High-Precision Lensless Microscope on a Chip Based on In-Line Holographic Imaging

The lensless on-chip microscope is an emerging technology in the recent decade that can realize the imaging and analysis of biological samples with a wide field-of-view without huge optical devices and any lenses. Because of its small size, low cost, and being easy to hold and operate, it can be used as an alternative tool for large microscopes in resource-poor or remote areas, which is of great significance for the diagnosis, treatment, and prevention of diseases. To improve the low-resolution characteristics of the existing lensless shadow imaging systems and to meet the high-resolution needs of point-of-care testing, here, we propose a high-precision on-chip microscope based on in-line holographic technology. We demonstrated the ability of the iterative phase recovery algorithm to recover sample information and evaluated it with image quality evaluation algorithms with or without reference. The results showed that the resolution of the holographic image after iterative phase recovery is 1.41 times that of traditional shadow imaging. Moreover, we used machine learning tools to identify and count the mixed samples of mouse ascites tumor cells and micro-particles that were iterative phase recovered. The results showed that the on-chip cell counter had high-precision counting characteristics as compared with manual counting of the microscope reference image. Therefore, the proposed high-precision lensless microscope on a chip based on in-line holographic imaging provides one promising solution for future point-of-care testing (POCT).


Introduction
Optical microscopes play a significant role in scientific study and clinical testing in modern medicine and life sciences, as they can expand and identify morphological features of samples (including cells, bacteria, marine microorganisms, etc.) that cannot be enlarged and seen by the naked eyes. With the iterative upgrade of the spatial resolution of optical microscopes, microscopes with various extended functions, including scattering, absorption, refraction, phase modulation, etc., have also emerged so that the morphological characteristics of transparent samples [1][2][3][4][5][6], the subtle internal changes of thick samples [7][8][9], and structural details even smaller than the wavelength of the light source [10,11] can be easily obtained. However, due to large size, high cost, and complicated operation, these microscope detection platforms can only be used in advanced laboratories and medical institutions. Hence, their scope and conditions of application are limited, especially in resource-limited areas where infectious diseases such as tuberculosis, malaria, sickle cell virus infection, and other diseases are common. Therefore, the use of portable optical microscopes in resource-limited areas to improve detection efficiency is vital for preventing the spread of infectious diseases [12][13][14].
To meet such needs, in recent years, the combination of Complementary Metal Oxide Semiconductor (CMOS) image sensor and microfluidic technology provides an opportu-microscope [31]. Fang et al. have developed an on-chip lensless flow cytometer, which uses the holographic imaging principle and the broad FOV of the S-shaped pipe to achieve a cell counting error of less than 2% [32]. Since the experimental device of holographic imaging is simple, and the resolution can be improved through phase recovery, it has been widely studied and applied in recent years [33][34][35].
Therefore, to overcome the shortcomings of shadow imaging and fluorescence imaging, this paper demonstrates an alternative method of lensless on-chip holographic imaging towards telemedicine applications. It is a portable high-precision detection device based on lensless holographic imaging to capture cells on the glass smear, and uses machine learning to classify and count mouse ascites tumor cells and polystyrene particles in holographic phase recovery images. Experiments show that the resolution of the platform is 1.41 times that of the shadow imaging platform, and the accuracy of cell counting is similar to the manual counting results of the microscope reference image. Besides, the platform has no complex optical path system, simple operation, small size, no damage to samples, low cost, and can be applied in resource-poor areas for point-of-care testing (POCT), which has specific application prospects in preventing the spread of diseases and early detection.

System Setup
This system is built using the imaging principle of in-line holography, and the overall structure is shown in Figure 1. The system mainly consists of a CMOS image sensor (IMX219PQ, Sony, Tokyo, Japan, 1.12 µm pixel size, 3280 H × 2464 V), a yellow Light Emitting Diode (LED) light source (LY-E65B, OSRAM Opto Semiconductors Inc., Regensburg, Germany, λ = 587 nm), and a pinhole (100 µm in diameter). To make full use of the imaging area of the image sensor, a cover glass (with a thickness of 0.5 mm) is directly covered on the image sensor and glued with liquid glue to prevent misalignment due to moving the experimental device. It not only achieves the conditions of static imaging but also controls the distance between the cover glass and the image sensor in a small range so that the magnification ratio of the sample imaging pattern can also be controlled to avoid imaging distortion. In order to obtain a holographic interference pattern on the surface of the image sensor, the LED light is controlled at a distance of 5 cm from above the image sensor. Besides, the pinhole is placed under the LED to improve the coherence of the LED light source. All the experimental structural components are finally assembled by a 3D-printed dark box (6.5 × 6.5 × 7 cm 3 ) to form a miniaturized on-chip lensless holographic imaging detection system. Note that the LED is powered by an external Raspberry Pi circuit board through a power line. The Raspberry Pi board is also connected with the CMOS image sensor board through an Mobile Industry Processor Interface (MIPI) interface. The captured holographic images are then transferred to the PC via the Raspberry Pi for further analysis.

147
In order to evaluate the imaging effect of the holographic imaging platform, we 148 prepared two different experimental samples. One is the optical positive film resolution 149 plate (USAF-1951, Yaopu Optics, Chengdu, China), which is used to measure the resolu-150 tion of the imaging system. There are some particular patterns on the resolution board, 151 and its line width and interval have been precisely set. By identifying the most indistin-152 guishable reference line, the resolution capability of the system can be determined. The 153 resolution board was cleaned by wipe and placed above the CMOS image sensor for 154 testing. Another is the mixed solution of mouse ascites tumor cells and polystyrene par-155 ticles (15 μm). First, some suspended malignant tumor cells were inoculated into the 156 abdominal cavity of mice. A few days later, the cells proliferated in the abdominal cavity 157 of the mice to produce a large number of offspring to form mice with ascites tumors, and 158 ascites were drawn for later use. In order to ensure that clear wavefront information was 159 observed in the coaxial holographic experiment, we diluted the mixed solution, extracted 160 1 μL of mouse ascites and 1 μL of polystyrene particles to mix, and then extracted 200 μL 161 of phosphate buffered solution (PBS) and mixed with 2 μL of the cell solution. The di-162 luted solution was made into a glass smear for testing. 163

164
In the on-chip lensless holographic imaging detection system, a translucent sample 165 is placed above the image sensor, usually 2 (<1 mm) from the image sensor. An inco-166 herent light source is fixed at a distance 1 from the sample, and a pinhole is set directly 167 below the light source so that the sample is irradiated by the light source and instantly 168 forms a holographic pattern on the image sensor, and the image sensor encodes the hol-169 ographic pattern by intensity. 170 The on-chip lensless holography is derived from the holography invented by Gabor 171 in 1948 [36]. This method not only records the amplitude information of the light field but 172 also records the phase information. Therefore, holography records the complete infor-173 mation of an object. In the holographic recording process, the recording medium records 174 the complex amplitude, that is, simultaneously records the amplitude and phase infor-175 mation of the original object light wave. The intensity change recorded in this way is 176 called a hologram. 177 In in-line holography, assuming that the object is semi-transparent, it can be ap-178 proximated as:

Sample Preparation
In order to evaluate the imaging effect of the holographic imaging platform, we prepared two different experimental samples. One is the optical positive film resolution plate (USAF-1951, Yaopu Optics, Chengdu, China), which is used to measure the resolution of the imaging system. There are some particular patterns on the resolution board, and its line width and interval have been precisely set. By identifying the most indistinguishable reference line, the resolution capability of the system can be determined. The resolution board was cleaned by wipe and placed above the CMOS image sensor for testing. Another is the mixed solution of mouse ascites tumor cells and polystyrene particles (15 µm). First, some suspended malignant tumor cells were inoculated into the abdominal cavity of mice. A few days later, the cells proliferated in the abdominal cavity of the mice to produce a large number of offspring to form mice with ascites tumors, and ascites were drawn for later use. In order to ensure that clear wavefront information was observed in the coaxial holographic experiment, we diluted the mixed solution, extracted 1 µL of mouse ascites and 1 µL of polystyrene particles to mix, and then extracted 200 µL of phosphate buffered solution (PBS) and mixed with 2 µL of the cell solution. The diluted solution was made into a glass smear for testing.

Imaging Principle
In the on-chip lensless holographic imaging detection system, a translucent sample is placed above the image sensor, usually z 2 (<1 mm) from the image sensor. An incoherent light source is fixed at a distance z 1 from the sample, and a pinhole is set directly below the light source so that the sample is irradiated by the light source and instantly forms a holographic pattern on the image sensor, and the image sensor encodes the holographic pattern by intensity.
The on-chip lensless holography is derived from the holography invented by Gabor in 1948 [36]. This method not only records the amplitude information of the light field but also records the phase information. Therefore, holography records the complete information of an object. In the holographic recording process, the recording medium records the complex amplitude, that is, simultaneously records the amplitude and phase information of the original object light wave. The intensity change recorded in this way is called a hologram.
In in-line holography, assuming that the object t is semi-transparent, it can be approximated as: Here, ∆t is the transmittance fluctuation and ∆t<<1. When an object is locally illuminated by plane wave A, it will coherently propagate z 2 distance (distance from the sample to the image sensor): Here, P[z 2 ]{ * } is the transfer function acting on z 2 , ε and η are frequency domain coordinates, and λ is the wavelength of the light source.
On the image sensor plane, the object light wave a(x, y) passing through the object interferes with the reference light wave A to form a hologram, and the intensity information I(x, y) is recorded: In (4), the second and third items are related to the reconstruction of object information. The first item is the reference light information, which can be removed by a sample-free background image, the fourth item is the object self-interference information, it can be ignored when ∆t<<1, because for holography, it does not include any useful information, and during the holographic reconstruction process, the focused image of the object and the out-of-focus image will overlap, and the twin image will form. In the on-chip holographic imaging, z 2 is usually very small. The twin image has a severe impact on the image of the actual object, so it needs to be removed by related methods.
For digital holographic imaging, according to the angular spectrum theory, sample information, including amplitude and phase, can be decoded by back propagation: In (5), A * is the conjugate of the plane wave and I(x, y) is the recorded hologram. On the right side of the Equation (5), the first term is the background light, the second term is the actual sample, the third term is the twin image interference, and the fourth term is the self-interference term backpropagation interference. For smaller or more scattered samples, the twin image interference will not cause interference to the reconstructed image, and routine analysis can be satisfied by simple backpropagation. For other samples, the existence of the twin image will interfere with the analysis of the results, making the recovered sample information unclear. Therefore, proper methods are needed to reduce the influence of the twin image, such as the phase iterative recovery method.
Regarding the recorded hologram as just ordinary diffraction field intensity information, the phase information is lost. Mudanyali et al. proposed a phase iteration method, which uses a threshold definition method to determine the boundary of the sample object [37]. After backpropagation, the twin image interference information which is outside the edge of the object can be removed iteratively by imposing constraints. The method consists of the following steps: 1.
The root mean square of the holographic image information I(x, y) recorded by the image sensor is propagated back to the object surface, the phase information on the object surface is assumed to be zero at this time, and the phase information is finally restored on the object surface through an iterative method. At the same time, the threshold segmentation method is used to determine the boundary of the sample object.
In Equation (6), U 1 −z 2 represents the real image field distribution after the first iteration. 2.
The information inside the boundary of the object is retained, and the information outside the boundary is replaced by the information after the backpropagation of the sample-free background image: In Equation (7), D −z 2 (x, y) is obtained by backpropagating the root mean square of the background image without samples, m is the iteration coefficient, and U i −z 2 represents the real image field distribution after the ith iteration. 3.
The reconstructed field after being constrained in the second step is propagated forward to the surface of the image sensor. At this time, the phase value is no longer zero, and the phase value is retained. The amplitude value is determined by the root mean square band of the original recorded holographic image, U 0 0 (x, y), amplitude. The diffraction field, U i 0 (x, y), after the ith iteration is expressed as follows: where φ i 0 (x, y) denotes the phase of the field after the ith iteration. Steps 1 to 3 can be iterated until the phase recovery converges. Typically, the results are obtained with less than 15 iterations, and the results are shown in Figure 2b. represents the real image field distribution after the first 220 iteration. 221 2. The information inside the boundary of the object is retained, and the information 222 outside the boundary is replaced by the information after the backpropagation of the 223 sample-free background image: In Equation (7), − 2 ( , ) is obtained by backpropagating the root mean 225 square of the background image without samples, is the iteration coefficient, and 226 − 2 represents the real image field distribution after the ith iteration.
3. The reconstructed field after being constrained in the second step is propagated 228 forward to the surface of the image sensor. At this time, the phase value is no longer 229 zero, and the phase value is retained. The amplitude value is determined by the root 230 mean square band of the original recorded holographic image, 0 0 ( , ), amplitude. 231 The diffraction field, 0 ( , ), after the ith iteration is expressed as follows: where 0 ( , ) denotes the phase of the field after the ith iteration. 233 Steps 1 to 3 can be iterated until the phase recovery converges. Typically, the results 234 are obtained with less than 15 iterations, and the results are shown in Figure 2b.

239
In order to test the performance of the algorithm, we used two imaging methods, 240 shadow imaging and holographic imaging, to shoot experiments on the United States Air 241 Force (USAF) resolution plate. The experimental conditions were set with the same pa-242 rameters. The center wavelength of the light source is 587 nm, the distance between the 243

Image Quality Assessment
In order to test the performance of the algorithm, we used two imaging methods, shadow imaging and holographic imaging, to shoot experiments on the United States Air Force (USAF) resolution plate. The experimental conditions were set with the same parameters. The center wavelength of the light source is 587 nm, the distance between the USAF resolution plate and the image sensor is 0.5 mm, and the pixel size is 1.12 µm. In addition, we also used a 10× objective microscope to photograph the same area of the USAF resolution plate as a comparison image. The comparison of the holographic image after iterative phase recovered, shadow image, and 10× ocular lens is shown in Figure 3.
In order to more intuitively evaluate the image quality of different imaging methods, we introduced image quality evaluation algorithms, which are divided into non-reference image quality evaluation algorithm [38] and reference-quality evaluation algorithm [39].

•
Non-reference image quality evaluation In the non-reference image quality evaluation, we used the Brisque algorithm to perform global scoring and evaluation on the holographic restored image and the shadow image. The overall principle of the algorithm is to extract the MSCN (Mean Subtracted Contrast Normalized) coefficients from the normalized image and fit the MSCN coefficients to an asymmetric generalized Gaussian distribution, extract the fitted Gaussian distribution feature, then input it into the support vector machine (SVM) for regression calculation, thereby obtaining the image quality evaluation result, and the score results are shown in Figure 3a,b. Based on the Brisque algorithm, lower score indicates better quality. •

Reference image quality evaluation
In the reference image quality evaluation, we used two evaluation parameters, namely the blur coefficient (K blur ) and quality index (Q). The 10× microscope image is used as the reference image, and the holographic recovered image and shadow image are used as the images to be evaluated. Among them, the blur coefficient is defined as follows: Among them, the energy characteristic of the oblique edge, S i , is In (11), y i f (i, j, k) is the value obtained after the brightness value of the kth frame, the ith row, and the jth column, which are processed by an oblique space differential filter.
It can be seen that K blur is the ratio of the output edge energy to the input edge energy. Assuming that the image sequence has no other distortion, the range of value K blur is generally between 0 and 1. The closer the K blur value is to 1, the higher the image clarity. The result of K blur is shown in Table 1. The K blur value 0.9738 of the recovered hologram is between 0 and 1 and is closer to 1, so the quality is better.
The quality index is defined as follows: In (12), where x and y are the reference image and the image to be tested respectively, x and y are pixel mean value, σ 2 x and σ 2 y are pixel variance, and σ xy is the standard deviation. The value range of the quality index Q is usually between [−1, 1], the closer to 1, the higher the image quality. The result of Q is shown in Table 1. The Q value of the shadow image and the recovered hologram image are both between −1 and 1, but the Q value of the recovered hologram image 0.2174 is closer to 1, so the quality of the holographic restored image is higher.

288
In the miniaturized on-chip biological detection equipment, the cell solution was 289 dropped on a cover glass with a thickness of 0.5 mm through a pipette, and a glass smear 290 was made and placed above the image sensor. Under the irradiation of an incoherent 291 LED light source, the holographic diffraction pattern of the cells was recorded by the 292 image sensor. In order to reduce the volume and cost of the equipment, we used ordinary 293 yellow LED as the light source, and used 3D printing technology to build a dark box with 294 a volume of 6.5 × 6.5 × 7 cm 3 . The light source was fixed to the pinhole, and the image 295 sensor was placed at the bottom of the box. The smear was attached to the image sensor 296 by liquid glue. After iteratively recovering the captured cell holographic image using the 297 above image recovery algorithm, the Fiji tool is introduced to classify, identify, and count 298 the cells. 299 Classification and recognition are performed by taking an image containing differ-300 ent cells and use the Trainable Weka Segmentation tool to mark the different cells in color 301 [40]. Trainable Weka Segmentation is a plug-in of Fiji that combines a set of machine 302 learning algorithms and a set of selected image features to generate pixel-based seg-303 mentation. Weka includes a set of visualization tools and algorithms for data analysis 304 and predictive modeling and a graphical user interface (GUI) for easy access to this fea-305 ture. Next, the cell images are binarized, the adhered cells are segmented using the wa-306 tershed segmentation method, and then the Cell Counter plug-in is used to count the 307 cells of the entire image and display the counting results. 308

309
In order to test the imaging performance of the designed holographic imaging sys-310 tem, we captured the holographic images of mixed solution of mouse ascites tumor cells 311 and polystyrene particles (15 μm). The same chosen area was shown for comparison. 312 Figure 4a is a microscopic image under 10× objective. In this figure, the arrows point to 313 the polystyrene particles, and the dotted circles indicate the cells. The holographic im-314 aging experiment process was as follows: First, a background image was taken without 315 any sample solution to use the phase recovery algorithm to remove the background, 316 second, a pipette was used to drop 10 μL of the mixed solution onto a cover glass with a 317 thickness of 0.5 mm and generate the cell smears, from which the holographic imaging 318

Cell Analysis
In the miniaturized on-chip biological detection equipment, the cell solution was dropped on a cover glass with a thickness of 0.5 mm through a pipette, and a glass smear was made and placed above the image sensor. Under the irradiation of an incoherent LED light source, the holographic diffraction pattern of the cells was recorded by the image sensor. In order to reduce the volume and cost of the equipment, we used ordinary yellow LED as the light source, and used 3D printing technology to build a dark box with a volume of 6.5 × 6.5 × 7 cm 3 . The light source was fixed to the pinhole, and the image sensor was placed at the bottom of the box. The smear was attached to the image sensor by liquid glue. After iteratively recovering the captured cell holographic image using the above image recovery algorithm, the Fiji tool is introduced to classify, identify, and count the cells.
Classification and recognition are performed by taking an image containing different cells and use the Trainable Weka Segmentation tool to mark the different cells in color [40]. Trainable Weka Segmentation is a plug-in of Fiji that combines a set of machine learning algorithms and a set of selected image features to generate pixel-based segmentation. Weka includes a set of visualization tools and algorithms for data analysis and predictive modeling and a graphical user interface (GUI) for easy access to this feature. Next, the cell images are binarized, the adhered cells are segmented using the watershed segmentation method, and then the Cell Counter plug-in is used to count the cells of the entire image and display the counting results.

Discussion
In order to test the imaging performance of the designed holographic imaging system, we captured the holographic images of mixed solution of mouse ascites tumor cells and polystyrene particles (15 µm). The same chosen area was shown for comparison. Figure 4a is a microscopic image under 10× objective. In this figure, the arrows point to the polystyrene particles, and the dotted circles indicate the cells. The holographic imaging experiment process was as follows: First, a background image was taken without any sample solution to use the phase recovery algorithm to remove the background, second, a pipette was used to drop 10 µL of the mixed solution onto a cover glass with a thickness of 0.5 mm and generate the cell smears, from which the holographic imaging device would capture the images of mixed sample solution (Figure 4b). Third, the self-designed holographic phase recovery algorithm based on Matlab was employed to reconstruct the captured holographic image (Figure 4c). The results show that in the cell image after holographic phase recovery, the gray value of the low refractive index cells is generally higher than that of the high refractive index polystyrene particles, and the contour and sharpness of the cell edges is better recovered. The inset in Figure 4d, enclosed with the dashed rectangle, shows the polystyrene particle and cells after iterative phase recovery algorithm, further validating the imaging performance of our holographic microscope. device would capture the images of mixed sample solution (Figure 4b). Third, the 319 self-designed holographic phase recovery algorithm based on Matlab was employed to 320 reconstruct the captured holographic image (Figure 4c). The results show that in the cell 321 image after holographic phase recovery, the gray value of the low refractive index cells is 322 generally higher than that of the high refractive index polystyrene particles, and the 323 contour and sharpness of the cell edges is better recovered. The inset in Figure 4d, en-324 closed with the dashed rectangle, shows the polystyrene particle and cells after iterative 325 phase recovery algorithm, further validating the imaging performance of our holo-326 graphic microscope.  The image processing flow consists of two steps: The first step is cell identification 330 and segmentation. We used Fiji's Trainable Weka Segmentation plug-in to train the clas-331 sifier. A small number of cells, particles, and backgrounds in Figure 4c are first selected 332 and set into three different labels. Each label generally contains sampling information of 333 3-4 different positions. The classification results can be obtained through training, as 334 shown in Figure 5a. Among them, the red parts represent polystyrene particles, the green 335 parts represent mouse ascites tumor cells, and the purple parts represent the background. 336 The second step is the cell counting. First, the particles and cells with incomplete edges in 337 Figure 5a were removed by setting a threshold, then we binarized the image and filled in 338 the holes, then broke the adherent cells, and finally counted the remaining cells in the 339 image. The counting result is shown in Figure 5b. It can be seen from the results that the 340 number of cells is 62, and the count value is marked inside the cell edge. The count result 341 and manual count result of reference are similar to each other, which preliminarily veri-342 fies the accuracy of the on-chip holographic microscope. The image processing flow consists of two steps: The first step is cell identification and segmentation. We used Fiji's Trainable Weka Segmentation plug-in to train the classifier. A small number of cells, particles, and backgrounds in Figure 4c are first selected and set into three different labels. Each label generally contains sampling information of 3-4 different positions. The classification results can be obtained through training, as shown in Figure 5a. Among them, the red parts represent polystyrene particles, the green parts represent mouse ascites tumor cells, and the purple parts represent the background. The second step is the cell counting. First, the particles and cells with incomplete edges in Figure 5a were removed by setting a threshold, then we binarized the image and filled in the holes, then broke the adherent cells, and finally counted the remaining cells in the image. The counting result is shown in Figure 5b. It can be seen from the results that the number of cells is 62, and the count value is marked inside the cell edge. The count result and manual count result of reference are similar to each other, which preliminarily verifies the accuracy of the on-chip holographic microscope.

345
In this paper, we demonstrated a lensless on-chip holographic imaging platform 346 using in-line holography technology and used an iterative phase recovery algorithm to 347 achieve the phase recovery of the holographic image. The resolution of the reconstructed 348 hologram image was improved by 1.41 times compared with the traditional shadow 349 imaging method, and the image sharpness was also improved. In the reconstructed hol-350 ogram (Figure 3a), all the bars of group 6, element 4, can be identified (90.5 Line 351 Pairs/mm), but in the traditional shadow image (Figure 3b), only group 6, element 1, can 352 be completely identified (64 Line Pairs/mm), and the edge is out of focus. Moreover, 353 compared with the traditional manual counting of blood smears, this paper realizes the 354 function of automatically identifying and counting cells. Finally, because the system is 355 small in size and low in price, it can be promoted and used in poor and remote areas and 356 has the application prospect of point-of-care testing (POCT).

Conclusions
In this paper, we demonstrated a lensless on-chip holographic imaging platform using in-line holography technology and used an iterative phase recovery algorithm to achieve the phase recovery of the holographic image. The resolution of the reconstructed hologram image was improved by 1.41 times compared with the traditional shadow imaging method, and the image sharpness was also improved. In the reconstructed hologram (Figure 3a), all the bars of group 6, element 4, can be identified (90.5 Line Pairs/mm), but in the traditional shadow image (Figure 3b), only group 6, element 1, can be completely identified (64 Line Pairs/mm), and the edge is out of focus. Moreover, compared with the traditional manual counting of blood smears, this paper realizes the function of automatically identifying and counting cells. Finally, because the system is small in size and low in price, it can be promoted and used in poor and remote areas and has the application prospect of point-of-care testing (POCT).