Open Access
Add to BibSonomy
Abstract
Digital holographic microscopy (DHM) has the potential to reconstruct the 3D shape of volumetric samples from a single-shot hologram in a label-free and noninvasive manner. However, the holographic reconstruction is significantly compromised by the out-of-focus image resulting from the crosstalk between refocused planes, leading to the low fidelity of the results. In this paper, we propose a crosstalk suppression algorithm-assisted 3D imaging method combined with a home built DHM system to achieve accurate 3D imaging of ocean algae using only a single hologram. As a key step in the algorithm, a hybrid edge detection strategy using gradient-based and deep learning-based methods is proposed to offer accurate boundary information for the downstream processing. With this information, the crosstalk of each refocused plane can be estimated with adjacent refocused planes. Empowered by this method, we demonstrated successful 3D imaging of six kinds of ocean algae that agree well with the ground truth; we further demonstrated that this method could achieve real-time 3D imaging of the quick swimming ocean algae in the water environment. To our knowledge, this is the first time single-shot DHM is reported in 3D imaging of ocean algae, paving the way for on-site monitoring of the ocean algae.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fast recognition of ocean algae is essential to accurately predicting the algae bloom, reducing the detrimental impact to the marine ecological environment and the loss of costal economy. To date, most ocean algae monitoring methods are based on the two-dimensional (2D) imaging, which is less than efficient due to the limited information of the sample it can provide. A 3D shape can offer a full view of ocean algae, thus to increase the recognition accuracy [1,2]. Digital holographic microscopy (DHM) has emerged as a promising 3D imaging tool that has been widely used in a broad range of biological applications [3–8], showing great potential in the on-site 3D monitoring of ocean algae in complex water environment. It can encode a complex optical field of volumetric sample using only a single 2D hologram (single-shot DHM) [9–11] and produce the sample’s 3D shape by numerical reconstruction, without the need of sample preparation and mechanical scanning that are required in other 3D imaging methods such as scanning electron microscope (SEM) [12,13] and optical diffraction tomography (ODT) [14–21]. However, the reconstruction quality is significantly limited by the holographic artifacts including twin-image, speckle noise and crosstalk between the refocused planes [9]. Among them, the twin-image and speckle noise can be efficiently suppressed through specialized hardware design [18,22] and algorithmic processing [23,24], while the crosstalk between the refocused planes (a main cause of the out-of-focus image) is difficult to be removed due to the diffraction nature of the hologram, and has been the main challenge of the DHM. As a result, the traditional DHM is limited in imaging of simple samples with small size (below ∼20 µm) [25–27] or using the fusion of multiple holograms (at least 80 frames) to produce a 3D shape. For example, Merola et al [28] reported using a DHM-based tomographic flow cytometry to image the red blood cells using about 200 holograms that are measured during 360° rotation of the cells in a microfluidic channel. Obviously, this strategy must compromise imaging speed and throughput to compensate the reconstruction accuracy, which is difficult to be applicable to the 3D tracking of living sample. As a promising alternate, data processing methods such as compressive sensing (CS) [29,30] and volumetric deconvolution (VD) [31,32], can be used to suppress the crosstalk to improve the holographic reconstruction accuracy. CS uses less pixels to reconstruct the 3D object, and part of the crosstalk can be simultaneously removed as an auxiliary effect due to the down-sampling of the image pixels. Nevertheless, part of the information will be abandoned together, leading to over smoothing of the results. The VD considers the reconstructed complex amplitude at a specific refocused plane as a convolution of the object’s actual 3D shape and the point-spread function (PSF) of the DHM system. Thus, the object’s 3D shape can be calculated by a deconvolution of the reconstructed complex amplitude with the PSF. Since the PSF is partially resulted from the crosstalk, this method can suppress the crosstalk to a certain degree. However, the performance of these algorithms is still insufficient to the accurate 3D reconstruction of the complex volumetric samples, such as the ocean algae which plays an important role in the marine ecology. For example, Joonku et al [33] demonstrated a 3D visualization of water cyclopse with the compressive holography, Eom et al [31] reported a 3D volumetric image of a kidney tissue sample with the volume deconvolution, but these results were incomplete. Besides, the 3D image obtained by a Gabor (in-line) configuration has a low resolution, it is difficult to distinguish the details of the ocean algae. Recently, deep learning was introduced to suppress the crosstalk, and obtained some good results [34,35]. However, the accurate registration of holographic image with the bright-field microscope image is complicated and time consuming. Yet, real-time 3D imaging with single-shot DHM has not been reported so far.
In this paper, we propose a crosstalk suppression algorithm assisted 3D imaging method to reconstruct 3D shape of the ocean algae. First, the refocused planes are preprocessed by the volumetric deconvolution to reduce the influence of the PSF of DHM system. Then, the edge of the ocean algae at each refocused plane is delineated by a hybrid method which combines a gradient-based approach and a deep learning-based approach. Next, backgrounds that are free of ocean algae are selected to produce the background refocused planes. Finally, each refocused plane is processed by its adjacent background refocused planes according to a method of crosstalk suppression, so as to eliminate the crosstalk between the refocused planes. Furthermore, since the ocean algae are non-transparent, to ensure the laser can completely penetrate it, a laser diode with coherent length of 50 m and a cuvette with thickness of 0.2 mm are employed in the optical setup. The optical setup is a co-axis configuration for a high quality of holographic reconstruction, and the magnification of the optical setup is 30 so that the influence of twin-image on real image (refocused ocean algae) can be negligible [24]. With this specialized DHM setup and the proposed method, the clear 3D shape of the ocean algae can be obtained quickly. We reconstructed the 3D shapes of six kinds of ocean algae by the proposed single-shot DHM 3D imaging method, with a running time of 70s for 41 refocused planes (120×120 pixels) and a transverse resolution of 0.18 µm. We also imaged five kinds of the six ocean algae by SEM and ODT (the last one has large size cannot be directly imaged by them), and impressively found that the DHM’s results showed high consistency with SEM and ODT. Furthermore, real-time 3D imaging of the quick swimming algae in the water environment was also presented. The results demonstrate that the proposed method can accurately reconstruct the 3D shapes of the ocean algae, making the on-site monitoring of ocean algae possible.
2. Principle of 3D imaging with single-shot DHM
The overview of 3D imaging with single-shot DHM can be illustrated in Fig. 1(a). The 2D holograms of the ocean algae (placed in cuvette C1) are captured by a home built DHM system, and one hologram containing ocean algae is selected to refocus the image plane-by-plane with a standard numerical reconstruction (NR) method [36], producing a stack of refocused planes. Next, the refocused planes are processed by the proposed crosstalk suppression method to obtain clear ones. Finally, the isosurfaces of the clear refocused planes are rendered to reconstruct the 3D shapes of the ocean algae.
Fig. 1. Scheme of the 3D reconstruction of ocean algae with single-shot DHM. (a) Overview of the 3D reconstruction of ocean algae using a single hologram. Denotation: spatial filter (SP); lens (L); beam splitter (BS); mirror (M); microscope objective (MO); cuvette with ocean algae (C1); cuvette with reference liquid (C2); numerical reconstruction (NR), isosurfaces rendering (IR). (b)The instrumentation setup of the DHM. (c) Scheme of the principle of DHM. Denotation: back propagation (BP); forward propagation (FP); O(x,y) is the wave field of object beam; R(x,y) is the wave field of reference beam; ‘δ’ is the deviation of the object plane (e.g. O1) from the focused plane (A) of MO; ‘l’ is the reconstruction distance.
The instrumental setup of the DHM system is a co-axis configuration based on a mach-zehnder interferometer working in transmission mode (Fig. 1(b)). A co-axis configuration rather than an off-axis configuration was employed in our setup. That is because the off-axis configuration has a small space-bandwidth product, which will results in the missing of edge of ocean algae and an inferior quality of refocused planes (see Fig.S1 in supplementary information). The laser beam generated by a single-longitudinal mode laser diode (MSL-DS-532, Changchun New industries opto-electronics Tech, co., Ltd) is expanded by a spatial filter (SP, 57-739, Edmund) to obtain a high-quality collimated plane wave, it is then divided into an object beam and a reference beam by the first cube non-polarizing beam splitter (BS1, 35-960, Edmund). The object beam, after reflecting from mirror (M1, NB1-K13, Thorlabs), passes through a cuvette (C1, 6 mm×0.2 mm) containing an ocean algae volume, and the reference beam transmits through another cuvette (C2, 6 mm×0.2 mm) filled with reference liquid after reflecting from mirror (M2, NB1-K13, Thorlabs). Two microscope objectives (MO1 and MO2, LMPLFLN10×, Olympus) are added after the two cuvettes to magnify the images of the ocean algae and reference liquid. The two arms of the interferometer are joined by a second cube non-polarizing beam splitter (BS2, 35-960, Edmund), where the object beam interferes with the reference beam, producing an interference pattern. The pattern is then captured as a 2D hologram by a camera (Mako-G419B, Allied Vision). A personal computer is used to store the hologram and perform the numerical calculations to reconstruct the 3D shape of the ocean algae. Considering the fact that the ocean algae is nontransparent, to ensure the laser beam penetrate the ocean algae as much as possible, a laser diode with a coherent length of 50 m is used as the light source, and the optical path length of the cuvette is 0.2 mm. An example video of refocused planes of an ocean algae sample (HAZJ) acquired using this home built DHM system is shown in the supplementary material (Visualization 1). In spite of the out-of-focus image, one can still roughly observe the change of the edge of the HAZJ, indicating that the laser beam can fully penetrate the sample. According to our previous work [37], for the purpose of obtaining a large refocus depth range, the camera has a large image sensor size (11.264 mm×11.264 mm) and the two microscope objectives have a long working distance (21 mm). The maximum measurement volume is 0.375×0.375×0.2 mm3, and the actual maximum reconstruction volume of the sample is 11.264×11.264×180 mm3 with a system magnification rate of 30.
The scheme of the principle of DHM can be illustrated in Fig. 1(c). Denoting the intensity distribution of the hologram as h(x,y,z), it performs numerical reconstruction to obtain the refocused planes. The complex amplitude of the refocused plane (P1) with reconstruction distance of l1’ can be expressed as:
Equation (1) and (2) can also be called as back propagation of the hologram, if ‘BP’ is used to denote the back propagation, then Eq. (1) can be rewritten as:
Actually, P2 is also a back propagation of P1, this can be expressed as:
According to the reversibility of light, P1 is a forward propagation of P2, which can be expressed as:
3. Crosstalk suppression algorithm-assisted 3D imaging method
Figure 2 gives a detailed pipeline of the proposed method using a single-shot hologram to produce accurate 3D shape of the ocean algae. Specifically, this method includes 6 steps.
Fig. 2. Pipeline of crosstalk suppression algorithm enabled 3D imaging using a single hologram. (a) Background removal of the target hologram. (b) Raw refocused planes using numerical reconstruction with the background corrected hologram. (c) Basic denoising of the raw refocused planes using volumetric deconvolution method. (d) Edge detection combined gradient based method with HED network based method to delineate the boundary of the ocean algae for each refocused plane. (e) Crosstalk suppression using the background extracted from the subsequent refocused planes after edge detection (the image information out of the edge is considered as the background), the BE denotes background extraction. (f) 3D reconstruction by IR and axes calibration using the refocused planes after crosstalk suppression. The color code indicates the gray scale value.
Step 1. Preprocessing
Remove the background noise of the target hologram (Fig. 2(a), left) using a neighboring hologram without target (Fig. 2(a), middle), obtaining the background corrected hologram.
Step 2. Numerical reconstruction
Reconstruct a raw refocused planes (PC-n, …, PC, …, PC+n) by performing numerical reconstruction of the corrected hologram with a series of reconstruction distances.
The refocused planes are divided into front half of ocean algae and back half of ocean algae (in the direction of the illumination incidence), as shown in Fig. 2(b), to be processed by the method of crosstalk suppression.
Step 3. Volumetric deconvolution
Reduce the influence of the PSF of the DHM system on the raw refocused planes by the volumetric deconvolution (detail methods and steps of volume deconvolution can be found in the Supplement 1) to produce the basic denoised refocused planes which are denoted as P'C-n, …, P'C, …, P'C+n (Fig. 2(c)).
The basic denoising of the raw refocused planes is performed by the volumetric deconvolution rather than the compressive sensing can be illustrated as follows. The compressive sensing usually decreases the pixel number of hologram for saving computing time, but a smaller or coarser hologram with fewer pixels result in a lower reconstruction quality, whereas in the volumetric deconvolution, hologram is reconstructed with original size, it is the refocused planes that go through cropping for deconvolution. Comparison results are presented in the Fig. S2 of the Supplement 1, it indicates that the VD outperforms the compressive sensing much better.
Step 4. Edge detection
Reduce the speckle noise and background noise of the basic denoised refocused planes by a non-local means (NLM) filter algorithm and an iterative thresholding algorithm firstly. After that, a hybrid edge detection strategy which leverages the advantage of the HED [38] neural network and a gradient-based method [39] to calculate the accurate edge of the focused ocean algae at each refocused plane, the edges detected by the two methods are concatenated by Boolean AND to output the final binary edge (Fig. 2(d)). More examples see Fig.S4 of the Supplement 1.
The details of the proposed method of edge detection is described in the edge detection of the Supplement 1. The HED neural network is trained on a manually labeled holographic image dataset, which contains 3520 image pairs. The detail architecture of the HED can be found in the details of network and training of the Supplement 1.
Step 5. Crosstalk suppression
Perform a background extraction (BE) on the basic denoised refocused planes according to the edges detected by Step 4 (e.g. EC-2S, EC-S, EC), producing the background refocused planes (e.g. BC-2S, BC-S, BC). Then they are propagated to the target refocused plane (e.g. P'C-2S-i) to produce the propagated ones (e.g. B'C-2S, B'C-S, B'C). The crosstalk of the target refocused plane can be suppressed by subtracting these adjacent propagated background refocused planes. The details are described as follows.
Suppose the number of the refocused planes that include the entire ocean algae is N (e.g. N = 41). Usually, refocused planes near the middle of the ocean algae have little holographic artifacts, they are selected as standard refocused planes to perform the crosstalk suppression for other refocused planes in the two ends (target refocused planes). For example, in Fig. 2(e), P'C is located at the middle of the ocean algae, P'C-2S, P'C-S near the middle of the ocean algae, so P'C-2S, P'C-S, P'C are standard refocused planes. P'C-2S-i is target refocused plane to be processed. The reconstruction distances of P'C-2S, P'C-S, P'C are l'C-2S, l'C-S, l'C, respectively, the interval of the above refocused planes is Δl’, which can be expressed as:
1. Select three standard refocused planes (P'C-2S, P'C-S, P'C) and S target refocused planes. The reconstruction distance of each target refocused plane (P'C-2S-i) can be expressed as:
2. Detect edges of ocean algae (EC-2S, EC-S, EC) in the standard refocused planes by the hybrid edge detection method to obtain the corresponding background refocused planes (BC-2S, BC-S, BC).
3. Forward propagate the background refocused planes (BC-2S, BC-S, BC) to the target refocused plane (P'C-2S-i) for subtracting the complex amplitude, longer propagation distance is given smaller weight. Then the complex amplitude of the clear refocused planes (P”C-2S-i (x,y)) can be expressed as:
4. Replace P'C-2S, P'C-S, P'C by P'C-3S, P'C-2S, P'C-S, respectively, to make up a new group of standard refocused planes, in other words, decreasing l'C, l'C-S and l'C-2S by Δl’. Then repeat step 2 to step 4 to suppress the crosstalk of the target refocused planes in the next batch (P'C-3S-i, i = 1,2, …, S), until all the target refocused planes are processed.
The steps for the refocused planes in the back half of ocean algae are similar except that the standard refocused planes are back propagated instead of forward propagated, also they are refreshed by increasing reconstruction distances by Δl’ instead of decreasing them.
Step 6. 3D reconstruction
Select the ocean algae in the crosstalk suppressed (clear) refocused planes by the hybrid edge detection method again, then render their isosurfaces with seven colors according to the gray value, higher gray value is closer to red, as shown in Fig. 2(f). In order to achieve a realistic shape, the scales of the length (y), width (x) and height (z) (3D axes) should be correctly calibrated, the details are described in determination of scales of the Supplement 1.
4. Results and discussion
4.1 Materials
To evaluate the performance of the proposed crosstalk suppression algorithm assisted 3D imaging method, six kinds of ocean algae are tested in our work. They are Amphidinium carterae Hulburt (ACZJ), Heterosigma akashiwo (HAZJ), Skeletonema costatum (SCYW), Scrippsiella trochoidea (STNJ), Alexandrium tamarense (ATEC) and Chattonella marinal (CMSH), the size and sample sites are list in Table 1. The ocean algae sample is diluted before be dropt into the thin cuvette, so that each ocean algae can be separated completely in the target hologram.
Table 1. The size and sample sites of the ocean algae
4.2 Reduction of crosstalk
Figure 3(a) shows some basic denoised refocused planes of the HAZJ. As can be seen, the out-of-focus image resulted from the crosstalk significantly decreased the contrast of the refocused planes and posed a great challenge for selection of ocean algae to reconstruct its true 3D shape. Actually, in the two refocused planes located at the ends of HAZJ (l'=64482 µm and l'=93867 µm), only a small part (circled by the red edge labelled by human expert) is the true body of the HAZJ, the rest are out-of-focus images. The edges of HAZJ detected by the proposed hybrid method are shown in Fig. 3(b), which are consistent well with the manual annotated ones (Fig. 3(a)). Figure 3(c) shows the clear refocused planes and detected edges after applying the proposed crosstalk suppression method, which efficiently eliminates the out-of-focus image, and produces clear edges of HAZJ. Table 2 lists the intersection over union (IoU) between regions filled by edges in Fig. 3(a) and Fig. 3(b), and that in Fig. 3(a) and Fig. 3(c). As can be seen, in most cases (except l'=64482 µm and l'=69992 µm), the later one presented a higher value of IoU than the former one. This fact indicates that the edges detected by the hybrid method are closer to the true contours of the sample after crosstalk suppression.
Fig. 3. Performance of the proposed crosstalk suppression method for HAZJ. (a) Basic denoised refocused planes before the use of the proposed crosstalk suppression method, the red lines are manual annotated edges. (b) Edges of HAZJ detected by the hybrid method combing the gradient magnitude-based approach and the deep learning-based approach, (c) Clear refocused planes and detected edges after applying the proposed crosstalk suppression method. The unit of l’ is in µm.
4.3 3D reconstruction of ocean algae
After crosstalk suppression and edge detection, an accurate 3D shape of the ocean algae can be obtained. Figure 4(a) shows the 3D shapes of six kinds of the ocean algae. As comparison, the 3D RI distributions obtained by ODT using a commercial holotomographic microscopy (HT-2H, Tomocube, Inc.) and the surface morphologies obtained by SEM (Regulus-8100, HITACHI) are also presented in Fig. 4(b) and (c), respectively. The experimental details can be found in the Supplement 1. As can be seen, the 3D shapes of the ocean algae obtained by DHM with the proposed crosstalk suppression algorithm assisted 3D imaging method agreed well with those obtained by SEM and ODT. For example, the hook in the end of the ACZJ, the bulge of the HAZJ, the rib (cannot be discerned by DHM and ODT) of the SCYW, the cone of the STNJ, and the chip of ATEC. Impressively, we also successfully reconstructed the 3D shape of CMSH that cannot be directly obtained by ODT and SEM due to its large size. It should be noted that the relative sizes of the six ocean algae in the Fig. 4(a) do not represent their true relative sizes because each of the 3D shapes was scaled with different zoom factor. For example, the length of the STNJ takes account about 80 pixels while CMSH takes account near 300 pixels. The calculated volumes for ACZJ, HAZJ, SCYW, STNJ, ATEC, CMSH are 355.64 µm3, 428.88 µm3, 80.12 µm3, 396.16 µm3, 4567.30 µm3 and 6500.00 µm3, respectively. More views observed from different visual angles are presented in Fig. S6 of the Supplement 1.
Fig. 4. 3D imaging of the ocean algae. (a) 3D shapes of six kinds of ocean algae by the proposed crosstalk suppression algorithm assisted 3D imaging method. (b) 3D RI distributions of five kinds of ocean algae by the ODT. (c) Surface morphologies of five kinds of ocean algae obtained by the SEM. (d-e) Real time 3D imaging of the ATEC (taken in December 20th, 2020) and HAZJ (taken in December 5th, 2020). The time near the 3D shape indicates the order of the record time of the holograms from which the 3D shapes are reconstructed, the blue arrows point the moving direction.
For saving time, each 3D shape was reconstructed using a small stack (41 frames, each contains 120×120 pixels) of clear refocused planes in this paper. It took 70s to obtain a 3D shape of ocean algae from 41 original refocused planes with size of 120×120 pixels, where the non-local means (NLM) filter algorithm in edge detection took up 57s. As comparison, due to the time-consuming preparation of sample, the time for the ODT to obtain a 3D RI distribution of ocean algae was nearly one hour, and the time for the SEM to obtain a surface morphology of ocean algae was about 30 h.
The transverse resolution of the 3D shape can be calculated according to the magnification of the optical system and the pixel pitch of the camera, which was 0.18 µm in our system. The axial resolution varies with the range of reconstruction distance, values for ACZJ, HAZJ, SCYW, STNJ, ATEC and CMSH were 1.26 µm, 1.02 µm, 0.23 µm, 1.12 µm, 2.17 µm and 2.30 µm, respectively.
We further presented the real time 3D imaging of the ATEC and HAZJ in Fig. 4(d) and (e) with the proposed method, each contained four consecutive 3D shapes of the ocean algae in the field of view when it swam at different positions in the water. The four consecutive 3D shapes were reconstructed and selected from four different background corrected holograms captured with an interval of 0.2 second, then they were fused together in the real-time 3D image according to their corresponding position. All the methods or algorithms were coded in Matlab (version R2018a), and could run automatically without user’s manual input.
The above results demonstrate that the proposed method allows DHM to obtain a 3D shape of ocean algae with a single-shot hologram, achieve the real-time 3D imaging of the ocean algae. This makes DHM a promising tool for on-site 3D monitoring of ocean algae.
5. Conclusion
DHM is a powerful imaging method which can provide the sample’s 3D shape with only a single hologram, thereby, it can be used in the real-time tracking of living samples. However, the holographic reconstruction cannot achieve ideal 3D accuracy due to the crosstalk of the out-of-focus images, thus, limiting the broad application of DHM. Here we demonstrate that a crosstalk suppression algorithm could facilitate the 3D imaging with single-shot DHM. Basically, this algorithm contains six main steps, that is, preprocessing, numerical reconstruction, volumetric deconvolution, edge detection, crosstalk suppression and 3D reconstruction. As a key step of this algorithm, the edge detection is achieved by a hybrid strategy which combines a gradient magnitude-based and a deep learning-based method to provide accurate boundary information so that crosstalk of each image slice can be suppressed efficiently. Besides, a specialized DHM system with long coherent length and thin imaging depth is built to facilitate the 3D imaging of opacity volumetric samples with complex external and internal structure. We demonstrated that the crosstalk suppression algorithm can efficiently improve the single-shot 3D imaging. Specifically, the 3D shapes of six kinds of ocean algae were successfully reconstructed using the proposed method. Expectedly, these 3D shapes showed high consistency with the results obtained by SEM and ODT method. Moreover, the proposed single-shot DHM showed advantages in large volumetric sample imaging which couldn’t be directly imaged by SEM and ODT, for example, the CMSH demonstrated in this paper. At last, we further demonstrated the proposed method could be used in real-time 3D imaging of the quick swimming ocean algae in the water environment with a frame rate of 5 Hz. To our knowledge this is the first time single-shot DHM is used in 3D imaging of ocean algae, which provides important guidance for on-site 3D imaging of ocean algae using single-shot DHM, and helps to fast recognize ocean algae for predicting the algae bloom.
Funding
China Postdoctoral Science Foundation (2022M711482); National Natural Science Foundation of China (42165007, 62163024).
Acknowledgments
The authors would like to thank Prof. Xiaoping Wang (Zhejiang University) for providing the ocean algae samples.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. P. Memmolo, P. Carcagni, V. Bianco, F. Merola, A. G. da Silva Junior Jr., L. M. Garcia Goncalves, P. Ferraro, and C. Distante, “Learning diatoms classification from a dry test slide by holographic microscopy,” Sensors 20(21), 6353 (2020). [CrossRef]
2. A. R. Nayak, E. Malkiel, M. N. McFarland, M. S. Twardowski, and J. M. Sullivan, “A review of holography in the aquatic sciences: in situ characterization of particles, plankton, and small scale biophysical interactions,” Front. Mar. Sci. 7, 1–16 (2021). [CrossRef]
3. G. Gao, J. Xia, J. Yu, J. Fan, and X. Zeng, “Regulation of inorganic carbon acquisition in a red tide alga (Skeletonema costatum): the importance of phosphorus availability,” Biogeosciences 15(16), 4871–4882 (2018). [CrossRef]
4. A. Anand, V. Chhaniwal, and B. Javidi, “Tutorial: Common path self-referencing digital holographic microscopy,” APL Photonics 3(7), 071101 (2018). [CrossRef]
5. V. Balasubramani, A. Kus, H.-Y. Tu, C.-J. Cheng, M. Baczewska, W. Krauze, and M. Kujawinska, “Holographic tomography: techniques and biomedical applications Invited,” Appl. Opt. 60(10), B65–B80 (2021). [CrossRef]
6. A. C. Monaldi, G. G. Romero, E. E. Alanis, and C. M. Cabrera, “Digital holographic microscopy for microalgae biovolume assessment,” Opt. Commun. 336, 255–261 (2015). [CrossRef]
7. S.-J. Park, B.-M. Kim, and E.-S. Kim, “Single-shot digital holographic microscopy based on computational telecentricity using a single-arm off-axis interferometer,” ICT Express 4(4), 186–193 (2018). [CrossRef]
8. B. Javidi, A. Carnicer, A. Anand, G. Barbastathis, W. Chen, P. Ferraro, J. W. Goodman, R. Horisaki, K. Khare, M. Kujawinska, R. A. Leitgeb, P. Marquet, T. Nomura, A. Ozcan, Y. Park, G. Pedrini, P. Picart, J. Rosen, G. Saavedra, N. T. Shaked, A. Stern, E. Tajahuerce, L. Tian, G. Wetzstein, and M. Yamaguchi, “Roadmap on digital holography Invited,” Opt. Express 29(22), 35078–35118 (2021). [CrossRef]
9. Y. Rivenson, Y. Wu, and A. Ozcan, “Deep learning in holography and coherent imaging,” Light: Sci. Appl. 8(1), 85 (2019). [CrossRef]
10. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008). [CrossRef]
11. Y. Wu, Y. Luo, G. Chaudhari, Y. Rivenson, A. Calis, K. de Haan, and A. Ozcan, “Bright-field holography: cross-modality deep learning enables snapshot 3D imaging with bright-field contrast using a single hologram,” Light: Sci. Appl. 8(1), 25 (2019). [CrossRef]
12. S. Becker, N. Raatz, S. Jankuhn, R. John, and J. Meijer, “Nitrogen implantation with a scanning electron microscope,” Sci. Rep. 8(1), 32 (2018). [CrossRef]
13. F. S. Hage, G. Radtke, D. M. Kepaptsoglou, M. Lazzeri, and Q. M. Ramasse, “Single-atom vibrational spectroscopy in the scanning transmission electron microscope,” Science 367(6482), 1124–1127 (2020). [CrossRef]
14. T. Chang, S. Shin, M. Lee, and Y. Park, “Computational approach to dark-field optical diffraction tomography,” APL Photonics 5(4), 040804 (2020). [CrossRef]
15. K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(01), 1–12 (2013). [CrossRef]
16. A. Kus, W. Krauze, P. L. Makowski, and M. Kujawinska, “Holographic tomography: hardware and software solutions for 3D quantitative biomedical imaging,” ETRI Journal 41(1), 61–72 (2019). [CrossRef]
17. J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23(13), 16933–16948 (2015). [CrossRef]
18. J. Min, B. Yao, V. Trendafilova, S. Ketelhut, L. Kastl, B. Greve, and B. Kemper, “Quantitative phase imaging of cells in a flow cytometry arrangement utilizing Michelson interferometer-based off-axis digital holographic microscopy,” J. Biophotonics 12(9), 1–24 (2019). [CrossRef]
19. P. Müller, M. Schürmann, and J. Guck, “The Theory of Diffraction Tomography,” Quantitative Biol. (2015).
20. Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009). [CrossRef]
21. J. Yoon, Y. Jo, M.-h. Kim, K. Kim, S. Lee, S.-J. Kang, and Y. Park, “Identification of non-activated lymphocytes using three-dimensional refractive index tomography and machine learning,” Sci. Rep. 7(1), 6654 (2017). [CrossRef]
22. Z. Zhong, H. Zhao, L. Cao, M. Shan, B. Liu, W. Lu, and H. Xie, “Automatic cross filtering for off-axis digital holographic microscopy,” Results Phys. 16, 102910 (2020). [CrossRef]
23. V. Bianco, P. Memmolo, M. Leo, S. Montresor, C. Distante, M. Paturzo, P. Picart, B. Javidi, and P. Ferraro, “Strategies for reducing speckle noise in digital holography,” Light: Sci. Appl. 7(1), 48 (2018). [CrossRef]
24. Y. Rivenson, A. Stern, and B. Javidi, “Improved depth resolution by single-exposure in-line compressive holography,” Appl. Opt. 52(1), A223–A231 (2013). [CrossRef]
25. A. Brodoline, N. Rawat, D. Alexandre, N. Cubedo, and M. Gross, “4D compressive sensing holographic microscopy imaging of small moving objects,” Opt. Lett. 44(11), 2827–2830 (2019). [CrossRef]
26. G. Situ, “Deep holography,” Light: Adv. Manuf. 3(1), 1–13 (2022). [CrossRef]
27. M. Toloui and J. Hong, “High fidelity digital inline holographic method for 3D flow measurements,” Opt. Express 23(21), 27159–27173 (2015). [CrossRef]
28. F. Merola, P. Memmolo, L. Miccio, R. Savoia, M. Mugnano, A. Fontana, G. D’Ippolito, A. Sardo, A. Iolascon, A. Gambale, and P. Ferraro, “Tomographic flow cytometry by digital holography,” Light: Sci. Appl. 6(4), e16241 (2017). [CrossRef]
29. Z. Wang, D. Ryu, K. He, R. Horstmeyer, A. Katsaggelos, and O. Cossairt, “High-speed holographic imaging using compressed sensing and phase retrieval,” in Conference on Computational Imaging II, Proceedings of SPIE (2017).
30. J. Weng, D. C. Clark, and M. K. Kim, “Compressive sensing sectional imaging for single-shot in-line self-interference incoherent holography,” Opt. Commun. 366, 88–93 (2016). [CrossRef]
31. J. Eom and S. Moon, “Three-dimensional high-resolution digital inline hologram reconstruction with a volumetric deconvolution method,” Sensors 18(9), 2918 (2018). [CrossRef]
32. T. Latychevskaia, “Three-dimensions volumetric deconvolution in coherent optics and holography,” Appl. Opt. 60(5), 1304–1314 (2021). [CrossRef]
33. J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19(8), 7289–7298 (2011). [CrossRef]
34. M. S. Sakib Rahman and A. Ozcan, “Computer-free, all-optical reconstruction of holograms using diffractive networks,” ACS Photonics 8(11), 3375–3384 (2021). [CrossRef]
35. J. Verduijn, L. Van der Meeren, D. V. Krysko, and A. G. Skirtach, “Deep learning with digital holographic microscopy discriminates apoptosis and necroptosis,” Cell Death Discov. 7(1), 229 (2021). [CrossRef]
36. K. Inoue, A. Anand, and M. Cho, “Angular spectrum matching for digital holographic microscopy under extremely low light conditions,” Opt. Lett. 46(6), 1470–1473 (2021). [CrossRef]
37. M. Tang, Z. Y. Tang, X. Qiao, K. Q. Lang, Y. Sun, and X. P. Wang, “Extension of refocus depth range in digital holographic microscopy,” Appl. Opt. 59(28), 8540–8552 (2020). [CrossRef]
38. S. Xie and Z. Tu, “Holistically-nested edge detection,” Int. J. Comput. Vis. 125(1-3), 3–18 (2017). [CrossRef]
39. B. Iqbal, W. Iqbal, N. Khan, A. Mahmood, and A. Erradi, “Canny edge detection and Hough transform for high resolution video streams using Hadoop and Spark,” Cluster Comput 23(1), 397–408 (2020). [CrossRef]
