Quantitative Phase Imaging with a Meta-Based Interferometric System (2025)

Introduction

Click to copy section linkSection link copied!

Traditional bright-field microscopy plays a crucial role in various biomedical applications. It typically relies on the opacity of specimens to generate sufficient contrast for visual observation. In cases involving nearly transparent materials, such as biological cells and tissues, contrast enhancement is often achieved through fluorescence and staining methods. However, these approaches have inherent limitations, as fluorescent dyes and staining agents can negatively affect the viability of live cells. (1−3) To address these challenges, label-free imaging modalities, such as Zernike phase contrast (ZPC) microscopy and differential interference contrast (DIC) microscopy, have been developed. (4−9) These techniques convert phase variations within transparent samples into detectable intensity contrasts, offering benefits such as reduced phototoxicity and minimal sample preparation. Nonetheless, while these methods are effective in providing qualitative visualizations, they are inadequate for quantitative phase profile mapping, which is essential for comprehensive morphological and structural analysis.

Quantitative phase imaging (QPI) techniques, including quantitative differential phase contrast (qDPC) microscopy, Fourier ptychographic microscopy (FPM), transport-of-intensity equation (TIE), cross-grating wavefront microscopy (CGM) and digital holographic microscopy (DHM), have significantly enhanced the capabilities of label-free microscopy. (10−19) These techniques enable the precise quantification of phase information in transparent specimens, thereby enriching our understanding of cellular structures. Notably, DHM excels in obtaining highly accurate quantitative phase information by capturing holographic interference patterns, which are subsequently processed through digital reconstruction. The standard DHM system uses either a Mach–Zehnder or Michelson interferometer, configured for transmission or reflection modes, and supports both on-axis (in-line) and off-axis setups. (20) Although the on-axis configuration, which involves copropagating reference and object beams, is relatively straightforward, it suffers from image clarity issues due to the overlap of the zero-order (direct current, DC) term and the virtual image (twin images). (21) In contrast, the off-axis configuration angles the reference and object beams with respect to each other, preventing overlap in the spatial frequency domain and thereby avoiding interference from the DC term and virtual image. (22) This configuration enhances real-time phase and amplitude imaging, which is critical for dynamic observations of biological samples. However, the separation of the beam paths in the off-axis makes it highly susceptible to environmental fluctuations, resulting in significant phase noise and compromised spatial and temporal stability. Recent advancements have seen a rise in common-path off-axis configurations due to their lower cost, robustness, and stability, as both the signal and reference beams traverse through the same optical components and follow nearly identical optical paths. (23) A key feature of these configurations is the use of a core optical element for beam splitting. Various optical elements have been proposed to fulfill this function, including Fresnel biprisms, diffraction gratings, and volume holographic grating, among others. (24−31) Among these approaches, diffraction phase microscopy (DPM) is a well-established and effective common-path DHM configuration that utilizes a diffraction grating to generate the necessary reference and object beams from its zero-order and first-order diffraction components. (24) However, conventional gratings introduce multiple diffraction orders, leading to power loss and unwanted signal contamination. As the demand for miniaturized optical systems continues to grow, ongoing research efforts in DHM are focused on developing more compact and flexible imaging solutions to address the limitations imposed by bulky traditional optical components.

Metasurfaces, ultrathin planar structures engineered from subwavelength features, are increasingly recognized for their unprecedented capability to precisely manipulate various degrees of freedom of electromagnetic waves, including phase, amplitude, polarization, and propagation direction. (32−45) Notably, dielectric metasurfaces can be manufactured using semiconductor fabrication processes, which significantly lower production costs and enable large-scale production. (46−48) By replacing bulky optical elements with compact, efficient designs, metasurfaces have revolutionized numerous optical applications, ranging from basic optics to advanced imaging and spectrometry, facilitating system miniaturization. Their potential in biomedical applications such as wide-field, tomographic, and endoscopic imaging, has garnered considerable attention, pushing the boundaries of traditional imaging modalities. (49−52)

Recent advances have seen the integration of metasurfaces into various phase contrast imaging techniques, marking a significant advancement. For example, an entirely metasurface-based spiral phase contrast imaging system has demonstrated, eliminating conventional optical elements while achieving compact and high-performance imaging. (53) Another recent study has shown that spiral metalens, combining both focusing and phase contrast imaging functionalities into a single metasurface, can achieve submicrometer resolution across a broadband visible spectrum. (54) The dynamic capabilities of metasurface are also demonstrated, such as the ability to switch between bright-field and edge-enhanced imaging, depending on the polarization state of the incident light. (55,56) Furthermore, their feasibility in QPI techniques has been proven with implementations in technologies based on TIE, phase shifting, DHM, and so on. (57−65) Despite the myriad advantages presented by metasurfaces, their integration into DHM remains relatively unexplored. Additionally, unlike TIE, phase-shifting methods, and qDPC, which typically require multiple images for phase reconstruction, DHM captures a full-field hologram in a single image. Moreover, its interferometric nature can offer the ability to digitally refocus and reconstruct different focal planes. Here we integrate the meta-biprism into the common-path off-axis DHM system to obtain the phase information on various objects. The ability to acquire and reconstruct complex optical fields with high stability is performed. Our results shed light on the advantages and prospective applications of metasurface in the ever-evolving world of imaging science.

Results and Discussion

Click to copy section linkSection link copied!

A schematic of a metasurface-based common-path off-axis DHM system is presented in Figure 1a, illustrating how the meta-biprism separates an incident beam into two beams with distinct angles, ultimately leading to the formation of their interference pattern. One of these beams is filtered using a pinhole located at the Fourier plane of 4f-imaging system, which serves as the reference beam, while the other beam functions as the object beam, carrying information about the scattered complex field of the object. The beam-splitting capability of the meta-biprism arises from the introduction of two opposing gradient phase distributions, as shown in Figure 1b. The phase distribution is defined by the equation:

$φ (x, λ) = - \frac{2 π}{λ} x \sin θ$

(1)

where x denotes the spatial coordinate, λ signifies the working wavelength, and θ represents the refraction angle. The angles θ are set at ± 9.28°, resulting in a phase distribution that corresponds to a conventional biprism with a 150° apex angle, as illustrated in Figure 1b. The optical phase modulation up to 2π at the working wavelength of 633 nm is achieved by arranging GaN nanopillars, each 850 nm in height and with diameters ranging from 120 to 240 nm, on a sapphire substrate, as shown in Figure 1c. Compared to a traditional biprism, this design not only reduces the thickness to the nanometer scale but also minimizes the optical path length by eliminating the need for the two beams to intersect, as depicted in the upper right inset. The nanopillars are fabricated using CMOS-compatible processes, including electron beam lithography followed by etching with inductively coupled plasma reactive ion (ICP-RIE). Further fabrication details are provided in the Methods section, and the SEM image of the fabricated nanopillars is shown in Figure 1d. The experimentally measured intensity distribution of the beam after passing through the meta-biprism along the x–z plane is presented in Figure S1. The two beams interfere off-axially on the image plane, positioned at the rear focal plane of a tube lens, and recorded by a CCD sensor (THORLABS, DCU223C). The complete optical setup is detailed in Figure S2.

Figure 1

High Resolution Image

Download MS PowerPoint Slide

The object beam (O) with an angle of θ and the reference beam (R) with an angle of −θ can be described as

$O = A_{o} (x, y) e^{i ϕ_{o} (x, y)} e^{- i k \sin (θ) x}$

(2)

$R = A_{r} (x, y) e^{i k \sin (θ) x}$

(3)

The resulting interference pattern can be expressed mathematically as follows:

$I_{H} (x, y) = {| R |}^{2} + {| O |}^{2} + R^{*} O + R O^{*} = {| A_{o} |}^{2} + {| A_{r} |}^{2} + A_{o} A_{r} e^{- i ϕ_{o} (x, y)} e^{i 2 k \sin (θ) x} + A_{o} A_{r} e^{i ϕ_{o} (x, y)} e^{- i 2 k \sin (θ) x}$

(4)

where |R|² represents the intensity of the reference beam, and |O|² represents the intensity of the object beam. The interference terms R*O and RO*, representing the real and virtual images, respectively, involve the complex conjugates of the reference (R*) and object (O*) beams. The corresponding spectrum can be described as

${\tilde{I}}_{H} = \tilde{O} (k_{x}, k_{y}) \otimes {\tilde{O}}^{*} (- k_{x}, {- k}_{y}) + {| A_{r} |}^{2} δ (k_{x}, k_{y}) + \tilde{O} (k_{x}, k_{y}) \otimes A_{r} δ (k_{x} - 2 k \sin (θ), k_{y}) + {\tilde{O}}^{*} (- k_{x}, {- k}_{y}) \otimes A_{r} δ (k_{x} + 2 k \sin (θ), k_{y})$

(5)

where Õ denotes the Fourier transform of O and (k_x, k_y) are the coordinates in the frequency domain. The symbol ⊗ represents the convolution operation, and δ is the delta function. The first two terms of the equation correspond to the DC component of the hologram. The third term contains the actual object information, while the fourth term contains the conjugate of this information. The term δ(k_x–2k sin(θ),k_y) results in a shift of object signal in the frequency domain, enabling its separation from the conjugate term and the DC component. By isolating the third term and performing an inverse Fourier transform, we can accurately retrieve the complex field of the object beam.

The reconstruction of digital holography is achieved using the spatial filtering method, as shown in Figure 2. The raw hologram image of the 1951 USAF resolution phase target, which includes zero padding, is depicted in Figure 2a. Figure 2b illustrates its spatial spectrum by using 2D Fourier transformation. The spectrum reveals three distinct components: the zero, first, and minus first orders, corresponding to the DC, primary, and conjugate terms of the hologram, respectively. By applying a windowing operation within the Fourier domain, either the first or the minus first orders can be singled out, as shown in Figure 2c. This isolation enables the reconstruction of the object’s amplitude and phase information, effectively mitigating the impact of the DC term and the twin image effect. The offset angle between the signal and reference beams is crucial; a larger angle not only increases the fringe frequency but also shifts the spatial frequencies of image away from the DC term in the frequency domain. This shift enables clearer differentiation and more precise filtering in holographic reconstruction. However, capturing these high-frequency details without aliasing requires higher sampling rates. Achieving these higher spatial sampling rates of the sensor is often constrained by several factors, especially the resolution of the CCD (charge-coupled device) camera, as each pixel represents a sampling point. In our setup, the produced image has dimensions of 470 × 500 pixels, and CCD has a pixel pitch of 4.65 μm. According to the Nyquist theorem, the maximum allowable frequency is about 0.1075 cycles/μm. To illustrate the impact of different offset angles on holographic reconstruction, we conducted simulations, as shown in Figures S3–S5. Subsequently, the inverse Fourier transform yields the reconstructed phase information on the target. Background noise is discernible within the image, attributed to the tilt or unevenness of the sample, as well as disparities in the distribution of the light source. To address this, we implement a phase compensation methodology. (66) By subtracting background noise, we achieve a quantitative phase image free from the interference of background artifacts, as shown in Figure 2d, with the detailed process illustrated in Figure S6.

Figure 2

High Resolution Image

Download MS PowerPoint Slide

The reconstructed phase images of the resolution phase target at 150, 200, and 300 nm in thickness are depicted in Figure 3. These images reveal a high-contrast depiction of the characteristics of the target, offering valuable quantitative phase information. The phase values obtained from these images represent the spatial distribution of phase discrepancies within the target, influenced by factors such as its thickness and the variation in refractive index relative to the surrounding medium. The thickness of samples can be calculated using the following equation:

$t = \frac{ϕ_{O} λ}{2 π Δ n}$

(6)

Figure 3

High Resolution Image

Download MS PowerPoint Slide

where ϕ_o is the phase distribution of the sample, λ represents the working wavelength, and Δn is the refractive index difference between the target and the ambient media, which is 1.52. The average thicknesses of the target structures measured by our DHM are 167, 243, and 369 nm, with corresponding Atomic Force Microscopy (AFM) measurements of 165.3, 211.4, and 324.7 nm, resulting in percentage differences of 0.45, 15.6, and 10.7%, respectively. Additionally, detailed three-dimensional information can be obtained from the complex amplitude of a captured hologram, enabling precise depth reconstruction. The capability is demonstrated in the Supporting Information (Figure S7), which includes the defocused hologram of the amplitude resolution target, its corresponding bright-field image, and the reconstructed complex field computed using the angular spectrum method.

We experimentally validate the imaging capabilities of the proposed system using two human lung cell lines, H1299 and A549, as illustrated in Figure 4a,b. These figures show the raw hologram images of these cells alongside with their corresponding quantitative unwrapped phase images. H1299 cells represent a human lung adenocarcinoma cell line commonly utilized in cancer research, characterized by the absence of functional p53. In contrast, A549 cells are another lung adenocarcinoma line notable for retaining wild-type p53, making them complementary models for studying p53-related cancer mechanisms. Both cell lines are valuable for investigating lung cancer biology, drug screening, and resistance mechanisms. The cells are fixed on a glass slide, immersed in phosphate-buffered saline (PBS) with a refractive index of approximately 1.335, and mounted on the stage for hologram recording. Following phase reconstruction, we use a phase unwrapping algorithm to address the issue of cell thickness exceeding the 2π phase limit. (67)

Figure 4

High Resolution Image

Download MS PowerPoint Slide

We also evaluated the temporal stability of our system using a blank glass slide as the test sample, with the results presented in Figure 5. A total of 150 holograms are captured at 10 frames per second over a 15 s duration. Each hologram consists of 273 × 450 pixels (122,850 individual data points), which are analyzed to compute the standard deviation (σ) of phase fluctuations. Figure 5a presents the pixel-wise standard deviation map across all frames, providing a spatial assessment of phase stability. Figure 5b summarizes the distribution of these standard deviation values as a histogram, offering a comprehensive statistical analysis of the system’s temporal stability over time. Our system achieves an average standard deviation of 85 mrad, demonstrating superior temporal stability compared to traditional off-axis DHM setups, particularly those based on Mach–Zehnder and Michelson interferometer configurations, which are more susceptible to environmental disturbances due to their separate reference and object beam paths. In contrast, our common-path configuration inherently minimizes these fluctuations, making it well-suited for long-term imaging applications, such as biomedical diagnostics, live-cell monitoring, and semiconductor process control.

Figure 5

High Resolution Image

Download MS PowerPoint Slide

Conclusions

Click to copy section linkSection link copied!

We have successfully integrated the meta-biprism into the common-path off-axis DHM system, marking a significant advancement in the field of QPI. The meta-biprism, engineered from GaN nanopillars, serves as a robust and compact beam splitter, enabling a streamlined optical setup that effectively reduces susceptibility to environmental disturbances. Our findings from studies involving resolution targets and human lung cell lines demonstrate the system’s capability to deliver high-contrast, low-noise phase images, allowing for precise thickness measurement down to the nanometer scale. The compact metasurface-based DHM platform is well-suited for point-of-care diagnostics, noninvasive imaging, and portable optical systems. Its compatibility with multimodal imaging approaches, such as fluorescence or polarization imaging, further extends its utility in tissue pathology, drug screening, and personalized medicine.

Conventional biprisms are typically fabricated through grinding and polishing processes, which become increasingly challenging and complex as the element size decreases, particularly in the development of miniaturized optical systems. In contrast, the meta-biprism leverages mature semiconductor fabrication processes, enabling precise nanostructure patterning at extremely small scales. This approach not only facilitates high-volume production and long-term reliability but also ensures the feasibility of integrating metasurfaces into compact optical systems, making them a strong candidate for widespread adoption. Furthermore, the meta-biprism, unlike traditional diffractive gratings that produce undesired higher-order diffraction, leverages engineered subwavelength structures for precise phase control and efficient beam splitting, making it a superior choice for compact, high-performance optical systems.

Additionally, metasurfaces enable asymmetric beam splitting, allowing them to be designed to accommodate light with different angles of incidence, making them adaptable to specific imaging conditions, such as a folded optical system for compact setups. By tailoring the nanostructure arrangement, metasurfaces can also introduce additional phase shifts at the same beam-splitting angle, making them suitable for phase-shifting digital holography. Moreover, metasurfaces can be designed with polarization-selective functionality, enabling applications in multiplexed holography and polarization-selective imaging. This capability allows for the simultaneous measurement of different physical properties of samples, such as birefringence or optical activity, which is particularly advantageous in biological and materials science applications, where polarization analysis can reveal structural and compositional details. Beyond digital holography, the meta-biprism design can be utilized in various optical experiments. For example, it could be employed to generate two identical light sources for quantum optics interference experiments, which traditionally require bulkier and more complex systems.

Looking ahead, future research could focus on enhancing spatial and temporal resolution, integrating multiwavelength capabilities, and incorporating AI-driven image processing for real-time analysis. By leveraging metasurface technology, these developments will push the boundaries of DHM, enabling deeper insights into biological structures and processes.

Methods

Click to copy section linkSection link copied!

Numerical Simulations

The design of the unit cell is conducted using CST Microwave Studio, employing the finite integral technique. The structure comprises cylindrical GaN nanopillars, each with a height of 850 nm, arranged on a sapphire substrate with a periodicity of 280 nm. A plane wave with a wavelength of 633 nm, polarized along either the x- or y-axis, is incident from the substrate side to illuminate the nanopillars. Periodic boundary conditions are applied along the x and y axes, while an open boundary condition is utilized in the z direction. The phase shifts and power transmission are analyzed by varying the diameters of the nanopillars between 120 and 240 nm.

Fabrication of Metasurface

The GaN meta-biprism is fabricated using a conventional electron beam lithography technique, followed by ICP-RIE processes. The pattern is generated in a PMMA A4 electron beam resist by using an electron beam writer (Elionix ELS-HS50) on the SiO₂/GaN/sapphire substrate. This pattern is then transferred to a chromium mask using a lift-off process. The GaN nanopillars are then formed through a two-step RIE process, followed by the removal of the chromium and SiO₂ masks using chromium etchant and buffered oxide etch (BOE) solution, respectively.

Supporting Information

Click to copy section linkSection link copied!

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsami.5c02901.

Beam profile measurement of meta-biprism; detailed schematic of the proposed metasurface-based common-path off-axis DHM system; simulated interference pattern of two beams under different offset angles from 0.2 to 2°; simulated hologram under different offset angles between signal and reference beams, ranging from 0.2 to 2°; simulated spectrum under different offset angles between signal and reference beam, ranging from 0.2 to 2°; phase compensation method; and depth reconstruction by angular spectrum method (PDF)

am5c02901_si_001.pdf (1.18 MB)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

Click to copy section linkSection link copied!

Corresponding Authors
- Yuan Luo - YongLinInstitute of Health, National Taiwan University, Taipei 10672, Taiwan; Instituteof Medical Device and Imaging, NationalTaiwan University, Taipei 10051, Taiwan; Programfor Precision Health and Intelligent Medicine, National Taiwan University, Taipei 106319, Taiwan; Instituteof Biomedical Engineering, National TaiwanUniversity, Taipei 10051, Taiwan; https://orcid.org/0000-0001-9776-7897; Email: [emailprotected]
- Din Ping Tsai - Departmentof Electrical Engineering, City Universityof Hong Kong, Kowloon, Hong Kong 999077, China; Centrefor Biosystems, Neuroscience, and Nanotechnology, City University of Hong Kong, Kowloon, Hong Kong 999077, China; TheState Key Laboratory of Terahertz and Millimeter Waves, City University of Hong Kong, Kowloon, Hong Kong 999077, China; https://orcid.org/0000-0002-0883-9906; Email: [emailprotected]
Authors
- Cheng Hung Chu - YongLinInstitute of Health, National Taiwan University, Taipei 10672, Taiwan; https://orcid.org/0000-0002-8749-3930
- Chen-Ming Tsai - Instituteof Medical Device and Imaging, NationalTaiwan University, Taipei 10051, Taiwan
- Takeshi Yamaguchi - InnovativePhoton Manipulation Research Team, RIKENCenter for Advanced Photonics, Saitama 351-0198, Japan; https://orcid.org/0000-0002-7085-455X
- Yu-Xiang Wang - Programfor Precision Health and Intelligent Medicine, National Taiwan University, Taipei 106319, Taiwan
- Takuo Tanaka - InnovativePhoton Manipulation Research Team, RIKENCenter for Advanced Photonics, Saitama 351-0198, Japan; MetamaterialsLaboratory, RIKEN Cluster for PioneeringResearch, Saitama 351-0198, Japan; https://orcid.org/0000-0001-5714-5401
- Huei-Wen Chen - GraduateInstitute of Toxicology, College of Medicine, National Taiwan University, Taipei 100, Taiwan; Genomeand Systems Biology Degree Program, NationalTaiwan University and Academia Sinica, Taipei 100, Taiwan
Author Contributions
C.H.C. and C.-M.T. contributed equally to this paper. C.H.C., Y.L., and D.P.T. developed the experimental concept and methodology, as well as designed the metasurfaces. C.-H.C., T.Y., and T.T. were responsible for fabricating the metasurfaces. C.H.C., C.-M.T., and Y.-X.W. conducted the optical measurements and performed data analysis. H.-W.C. contributed to the human cell line experiments. Y.L. and D.P.T. coordinated the project and experiments. All authors contributed to discussing and analyzing the results, as well as preparing the manuscript. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
Notes
The authors declare no competing financial interest.

Acknowledgments

Click to copy section linkSection link copied!

We acknowledge the financial support from the National Science and Technology Council, Taiwan, R.O.C. (Grant Nos. NSTC 112-2221-E-002-055 -MY3, NSTC 112-2221-E-002-212 -MY3, NSTC 113-2221-E-007-061-MY3 and NSTC 110-2221-E-007-068-MY3), National Taiwan University, Taiwan, R.O.C. (Grant No. NTU-CC-112L892902, NTU-113L8507, and NTU-CC-113L891102), National Health Research Institutes, Taiwan, R.O.C. (Grant No. NHRI-EX113-11327EI), Fitipower Integrated Technology Inc, Taiwan, R.O.C. (Grant No. 113H1010-C01), the University Grants Committee/Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. AoE/P-502/20, CRF Project C5031-22G, GRF Project: CityU11305223; CityU11300224), City University of Hong Kong (Project No. 9380131) and JST CREST (Grant No. JPMJCR1904). We acknowledge Dr. Junxiao Zhou for her valuable suggestions for this work.

Abbreviations

Click to copy section linkSection link copied!

DHM	digital holographic microscopy
ZPC	Zernike phase contrast
DIC	differential interference contrast
QPI	quantitative phase imaging
qDPC	quantitative differential phase contrast
FPM	Fourier ptychographic microscopy
TIE	transport-of-intensity equation
CGM	cross-grating wavefront microscopy
DPM	diffraction phase microscopy
DC	direct current
SEM	scanning electron microscopy
ICP-RIE	inductively coupled plasma reactive ion
AFM	atomic force microscopy
PBS	phosphate-buffered saline
BOE	buffered oxide etch

References

Click to copy section linkSection link copied!

This article references 67 other publications.

1
Diaspro, A. OpticaL Fluorescence Microscopy: from the Spectral to the Nano Dimension; Springer Science & Business Media, 2010.
Google Scholar
There is no corresponding record for this reference.
2
Alford, R.; Simpson, H. M.; Duberman, J.; Hill, G. C.; Ogawa, M.; Regino, C.; Kobayashi, H.; Choyke, P. L. Toxicity of organic fluorophores used in molecular imaging: literature review. Mol. Imaging 2009, 8 (6), 341– 354, DOI: 10.2310/7290.2009.00031
Google Scholar
There is no corresponding record for this reference.
3
Lichtman, J. W.; Conchello, J.-A. Fluorescence microscopy. Nat. Methods 2005, 2 (12), 910– 919, DOI: 10.1038/nmeth817
Google Scholar
There is no corresponding record for this reference.
4
Liang, R.; Erwin, J. K.; Mansuripur, M. Variation on Zernike’s phase-contrast microscope. Appl. Opt. 2000, 39 (13), 2152– 2158, DOI: 10.1364/AO.39.002152
Google Scholar
There is no corresponding record for this reference.
5
Arnison, M. R.; Larkin, K. G.; Sheppard, C. J.; Smith, N. I.; Cogswell, C. J. Linear phase imaging using differential interference contrast microscopy. J. Microsc. 2004, 214 (1), 7– 12, DOI: 10.1111/j.0022-2720.2004.01293.x
Google Scholar
See Also
Contiguous Mo Species and SMSI Effect in MoOx Reinforce Catalytic Performance in Reverse Water–Gas Shift Reaction Ultrahigh Energy Storage Density and Efficiency Achieved in PbZrO3-Based Antiferroelectric Ceramics via Phase Modulation Engineering Unraveling the Diversity of the Storage Mechanism in Carbonyl Materials toward Different Metal Ions Atomic Layer Deposition of Al2O3/TiO2 Multilayer Films on Silk for High-Efficiency UV Shielding Properties
There is no corresponding record for this reference.
6
Gao, P.; Yao, B.; Harder, I.; Lindlein, N.; Torcal-Milla, F. J. Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement. Opt. Lett. 2011, 36 (21), 4305– 4307, DOI: 10.1364/OL.36.004305
Google Scholar
There is no corresponding record for this reference.
7
Franz, G.; Kross, J. Generation of two-dimensional surface profiles from differential interference contrast (DIC)─images. Optik 2001, 112 (8), 363– 367, DOI: 10.1078/0030-4026-00063
Google Scholar
There is no corresponding record for this reference.
8
Zernike, F. Phase contrast, a new method for the microscopic observation of transparent objects. Physica 1942, 9 (7), 686– 698, DOI: 10.1016/S0031-8914(42)80035-X
Google Scholar
There is no corresponding record for this reference.
9
Zernike, F. How I discovered phase contrast. Science 1955, 121 (3141), 345– 349, DOI: 10.1126/science.121.3141.345
Google Scholar
There is no corresponding record for this reference.
10
Baffou, G. Wavefront microscopy using quadriwave lateral shearing interferometry: From bioimaging to nanophotonics. ACS Photonics 2023, 10 (2), 322– 339, DOI: 10.1021/acsphotonics.2c01238
Google Scholar
There is no corresponding record for this reference.
11
Vyas, S.; Li, A.-C.; Lin, Y.-H.; Yeh, J. A.; Luo, Y. Isotropic quantitative differential phase contrast imaging techniques: a review. J. Phys. D: Appl. Phys. 2022, 55 (18), 183001 DOI: 10.1088/1361-6463/ac43da
Google Scholar
There is no corresponding record for this reference.
12
Lin, Y.-H.; Li, A.-C.; Vyas, S.; Huang, Y.-Y.; Yeh, J. A.; Luo, Y. Isotropic quantitative differential phase contrast microscopy using radially asymmetric color-encoded pupil. J. Phys.: Photonics 2021, 3 (3), 035001 DOI: 10.1088/2515-7647/abf02d
Google Scholar
There is no corresponding record for this reference.
13
Chaumet, P. C.; Bon, P.; Maire, G.; Sentenac, A.; Baffou, G. Quantitative phase microscopies: accuracy comparison. Light:Sci. Appl. 2024, 13 (1), 288 DOI: 10.1038/s41377-024-01619-7
Google Scholar
There is no corresponding record for this reference.
14
Park, Y.; Depeursinge, C.; Popescu, G. Quantitative phase imaging in biomedicine. Nat. Photonics 2018, 12 (10), 578– 589, DOI: 10.1038/s41566-018-0253-x
Google Scholar
There is no corresponding record for this reference.
15
Zheng, G.; Shen, C.; Jiang, S.; Song, P.; Yang, C. Concept, implementations and applications of Fourier ptychography. Nat. Rev. Phys. 2021, 3 (3), 207– 223, DOI: 10.1038/s42254-021-00280-y
Google Scholar
There is no corresponding record for this reference.
16
Tian, L.; Waller, L. 3D intensity and phase imaging from light field measurements in an LED array microscope. Optica 2015, 2 (2), 104– 111, DOI: 10.1364/OPTICA.2.000104
Google Scholar
There is no corresponding record for this reference.
17
Zuo, C.; Li, J.; Sun, J.; Fan, Y.; Zhang, J.; Lu, L.; Zhang, R.; Wang, B.; Huang, L.; Chen, Q. Transport of intensity equation: a tutorial. Opt Lasers Eng. 2020, 135, 106187 DOI: 10.1016/j.optlaseng.2020.106187
Google Scholar
There is no corresponding record for this reference.
18
Kim, M. K. Principles and techniques of digital holographic microscopy. SPIE Rev. 2010, 1 (1), 018005 DOI: 10.1117/6.0000006
Google Scholar
There is no corresponding record for this reference.
19
Durdevic, L.; Relaño Ginés, A.; Roueff, A.; Blivet, G.; Baffou, G. Biomass measurements of single neurites in vitro using optical wavefront microscopy. Biomed. Opt. Express 2022, 13 (12), 6550– 6560, DOI: 10.1364/BOE.471284
Google Scholar
There is no corresponding record for this reference.
20
Sirico, D. G.; Miccio, L.; Wang, Z.; Memmolo, P.; Xiao, W.; Che, L.; Xin, L.; Pan, F.; Ferraro, P. Compensation of aberrations in holographic microscopes: main strategies and applications. 2022, 1284. 78. DOI: 10.1007/s00340-022-07798-8 .
Google Scholar
There is no corresponding record for this reference.
21
Garcia-Sucerquia, J.; Xu, W.; Jericho, S. K.; Klages, P.; Jericho, M. H.; Kreuzer, H. J. Digital in-line holographic microscopy. Appl. Opt. 2006, 45 (5), 836– 850, DOI: 10.1364/AO.45.000836
Google Scholar
There is no corresponding record for this reference.
22
Leith, E. N.; Upatnieks, J. Reconstructed wavefronts and communication theory. J. Opt. Soc. Am. 1962, 52 (10), 1123– 1130, DOI: 10.1364/JOSA.52.001123
Google Scholar
There is no corresponding record for this reference.
23
Zhang, J.; Dai, S.; Ma, C.; Xi, T.; Di, J.; Zhao, J. A review of common-path off-axis digital holography: towards high stable optical instrument manufacturing. Light: Adv. Manuf. 2021, 2 (3), 333– 349, DOI: 10.37188/lam.2021.023
Google Scholar
There is no corresponding record for this reference.
24
Bhaduri, B.; Edwards, C.; Pham, H.; Zhou, R.; Nguyen, T. H.; Goddard, L. L.; Popescu, G. Diffraction phase microscopy: principles and applications in materials and life sciences. Adv. Opt. Photonics 2014, 6 (1), 57– 119, DOI: 10.1364/AOP.6.000057
Google Scholar
There is no corresponding record for this reference.
25
Cuche, E.; Marquet, P.; Depeursinge, C. Spatial filtering for zero-order and twin-image elimination in digital off-axis holography. Appl. Opt. 2000, 39 (23), 4070– 4075, DOI: 10.1364/AO.39.004070
Google Scholar
There is no corresponding record for this reference.
26
Vora, P.; Trivedi, V.; Mahajan, S.; Patel, N.; Joglekar, M.; Chhaniwal, V.; Moradi, A.-R.; Javidi, B.; Anand, A. Wide field of view common-path lateral-shearing digital holographic interference microscope. J. Biomed. Opt. 2017, 22 (12), 1– 11, DOI: 10.1117/1.JBO.22.12.126001
Google Scholar
There is no corresponding record for this reference.
See Also
Ionic-Liquid-Mimetic Surface Engineering of WS2 Nanosheets via Amine-Phosphate Functionalization for Enhanced Tribological Performance
27
Ebrahimi, S.; Dashtdar, M.; Anand, A.; Javidi, B. Common-path lensless digital holographic microscope employing a Fresnel biprism. Opt. Lasers Eng. 2020, 128, 106014 DOI: 10.1016/j.optlaseng.2020.106014
Google Scholar
There is no corresponding record for this reference.
28
Tsai, C.-M.; Vyas, S.; Luo, Y. Common-path digital holographic microscopy based on a volume holographic grating for quantitative phase imaging. Opt. Express 2024, 32 (5), 7919– 7930, DOI: 10.1364/OE.514225
Google Scholar
There is no corresponding record for this reference.
29
Chhaniwal, V.; Singh, A. S.; Leitgeb, R. A.; Javidi, B.; Anand, A. Quantitative phase-contrast imaging with compact digital holographic microscope employing Lloyd’s mirror. Opt. Lett. 2012, 37 (24), 5127– 5129, DOI: 10.1364/OL.37.005127
Google Scholar
There is no corresponding record for this reference.
30
Singh, V.; Tayal, S.; Mehta, D. S. Highly stable wide-field common path digital holographic microscope based on a Fresnel biprism interferometer. OSA Continuum 2018, 1 (1), 48– 55, DOI: 10.1364/OSAC.1.000048
Google Scholar
There is no corresponding record for this reference.
31
Kumar, M.; Pensia, L.; Kumar, R. Single-shot off-axis digital holographic system with extended field-of-view by using multiplexing method. Sci. Rep. 2022, 12 (1), 16462 DOI: 10.1038/s41598-022-20458-3
Google Scholar
There is no corresponding record for this reference.
32
Kim, J.; Jeon, D.; Seong, J.; Badloe, T.; Jeon, N.; Kim, G.; Kim, J.; Baek, S.; Lee, J.-L.; Rho, J. Photonic encryption platform via dual-band vectorial metaholograms in the ultraviolet and visible. ACS Nano 2022, 16 (3), 3546– 3553, DOI: 10.1021/acsnano.1c10100
Google Scholar
There is no corresponding record for this reference.
33
Zhang, X.; Li, X.; Zhou, H.; Wei, Q.; Geng, G.; Li, J.; Li, X.; Wang, Y.; Huang, L. Multifocal Plane Display Based on Dual Polarity Stereoscopic Metasurface. Adv. Funct. Mater. 2022, 32, 2209460 DOI: 10.1002/adfm.202209460
Google Scholar
There is no corresponding record for this reference.
34
Guo, Y.; Zhang, S.; Pu, M.; He, Q.; Jin, J.; Xu, M.; Zhang, Y.; Gao, P.; Luo, X. Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation. Light:Sci. Appl. 2021, 10 (1), 63 DOI: 10.1038/s41377-021-00497-7
Google Scholar
There is no corresponding record for this reference.
35
Luo, Y.; Chu, C. H.; Vyas, S.; Kuo, H. Y.; Chia, Y. H.; Chen, M. K.; Shi, X.; Tanaka, T.; Misawa, H.; Huang, Y.-Y.; Tsai, D. P. Varifocal metalens for optical sectioning fluorescence microscopy. Nano Lett. 2021, 21 (12), 5133– 5142, DOI: 10.1021/acs.nanolett.1c01114
Google Scholar
There is no corresponding record for this reference.
36
Arbabi, E.; Arbabi, A.; Kamali, S. M.; Horie, Y.; Faraji-Dana, M.; Faraon, A. MEMS-tunable dielectric metasurface lens. Nat. Commun. 2018, 9 (1), 812 DOI: 10.1038/s41467-018-03155-6
Google Scholar
There is no corresponding record for this reference.
37
Zhang, F.; Guo, Y.; Pu, M.; Chen, L.; Xu, M.; Liao, M.; Li, L.; Li, X.; Ma, X.; Luo, X. Meta-optics empowered vector visual cryptography for high security and rapid decryption. Nat. Commun. 2023, 14 (1), 1946 DOI: 10.1038/s41467-023-37510-z
Google Scholar
There is no corresponding record for this reference.
38
Arbabi, A.; Horie, Y.; Bagheri, M.; Faraon, A. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 2015, 10 (11), 937– 943, DOI: 10.1038/nnano.2015.186
Google Scholar
There is no corresponding record for this reference.
39
Lin, R. J.; Su, V.-C.; Wang, S.; Chen, M. K.; Chung, T. L.; Chen, Y. H.; Kuo, H. Y.; Chen, J.-W.; Chen, J.; Huang, Y.-T. Achromatic metalens array for full-colour light-field imaging. Nat. Nanotechnol. 2019, 14 (3), 227– 231, DOI: 10.1038/s41565-018-0347-0
Google Scholar
There is no corresponding record for this reference.
40
Liu, X.; Zhang, J.; Leng, B.; Zhou, Y.; Cheng, J.; Yamaguchi, T.; Tanaka, T.; Chen, M. K. Edge enhanced depth perception with binocular meta-lens. Opto-Electron. Sci. 2024, 3, 230033 DOI: 10.29026/oes.2024.230033
Google Scholar
There is no corresponding record for this reference.
41
Li, L.; Liu, Z.; Ren, X.; Wang, S.; Su, V.-C.; Chen, M.-K.; Chu, C. H.; Kuo, H. Y.; Liu, B.; Zang, W. Metalens-array–based high-dimensional and multiphoton quantum source. Science 2020, 368 (6498), 1487– 1490, DOI: 10.1126/science.aba9779
Google Scholar
There is no corresponding record for this reference.
42
Lin, D.; Fan, P.; Hasman, E.; Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 2014, 345 (6194), 298– 302, DOI: 10.1126/science.1253213
Google Scholar
There is no corresponding record for this reference.
43
Ni, X.; Wong, Z. J.; Mrejen, M.; Wang, Y.; Zhang, X. An ultrathin invisibility skin cloak for visible light. Science 2015, 349 (6254), 1310– 1314, DOI: 10.1126/science.aac9411
Google Scholar
There is no corresponding record for this reference.
44
Zhou, J.; Zhang, W.; Liu, Y.; Ke, Y.; Liu, Y.; Luo, H.; Wen, S. Spin-dependent manipulating of vector beams by tailoring polarization. Sci. Rep. 2016, 6 (1), 34276 DOI: 10.1038/srep34276
Google Scholar
There is no corresponding record for this reference.
45
Luo, Y.; Tseng, M. L.; Vyas, S.; Kuo, H. Y.; Chu, C. H.; Chen, M. K.; Lee, H. C.; Chen, W. P.; Su, V. C.; Shi, X. Metasurface-based abrupt autofocusing beam for biomedical applications. Small Methods 2022, 6 (4), 2101228 DOI: 10.1002/smtd.202101228
Google Scholar
There is no corresponding record for this reference.
46
Park, J.-S.; Lim, S. W. D.; Amirzhan, A.; Kang, H.; Karrfalt, K.; Kim, D.; Leger, J.; Urbas, A.; Ossiander, M.; Li, Z.; Capasso, F. All-glass 100 mm diameter visible metalens for imaging the cosmos. ACS Nano 2024, 18 (4), 3187– 3198, DOI: 10.1021/acsnano.3c09462
Google Scholar
There is no corresponding record for this reference.
47
Kim, J.; Seong, J.; Kim, W.; Lee, G.-Y.; Kim, S.; Kim, H.; Moon, S.-W.; Oh, D. K.; Yang, Y.; Park, J. Scalable manufacturing of high-index atomic layer–polymer hybrid metasurfaces for metaphotonics in the visible. Nat. Mater. 2023, 22 (4), 474– 481, DOI: 10.1038/s41563-023-01485-5
Google Scholar
There is no corresponding record for this reference.
48
Yang, W.; Zhou, J.; Tsai, D. P.; Xiao, S. Advanced manufacturing of dielectric meta-devices. Photonics Insights 2024, 3 (2), R04, DOI: 10.3788/PI.2024.R04
Google Scholar
There is no corresponding record for this reference.
49
Chia, Y. H.; Liao, W. H.; Vyas, S.; Chu, C. H.; Yamaguchi, T.; Liu, X.; Tanaka, T.; Huang, Y. Y.; Chen, M. K.; Chen, W. S. In Vivo Intelligent Fluorescence Endo-Microscopy by Varifocal Meta-Device and Deep Learning. Adv. Sci. 2024, 11, 2307837 DOI: 10.1002/advs.202307837
Google Scholar
There is no corresponding record for this reference.
50
Chu, C. H.; Vyas, S.; Luo, Y.; Yang, P.-C.; Tsai, D. P. Recent developments in biomedical applications of metasurface optics. APL Photonics 2024, 9 (3), 030901 DOI: 10.1063/5.0190758
Google Scholar
There is no corresponding record for this reference.
51
Luo, Y.; Tseng, M. L.; Vyas, S.; Hsieh, T.-Y.; Wu, J.-C.; Chen, S.-Y.; Peng, H.-F.; Su, V.-C.; Huang, T.-T.; Kuo, H. Y. Meta-lens light-sheet fluorescence microscopy for in vivo imaging. Nanophotonics 2022, 11 (9), 1949– 1959, DOI: 10.1515/nanoph-2021-0748
Google Scholar
There is no corresponding record for this reference.
52
Pahlevaninezhad, H.; Khorasaninejad, M.; Huang, Y.-W.; Shi, Z.; Hariri, L. P.; Adams, D. C.; Ding, V.; Zhu, A.; Qiu, C.-W.; Capasso, F.; Suter, M. J. Nano-optic endoscope for high-resolution optical coherence tomography in vivo. Nat. Photonics 2018, 12 (9), 540– 547, DOI: 10.1038/s41566-018-0224-2
Google Scholar
There is no corresponding record for this reference.
53
Chu, C. H.; Chia, Y.-H.; Hsu, H.-C.; Vyas, S.; Tsai, C.-M.; Yamaguchi, T.; Tanaka, T.; Chen, H.-W.; Luo, Y.; Yang, P.-C.; Tsai, D. P. Intelligent Phase Contrast Meta-Microscope System. Nano Lett. 2023, 23 (24), 11630– 11637, DOI: 10.1021/acs.nanolett.3c03484
Google Scholar
There is no corresponding record for this reference.
54
Kim, Y.; Lee, G. Y.; Sung, J.; Jang, J.; Lee, B. Spiral metalens for phase contrast imaging. Adv. Funct. Mater. 2022, 32 (5), 2106050 DOI: 10.1002/adfm.202106050
Google Scholar
There is no corresponding record for this reference.
55
Huo, P.; Zhang, C.; Zhu, W.; Liu, M.; Zhang, S.; Zhang, S.; Chen, L.; Lezec, H. J.; Agrawal, A.; Lu, Y.; Xu, T. Photonic spin-multiplexing metasurface for switchable spiral phase contrast imaging. Nano Lett. 2020, 20 (4), 2791– 2798, DOI: 10.1021/acs.nanolett.0c00471
Google Scholar
There is no corresponding record for this reference.
56
Zhang, Y.; Lin, P.; Huo, P.; Liu, M.; Ren, Y.; Zhang, S.; Zhou, Q.; Wang, Y.; Lu, Y.-q.; Xu, T. Dielectric Metasurface for Synchronously Spiral Phase Contrast and Bright-Field Imaging. Nano Lett. 2023, 23, 2991– 2997, DOI: 10.1021/acs.nanolett.3c00388
Google Scholar
There is no corresponding record for this reference.
57
Zhou, J.; Tian, F.; Hu, J.; Shi, Z.; Godinez, V. G.; Tsai, D. P.; Liu, Z. Eagle-Eye Inspired Meta-Device for Phase Imaging. Adv. Mater. 2024, 36, 2402751 DOI: 10.1002/adma.202402751
Google Scholar
There is no corresponding record for this reference.
58
Liu, B.; Cheng, J.; Zhao, M.; Yao, J.; Liu, X.; Chen, S.; Shi, L.; Tsai, D. P.; Geng, Z.; Chen, M. K. Metalenses phase characterization by multi-distance phase retrieval. Light:Sci. Appl. 2024, 13 (1), 182 DOI: 10.1038/s41377-024-01530-1
Google Scholar
There is no corresponding record for this reference.
59
Engay, E.; Huo, D. W.; Malureanu, R.; Bunea, A. I.; Lavrinenko, A. Polarization-Dependent All-Dielectric Metasurface for Single-Shot Quantitative Phase Imaging. Nano Lett. 2021, 21 (9), 3820– 3826, DOI: 10.1021/acs.nanolett.1c00190
Google Scholar
There is no corresponding record for this reference.
60
Sardana, J.; Devinder, S.; Zhu, W. Q.; Agrawal, A.; Joseph, J. Dielectric Metasurface Enabled Compact, Single-Shot Digital Holography for Quantitative Phase Imaging. Nano Lett. 2023, 23 (23), 11112– 11119, DOI: 10.1021/acs.nanolett.3c03515
Google Scholar
There is no corresponding record for this reference.
61
Kwon, H.; Arbabi, E.; Kamali, S. M.; Faraji-Dana, M.; Faraon, A. Single-shot quantitative phase gradient microscopy using a system of multifunctional metasurfaces. Nat. Photonics 2020, 14 (2), 109– 114, DOI: 10.1038/s41566-019-0536-x
Google Scholar
There is no corresponding record for this reference.
62
Wang, J.; Yu, R.; Ye, X.; Sun, J.; Li, J.; Huang, C.; Xiao, X.; Ji, J.; Shen, W.; Tie, Z. Quantitative phase imaging with a compact meta-microscope. npj Nanophotonics 2024, 1 (1), 4 DOI: 10.1038/s44310-024-00007-8
Google Scholar
There is no corresponding record for this reference.
63
Wu, Q. Y.; Zhou, J. X.; Chen, X. Y.; Zhao, J. X.; Lei, M.; Chen, G. H.; Lo, Y. H.; Liu, Z. W. Single-shot quantitative amplitude and phase imaging based on a pair of all-dielectric metasurfaces. Optica 2023, 10 (5), 619– 625, DOI: 10.1364/OPTICA.483366
Google Scholar
There is no corresponding record for this reference.
64
Zhou, J.; Wu, Q.; Zhao, J.; Posner, C.; Lei, M.; Chen, G.; Zhang, J.; Liu, Z. Fourier optical spin splitting microscopy. Phys. Rev. Lett. 2022, 129 (2), 020801 DOI: 10.1103/PhysRevLett.129.020801
Google Scholar
There is no corresponding record for this reference.
65
Li, L.; Wang, S.; Zhao, F.; Zhang, Y.; Wen, S.; Chai, H.; Gao, Y.; Wang, W.; Cao, L.; Yang, Y. Single-shot deterministic complex amplitude imaging with a single-layer metalens. Sci. Adv. 2024, 10 (1), eadl0501 DOI: 10.1126/sciadv.adl0501
Google Scholar
There is no corresponding record for this reference.
66
Pham, H. V.; Edwards, C.; Goddard, L. L.; Popescu, G. Fast phase reconstruction in white light diffraction phase microscopy. Appl. Opt. 2013, 52 (1), A97– A101, DOI: 10.1364/AO.52.000A97
Google Scholar
There is no corresponding record for this reference.
67
Martinez-Carranza, J.; Falaggis, K.; Kozacki, T. Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation. Appl. Opt. 2017, 56 (25), 7079– 7088, DOI: 10.1364/AO.56.007079
Google Scholar
There is no corresponding record for this reference.

Cited By

Click to copy section linkSection link copied!

This article has not yet been cited by other publications.

Download PDF