Quantitative Phase Imaging with a Compact Meta- microscope

doi:10.21203/rs.3.rs-3635679/v1

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Quantitative Phase Imaging with a Compact Meta- microscope

https://doi.org/10.21203/rs.3.rs-3635679/v1

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Quantitative phase imaging (QPI) based on the transport-of-intensity equation (TIE) is a powerful technique in label-free microscopy. The image stack required for a successful TIE-QPI is traditionally obtained by translating the object or image plane, and the optical elements used in the conventional TIE-QPI systems are usually bulky and cumbersome. Stable and compact TIE-QPI methods capable of non-motion optical zooming can significantly facilitate applications that demand portability. Here, we propose a non-motion TIE-QPI method based on a dispersive metalens. The dispersive nature of the metalens is utilized to provide a spectral focal tuning. With fixed object and image planes, seven through-focus intensity images are captured by changing the illumination wavelength. The QPI performance is validated by retrieving the surface phase profiles of a microlens array and a phase resolution target, showing a high phase detection accuracy (deviation less than 0.03 wavelength). Subsequently, we established a compact meta-microscope by integrating the metalens with a commercially available CMOS image sensor, which shows good performance in microscopic imaging of unstained bio-samples. Our approach, based on the large-dispersive metalens, facilitates a compact and robust QPI system for optical metrology and label-free microscopy.

Physical sciences/Optics and photonics/Optical physics/Nanophotonics and plasmonics

Physical sciences/Optics and photonics/Optical techniques/Microscopy/Phase contrast microscopy

Physical sciences/Optics and photonics/Optical techniques/Imaging and sensing

Traditional bright-field microscopes mainly utilize opaque specimens to provide sufficient contrast for observation. For near-transparent samples with little contrast, like bio-cells and tissues, fluorescence or staining methods are widely used to enhance intensity contrast. However, exogenous fluorescent agents or staining labels may be toxic to living cells^1,2. Label-free microscopy, serving as a complementary technique to fluorescence or staining methods, can provide low phototoxicity and does not demand sophisticated sample preparation procedures. It transfers the intrinsic phase information of the intensity-transparent samples into intensity contrast. Typical examples of label-free microscopy are Zernike phase contrast microscopy³ (ZPC) and differential interference contrast microscopy⁴ (DIC). However, they provide only qualitative visualization instead of quantitative mapping of the phase profile.

Quantitative phase imaging (QPI) techniques, such as digital holographic microscopy⁵, Fourier ptychographic microscopy⁶, quantitative differential phase contrast microscopy^7,8, the transport-of-intensity equation (TIE)^9–11, have proven to be powerful tools in label-free microscopy¹², and have witnessed rapid development in recent decades. The images provided by QPI, unlike ZPC or DIC outputs, can be put to automated analysis like cell segmentation¹³, facilitating research on cell structures, cell dynamics, and the calculation of cell mass and volume, etc. Among diverse QPI methods, TIE is non-interferometric and highly compatible with conventional microscope setups with Köhler illumination. It requires only multiple intensity measurements from axially displaced planes for deterministic phase retrieval. Due to the less demanding experimental configuration, TIE-QPI methods have found great potential in biomedical and metrological applications^14,15. Nevertheless, traditional TIE-QPI methods mostly require mechanical translation of the camera or the object to capture raw data, which relies on cumbersome setups and potentially brings instability to image acquisition. This is unfavorable in applications that call for compactness and portability, such as point-of-care testing.

Imaging system miniaturization has advanced rapidly in past years, bringing about technological developments like miniaturized fluorescence microscopes^16,17, lensless microscopy¹⁸, chip-scale metalens microscopes^19,20, etc. Among these, metalenses, with flat and ultrathin architectures composed of subwavelength units^21,22, have shown massive potential in providing miniaturized solutions for diverse imaging applications^23,24, like fluorescence imaging^25,26, polarization imaging²⁷, ultraspectral imaging²⁸, phase imaging^29–35, tomographic imaging^36,37, multimode imaging³⁸, wide-angle imaging³⁹, etc. Current metasurface-based QPI or quantitative phase gradient imaging (QPGI) methods either require two cascaded metasurfaces³⁰, or place the metasurface at the Fourier plane, both of which complicate the entire system^29,35. Therefore, a QPI method composed of a single-layered metalens in a fixed system free of complicated configurations is highly desirable.

In this article, we propose and experimentally demonstrate a dispersive metalens based TIE method to realize QPI without mechanically translating the image or object plane. We exploit the dispersive nature of metalenses, which can introduce spectral dispersion large enough to provide evident focal length deviations, thereby enabling non-mechanical optical zooming. Specifically, by sweeping the illumination wavelength while fixing the image and object planes, we obtain a stack of through-focus intensity images bound for a multi-plane TIE phase recovery method^40,41 to retrieve the in-focus phase information. The QPI performance of the proposed method is characterized on a commercial microlens array, showing the phase deviation is less than 0.03 wavelength (i.e., 0.1 rad by calculation) as compared with the atomic force microscope (AFM) measured surface profile. Its powerful capability in phase measurement on the near-transparent samples is further validated on a phase resolution target. Moreover, the dispersive metalens based TIE method, free of mechanical translation of the image or object plane, enables the direct integration of the metalens with a commercial image sensor to establish a meta-microscope. The QPI performance of the meta-microscope is tested on unstained bio-samples, also showing good results.

2.1 Concept of the metalens-based QPI

The quantitative relationship between the axial intensity derivative and the phase of the transverse optical field was first derived by Teague in a second-order elliptic partial differential equation, later termed TIE, which is written as

$$- k\frac{{\partial I(x,y)}}{{\partial z}}={\nabla _ \bot } \cdot \left[ {I(x,y){\nabla _ \bot }\varphi (x,y)} \right]$$

where k is the wavenumber ${{2\pi } \mathord{\left/ {\vphantom {{2\pi } \lambda }} \right. \kern-0pt} \lambda }$, $\lambda$ is the wavelength, z is the coordinate along the optical axis, I and $\varphi$ are the intensity and phase distributions at the recorded plane (generally the focal plane), and ${\nabla _ \bot }$ is the two-dimensional gradient operator over the transverse coordinates x and y. When satisfying certain boundary conditions, the absolute phase can be deterministically retrieved without phase unwrapping or iterative approximations. Due to the convenience of being non-interferometric and highly compatible with basic microscope setups, TIE is chosen as the phase solver to achieve a metalens-based QPI. According to the working principle of TIE, a precise axial intensity derivative is necessary, which can be approximately obtained with different methods. The most straightforward approach is to use the difference between two intensity images. However, the result is usually sensitive to the choice of defocus distance in practical experiments. In comparison, acquiring multiple through-focus images^40,41 can provide a more robust approximation of the axial intensity derivative (see Supplementary Note 1 for details about the multi-plane methods). The image stack is traditionally acquired by mechanically scanning the object plane (or the conjugate image plane), undoubtedly involving complicated mechanical elements. Inspired by the large dispersive nature of metalenses, which has been used to access a microscope tomography³⁶, we conceived the concept of non-motion scanning using a dispersive metalens, as schematically shown in Fig. 1. In this case, the TIE should be converted to a more general form⁴² as

$$- 2\pi \frac{{\partial I(x,y)}}{{\partial \xi }}={\nabla _ \bot } \cdot \left[ {I(x,y){\nabla _ \bot }\varphi (x,y)} \right]$$

where $\xi =\lambda z$ represents the general defocus distance, and the TIE-solving process remains similar. The dispersive nature of metalenses allows optical zooming to capture multiple through-focus images with much smaller wavelength alterations than their refractive counterparts⁴². In the experiment, we captured seven images with varied defocus distances while changing the illumination wavelength from 420 nm to 480 nm with a 10-nm-interval (the center wavelength ${\lambda _0}$ is 450 nm). The small wavelength sweeping range makes it possible to use a single light-emitting diode (LED, GCI-060404, Daheng Optics Co. Ltd., China) as the light source, accompanied by filters of 10-nm bandwidth (hard-coated bandpass filters from Thorlabs, Inc.). Considering the non-motion optical zooming and the compactness of the single-layered metalens and the LED light source, our dispersive metalens based QPI method shows great prospects in a miniaturized and stable platform.

2.2 Design and Characterization of the metalens

The capability of defocus to transfer phase into intensity variations stems from the imaginary part introduced to the coherent transfer function of the imaging system, as do most optical aberrations. If we assume the phase of a metalens is introduced by the Pancharatnam-Berry (PB) phase and takes the normally used hyperbolic form as

$${\varphi _{hyperbolic}}= - \frac{{2\pi }}{{{\lambda _0}}}(\sqrt {{f^2}+{r^2}} - f)$$

where f is the focal length at ${\lambda _0}$, and r is the radial position, it will induce considerable spherical aberration when the wavelength deviates from ${\lambda _0}$, and it is not suitable for microscopic imaging applications (see Supplementary Note 2 for detailed discussion). To deliver an accurate phase retrieval, it is important to alleviate the influence of unwanted aberrations. Under the microscopic imaging setup, it is proven that the spherical aberration can be significantly reduced by using an aplanatic phase profile³⁶. The aplanatic phase is deduced as a function of the object distance based on the generalized law of refraction, written as

$${\varphi _{aplanatic}}= - \frac{{2\pi }}{{{\lambda _0}}}\left[ {\sqrt {{s^2}+{r^2}} +\sqrt {{{\left( {\frac{{sf}}{{f - s}}} \right)}^2}+{r^2}} } \right]$$

where s is the object distance. The aplanatic phase profile is delivered based on the PB phase method via distributing SiN_x nanofins (height H = 1000 nm, length Dx = 90 nm, width Dy = 215 nm) in a rectangle lattice (lattice period P = 300 nm, meeting the Nyquist sampling criterion) on a SiO₂ substrate. Figure 2a depicts that the selected nanofin possesses high polarization conversion ratio (PCR) across the targeted spectrum (see Methods for the simulation details). The average PCR is 95%. Figure 2b demonstrates the photograph of the fabricated metalens with a diameter D = 2 mm and the optical and scanning electron microscope (SEM) images (see Methods for the fabrication details). The numerical aperture (NA) of the metalens was set as 0.58 at ${\lambda _0}$ = 450 nm (the corresponding ideal focal length is 1.4 mm), and the metalens was designed with an imaging magnification of 4 at ${\lambda _0}$ = 450 nm.

Figure 2c demonstrates apparent focal shifts with different illumination wavelengths. The imaging performance of the metalens is good according to the captured images of the 1951 United States Air Force (USAF) resolution test chart shown in Fig. 2d. The measured intensity distributions of longitudinal cross-sections of the optical field are obtained with normally incident light. This is unsuitable for determining the actual defocus distances at different wavelengths because the aplanatic phase is designed under the illumination of an on-axis point source with a small object distance. When the image distance is set, the exact defocus distances from spectral zooming can be obtained through refocusing experiments shown in Fig. 2d. The defocus distance equals the negative number of the refocusing distance when the illumination wavelength deviates from ${\lambda _0}$ = 450 nm. The defocus distances are measured as -172 µm, -111 µm, -55 µm, 0 µm, 52 µm, 101 µm, and 147 µm for illumination wavelengths ranging from 420 nm to 480 nm with a 10-nm-interval. The measured seven defocus distances show good accordance with the theoretically predicted ones following the equation as

$${z_{defocus}}={s_0} - \sqrt {{{\left\{ {{{{r_p}} \mathord{\left/ {\vphantom {{{r_p}} {[\frac{\lambda }{{{\lambda _0}}}(\frac{{{r_p}}}{{\sqrt {r_{p}^{2}+s{{_{0}^{\prime }}^2}} }}+\frac{{{r_p}}}{{\sqrt {r_{p}^{2}+s_{0}^{2}} }})] - \frac{{{r_p}}}{{\sqrt {r_{p}^{2}+s{{_{0}^{\prime }}^2}} }}}}} \right. \kern-0pt} {[\frac{\lambda }{{{\lambda _0}}}(\frac{{{r_p}}}{{\sqrt {r_{p}^{2}+s{{_{0}^{\prime }}^2}} }}+\frac{{{r_p}}}{{\sqrt {r_{p}^{2}+s_{0}^{2}} }})] - \frac{{{r_p}}}{{\sqrt {r_{p}^{2}+s{{_{0}^{\prime }}^2}} }}}}} \right\}}^2} - r_{p}^{2}}$$

when the r_p is set as half of the radius of the metalens. The s₀ and s₀^’ represent the object and image distance at the center wavelength. The details and illustrations of the experimental setups to measure the chromatic dispersion and imaging performance can be found in Methods and Supplementary Fig. S2.

2.3 QPI performance

We first characterized the QPI capability of the dispersive metalens based system using a commercial microlens array made of fused silica (pitch = 21 µm, f = 500 µm, sublenses are plane-convex lenses, refractive index is 1.47). The experimental setup is the same as used in the imaging performance characterization above. In the imaging experiment, we fixed the image and object distances the same as the ones at ${\lambda _0}$ = 450 nm. The magnification of the singlet imaging system inevitably changes with the wavelength-switching induced focal shifts. The magnification at each wavelength is calibrated as 3.64, 3.76, 3.89, 4, 4.12, 4.24, and 4.37, respectively. Although the aplanatic phase of the metalens was designed for imaging magnification of 4, the change of magnification only brings marginal spherical aberrations, which will not significantly influence the phase retrieval (see Supplementary Note 2 for detailed discussion).

The image stack of the microlens array captured by the dispersive metalens is shown in Fig. 3a, b. The magnification and defocus effects can be easily observed, which validates the design concept. Before the phase retrieval, we rescaled the captured images with respect to the one with the lowest imaging magnification. The scaling process is carried out in the frequency domain to avoid undesired scaling errors in the real space. The cut-off frequency of the intensity spatial spectrum will increase with magnification. Thus, we cut out the spectrum range for all images to match that of the image shot at $\lambda$ = 420 nm, which has the lowest cut-off frequency. Afterwards, inverse Fourier transformation is employed to get rescaled real-space images, and the missing pixels at the edge of the images were made up with zero. Then, the axial intensity derivative is obtained from the seven through-focus images with precision to the sixth order. The retrieved in-focus phase at ${\lambda _0}$ = 450 nm is demonstrated in Fig. 3c. The cross-sectional phase profile (radial average) of a single microlens indicated by the red-dashed box shows good accordance with the surface profile measured by AFM, as is shown in Fig. 3d, and the profile difference is less than 15 nm (approximately 0.03${\lambda _0}$, i.e., 0.1 rad by calculation). We then utilized the angular spectrum method⁴³ to numerically calculate the field distribution transmitted through the microlens array with a distance of 100 µm to 500 µm with an interval of 100 µm. The calculated results agree well with the measured field distributions as depicted in Fig. 3e, f.

To further verify the QPI capability of our method, we fabricated a phase resolution target with sharp surface profile gradients using SiN_x based on the same fabrication method used on the metasurface (see Methods for the fabrication details). The thickness of the sample was measured by a stylus profilometer (KLA, Tencor P-7) to be 100 nm ± 10 nm. The sizes of the line pairs are set to match group 7 and group 8 of the 1951 USAF resolution test chart. Figure 4a, b show the captured image stack, and Fig. 4c depicts the reconstructed surface phase profile at ${\lambda _0}$ = 450 nm. The horizontal and longitudinal cutlines of the surface profile of group 7 indicated by the yellow dashed lines are shown in the inset of Fig. 4c, where the blue dashed line indicates the thickness of 100 nm. The feature size of group 7 element 5 (2.46 µm half-pitch resolution) can be resolved in the reconstructed phase image, as is shown in the inset. The performance of phase resolution is less than the intensity image because the smallest defocus distance here is approximately 50 µm, which is too large to transfer the high-frequency phase information completely. The smallest defocus distance here is limited by the bandwidth of the filter, which would be possibly improved by alternating filters.

After validating the accuracy of our QPI method, we integrated the metalens on a CMOS chip (Imaging source: DMM 27UJ003-ML, pixel size: 1.67 µm×1.67 µm) to establish a meta-microscope, demonstrating its potential in system miniaturization, as is shown in Fig. 5a, b. We tested the QPI performance of the integrated system on unstained bio-samples (HeLa and 4T1 cells). Figure 5c, e show the in-focus images obtained by the metalens at ${\lambda _0}$ = 450 nm (the other through-focus images of the two cells can be found in Supplementary Fig. S3). The intensity images can hardly distinguish details due to the low image contrast. By comparison, the reconstructed phase profiles shown in Fig. 5d, f clearly display the structure features, like the cell size, thickness, etc., which could facilitate structure analysis and medical diagnosis. In addition, the quantitative phase information is directly related to the ‘dry mass’ density map of the cellular structure^12,44 making it convenient for further medical research.

In this article, we have proposed and experimentally demonstrated the proof-of-concept of a compact QPI microscope composed of a single-layered dispersive metalens. The large spectral dispersion of the metalens makes the non-motion optical zooming possible simply by sweeping the illumination wavelength. This enables the direct integration of the metalens with a commercially available CMOS image sensor, which demonstrates the prospect of developing a compact and stable platform for a miniaturized QPI system. The QPI results of the microlens array and phase resolution target clearly validate the reconstruction reliability of our method. The QPI images of the unstained bio-samples, which are reconstructed from raw images captured by the meta-microscope, display distinct image contrast, proving the feasibility of our method for biological applications. We envision that the dispersive metalens based QPI will cast new light on the development of miniaturized QPI systems and facilitate applications like point-of-care testing, industrial measurements, etc.

Simulations

We conducted the full-wave simulation using a commercial finite-difference time-domain (FDTD) solver (Lumerical, Ansys). The refractive indices of SiN_xare 2.0908, 2.0824, 2.0746, 2.0673, 2.0606, 2.0544, and 2.0486 at = 420 nm, 430 nm, 440 nm, 450 nm, 460nm, 470 nm, and 480 nm. The refractive indices of SiO₂ are 1.4748, 1.4738, 1.4728, 1.4720, 1.4711, 1.4703, and 1.4696 accordingly. The wavelength-dependent refractive indices were measured using a spectroscopic ellipsometer (J.A.Woollam, RC2). Periodic boundary condition was used in the simulation for calculating the polarization conversion ratio. The SiN_x nanofins were set as 1000 nm tall with a rectangle lattice period of 300 nm. The length Dx and width Dy were set to range from 80 nm to 250 nm with a 5-nm-interval. Simulation results of the transmittance and phase modulations of x and y polarized light as a function of Dx and Dy at = 450 nm are presented in Supplementary Fig. S4.

Metasurface and phase resolution target fabrication

The SiNx layer was deposited on a 500-μm-thick fused silica substrate by plasma-enhanced chemical vapor deposition at 300 to a final thickness of 1 μm for the metasurface. Then, a positive electron beam resist (200 nm, PMMA A4) was spin-coated onto the substrate and baked at 170 for 5 min. Next, a 100-nm-thick layer of a water-soluble conductive polymer (AR-PC 5090) was spin-coated on the resist for the dissipation of electron beam charges. The metalens pattern was written on an electron beam resist using electron beam lithography (EBL, ELS-F125, Elionix). The conductive polymer was then dissolved in water, and the resist was developed in a resist developer solution. Then, the pattern was transferred into a 40-nm-thick chromium layer deposited by electron beam evaporation (EBE) using the lift-off technique. The pattern chromium served as a hard mask for the dry etching of the SiNx layer in a mixture of CHF₃ and SF₆ plasma (Oxford Instruments, PlasmaPro100 Cobra300). The flow rates of the two gases were 60 sccm:6 sccm. Finally, the chromium mask was removed using a solution of ammonium cerium nitrate. The fabrication procedure for the phase resolution target was identical to the one above with one difference in the thickness of the SiN_x layer being 100 nm.

Experimental setup

The schematic of chromatic dispersion characterization is shown in Supplementary Fig. S2. A white-light laser (Fianium Super-continuum, 4 W), accompanied by filters of 10 nm bandwidth, was used for incidence. A left circularly polarized (LCP) film (#88-084, Edmund Optics) was inserted after the source to confirm the incident polarization state. The metalens was mounted on a translation stage. A custom-built microscope consisted of an objective lens (Mitutoyo, NA = 0.42, 20X) and a tube lens (Jcoptix, OLD2466-T2M, f = 20 cm) was used to relay the light focused by the metalens to a CMOS image sensor (FLIR, BFS-U3-200S6C-C, pixel size: 2.4 μm´2.4 μm). A right circularly polarized film (#11-047, Edmund Optics) was inserted between the objective lens and the tube lens to filter the background signals.

The imaging performance of the metalens was characterized using the setups shown schematically in Supplementary Fig. S2. A blue LED (GCI-060404, Daheng Optics Co. Ltd., China) was chosen as light source, and filters of 10 nm bandwidth were utilized to tune the incident wavelength. A 4f system with a magnification of 2.7 was utilized to relay the source to the aperture stop. Another 4f system with a magnification of 1/3 relayed the field stop onto the object plane. The two 4f systems together formed a Köhler illumination system to provide uniform illumination. The metalens and imaging samples were mounted on separate translation stages. The images formed by the metalens were relayed to the same CMOS image sensor by a custom-built microscope consisting of an objective lens (Mitutoyo, NA = 0.28, 10X) and a tube lens (Jcoptix, OLD2466-T2M, f = 20 cm). The same pair of orthogonal circularly polarized films used in the chromatic dispersion characterization were inserted after the source and before the tube lens functioning as the polarizer and corresponding analyzer.

Acknowledgements

The authors thank Dr. Wei Jiang for the help in preparing cell samples and Dr. Lintao Li for the assistance in the AFM analysis. The authors acknowledge the funding provided by National Key R&D Program of China (2022YFA1404301), National Natural Science Foundation of China (Nos. 62325504, 62305149, 92250304, 62288101), and Dengfeng Project B of Nanjing University. The authors acknowledge the micro-fabrication center of the National Laboratory of Solid State Microstructures (NLSSM) for technical support.

Author contributions

J.W., R.Y., X.Y., and T.L. conceived the idea. J.W. and R.Y. conducted the imaging experiments and completed the numerical calculations. X.X., J.J., W.S., and Z.T. helped with the calculations. X.Y. and J.W. performed the simulations and characterizations of the metalens. J.S., J.L., and C.H. fabricated the metalens and the phase resolution target. J.W., R.Y., X.Y., C.C., and T.L. wrote the manuscript. C.C., S.Z., and T.L. supervised the project. All the authors analyzed the data and discussed the results. All the authors read and approved the final manuscript.

Competing interests

All authors declare no financial or non-financial competing interests.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

The underlying code for this study is not publicly available but may be made available to qualified researchers on reasonable request from the corresponding author.

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Quantitative Phase Imaging with a Compact Meta- microscope

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1. Introduction

2. Results

2.1 Concept of the metalens-based QPI

2.2 Design and Characterization of the metalens

2.3 QPI performance

3. Discussion and Conclusion

Methods

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