, demonstrated its effectiveness in automated cell segmentation, confluence measurement, and phase map calculations for HeLa cell samples.

The system achieved high accuracy rates of 98% for low-density samples, 95% for medium-density samples, and 87% for high-density samples. Despite the lower signal-to-noise ratio (SNR) in low-density samples, which naturally reduces the accuracy of the analysis, our system still maintained commendable performance, underscoring its robustness. As shown in Fig. 3(a)), the predicted confluence values generally followed the trends observed in the ground truth (GT) across all sample densities, although discrepancies were more pronounced in the low and mid-density samples. This demonstrates the system’s capacity to handle varying cell densities while providing reliable data.

A key advantage of our QPM system is its ability to leverage the high contrast provided by the setup to implement computational algorithms for automated and precise analysis. The phase information generated by the system can be utilized in two important ways: first, to improve confluence measurements in low SNR scenarios, and second, to remove background noise by masking the phase information with binary masks generated during image processing. By applying these masks to the phase maps, background noise is effectively eliminated, enabling the extraction of additional sample characteristics, such as cell mass and morphology. This integration of advanced image processing techniques allows for the extraction of precise quantitative information, reducing subjectivity and improving reproducibility.

Additionally, the system operates under low-intensity illumination, minimizing the risk of phototoxicity and cytotoxicity, making it suitable for long-term monitoring of cell cultures. The common-path configuration also ensures robustness against vibrations, enhancing the system's stability and reliability during extended imaging sessions.

Another significant advantage of our QPM system is its cost-effectiveness [18], our setup provides a budget-friendly alternative without compromising the quality of the information obtained. This affordability, combined with its advanced capabilities, makes our system an accessible tool for researchers in both optical science and biology.

In conclusion, our QPM system offers a powerful, versatile, and cost-effective solution for cell analysis. It integrates multiple functionalities into a single apparatus, simplifying experimental setups and improving data collection efficiency. The system's ability to capture extensive information in a single shot positions it as a valuable addition to the arsenal of techniques available for advanced biological imaging and analysis. The findings of this study validate the system's potential for routine use in biological laboratories, where accurate, non-invasive, and cost-effective tools are essential.

Funding

NSF Directorate for Engineering10.13039/100000084 (2047592); Research Corporation for Science Advancement10.13039/100001309 (#CS-CSA-2021-111); University of North Carolina at Charlotte10.13039/100010942 (678237).

Disclosures

The authors declare no conflicts of interest.

Data availability

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.