Abstract

Various speckle-based computational imaging techniques that exploit the ability of scattering media to transfer hidden information into the speckle pattern have recently been demonstrated. Current implementations suffer from several drawbacks associated with the use of conventional scattering media (CSM), such as their time-consuming characterization, instability with time, and limited memory-effect range. Here we show that by using a random dielectric metasurface diffuser (MD) with known scattering properties, many of these issues can be addressed. We experimentally demonstrate an imaging system with the ability to retrieve complex field values using a MD and the speckle-correlation scattering matrix method. We explore the mathematical properties of the MD transmission matrix such as its correlation and singular value spectrum to expand the understanding about both MDs and the speckle-correlation scattering matrix approach. In addition to a large noise tolerance, reliable reproducibility, and robustness against misalignments, using the MD allows us to substitute the laborious experimental characterization procedure of the CSM with a simple simulation process. Moreover, dielectric MDs with identical scattering properties can easily be mass-produced, thus enabling real-world applications. Representing a bridge between metasurface optics and speckle-based computational imaging, this work paves the way to extending the potentials of diverse speckle-based computational imaging methods for various applications such as biomedical imaging, holography, and optical encryption.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (10)

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).
[Crossref]

M. Jang, Y. Horie, A. Shibukawa, J. Brake, Y. Liu, S. M. Kamali, A. Arbabi, H. Ruan, A. Faraon, and C. Yang, “Wavefront shaping with disorder-engineered metasurfaces,” Nat. Photonics 12, 84–90 (2018).
[Crossref]

F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep. Prog. Phys. 81, 026401 (2018).
[Crossref]

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

L. Gong, Q. Zhao, H. Zhang, X. Hu, and Y. Li, “Exploiting scattering for single-shot measurement of the orbital angular momentum spectrum of light fields,” Proc. SPIE 10712, 107121F (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141 (2018).
[Crossref]

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5, 1–9 (2018).
[Crossref]

Y. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).
[Crossref]

2017 (16)

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics,” Optica 4, 625–632 (2017).
[Crossref]

Y. Kashter, A. Vijayakumar, and J. Rosen, “Resolving images by blurring: superresolution method with a scattering mask between the observed objects and the hologram recorder,” Optica 4, 932–939 (2017).
[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
[Crossref]

S. Sahoo, D. Tang, and C. Dang, “Single-shot multispectral imaging with a monochromatic camera,” Optica 4, 1209–1213 (2017).
[Crossref]

P. Berto, H. Rigneault, and M. Guillon, “Wavefront sensing with a thin diffuser,” Opt. Lett. 42, 5117–5120 (2017).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

H. C. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3, e1701477 (2017).
[Crossref]

J. K. Adams, V. Boominathan, B. W. Avants, D. G. Vercosa, F. Ye, R. G. Baraniuk, J. T. Robinson, and A. Veeraraghavan, “Single-frame 3D fluorescence microscopy with ultraminiature lensless FlatScope,” Sci. Adv. 3, e1701548 (2017).
[Crossref]

M. Castro-Lopez, M. Gaio, S. Sellers, G. Gkantzounis, M. Florescu, and R. Sapienza, “Reciprocal space engineering with hyperuniform gold metasurfaces,” APL Photon. 2, 061302 (2017).
[Crossref]

E. Maguid, M. Yannai, A. Faerman, I. Yulevich, V. Kleiner, and E. Hasman, “Disorder-induced optical transition from spin Hall to random Rashba effect,” Science 358, 1411–1415 (2017).
[Crossref]

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17, 4902–4907 (2017).
[Crossref]

H. H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).
[Crossref]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11, 415–420 (2017).
[Crossref]

A. Singh, D. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).
[Crossref]

2016 (8)

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11, 23–36 (2016).
[Crossref]

S. M. Kamali, A. Arbabi, E. Arbabi, Y. Horie, and A. Faraon, “Decoupling optical function and geometrical form using conformal flexible dielectric metasurfaces,” Nat. Commun. 7, 11618 (2016).
[Crossref]

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7, 13359 (2016).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
[Crossref]

A. Pors, F. Ding, Y. Chen, I. P. Radko, and S. I. Bozhevolnyi, “Random-phase metasurfaces at optical wavelengths,” Sci. Rep. 6, 28448 (2016).
[Crossref]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref]

R. Horisaki, R. Egami, and J. Tanida, “Single-shot phase imaging with randomized light (SPIRaL),” Opt. Express 24, 3765–3773 (2016).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3, 1504–1505 (2016).
[Crossref]

2015 (11)

H. Lee, Y. Lee, C. Song, H. R. Cho, R. Ghaffari, T. K. Choi, K. H. Kim, Y. B. Lee, D. Ling, H. Lee, S. J. Yu, S. H. Choi, T. Hyeon, and D. H. Kim, “An endoscope with integrated transparent bioelectronics and theranostic nanoparticles for colon cancer treatment,” Nat. Commun. 6, 10059 (2015).
[Crossref]

H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Speckle correlation resolution enhancement of wide-field fluorescence imaging,” Optica 2, 424–429 (2015).
[Crossref]

H.-Y. Liu, E. Jonas, L. Tian, J. Zhong, B. Recht, and L. Waller, “3D imaging in volumetric scattering media using phase-space measurements,” Opt. Express 23, 14461–14471 (2015).
[Crossref]

M. Chakrabarti, M. L. Jakobsen, and S. G. Hanson, “Speckle-based spectrometer,” Opt. Lett. 40, 3264–3267 (2015).
[Crossref]

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic illustration of computational complex field retrieval using a designed MD. Light from the object is scattered by the metasurface, resulting in a speckle pattern. The known phase profile of the MD is then used in a computational procedure based on the SSM method to retrieve the complex fields of the object from the captured speckle pattern.
Fig. 2.
Fig. 2. MD structure and design. (a) Schematic illustration of the side and top views of the MD. The α-Si meta-atoms are arranged in a square lattice on a fused silica substrate. A gold layer is deposited to block the light outside the diffuser aperture. (b) Schematics of a uniform array (top) and a unit cell of the metasurface (bottom), showing the parameter definitions. The transmission phase of the two orthogonal polarizations can be manipulated using the meta-atoms. (c) Calculated in-plane dimensions of the meta-atoms (Dx and Dy) as functions of the required transmission phases for x- and y-polarized light (ϕx and ϕy, respectively). The black dashed lines show the meta-atoms that work as a half-wave plate (i.e., |ϕxϕy|=π). (d) Calculated amplitude of the Fourier transform of the MD’s phase mask. (e) Optical image of the fabricated MD array. (f) Bird's-eye-view scanning electron microscope image of a portion of the metasurface. The scale bar is 1 μm.
Fig. 3.
Fig. 3. Numerical investigation of the ability of the MD to retrieve complex fields. (a) Simulated speckle amplitudes and phases for sample input modes, which are then shaped as complex M×1 vectors and form the columns of T. (b) The G matrix formed from the inner product mapping of the normalized vectors of T. Gij represents the absolute value of the inner product of normalized ti and tj. The 130×130 elements located at the center of G are magnified in the inset. (c) Eigenvalue distribution of the TT/M matrix. The solid red line is the Marchenko-Pastur law prediction for a random M×N matrix. (d), (e) The sample amplitude and phase objects. (f), (g) Simulated speckle patterns of the amplitude and phase objects. (h)–(k) Amplitude and phase maps of the initially retrieved complex fields. (h), (j) Amplitude object. (i), (k) Retrieved fields for the phase object. (l)–(o) Amplitude and phase maps of the retrieved complex fields after 20 iterations.
Fig. 4.
Fig. 4. Experimental retrieval of amplitude objects: (a), (b) in-focus images of targets captured by a custom-built microscope; (c), (d) the resulting speckle patterns of the samples after passing through the MD; (e), (f) the retrieved object amplitudes; (g), (h) phases from the captured speckle patterns. The scale bars are 25 μm.
Fig. 5.
Fig. 5. Numerical noise tolerance analysis. (a)–(d) Retrieved amplitudes and phases for the amplitude and phase objects in Figs. 3(d) and 3(e) for SNR values from 0.5 to 1000. A Gaussian noise is added to the simulated speckle patterns to test the noise tolerance. (e)–(h) Reconstructed objects after performing 20 iterations of the GS algorithm using the results in (a)–(d) as initial points. (i), (j) Retrieved intensity and phase maps for the object shown in Fig. 4(a) when changing the SNR from 0.5 to 1000. A Gaussian noise is added to the measured speckle pattern shown in Fig. 4(c). (k), (l) Reconstructed intensity and phase maps after conducting 20 iterations of the GS algorithm using (i) and (j). The scale bars in (i)–(l) are 25 μm.
Fig. 6.
Fig. 6. Experimental results of complex field retrieval for holographic imaging. (a) Schematic drawing of the measurement setup showing the computational steps. The complex field is retrieved at the 150 μm aperture using the captured speckle pattern. The field is then backpropagated to reconstruct the object at different distances from the aperture. (b) Reconstructed images for different objects at point A. (c) Reconstructed images for a target shaped like the number 5 at different distances from the aperture. (d) Schematic drawing of a microscope setup that images the target through the same aperture for comparison. (e) Captured in-focus images with the microscope for the same objects as in (b). (f) Captured in-focus images with the microscope for the same object and distances as in (c). The distances between the points and the aperture are as follows: A, 1.5 mm; B, 2 mm; C, 2.5 mm; D, 3.5 mm; and E, 4.5 mm. Scale bars are 25 μm.

Equations (1)

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Zij=1ij[ti*tjy*yti*tjy*y],

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