It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over a large continuous bandwidth with a single diffractive surface. In contrast to conventional lens design, we utilize inverse design, where the phase in the focal plane is treated as a free parameter. This approach attains a phase-only (lossless) pupil function, which can be implemented as a multi-level diffractive flat lens that achieves achromatic focusing and imaging. In particular, we experimentally demonstrate imaging using a single flat lens of diameter > 3 mm and focal length = 5 mm (NA = 0.3, f/1.59) that is achromatic from λ = 450 nm (blue) to 1 μm (NIR). This simultaneous achievement of large size, NA, and broad operating bandwidth has not been demonstrated in a flat lens before. We experimentally characterized the point-spread functions, off-axis aberrations, and broadband imaging performance of the lens.
References
1.
M.
Born
and E.
Wolf
, Principle of Optics
, 7th ed. (Cambridge University Press
, Cambridge
, 1999
).2.
P.
Wang
and R.
Menon
, “Computational multi-spectral video imaging
,” J. Opt. Soc. Am. A
35
(1
), 189
–199
(2018
).3.
R.
Menon
, P.
Rogge
, and H.-Y.
Tsai
, “Design of diffractive lenses that generate optical nulls without phase singularities
,” J. Opt. Soc. Am. A
26
(2
), 297
(2009
).4.
S. R. R.
Pavani
, M. A.
Thompson
, J. S.
Biteen
, S. J.
Lord
, N.
Liu
, R. J.
Tweig
, R.
Piestun
, and W. E.
Moerner
, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point-spread function
,” Proc. Natl. Acad. U. S. A.
106
(9
), 2995
–2999
(2009
).5.
M.
Khorasaninejad
, W. T.
Chen
, A. Y.
Zhu
, J.
Oh
, R. C.
Devlin
, C.
Roques-Carmes
, I.
Mishra
, and F.
Capasso
, “Visible wavelength planar metalenses based on titanium dioxide
,” IEEE J. Sel. Top. Quantum Electron.
23
(3
), 4700216
(2017
).6.
M.
Meem
, A.
Majumder
, and R.
Menon
, “Multi-plane, multi-band image projection via broadband diffractive optics
,” Appl. Opt.
59
, 38
–44
(2020
).7.
N.
Mohammad
, M.
Meem
, X.
Wan
, and R.
Menon
, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics
,” Sci. Rep.
7
, 5789
(2017
).8.
G.
Kim
, N.
Nagarajan
, E.
Pastuzyn
, K.
Jenks
, M.
Capecchi
, J.
Sheperd
, and R.
Menon
, “Deep-brain imaging via epi-fluorescence computational cannula microscopy
,” Sci. Rep.
7
, 44791
(2017
).9.
G.
Kim
, N.
Nagarajan
, M.
Capecchi
, and R.
Menon
, “Cannula-based computational fluorescence microscopy
,” Appl. Phys. Lett.
106
, 261111
(2015
).10.
G.
Kim
and R.
Menon
, “Computational imaging enables a “see-through” lensless camera
,” Opt. Express
26
(18
), 22826
–22836
(2018
).11.
G.
Kim
, K.
Isaacson
, R.
Palmer
, and R.
Menon
, “Lensless photography with only an image sensor
,” Appl. Opt.
56
(23
), 6450
–6456
(2017
).12.
G.
Kim
, S.
Kapetanovic
, R.
Palmer
, and R.
Menon
, “Lensless-camera based machine learning for image classification
,” arXiv:1709.00408.13.
G. C.
Sherman
, “Integral-transform formulation of diffraction theory
,” J. Opt. Soc. Am. A
57
(12
), 1490
–1498
(1967
).14.
M.
Meem
, S.
Banerji
, A.
Majumder
, P.
Hon
, J. C.
Garcia
, B.
Sensale-Rodriguez
, and R.
Menon
, “Imaging from the visible to the longwave infrared via an inverse-designed flat lens
,” arXiv:2001.03684.15.
M.
Meem
, S.
Banerji
, A.
Majumder
, C.
Dvonch
, B.
Sensale-Rodriguez
, and R.
Menon
, “Imaging across the short-wave infra-red (SWIR) band via a flat multi-level diffractive lens
,” OSA Continuum
2
(10
), 2968
–2974
(2019
).16.
S.
Banerji
, M.
Meem
, A.
Majumder
, B.
Sensale-Rodriguez
, and R.
Menon
, “Imaging over an unlimited bandwidth with a single diffractive surface
,” arXiv:1907.06251.17.
M.
Meem
, S.
Banerji
, A.
Majumder
, F. G.
Vasquez
, B.
Sensale-Rodriguez
, and R.
Menon
, “Broadband lightweight flat lenses for longwave-infrared imaging
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 21375
(2019
).18.
N.
Mohammad
, M.
Meem
, B.
Shen
, P.
Wang
, and R.
Menon
, “Broadband imaging with one planar diffractive lens
,” Sci. Rep.
8
, 2799
(2018
).19.
S.
Banerji
, M.
Meem
, A.
Majumder
, B.
Sensale-Rodriguez
, and R.
Menon
, “Diffractive flat lens enables extreme depth-of-focus imaging
,” Optica
7
(3
), 214
–2017
(2020
).20.
M.
Meem
, S.
Banerji
, A.
Majumder
, C.
Pies
, T.
Oberbiermann
, B.
Sensale-Rodriguez
, and R.
Menon
, “Large-area, high-NA multi-level diffractive lens via inverse design
,” Optica
7
(3
), 252
–253
(2020
).21.
H.
Liang
, A.
Martins
, B. H. V.
Borges
, J.
Zhou
, E. R.
Martins
, J.
Li
, and T. F.
Krauss
, “High performance metalenses: Numerical aperture, aberrations, chromaticity, and trade-offs
,” Optica
6
(12
), 1461
–1470
(2019
).22.
W. T.
Chen
, A. Y.
Zhu
, J.
Sisler
, Z.
Bharwani
, and F.
Capasso
, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures
,” Nat. Commun.
10
(1
), 355
(2019
).23.
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
).24.
Y.
Liang
, H.
Liu
, F.
Wang
, H.
Meng
, J.
Guo
, J.
Li
, and Z.
Wei
, “High-efficiency, near-diffraction limited, dielectric metasurface lenses based on crystalline titanium dioxide at visible wavelengths
,” Nanomaterials
8
(5
), 288
(2018
).25.
M.
Ye
, V.
Ray
, and Y. S.
Yi
, “Achromatic flat subwavelength grating lens over whole visible bandwidths
,” IEEE Photonics Technol. Lett.
30
(10
), 955
–958
(2018
).26.
H. C.
Wang
, C. H.
Chu
, P. C.
Wu
, H. H.
Hsiao
, H. J.
Wu
, J. W.
Chen
, W. H.
Lee
, Y. C.
Lai
, Y. W.
Huang
, M. L.
Tseng
, S. W.
Chang
, and D. P.
Tsai
, “Ultrathin planar cavity metasurfaces
,” Small
14
, 1703920
(2018
).27.
M.
Khorasaninejad
, Z.
Shi
, A. Y.
Zhu
, W. T.
Chen
, V.
Sanjeev
, A.
Zaidi
, and F.
Capasso
, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion
,” Nano Lett.
17
(3
), 1819
–1824
(2017
).28.
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
(2018
).29.
S.
Banerji
, M.
Meem
, A.
Majumder
, B.
Sensale-Rodriguez
, and R.
Menon
, “Imaging with flat optics: Metalenses or diffractive lenses?
,” Optica
6
(6
), 805
–810
(2019
).30.
S.
Banerji
and B.
Sensale-Rodriguez
, “A computational design framework for efficient, fabrication error-tolerant, planar THz diffractive optical elements
,” Sci. Rep.
9
, 5801
(2019
).31.
J. J.
Stamnes
and V.
Dhayalan
, “Focusing of electric-dipole waves
,” Pure Appl. Opt.
5
, 195
–225
(1996
).32.
J. J.
Stamnes
and V.
Dhayalan
, “Focusing of electric-dipole waves in the Debye and Kirchoff approximations
,” Pure Appl. Opt.
6
, 347
–372
(1997
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
