Imaging of transparent samples such as cells is important in the biomedicine field; however, insignificant absorption and weakly scattering limit the imaging contrast of phase objects. Here, we propose and demonstrate Brewster differential microscopy based on simple optical reflection at the glass interface. The combination of spin–orbit interaction of light and the Brewster effect can perform two-dimensional differentiation to the incident light distribution and, thus, achieves isotropic edge-enhanced imaging of pure phase objects, which overcomes the limitation of traditional one-dimensional imaging. Furthermore, by introducing bias retardation, we also reconstruct the original phase distribution. The proposed microscopic imaging mechanism does not involve any complex modulation devices and takes advantages of simple and low-cost structure. The results indicate that our research shows promising applications for nondestructive imaging of biological cells.

Light microscopy is a powerful tool to observe the microscopic structure and understand dynamics of living systems.1–31. T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “ Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8, 210 (2017). https://doi.org/10.1038/s41467-017-00190-72. Y. Park, C. Depeursinge, and G. Popescu, “ Quantitative phase imaging in biomedicine,” Nat. Photonics 12, 578 (2018). https://doi.org/10.1038/s41566-018-0253-x3. C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, “ Quantum-enhanced nonlinear microscopy,” Nature 594, 201 (2021). https://doi.org/10.1038/s41586-021-03528-w Conventional imaging techniques easily detect intensity information, while for phase objects, including cells, tissues, and biomolecules, they exhibit low contrast under bright field microscopy owing to insignificant absorption and weak scattering in visible spectroscopy.4–74. P. M. S. Roma, L. Siman, F. T. Amaral, U. Agero, and O. N. Mesquita, “ Total three-dimensional imaging of phase objects using defocusing microscopy: Application to red blood cells,” Appl. Phys. Lett. 104, 251107 (2014). https://doi.org/10.1063/1.48844205. H. Kwon, E. Arbabi, S. M. Kamali, M. Seyedeh, M. Faraji-Dana, and A. Faraon, “ Single-shot quantitative phase gradient microscopy using a system of multifunctional metasurfaces,” Nat. Photonics 14, 109 (2020). https://doi.org/10.1038/s41566-019-0536-x6. S. Ebrahimi and M. Dashtdar, “ Quantitative phase imaging based on Fresnel diffraction from a phase plate,” Appl. Phys. Lett. 115, 203702 (2019). https://doi.org/10.1063/1.51233537. Y. Fan, J. Sun, Q. Chen, X. Pan, M. Trusiak, and C. Zuo, “ Single-shot isotropic quantitative phase microscopy based on color-multiplexed differential phase contrast,” APL Photonics 4, 121301 (2019). https://doi.org/10.1063/1.5124535 Staining biological samples allow for their conversion into intensity objects but may affect the structure of the subjects.8,98. S. B. Mehta and C. J. R. Sheppard, “ Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast,” Opt. Lett. 34, 1924 (2009). https://doi.org/10.1364/OL.34.0019249. S. Koppell and M. Kasevich, “ Information transfer as a framework for optimized phase imaging,” Optica 8, 493 (2021). https://doi.org/10.1364/OPTICA.412129 Traditional phase contrast imaging methods, such as Zernike phase contrast microscopy1010. F. Zernike, “ How I discovered phase contrast,” Science 121, 345 (1955). https://doi.org/10.1126/science.121.3141.345 and differential interference contrast microscopy,1111. R. Allen, G. David, and G. Nomarski, “ The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. Mikrosk. Tech. 69, 193 (1969). extend the capability of label-free optical imaging of phase objects by employing phase filters or Nomarski prism. However, phase contrast microscopy is only suitable for thin phase objects and halo effects will disturb observation,1212. C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “ Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006). https://doi.org/10.1063/1.2397030 and differential interference contrast microscopy involves precise alignment, expensive sensing equipment,1313. X. Cui, M. Lew, and C. Yang, “ Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. 93, 091113 (2008). https://doi.org/10.1063/1.2977870 and requires images on multiple directions to break through the limitation of one-dimensional imaging.The Brewster effect is well-known as a special phenomenon, where the p-polarized light in reflected waves will vanish when unpolarized waves impinge onto a dielectric surface at a specific incidence angle.1414. D. Brewster, “ On the laws which regulate the polarisation of light by reflexion from transparent bodies,” Philos. Trans. R. Soc. London 105, 125 (1815). https://doi.org/10.1098/rstl.1815.0010 Recently, the Brewster effect has attracted great scientific interest15,1615. A. Youssefi, F. Zangeneh-Nejad, S. Abdollahramezani, and A. Khavasi, “ Analog computing by Brewster effect,” Opt. Lett. 41, 3467 (2016). https://doi.org/10.1364/OL.41.00346716. K. V. Sreekanth, M. ElKabbash, R. Medwal, J. Zhang, T. Letsou, G. Strangi, M. Hinczewski, R. S. Rawat, C. Guo, and R. Singh, “ Generalized Brewster angle effect in thin-film optical absorbers and its application for graphene hydrogen sensing,” ACS Photonics 6, 1610 (2019). https://doi.org/10.1021/acsphotonics.9b00564 and gained prominent applications in polarizers and optical broadband angular selectivity.1717. Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “ Optical broadband angular selectivity,” Science 343, 1499 (2014). https://doi.org/10.1126/science.1249799 Remarkably, Brewster angle microscopy has been proposed to observe state changes on the liquidoid surface.1818. D. Hoenig and D. Moebius, “ Direct visualization of monolayers at the air-water interface by Brewster angle microscopy,” J. Phys. Chem. 95, 4590 (1991). https://doi.org/10.1021/j100165a003 This is attributed to the fact that slight perturbations in the observation system will affect the faintest intensity of the reflection field near the Brewster angle, so that the monolayer at the interface will be observed.In this Letter, we propose differential microscopy based on the Brewster effect, for the purpose of phase-contrast imaging. As an important physical effect in light–matter interaction, spin–orbit interaction of light can be used as a promising tool in precision measurement,19–2119. X. Zhou, X. Ling, H. Luo, and S. Wen, “ Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101, 251602 (2012). https://doi.org/10.1063/1.477250220. S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “ Precision measurement of the optical conductivity of atomically thin crystals via the photonic spin Hall effect,” Phys. Rev. Appl. 13, 014057 (2020). https://doi.org/10.1103/PhysRevApplied.13.01405721. T. Tang, Y. Tang, L. Bi, T. Kang, X. Liang, J. Qin, J. Li, L. Luo, and C. Li, “ Highly sensitive real-time detection of phase change process based on photonic spin Hall effect,” Appl. Phys. Lett. 120, 191105 (2022). https://doi.org/10.1063/5.0094961 biochemical sensing,22,2322. R. Wang, J. Zhou, K. Zeng, S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “ Ultrasensitive and real-time detection of chemical reaction rate based on the photonic spin Hall effect,” APL Photonics 5, 016105 (2020). https://doi.org/10.1063/1.513118323. R. Wang, S. He, S. Chen, W. Shu, S. Wen, and H. Luo, “ Computing metasurfaces enabled chiral edge image sensing,” iScience 25, 104532 (2022). https://doi.org/10.1016/j.isci.2022.104532 and microscopic imaging.24–2624. M. Benelajla, E. Kammann, B. Urbaszek, and K. Karrai, “ Physical origins of extreme cross-polarization extinction in confocal microscopy,” Phys. Rev. X 11, 021007 (2021). https://doi.org/10.1103/PhysRevX.11.02100725. J. Liu, Q. Yang, S. Chen, Z. Xiao, S. Wen, and H. Luo, “ Intrinsic optical spatial differentiation enabled quantum dark-field microscopy,” Phys. Rev. Lett. 128, 193601 (2022). https://doi.org/10.1103/PhysRevLett.128.19360126. S. Liu, S. Chen, S. Wen, and H. Luo, “ Photonic spin Hall effect: Fundamentals and emergent applications,” Opto-Electron. Sci. 1, 220007 (2022). https://doi.org/10.29026/oes.2022.220007 Here, by incorporating with spin–orbit interaction of light,27–2927. R. Barczyk, S. Nechayev, M. A. Butt, G. Leuchs, and P. Banzer, “ Vectorial vortex generation and phase singularities upon Brewster reflection,” Phys. Rev. A 99, 063820 (2019). https://doi.org/10.1103/PhysRevA.99.06382028. D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “ Optical analog computing of two-dimensional spatial differentiation based on the Brewster effect,” Opt. Lett. 45, 6867 (2020). https://doi.org/10.1364/OL.41310429. R. Wang, S. He, and H. Luo, “ Photonic spin-Hall differential microscopy,” Phys. Rev. Appl. 18, 044016 (2022). https://doi.org/10.1103/PhysRevApplied.18.044016 the conversion of incident elliptic polarization to vortex light is realized, which further allows for two-dimensional spatial differentiation. The proposed scheme can be applied for edge-enhanced imaging of phase objects, since for phase objects, the phase gradients usually exist at the edges. There are several appealing features for our Brewster differential microscopy. (1) Two-dimensional differential operation achieves edge-enhanced imaging of biological samples and avoids biophysical damages caused by staining or fluorescence. (2) The system is capable of a switch between bright-field imaging and differential imaging and, thus, enables the adjustment of the output image contrast. (3) Our device does not involve any complex and expensive nanostructures, and isotropic edge-enhanced imaging is easy to implement due to the simple and flexible operability.As shown in Fig. 1(a), our proposed Brewster differential microscopy is based on air–glass interface used as a planar reflector. The scheme achieves differential microscopic imaging of input phase distribution and especially can be applied for the visualization of the transparent phase objects. In momentum space, the input field can be considered as Ẽin=Ẽin(cos αex+sin αey).(1)Here, α is the incident polarization angle and the incident field with Gaussian distribution can be specified by the following expression: Ẽin=w2πexp [−w2(kx2+ky2)4],(2)where w is the beam waist. With the polarization axis of the Glan laser polarizer (GLP2) set to be horizontal direction, the output wave function in the momentum space can be obtained as (see a detailed theory in Sec. I of the supplementary material) Ẽout∝Ẽin[exp (Δxkx+iΔyky)−exp (−Δxkx−iΔyky)].(3)Here, Δx=rprstanαk0∂Inrp∂θi (k0=2πλ is the wave vector in the vacuum, θi is the incident angle, and rp and rs are the Fresnel reflection coefficients of p and s polarizations) is the Brewster effect term, which originates from the vanishment of p-polarized light upon reflection at the Brewster angle. Δy=(rp+rs)cotθik0rs is the spin–orbit interaction term, which is attributed to the transverse wave property of the photon polarization. The schematic diagram of two-dimensional phase contrast imaging based on the Brewster effect and spin–orbit interaction of light is depicted in Fig. S1, which shows the field transformation during optical reflection (see Fig. S1 in Sec. II of the supplementary material). The spatial transformation between the incident field and the output field is described by a spatial spectral transfer function H(kx,ky)=Ẽout(kx,ky)Ẽin(kx,ky)∝Δxkx+iΔyky.(4)By the spatial Fourier transform, the final output field in the spatial domain can be given by Eout=∬Ẽout exp [i(kxx+kyy)]dkxdky.(5)Substituting Eq. (3) into Eq. (5), the output field can be rewritten as Eout∝Δx∂Ein(x,y)∂x+iΔy∂Ein(x,y)∂y.(6)It is shown that the proposed mechanism can achieve the two-dimensional spatial differentiation of the input field. The spin–orbit interaction of light is related to the geometric phase, and although the specific Brewster angle can be affected by wavelength, the occurrence of the Brewster effect was unaffected. These features make the system wavelength-independent and ensure broadband phase-contrast imaging.For pure phase object with phase distribution φ(x,y), its output bright-field can be obtained as Eout(x,y)=exp [iφ(x,y)]. Due to Iout(x,y)=| exp [iφ(x,y)|2=1, the output intensity of bright-field image shows no contrast.2929. R. Wang, S. He, and H. Luo, “ Photonic spin-Hall differential microscopy,” Phys. Rev. Appl. 18, 044016 (2022). https://doi.org/10.1103/PhysRevApplied.18.044016 However, after our differential scheme, the output field can be written as Eout∝[Δx∂φ(x,y)∂x+iΔy∂φ(x,y)∂y]exp [iφ(x,y)].(7)Then, the output intensity of differential image can be obtained as Iout=Eout·Eout*∝|Δx∂φ(x,y)∂x|2+|Δy∂φ(x,y)∂y|2.(8)It is indicated that the differential operation on phase distribution makes the output intensity visible where phase gradients exist, which is the edge of the phase object.30–3530. T. Zhu, J. Huang, and Z. Ruan, “ Optical phase mining by adjustable spatial differentiator,” Adv. Photonics 2, 016001 (2020). https://doi.org/10.1117/1.AP.2.1.01600131. S. He, J. Zhou, S. Chen, W. Shu, H. Luo, and S. Wen, “ Wavelength-independent optical fully differential operation based on the spin-orbit interaction of light,” APL Photonics 5, 036105 (2020). https://doi.org/10.1063/1.514495332. X. Zhu, H. Yao, J. Yu, G. Gbur, F. Wang, Y. Chen, and Y. Cai, “ Inverse design of a spatial filter in edge enhanced imaging,” Opt. Lett. 45, 2542 (2020). https://doi.org/10.1364/OL.39142933. T. Zhu, C. Guo, J. Huang, H. Wang, M. Orenstein, Z. Ruan, and S. Fan, “ Topological optical differentiator,” Nat. Commun. 12, 680 (2021). https://doi.org/10.1038/s41467-021-20972-434. L. Wesemann, T. J. Davis, and A. Roberts, “ Meta-optical and thin film devices for all-optical information processing,” Appl. Phys. Rev. 8, 031309 (2021). https://doi.org/10.1063/5.004875835. M. Zhao, X. Liang, J. Li, M. Xie, H. Zheng, Y. Zhong, J. Yu, J. Zhang, Z. Chen, and W. Zhu, “ Optical phase contrast microscopy with incoherent vortex phase,” Laser Photonics Rev. 16, 2200230 (2022). https://doi.org/10.1002/lpor.202200230 Recently, nanophotonic materials have widely been applied for optical differential operation to achieve edge details of image processing.36–4636. T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “ Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017). https://doi.org/10.1038/ncomms1539137. C. Guo, M. Xiao, M. Minkov, Y. Shi, and S. Fan, “ Photonic crystal slab Laplace operator for image differentiation,” Optica 5, 251 (2018). https://doi.org/10.1364/OPTICA.5.00025138. Z. Dong, J. Si, X. Yu, and X. Deng, “ Optical spatial differentiator based on subwavelength high-contrast gratings,” Appl. Phys. Lett. 112, 181102 (2018). https://doi.org/10.1063/1.502630939. A. Momeni, H. Rajabalipanah, A. Abdolali, and K. Achouri, “ Generalized optical signal processing based on multioperator metasurfaces synthesized by susceptibility tensors,” Phys. Rev. Appl. 11, 064042 (2019). https://doi.org/10.1103/PhysRevApplied.11.06404240. P. Huo, C. Zhang, W. Zhu, M. Liu, S. Zhang, S. Zhang, L. Chen, H. J. Lezec, A. Agrawal, Y. Lu, and T. Xu, “ Photonic spin-multiplexing metasurface for switchable spiral phase contrast imaging,” Nano Lett. 20, 2791 (2020). https://doi.org/10.1021/acs.nanolett.0c0047141. H. Wang, C. Guo, Z. Zhao, and S. Fan, “ Compact incoherent image differentiation with nanophotonic structures,” ACS Photonics 7, 338 (2020). https://doi.org/10.1021/acsphotonics.9b0146542. L. Wan, D. Pan, S. Yang, W. Zhang, A. A. Potapov, X. Wu, W. Liu, T. Feng, and Z. Li, “ Optical analog computing of spatial differentiation and edge detection with dielectric metasurfaces,” Opt. Lett. 45, 2070 (2020). https://doi.org/10.1364/OL.38698643. J. Zhou, H. Qian, J. Zhao, M. Tang, Q. Wu, M. Lei, H. Luo, S. Wen, S. Chen, and Z. Liu, “ Two-dimensional optical spatial differentiation and high-contrast imaging,” Natl. Sci. Rev. 8, nwaa176 (2021). https://doi.org/10.1093/nsr/nwaa17644. X. Zhang, Y. Zhou, H. Zheng, A. E. Linares, F. C. Ugwu, D. Li, H. B. Sun, B. Bai, and J. G. Valentine, “ Reconfigurable metasurface for image processing,” Nano Lett. 21, 8715 (2021). https://doi.org/10.1021/acs.nanolett.1c0283845. H. Yang, Z. Xie, H. He, Q. Zhang, J. Li, Y. Zhang, and X. Yuan, “ Switchable imaging between edge-enhanced and bright-field based on a phase-change metasurface,” Opt. Lett. 46, 3741 (2021). https://doi.org/10.1364/OL.42887046. F. Zangeneh-Nejad, D. L. Sounas, A. Alù, and R. Fleury, “ Analogue computing with metamaterials,” Nat. Rev. Mater. 6, 207 (2021). https://doi.org/10.1038/s41578-020-00243-2 However, our proposed imaging mechanism is based on simple optical reflection at the glass interface, without involving any complex nanofabrication.By incorporating a microscope with the differential apparatus mentioned in Fig. S2(a) (see the experimental scheme in Sec. III of the supplementary material), the proposed microscopic imaging scheme is now demonstrated to be applied in the measurement of a quantitative phase microscopy target (Benchmark Technologies). The experimental setup is shown in Fig. 2(a) by adding 10× microscope objectives based on Fig. S2(a). L1 and L2 make up the first 4f system and the sample is placed at 125 mm (the focal length of L1) before the L1. Then, we rotate the optical axis of GLP1 at 67.1° and use a quarter-wave plate (QWP) aligned with the x axis to adjust the polarization of the incident beam to the required elliptical polarized light. Here, our experiment is operated at the Brewster angle. After the light reflection on the prism interface, we use GLP2 to select the required output polarization. The second 4f system consists of L3 and L4 and CCD is placed at the back focal plane of L4 for recording an output image.Figure 2(c) shows the contrasted images of five focus stars with different thicknesses ranging from 150 to 350  nm in the resolution target. The black background represents 0 nm, while the gray parts are regarded as different phase gradients. Under coherent green-light illumination, the obtained bright-field images [Fig. 2(d)] show little contrast when the polarization axis of GLP2 is aligned with the y axis. However, with its polarization axis set to be the x axis, the differential images shown in Fig. 2(e) obviously enhance the edges of the phase object, which have relatively uniform brightness in different directions. The highest resolution of the detected edge is around 0.2 μm. The experimental results indicate that isotropic two-dimensional edge imaging of phase objects could be achieved by our scheme. Some slightly inhomogeneous edges are possibly caused by the uneven intensity distribution of light. To further illustrate the imaging resolution more intuitively, the light intensities along the white dashed lines are extracted and plotted in Fig. 2(f). It is found that the contrast of the image increases obviously as the phase gradient increases. For comparison, we also fit the average intensities along the white lines in five edge images varying with the phase of these five targets, which shows approximately linear in Fig. 2(b). These results indicate that the proposed microscopic imaging scheme achieves phase contrast imaging and is sensitive to different phase gradients.To further confirm the ability of our system for nondestructive imaging of transparent cells, we replace the pure phase resolution target with pakchoi cabbage epidermal cells as an imaging sample. Here, the four lens L1–L4 are 75, 125, 175, and 250 mm, respectively. Figure 3(a) shows the epidermal membrane on the pakchoi cabbage torn out by tweezers. The stripped-off epidermal sample for observation is placed on the glass slide as shown in Fig. 3(b). By the mentioned confocal microscope system, the bright-field image [Fig. 3(c)] and the differential image [Fig. 3(d)] are obtained. For detailed comparison, the intensity distributions along the white dashed lines in Figs. 3(c) and 3(d) are extracted, which are shown in Figs. 3(e) and 3(f). It is found that the differential image shows the cell structure clearly and improves the contrast evidently compared to the bright-field image.Finally, we reconstruct the phase distribution through our Brewster differential scheme with bias retardation. If the postselected polarization is set to be [ cos βi sin β] and the value of β is taken as δ and −δ, the derivative of the phase distribution with respect to the x direction can be obtained by subtracting the two corresponding output intensities |Eout1+δ(x,y)|2−|Eout1−δ(x,y)|2=4 sin2δ cot δΔx∂φ(x,y)∂x.(9)Similarly, with the postselected polarization set to be [ cos β sin β], the subtraction of the two corresponding intensities achieves the differentiation of phase on the y direction |Eout2+δ(x,y)|2−|Eout2−δ(x,y)|2=4 sin2δ cot δΔy∂φ(x,y)∂y.(10)Therefore, two-dimensional differentiation is obtained, which enables two-dimensional phase reconstruction. Through 2D Fourier integration, the phase distribution is finally given by Ref. 2929. R. Wang, S. He, and H. Luo, “ Photonic spin-Hall differential microscopy,” Phys. Rev. Appl. 18, 044016 (2022). https://doi.org/10.1103/PhysRevApplied.18.044016 (see theoretical calculation details in Sec. IV of the supplementary material) In the experiment, a 350-nm-height target is first selected for phase reconstruction. By introducing bias retardation of 0.2° and −0.2°, the biased contrast images are obtained in Figs. 4(a) and 4(b). The absolute value of two-dimensional spatial differentiation is shown in Fig. 4(c), which is obtained by the subtraction of Figs. 4(a) and 4(b). As shown in Fig. 4(d), the phase distribution is finally reconstructed through 2D Fourier integration. Figures 4(e) and 4(f) show the vertical-cut intensity distributions extracted from white lines in Figs. 4(c) and 4(d). The corresponding experimental results of phase reconstruction for the quantitative phase microscopy target at a 250-nm height are also obtained in Figs. 4(g)–4(l) for comparison. It can be seen that the reconstructed phase distributions have advantages of high contrast and uniformity, and especially for different phase gradients measurements, the intensities exhibit consistent distributions with the measured phase gradient, which allows for potential applications in quantitative phase imaging. Based on the Brewster differential scheme, we not only visualize the transparent phase objects by optical differential operation but also retrieve phase information of the object.

It is known that Brewster angle microscopy is used for studying thin films on liquid surfaces, most typically Langmuir films. However, in our proposed Brewster differential microscopy, the combination of spin–orbit interaction of light and the Brewster effect enables two-dimensional differentiation of phase objects, which can be mainly applied for visualization and edge imaging of phase objects. Different from the studies of isotropic differential interference contrast microscopy for pure phase imaging, Brewster differential microscopy is based on simple optical reflection at the glass interface, which does not involve any complex and expensive nanostructures. Our proposed method provides simplicity and operability and avoids complex adjustment.

In conclusion, we propose differential microscopy based on the Brewster effect and spin–orbit interaction of light and demonstrate the feasibility of visualizing phase objects both through theory and experiment. Edge-enhanced imaging of the observed phase target can be achieved by two-dimensional differentiation operation on the incident light field, and the adjustment of analyzer can control the switching between the bright field imaging and the differential imaging modes. The proposed microscopy enables nondestructive imaging of biological samples, which can lead to opportunities for label-free and high-resolution biological analysis. Furthermore, by biased imaging, the original phase distribution is also reconstructed. In addition, our scheme is mainly based on light reflection at the glass interface without any complex and expensive nanostructures, thus showing the advantages of simple and low-cost structure. It is believed that our proposed method will play a significant role in biomedical fields, such as cell imaging and tissue morphological feature analysis.

This work was supported by the National Natural Science Foundation of China (Grant No. 12174097) and the Natural Science Foundation of Hunan Province (Grant No. 2021JJ10008).

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Ruisi Wang: Writing – original draft (lead). Shanshan He: Writing – review & editing (equal). Shizhen Chen: Writing – review & editing (equal). Hailu Luo: Data curation (lead); Investigation (lead); Writing – review & editing (equal).

The data that support the finding of this study are available from the corresponding author upon reasonable request.

REFERENCES

1. T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “ Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8, 210 (2017). https://doi.org/10.1038/s41467-017-00190-7, Google ScholarCrossref, ISI2. Y. Park, C. Depeursinge, and G. Popescu, “ Quantitative phase imaging in biomedicine,” Nat. Photonics 12, 578 (2018). https://doi.org/10.1038/s41566-018-0253-x, Google ScholarCrossref, ISI3. C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, “ Quantum-enhanced nonlinear microscopy,” Nature 594, 201 (2021). https://doi.org/10.1038/s41586-021-03528-w, Google ScholarCrossref4. P. M. S. Roma, L. Siman, F. T. Amaral, U. Agero, and O. N. Mesquita, “ Total three-dimensional imaging of phase objects using defocusing microscopy: Application to red blood cells,” Appl. Phys. Lett. 104, 251107 (2014). https://doi.org/10.1063/1.4884420, Google ScholarScitation, ISI5. H. Kwon, E. Arbabi, S. M. Kamali, M. Seyedeh, M. Faraji-Dana, and A. Faraon, “ Single-shot quantitative phase gradient microscopy using a system of multifunctional metasurfaces,” Nat. Photonics 14, 109 (2020). https://doi.org/10.1038/s41566-019-0536-x, Google ScholarCrossref6. S. Ebrahimi and M. Dashtdar, “ Quantitative phase imaging bas