of 9
ARTICLE
Received 14 Jun 2016
|
Accepted 25 Oct 2016
|
Published 28 Nov 2016
Miniature optical planar camera based
on a wide-angle metasurface doublet corrected
for monochromatic aberrations
Amir Arbabi
1
, Ehsan Arbabi
1
, Seyedeh Mahsa Kamali
1
, Yu Horie
1
, Seunghoon Han
1,2
& Andrei Faraon
1
Optical metasurfaces are two-dimensional arrays of nano-scatterers that modify optical
wavefronts at subwavelength spatial resolution. They are poised to revolutionize optics by
enabling complex low-cost systems where multiple metasurfaces are lithographically stacked
and integrated with electronics. For imaging applications, metasurface stacks can perform
sophisticated image corrections and can be directly integrated with image sensors. Here we
demonstrate this concept with a miniature flat camera integrating a monolithic metasurface
lens doublet corrected for monochromatic aberrations, and an image sensor. The doublet
lens, which acts as a fisheye photographic objective, has a small
f
-number of 0.9, an angle-of-
view larger than 60
°

60
°
, and operates at 850 nm wavelength with 70% focusing
efficiency. The camera exhibits nearly diffraction-limited image quality, which indicates the
potential of this technology in the development of optical systems for microscopy,
photography, and computer vision.
DOI: 10.1038/ncomms13682
OPEN
1
T.J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125, USA.
2
Samsung
Advanced Institute of Technology, Samsung Electronics, Samsung-ro 130, Suwon-si, Gyeonggi-do 443-803, South Korea. Correspondence and requests
for
materials should be addressed to A.F. (email: faraon@caltech.edu).
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
1
O
ptical systems such as cameras, spectrometers and
microscopes are conventionally made by assembling
discrete bulk optical components like lenses, gratings
and filters. The optical components are manufactured separately
using cutting, polishing and grinding, and have to be assembled
with tight alignment tolerances, a process that is becoming more
challenging as the optical systems shrink in size. Furthermore, the
continuous progress of mobile, wearable, and portable consumer
electronics and medical devices has rapidly increased the demand
for high-performance and low-cost miniature optical systems.
Optical metasurfaces offer an alternative approach for realization
of optical components
1–5
. Recent advances have increased their
efficiency and functionalities, thus allowing metasurface
diffractive optical components with comparable or superior
performance than conventional optical components
6–10
. The
main advantage of metasurfaces stems from the capability to
make sophisticated planar optical systems composed of
lithographically stacked electronic and metasurface layers. The
resulting optical system is aligned lithographically, thus
eliminating the need for post-fabrication alignments.
The development of the optoelectronic image sensor has been a
significant step towards the on-chip integration of cameras
11
;
however, the camera lenses are yet to be fully integrated with the
image sensor. The freedom in controlling the metasurface phase
profiles has enabled the implementation of spherical-aberration-
free flat lenses that focus normally incident light to diffraction
limited spots
7,12–14
. Such lenses have been used in applications
requiring focusing of an optical beam or collimating emission
from an optical fibre
15
or a semiconductor laser
10
. However, the
metasurface lenses suffer from other monochromatic aberrations
(i.e., coma and astigmatism), which reduce their field of view and
hinder their adoption in imaging applications where having a
large field of view is an essential requirement. A metasurface lens
can be corrected for coma if it is patterned on the surface of a
sphere
16–18
, but direct patterning of nano-structures on curved
surfaces is challenging. Although conformal metasurfaces might
provide a solution
19
, the resulting device would not be flat. As we
show here, another approach for correcting monochromatic
aberrations of a metasurface lens is through cascading and
forming a metasurface doublet lens.
Here we show that a doublet lens formed by cascading two
metasurfaces can be corrected over a wide range of incident
angles. We also demonstrate an ultra-slim, low
f
-number camera,
composed of two metasurface lenses placed on top of an image
sensor. The camera represents an example of the optical systems
enabled by the metasurface vertical integration platform.
Results
Design and optimization of the metasurface doublet lens
.
Figure 1a schematically shows focusing by a spherical-aberration-
free metasurface lens. Simulated focal spots for such a lens are
shown in Fig. 1b, exhibiting diffraction limited focusing
for normal incidence and significant aberrations for incident
angles as small as a few degrees. The proposed doublet lens
(Fig. 1c) is composed of two metasurfaces behaving as polariza-
tion insensitive phase plates that are patterned on two sides of a
single transparent substrate. The aberrations of two cascaded
phase plates surrounded by vacuum have been studied previously
in the context of holographic lenses, and it has been shown that
such a combination can realize a fisheye lens with significantly
reduced monochromatic aberrations
20
. We used the ray tracing
approach to optimize the phase profiles of the two metasurfaces
when they are separated by a 1-mm-thick fused silica substrate.
Simulation results of the focal plane spot for different incident
angles (
y
) are presented in Fig. 1d, showing nearly diffraction
limited focusing by the doublet up to almost 30
°
incident angle.
The doublet lens has an input aperture diameter of 800
m
m and a
focal length of 717
m
m corresponding to an
f
-number of 0.9. In
the optimum design, the first metasurface operates as a corrector
plate and the second one performs the significant portion of
focusing; thus, we refer to them as correcting and focusing
metasurfaces, respectively. The metasurfaces are designed for the
operation wavelength of 850 nm, and are implemented using the
dielectric nano-post metasurface platform shown in Fig. 2a
(ref. 7). The metasurfaces are composed of hexagonal arrays of
amorphous silicon nano-posts with different diameters that rest
on a fused silica substrate and are covered by the SU-8 polymer.
The nano-posts behave as truncated waveguides with circular
cross sections supporting Fabry–Pe
́
rot resonances
7,9,19
. The high
refractive index between the nano-posts and their surroundings
leads to weak optical coupling among the nano-posts and allows
for the implementation of any phase profile with subwavelength
resolution by spatially varying the diameters of the nano-posts.
Simulated intensity transmission and phase of the transmission
coefficient for different nano-post diameters are presented in
Fig. 2b, showing that 2
p
phase coverage is achieved with an
average transmission over 96% (see Methods for details).
Device fabrication
. We fabricated the metasurfaces on both sides
of a fused silica substrate by depositing amorphous silicon and
defining the nano-post pattern using e-beam lithography and
dry etching (see Methods for the details). First, the correcting
metasurfaces were patterned on the top side of the substrate, and
then the focusing metasurfaces were aligned and patterned on the
substrate’s bottom side (as schematically shown in Fig. 2c). To
protect the metasurfaces while processing the other side of the
substrate, the metasurfaces were cladded by a layer of cured SU-8
polymer. Aperture and field stops were formed by depositing and
patterning opaque metal layers on the top and bottom sides of the
substrate, respectively, and anti-reflection layers were coated on
both sides of the device. Photos of the top and bottom sides of a
set of fabricated metasurface doublet lenses are shown in Fig. 2c.
Scanning electron microscope images of the nano-posts are
shown in Fig. 2d.
Focal spot and focusing efficiency characterizations
.We
characterized the fabricated metasurface doublet by illuminating
it with an 850 nm laser beam at different incident angles
(as shown in Fig. 3a), and measuring its focal spot and
focusing efficiency. For comparison, a spherical-aberration-
free singlet metasurface lens with the same aperture diameter
and focal length as the doublet lens (phase profile
fr
ðÞ¼
2
p
=
l
ðÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
2
þ
f
2
p
,
r
: radial coordinate,
f
¼
717
m
m:
focal length,
D
¼
800
m
m: aperture diameter) was also fabricated
and characterized. The focal spots of the metasurface doublet and
singlet lenses were measured with two different polarizations of
incident light and are shown along with the corresponding
simulation results in Fig. 3b,c, respectively (see Methods for
details). The doublet lens has a nearly diffraction limited focal
spot for incident angles up to more than 25
°
(with the criterion of
Strehl ratio of larger than 0.9, see Supplementary Fig. 1) while the
singlet exhibits significant aberrations even at incident angles of a
few degrees. As Fig. 3b,c shows, simulated and measured spot
shapes agree well. For the doublet lens, a small asymmetry in the
0
°
spot shape and slightly larger aberrations are observed in the
measured spots compared with the simulation results, which we
attribute to a misalignment (estimated
B
2
m
m along both
x
and
y
directions) between the top and bottom side patterns (Supple-
mentary Fig. 2).
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
2
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
The focusing efficiency (ratio of the focused power to the
incident power) for the metasurface doublet lens is shown in
Fig. 3d, and is
B
70% for normally incident light. The focusing
efficiency is polarization dependent, and its value for unpolarized
light drops at the rate of
B
1% per degree as the incident angle
increases. The measured focusing efficiency at normal incidence
is lower than the average of the transmission shown in Fig. 2b
because of the large numerical aperture (NA) of the focusing
metasurface
7
, undesired scattering due to the sidewall roughness
of the nano-posts, residual reflection at the air/SU-8 interfaces,
and measurement artefacts (see Methods for details). The
metasurfaces are polarization insensitive at normal incidence,
but their diffraction efficiency depends on the polarization
of incident light for non-zero incident angles. The focusing
efficiency is lower for the transverse magnetic polarized light
compared with the transverse electric polarized light because of
the excitation of some resonances of the nano-posts with the axial
component of the electric field of the incident light
19
. This also
causes the slight difference between the transverse electric and
transverse magnetic spot shapes for the 30
°
incident light shown
a
c
b

=0
°
2.5
°
1
°
0
1
Intensity (a.u.)
d
10
°
20
°
30
°
0
1
Intensity (a.u.)

=0
°


Figure 1 | Focusing by metasurface singlet and doublet lenses.
(
a
) Schematic illustration of focusing of on-axis and off-axis light by a spherical-
aberration-free metasurface singlet lens. (
b
) Simulated focal plane intensity for different incident angles. Scale bar, 2
m
m. (
c
,
d
) Similar illustration and
simulation results as presented in
a
,
b
but for a metasurface doublet lens corrected for monochromatic aberrations. Scale bar, 2
m
m. Both lenses have
aperture diameter of 800
m
m and focal length of 717
m
m(
f
-number of 0.9) and the simulation wavelength is 850 nm. See Methods for details.
cd
Top side
Bottom side
1 mm
ab
100
150
200
250
0
1
Diameter (nm)
|
t
|
2
t
/(2

)
1
t
Transmission (a.u.)
Fused silica
SU-8
Side view
Top view
Unit cell
Amorphous
silicon
Figure 2 | Monolithic metasurface doublet lens.
(
a
) A schematic illustration of the dielectric metasurface used to implement the metasurface doublet
lens. The metasurface is composed of an array of amorphous silicon nano-posts covered with a layer of SU-8 polymer and arranged in a hexagonal lattice.
(
b
) Simulated intensity transmission (|
t
|
2
) and the phase of transmission coefficient (
+
t
) of the metasurface shown in
a
with identical nano-posts as a
function of the nano-posts’ diameter. The diameters with low transmission values, which are highlighted by two grey rectangles, are excluded from th
e
designs. The nano-posts are 600 nm tall, the lattice constant is 450 nm, and the simulation wavelength is 850 nm. (
c
) Schematic drawing of the monolithic
metasurface doublet lens composed of two metasurfaces on two sides of a 1-mm-thick fused silica substrate, an aperture stop and a field stop. The
photographs of the top and bottom sides of an array of doublet lenses are also shown. (
d
) Scanning electron micrographs showing a top and an oblique
view of the amorphous silicon nano-posts composing the metasurfaces. Scale bars, 1
m
m.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
ARTICLE
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
3
in Fig. 3b. We measured a focusing efficiency of
B
75% for the
singlet, and did not observe a detectable difference between the
focal spots measured with transverse electric and transverse
magnetic polarizations. The measured relative location of the
doublet lens focal spot as a function of incident angle is shown in
Fig. 3e along with the
f
sin(
y
) curve. The good agreement between
the measured data and the curve indicates that the metasurface
doublet lens can be used as an orthographic fisheye lens or a wide
angle Fourier transform lens
20
. Also, the specific
f
sin(
y
) fisheye
distortion of the image leads to a uniform brightness over
the image plane
21
.
Imaging performance
. We characterized the imaging perfor-
mance of the metasurface doublet lens using the experimental
setup shown in Fig. 4a. A pattern printed on a letter-size paper
was used as an object. The object was placed
B
25 cm away from
the metasurface doublet lens and was illuminated by an LED
(centre wavelength: 850 nm, bandwidth: 40 nm, spectrum shown
in Supplementary Fig. 3). The image formed by the doublet lens
was magnified by approximately

10 using an objective and a
tube lens and captured by a camera. A bandpass filter with 10 nm
bandwidth (see Supplementary Fig. 3 for the spectrum) was used
to spectrally filter the image and reduce the effect of chromatic
aberration on the image quality. Figure 4b shows the image
captured by the camera, and its insets depict the zoomed-in views
of the image at 0
°
,15
°
and 30
°
view angles. For comparison, an
image captured using the same setup but with the metasurface
singlet lens is shown in Fig. 4c. The objective lens used for
magnifying the images has a smaller NA than the metasurface
lenses and limits the resolution of the captured images
(see Supplementary Fig. 4 for an image taken with a higher NA
objective).
Any imaging system can be considered as low pass spatial filter
whose transfer function varies across the field of view. For
incoherent imaging systems, the transfer function for each point
in the field of view can be obtained by computing the Fourier
transform of the focal spot intensity. The modulus of this transfer
0
20
40
60
80
Focusing efficiency (%)
Incident angle (degree)
TE
TM
10
02030
0
100
200
300
400
Focal spot location (
μ
m)
Incident angle (degree)
10
02030

=0°
10°
20°
30°
Measured TM
Measured TE
Simulated
0
1
Intensity (a.u.)

=0°
2.5°
0
1
Intensity (a.u.)
Simulated
Measured
Doublet lens
Camera
Tube lens
Polarizer
Collimator
Polarization
controller
Laser
×100
0.95 NA
z
x
y
x
y
x
y
a
b
c
d
e

Figure 3 | Measured and simulated focal spots of the metasurface doublet and singlet lenses.
(
a
) Schematic drawing of the measurement setup.
(
b
) Simulated and measured focal plane intensity profiles of the metasurface doublet lens for different incident angles (
y
). Simulation results are shown in
the top row, and the measurement results for the transverse electric (TE) and the transverse magnetic (TM) polarizations are shown in the second
and third rows, respectively. Simulation results are obtained using scalar approximation (that is, ignoring polarization dependence). Scale bar,
2
m
m.
(
c
) Simulated and measured focal plane intensity profiles for a metasurface singlet with the same aperture diameter and focal length as the metasurface
doublet. For the range of angles shown, the measured intensity distributions are polarization insensitive. Scale bar, 2
m
m. (
d
) Measured focusing efficiency
of the metasurface doublet for TE- and TM-polarized incident light as a function of incident angle. The measured data points are shown by the symbols an
d
the solid lines are eye guides. (
e
) Transverse location of the focal spot for the doublet lens as a function of incident angle. The measured data points are
shown by the symbols, and the solid line shows the
f
sin(
y
) curve, where
f
¼
717
m
m is the focal length of the metasurface doublet lens.
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
4
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
function is referred to as the modulation transfer function (MTF)
and represents the relative contrast of the image versus the spatial
details of the object. The MTFs for the metasurface doublet and
singlet lenses were computed using the measured focal spots
(Fig. 3b,c) and are shown in Fig. 4d,e, respectively. Both the
images and the MTFs shown in Fig. 4b–e demonstrate the
effectiveness of correction achieved by cascading two metasur-
faces, and the diffraction limited performance of the metasurface
doublet lens over a wide field of view.
Miniature metasurface camera
. To further demonstrate the
use of this technology in imaging applications, we realized a
miniature planar camera by using a metasurface doublet lens and
a CMOS image sensor as schematically shown in Fig. 4f.
To compensate for the light propagating through the cover glass
protecting the image sensor, another doublet lens was optimized
(see Metasurface Doublet Lens II in Supplementary Fig. 5). The
total dimensions of the camera (including the image sensor) are
1.6 mm

1.6 mm

1.7 mm. The miniature camera was char-
acterized using the setup shown in Fig. 4g and by imaging
the object shown in Fig. 4a, which was illuminated by a filtered
LED (centre wavelength: 850 nm, bandwidth: 10 nm, see
Supplementary Fig. 3 for the spectrum). The image captured by
the image sensor is also shown in Fig. 4g, which shows a wide
field of view. The camera’s image quality is reduced by the
0
400
800
1,200
MTF (a.u.)
0
0.5
1
Frequency (cycles per mm)
Diffraction limit
2.5°
0
400
800
1,200
0
0.5
1
Frequency (cycles per mm)
MTF (a.u.)
Diffraction limit
20°
10°
30°
LED
25 cm
740 pixels
Filter
1.7 mm
1.6 mm
Correcting metasurface
Focusing metasurface
CMOS image sensor
Stop
Camera
Tube lens
LED
Object
25 cm
01020
mm
01020
mm
01020
mm
28 cm
Filter
Image plane
Objective
lens
×10
0.3 NA
15°
30°
15°
30°
a
bc
de
fg
Figure 4 | Imaging with the metasurface doublet lens.
(
a
) Schematic of the measurement setup. A pattern printed on a letter-size paper is used as the
object. The image formed by the metasurface camera is magnified by the combination of the objective lens and the tube lens and is captured by the
camera. A bandpass filter (centre wavelength: 850 nm, FWHM bandwidth: 10 nm) is placed between the objective and tube lens to reduce chromatic
aberrations. (
b
) Image taken with the metasurface doublet lens and (
c
) with the spherical-aberration-free metasurface singlet lens. Scale bar, 100
m
m. The
insets show zoomed-in views of the images at the locations indicated by the rectangles with the same outline colours which correspond to viewing angle
s
of 0
°
,15
°
and 30
°
. Scale bar, 10
m
m. (
d
,
e
) Modulation transfer function (MTF) of the metasurface doublet and singlet lenses, respectively. The solid and
dashed lines show the MTF in the tangential plane (along
x
in Fig. 3b) and sagittal plane (along
y
in Fig. 3b), respectively. The diffraction limited MTF of a
lens with aperture diameter of 800
m
m and focal length of 717
m
m is also shown for comparison. (
f
) Schematic drawing of a miniature planar camera
realized using a metasurface doublet lens and a CMOS image sensor. (
g
) Imaging setup and the image captured by the miniature camera. Scale bar,
100
m
m. The bandpass filter (centre wavelength: 850 nm, FWHM bandwidth: 10 nm) placed in front of the LED reduces the chromatic aberration.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
ARTICLE
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
5
nonuniform sensitivity of the image sensor pixels to the 850 nm
light due to the colour filters, and by its larger-than-optimal pixel
size. Therefore, the image quality can be improved by using
a monochromatic image sensor with a smaller pixel size (the
optimum pixel size for the miniature camera is
B
0.4
m
m based
on the MTFs shown in Fig. 4d). Thus, the miniature camera
benefits from the current technological trend in pixel size
reduction.
The intensity of the image formed by a camera only depends
on the NA of its lens (it is proportional to 1/
f
-number
2
¼
4NA
2
(ref. 22)); therefore, the metasurface miniature camera collects a
small optical power but forms a high brightness image.
Furthermore, the metasurface doublet lens is telecentric in the
image space, and light is incident on the image sensor with the
uniform angular distribution (Supplementary Fig. 5), and thus
removing the need for the variable incident angle correction in
the image sensor.
Correcting chromatic abberations
. The metasurface doublet lens
suffers from chromatic aberrations that reduce the image quality
of the miniature camera as the illumination bandwidth increases.
Simulated focal spots of the metasurface doublet lens for different
illumination bandwidths and the corresponding MTFs are shown
in Fig. 5a,b, respectively. See Supplementary Fig. 6 for the off-axis
MTFs. As it can be seen from the MTFs, the imaging resolution
decreases as the illumination bandwidth increases. This effect can
be seen as reduced contrast and lower resolution in the image
shown in Fig. 5c (40 nm bandwidth illumination) compared with
the image shown in Fig. 5d (10 nm bandwidth illuminations). For
the imaging purpose, the fractional bandwidth of a metasurface
lens is proportional to
l
=
f
NA
2
ðÞ
(Supplementary Note 1) and
can be increased by reducing the NA of the metasurface lens and
its focal length. Also, since the MTFs of the metasurface doublet
lens shown in Fig. 5b have significant high-frequency compo-
nents, the unfavourable effect of chromatic aberration can to
some extent be corrected using Wiener deconvolution
23
.
Figure 5e shows the deconvolution results of the image shown
in Fig. 5c that is taken with a 40-nm-bandwidth illumination
(see Methods for the details). As expected, the deconvolved image
appears sharper and has a higher contrast than the original image;
however, deconvolution also amplifies the noise, limiting its
applicability for correcting the chromatic aberrations over a
significantly wider bandwidth.
Discussion
The metasurface doublet lens and camera can be further
miniaturized by reducing the thickness of the substrate, the
diameters of the metasurface lenses, the focal length of the lens,
and the distance to the image sensor by the same scale factor,
while using the same nano-post metasurface design presented in
Fig. 2. For example, a 10

smaller camera (160
m
m

160
m
m

170
m
m) can be designed and fabricated using a similar
procedure on a 100-
m
m-thick fused silica substrate. Such a
camera would have 10

larger bandwidth compared with the
miniature camera presented here, the same image plane intensity,
but with 10

smaller image and 100

lower number of
distinguishable pixels (94

94 pixels instead of 940

940).
Compared with other miniature lenses reported previously
24–26
and Awaiba NanEye camera (http://www.awaiba.com), the
metasurface doublet offers significantly smaller
f
-number
and better correction for monochromatic aberrations that
lead to brighter images with higher resolution; however,
they have larger chromatic aberration (that is, narrower
bandwidth).
The miniature metasurface camera concept can be extended for
colour and hyperspectral imaging by using a set of metasurfaces
that are designed for different centre wavelengths and fabricated
side by side on the same chip. Each of the metasurface doublet
lenses forms an image on a portion of a single monochromatic
image sensor. High-quality thin-film colour filters with different
centre wavelengths can be directly deposited on the correcting
metasurface of each doublet lens, and the colour filter efficiency
issues associated with small size colour filters will be avoided
27,28
.
Also, multiwavelength metasurface lenses that work at multiple
discrete wavelengths have been demonstrated
29–32
. However,
the multiwavelength metasurfaces exhibit the same chromatic
dispersion (that is, d
f
=
d
l
) and thus similar chromatic aberrations
as the single wavelength metasurface lenses. The amorphous
silicon metasurfaces have negligible absorption loss for wave-
lengths above 650 nm. For shorter wavelengths, materials with
lower absorption loss such as polycrystalline silicon, gallium
phosphide, titanium dioxide
33,34
or silicon nitride
35,36
can be
used.
The metasurface-enabled camera we reported here has a flat
and thin form factor, small
f
-number, and exhibits nearly
diffraction limited performance over a large field of view. From
a manufacturing standpoint, the metasurface doublets have
several advantages over conventional lens modules. Conventional
lens modules are composed of multiple lenses that are separately
manufactured and later aligned and assembled together to form
the module. On the other hand, the metasurface doublets are
batch manufactured with simultaneous fabrication of tens of
thousands of doublets on each wafer, and with the metasurfaces
aligned to each other using lithographic steps during fabrication.
Furthermore, the assembly of the conventional lens modules with
the image sensors has to be done in a back-end step, but the
metasurface doublet can be monolithically stacked on top of
image sensors. More generally, this work demonstrates a vertical
on-chip integration architecture for designing and manufacturing
optical systems, which is enabled through high performance
metasurfaces. This architecture will enable low-cost realization of
conventional optical systems (for example, spectrometers, 3D
scanners, projectors, microscopes and so on), and systems with
novel functionalities in a thin and planar form factor with
immediate applications in medical imaging and diagnostics,
surveillance and consumer electronics.
Methods
Simulation and design
.
The phase profiles of the two metasurfaces composing the
doublet lenses were obtained through the ray tracing technique using a commercial
optical design software (Zemax OpticStudio, Zemax LLC). The phase profiles were
defined as even order polynomials of the radial coordinate
r
as
fr
ðÞ¼
X
5
n
¼
1
a
n
r
R

2
n
;
ð
1
Þ
where
R
is the radius of the metasurface, and the coefficients
a
n
were optimized for
minimizing the focal spot size (root mean square spot size) at incident angles up
to 30
°
. Two different metasurface doublet lenses were designed. The first doublet
lens (metasurface doublet lens I) is optimized for focusing incident light in air,
and was used in measurements shown in Figs 3 and 4b,d. The second doublet lens
(metasurface doublet lens II) is optimized for focusing through the
B
445-
m
m-thick
cover glass of the CMOS image sensor, and was used in the implementation of
the miniature camera as shown in Fig. 4f,g. The optimal values of the coefficients
for the two doublet lenses are listed in Supplementary Tables 1 and 2, and
the corresponding phase profiles are plotted in Supplementary Fig. 7. The
phase profile for the spherical-aberration-free metasurface singlet is given by
fr
ðÞ¼
2
p
=
l
ðÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
2
þ
f
2
p
, where
f
¼
717
m
m is the focal length of the singlet
(which is the same as the focal length of the doublet lens I).
The simulation results shown in Figs 1b,d and 2b,c and Supplementary Fig. 2
were computed assuming the metasurfaces operate as ideal phase masks (that
is, their phase profile is independent of the incident angle). Incident light was
modelled as a plane wave and optical waves passing through the metasurfaces were
propagated through the homogeneous regions (that is, fused silica and air) using
the plane wave expansion technique
37
. The simulated focal plane intensity results
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
6
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
for wideband incident light, which are shown Fig. 5a, were obtained by computing
a weighted average of the optical intensity at several discrete wavelengths in
the bandwidth of the incident light. The weights were chosen according to the
power density of incident light (Fig. 5a, bottom) assuming the diffraction efficiency
of the metasurfaces is constant over the incident light’s bandwidth. This
assumption is justified because the efficiency of dielectric nano-post metasurfaces
does not vary significantly over
B
10% fractional bandwidth
7
. The simulated
bandwidth-dependent modulation transfer function of the metasurface doublet
lens shown in Fig. 5b and Supplementary Fig. 6 were obtained by taking the Fourier
transform of the simulated focal plane intensity distributions presented in Fig. 5a.
Simulated transmission data of the periodic array of amorphous silicon nano-
posts presented in Fig. 2b were obtained by using the rigorous coupled wave
analysis technique using a freely available software package
38
. The simulations were
performed at
l
¼
850 nm. The amorphous silicon nano-posts (with refractive
index of 3.6 at 850 nm) are 600 nm tall, rest on a fused silica substrate (refractive
index of 1.45), and are cladded with a layer of the SU-8 polymer (refractive index
of 1.58 at 850 nm). The imaginary part of the refractive index of amorphous silicon
is smaller than 10

4
at 850 nm and was ignored in the simulations. The nano-
posts are arranged in a hexagonal lattice with the lattice constant of
a
¼
450 nm.
For normal incidence, the array is non-diffractive in both SU-8 and fused silica at
wavelengths longer than
l
¼
n
SU

8
ffiffiffi
3
p
=
2
a
¼
616 nm. The refractive indices of
amorphous silicon and SU-8 polymer were obtained through variable angle
spectroscopic measurements.
The metasurface patterns were generated using their phase profiles
fr
ðÞ
and
the relation between the transmission and the diameter of the nano-posts shown
in Fig. 2b. The diameter of the nano-post at each lattice site (
d
) was chosen to
Deconvolved, FWHM: 40 nm
15°
Measured, FWHM: 10 nm
15°
0
10
20
40
FWHM (nm)
0
400
800
1,200
0
0.5
1
Frequency (cycles per mm)
MTF (a.u.)
0 nm
10 nm
20 nm
a
40 nm
0
1
Intensity (a.u.)
bc
de
850
Wavelength (nm)
Power density (a.u.)
0
1
0.5
FWHM
θ

=0°

=15°
FWHM:
Measured, FWHM: 40 nm
15°
x
z
y
x
y
Figure 5 | Chromatic aberration of metasurface doublet lens and its correction.
(
a
) Illustration of focusing of wideband light by a metasurface doublet
lens. The spectrum of the incident light (shown at the bottom) is assumed as a Gaussian function centred at the design wavelength of the doublet lens
(850 nm). Simulated focal plane intensity for the metasurface doublet lens as a function of incident light’s bandwidth for incident angles of 0
°
and 15
°
are
shown on the right. Scale bar, 2
m
m. (
b
) On-axis modulation transfer function (MTF) of the metasurface doublet lens for different bandwidth of incident
light. The MTF is computed using the simulation results shown in
a
.(
c
) Image formed by the metasurface doublet lens with unfiltered LED illumination
(40 nm FWHM bandwidth) and (
d
) with filtered LED illumination (10 nm FWHM bandwidth). Scale bar, 100
m
m. See Supplementary Fig. 3 for the spectra.
The images are captured using the setup shown in Fig. 4a but with a higher magnification objective (

20, 0.4 NA). (
e
) Result of chromatic aberration
correction for the image shown in
d
. Scale bar, 100
m
m. The insets in
c
e
show zoomed-in views of the images at the locations indicated by the rectangles
with the same outline colours corresponding to viewing angles of 0
°
(red border) and 15
°
(green border), and the scale bars shown in the insets represent
10
m
m. FWHM, full width at half maximum.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
ARTICLE
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
7
minimize the transmission error defined as
E
¼
td
ðÞ
exp
i
f
ðÞ
jj
, which is the
difference between the nano-post transmission
t
(
d
) and the desired transmission
exp
i
f
ðÞ
. The nano-posts diameters corresponding to low transmission, which are
highlighted in Fig. 2b, are automatically avoided in this selection process, as the low
transmission amplitude results in a large transmission error.
Device fabrication
.
The metasurfaces forming the doublet lenses shown in Fig. 2c
were fabricated on both sides of a 1-mm-thick fused silica substrate. The substrate
was cleaned using a piranha solution and an oxygen plasma. A 600-nm-thick
layer of hydrogenated amorphous silicon was deposited on each side of the
substrate using the plasma enhanced chemical vapour deposition technique with
a 5% mixture of silane in argon at 200
°
C. Next, the nano-post patterns for the
correcting metasurfaces were defined on one side of the substrate as follows. First
a
B
300-nm-thick positive electron resist (ZEP-520A) was spin coated on the
substrate and baked at 180
°
C for 5 min. Then a
B
60-nm-thick layer of a water
soluble conductive polymer (aquaSAVE, Mitsubishi Rayon) was spin coated on the
resist to function as a charge dissipating layer during electron-beam patterning.
The metasurface patterns and alignment marks were written on the resist using
electron-beam lithography. The conductive polymer was then dissolved in water
and the resist was developed in a resist developer solution (ZED-N50, Zeon
Chemicals). A 70-nm-thick layer of aluminium oxide was deposited on the resist
and was patterned by lifting-off the resist in a solvent (Remover PG, MicroChem).
The patterned aluminium oxide was then used as the hard mask in dry etching of
the underlying amorphous silicon layer. The dry etching was performed in a
mixture of SF
6
and C
4
F
8
plasmas using an inductively coupled plasma reactive ion
etching process. Next, the aluminium oxide mask was dissolved in a 1:1 mixture of
ammonium hydroxide and hydrogen peroxide heated to 80
°
C. Figure 2d shows
scanning electron micrographs of the top and oblique view of the nano-posts at this
step of the fabrication process. The metasurfaces were then cladded by the SU-8
polymer (SU-8 2002, MicroChem) that acts as a protective layer for the meta-
surfaces during the processing of the substrate’s backside. A
B
2-
m
m-thick layer of
SU-8 was spin coated on the sample, baked at 90
°
C for 5 min, and reflowed at
200
°
C for 30 min to achieve a completely planarized surface. The SU-8 polymer
was then ultraviolet exposed and cured by baking at 200
°
C for another 30 min. The
complete planarization of the metasurfaces, and the void-free filling of the gaps
between the nano-posts were verified by cleaving a test sample fabricated using
a similar procedure and inspecting the cleaved cross section using a scanning
electron microscope.
The focusing metasurfaces were patterned on the backside of the substrate using
a procedure similar to the one used for patterning the correcting metasurfaces.
To align the top and bottom metasurface patterns, a second set of alignment
marks was patterned on the backside of the substrate and aligned to the topside
alignment marks using optical lithography. The focusing metasurface pattern was
subsequently aligned to these alignment marks. The aperture and field stops were
then patterned by photo-lithography, deposition of chrome/gold (10 nm/100 nm)
layers, and photoresist lift-off. To reduce the reflection at the interface between
SU-8 and air, a
B
150-nm-thick layer of hydrogen silsesquioxane (XR-1541 from
Dow Corning with refractive index of 1.4 at 850 nm) was spin coated on both sides
of the substrate and baked at 180
°
C for 5 min.
Systematic fabrication errors due to non-optimal exposure dose in e-beam
lithography, or over and under etching will generally increase or decrease the nano-
post diameters almost by the same amount. To compensate for such errors, we
fabricated a set of devices (as shown in Fig. 2c) with all nano-post diameters biased
by the same amount (in steps of 5 nm) from their design values. All the devices in
the set showed similar focal spots, but with different focusing efficiencies. The
focusing efficiency at normal incidence decreased by
B
2.5% for every 5 nm error
in the nano-post diameters.
Measurement procedure and data analysis
.
The measurement results shown
in Fig. 3b–e were obtained using the experimental setup schematically shown in
Fig. 3a. An 850 nm semiconductor laser (Thorlabs L850P010, measured spectrum
shown in Supplementary Fig. 3) was coupled to a single mode fibre. The fibre
passed through a manual polarization controller and was connected to a fibre
collimation package (Thorlabs F220APC-780, 1/
e
2
beam diameter:
B
2.3 mm). The
collimated beam was passed through a linear polarizer (Thorlabs LPNIR050-MP)
that sets the polarization of light incident on the doublet. The collimator and the
polarizer were mounted on a rotation stage whose rotation axis coincides with the
metasurface doublet lens. The focal plane of the doublet lens was imaged using an
objective lens, a tube lens (Thorlabs AC254-200-B, focal length: 20 cm) and a
camera (Photometrics CoolSNAP K4, pixel size: 7.4
m
m). A

100 objective lens
(Olympus UMPlanFl, NA
¼
0.95) was used in measurements shown in Fig. 3b–d,
and a

50 objective lens (Olympus LMPlanFl N, NA
¼
0.5) with a larger field
of view was used for obtaining the focal spot position data shown in Fig. 3e.
A calibration sample with known feature sizes was used to accurately determine
the magnification of the objective/tube lens combination for both of the objectives.
The dark noise of the camera was subtracted from the measured intensity images
shown in Fig. 3b,c.
The focusing efficiency presented in Fig. 3d is defined as the ratio of the optical
power focused by the lens to the optical power incident on the lens aperture. The
focusing efficiency for the normal incidence (zero incident angle) was measured by
placing a 15-
m
m-diameter pinhole in the focal plane of the doublet lens and
measuring the optical power passed through the pinhole and dividing it by the
power of the incident optical beam. For this measurement, the 1/
e
2
diameter of the
incident beam was reduced to
B
500
m
m by using a lens (Thorlabs LB1945-B, focal
length: 20 cm) to ensure that more than 99% of the incident power passes through
the aperture of the doublet lens (800
m
m input aperture diameter). The incident
and focused optical powers were measured using an optical power meter (Thorlabs
PM100D with Thorlabs S122C power sensor). The pinhole was a 15-
m
m-diameter
circular aperture formed by depositing
B
100 nm chrome on a fused silica substrate
and had a transmission of
B
94% (that is, 6% of the power was reflected by the
two fused silica/air interfaces), therefore the reported focusing efficiency values
presented in Fig. 3d underestimate the actual values by a few percent.
The focusing efficiency values for non-zero incident angles were found using
the focal spot intensity distributions captured by the camera and the directly
measured focusing efficiency for normal incidence. First, the focused optical
powers for different incident angles were obtained by integrating the focal plane
intensity distributions within a 15-
m
m-diameter circle centred at the intensity
maximum. The intensity distributions were captured by the camera when the
doublet was illuminated by a large diameter beam (1/
e
2
beam diameter of
B
2.3 mm) and the dark noise of the camera was subtracted from the recorded
intensities before integration. Next, the focused optical powers for different
incident angles were compared with the focused power at normal incidence and
corrected for the smaller effective input aperture (that is, a cos(
y
) factor). The
measurement was performed for transverse electric (with electric field parallel to
the doublet lens’s surface) and transverse magnetic (with magnetic field parallel to
the doublet lens’s surface) polarizations of the incident beam.
The images presented in Fig. 4b,c were captured using the experimental setup
schematically shown in Fig. 4a. A pattern was printed on a letter-size paper
(
B
22 cm

28 cm) and used as an object. The object was placed in front of the
metasurface lens at a distance of
B
25 cm from it. Three ruler marks were also
printed as a part of the pattern at viewing angles of 0
°
,15
°
and 30
°
. The object was
illuminated by an 850 nm LED (Thorlabs LED851L, measured spectrum shown in
Supplementary Fig. 3). The images formed by the metasurface lenses were
magnified by approximately

10 using an objective lens (Olympus UMPlanFl,

10, NA
¼
0.3) and a tube lens (Thorlabs AC254-200-B, focal length: 20 cm).
A bandpass filter (Thorlabs FL850-10, centre wavelength: 850 nm, full width at half
maximum (FWHM) bandwidth: 10 nm) was placed between the objective lens and
the tube lens. The placement of the filter between the objective and the tube lens
did not introduce any discernible aberrations to the optical system. The magnified
images were captured using a camera (Photometrics CoolSNAP K4) with pixel
size of 7.4
m
m. The images shown in Fig. 5c,d and Supplementary Fig. 4 were
also captured using the same setup but with different objective lenses (Olympus
LMPlanFl,

20, NA
¼
0.4 for Fig. 5c,d and Olympus LMPlanFl N,

50, NA
¼
0.5
for Supplementary Fig. 4).
The miniature camera schematically shown in Fig. 4f is composed of the
metasurface doublet lens II (with parameters listed in Supplementary Table 2) and
a low-cost colour CMOS image sensor (OmniVision OV5640, pixel size: 1.4
m
m)
with a cover glass thickness of 445
±
20
m
m. An air gap of 220
m
m was set between
the metasurface doublet lens and the image sensor to facilitate the assembly of the
camera. The metasurface doublet was mounted on a 3-axis translation stage during
the measurements. To set the distance between the image sensor chip and the
doublet, a far object was imaged and the distance was adjusted until the image was
brought into focus.
The modulation transfer functions shown in Fig. 4d,e were computed by taking
the Fourier transform of the measured focal plane intensity distributions shown in
Fig. 3b,c, respectively. The dark noise of the camera was first subtracted from the
recorded intensity distributions. The diffraction limit curves shown in Fig. 4d,e are
the simulated modulation transfer function of a diffraction limited lens (that is,
Fourier transform of the diffraction limited Airy disk) with the same focal length
(
f
¼
717
m
m) and aperture diameter (
D
¼
800
m
m) as the metasurface doublet and
singlet lenses used in the measurements.
The image shown in Fig. 5e was obtained using Wiener deconvolution
23
, and by
filtering the image shown in Fig. 5c by the Wiener filter
H
n
ðÞ¼
MTF
n
ðÞ
MTF
2
n
ðÞþ
N
n
ðÞ
=
S
n
ðÞ
;
ð
2
Þ
where
n
is the spatial frequency, MTF
n
ðÞ
is the on-axis modulation transfer
function of the metasurface doublet lens for illumination with 40 nm FWHM
bandwidth (shown in Fig. 5b), and
N
n
ðÞ
and
S
n
ðÞ
are the power spectral densities
of the noise and the image, respectively. The noise was assumed to be white (that is,
constant power spectral density), and
S
n
ðÞ
was assumed to be equal to the power
spectral density of an image formed with a diffraction limited imaging system with
NA
¼
0.4 (that is, the NA of the objective lens used for magnification in the
experimental setup). The signal to noise ratio was found as
B
250 by estimating the
camera’s noise, and was used to set the constant value for
N
n
ðÞ
.
Data availability
.
The data that support the finding of this study are available
from the corresponding author upon request.
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
8
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
References
1. Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Planar photonics with
metasurfaces.
Science
339,
1232009 (2013).
2. Yu, N. & Capasso, F. Flat optics with designer metasurfaces.
Nat. Mater.
13,
139–150 (2014).
3. Meinzer, N., Barnes, W. L. & Hooper, I. R. Plasmonic meta-atoms and
metasurfaces.
Nat. Photon
8,
889–898 (2014).
4. Jahani, S. & Jacob, Z. All-dielectric metamaterials.
Nat. Nanotechnol.
11,
23–36
(2016).
5. Zhang, L., Mei, S., Huang, K. & Qiu, C.-W. Advances in full control of
electromagnetic waves with metasurfaces.
Adv. Opt. Mater.
4,
818–833 (2016).
6. Vo, S.
et al.
Sub-wavelength grating lenses with a twist.
IEEE Photon. Technol.
Lett.
26,
1375–1378 (2014).
7. Arbabi, A., Horie, Y., Ball, A. J., Bagheri, M. & Faraon, A. Subwavelength-thick
lenses with high numerical apertures and large efficiency based on high-
contrast transmitarrays.
Nat. Commun.
6,
7069 (2015).
8. Zheng, G.
et al.
Metasurface holograms reaching 80% efficiency.
Nat.
Nanotechnol.
10,
308–312 (2015).
9. 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.
10,
937–943 (2015).
10. Arbabi, A., Briggs, R. M., Horie, Y., Bagheri, M. & Faraon, A. Efficient dielectric
metasurface collimating lenses for mid-infrared quantum cascade lasers
Opt. Express
23,
33310–33317 (2015).
11. Fossum, E. R. CMOS image sensors: electronic camera-on-a-chip.
IEEE Trans.
Electron Devices
44,
1689–1698 (1997).
12. Fattal, D., Li, J. J., Peng, Z., Fiorentino, M. & Beausoleil, R. G. Flat dielectric
grating reflectors with focusing abilities.
Nat. Photon.
4,
466–470 (2010).
13. Aieta, F.
et al.
Aberration-free ultrathin flat lenses and axicons at telecom
wavelengths based on plasmonic metasurfaces.
Nano Lett.
12,
4932–4936 (2012).
14. Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient
metasurface optical elements.
Science
345,
298–302 (2014).
15. Arbabi, A.
et al.
In
CLEO: Optical Society of America STu3M.4
(San Jose,
CA, USA, 2014). Available at http://www.opticsinfobase.org/abstract.cfm?URI=
CLEO_SI-2014-STu3M.4.
16. Welford, W. T. Aplanatic hologram lenses on spherical surfaces.
Opt. Commun.
9,
268–269 (1973).
17. Bokor, N. & Davidson, N. Aberration-free imaging with an aplanatic curved
diffractive element.
Appl. Opt.
40,
5825–5829 (2001).
18. Aieta, F., Genevet, P., Kats, M. & Capasso, F. Aberrations of flat lenses and
aplanatic metasurfaces.
Opt. Express
21,
31530–31539 (2013).
19. Kamali, S. M., Arbabi, A., Arbabi, E., Horie, Y. & Faraon, A. Decoupling optical
function and geometrical form using conformal flexible dielectric metasurfaces.
Nat. Commun.
7,
11618 (2015).
20. Buralli, D. A. & Morris, G. M. Design of a wide field diffractive landscape lens.
Appl. Opt.
28,
3950–3959 (1989).
21. Reiss, M. Notes on the cos
4
law of illumination.
J. Opt. Soc. Am.
38,
980–986
(1948).
22. Smith, W. J.
Modern Optical Engineering: the Design of Optical Systems
4th edn
(McGraw Hill, 2008).
23. Wiener, N.
Extrapolation, Interpolation, and Smoothing of Stationary Time
Series
(The MIT Press, 1964).
24. Han, H., Kriman, M. & Boomgarden, M. in
2010 11th International Conference
on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP),
121-124 (Xi’an, China, 2010).
25. Wippermann, F., Mu
̈ller, M., Wa
̈
ny, M. & Voltz, S.
in SPIE Optical
Engineering
þ
Applications,
Vol. 9192, 91920Z-91920Z-6 (San Diego, CA, USA,
2014).
26. Gissibl, T., Thiele, S., Herkommer, A. & Giessen, H. Two-photon direct laser
writing of ultracompact multi-lens objectives.
Nat. Photon.
10,
554–560 (2016).
27. Xu, T., Wu, Y. K., Luo, X. G. & Guo, L. J. Plasmonic nanoresonators for high-
resolution colour filtering and spectral imaging.
Nat. Commun.
1,
59 (2010).
28. Fesenmaier, C. C., Huo, Y. & Catrysse, P. B. Optical confinement methods for
continued scaling of CMOS image sensor pixels.
Opt. Express
16,
20457–20470
(2008).
29. Aieta, F., Kats, M. A., Genevet, P. & Capasso, F. Multiwavelength achromatic
metasurfaces by dispersive phase compensation.
Science
347,
1342–1345 (2015).
30. Arbabi, E., Arbabi, A., Kamali, S. M., Horie, Y. & Faraon, A. Multiwavelength
polarization insensitive lenses based on dielectric metasurfaces with meta-
molecules.
Optica
3,
628–633 (2016).
31. Arbabi, E., Arbabi, A., Kamali, S. M., Horie, Y. & Faraon, A. High efficiency
double-wavelength dielectric metasurface lenses with dichroic birefringent
meta-atoms.
Opt. Express
24,
18468–18477 (2016).
32. Arbabi, E., Arbabi, A., Kamali, S. M., Horie, Y. & Faraon, A. Multiwavelength
metasurfaces through spatial multiplexing.
Sci. Rep.
6,
32803 (2016).
33. Lalanne, P., Astilean, S., Chavel, P., Cambril, E. & Launois, H. Blazed binary
subwavelength gratings with efficiencies larger than those of conventional
e
́
chelette gratings.
Opt. Lett.
23,
1081 (1998).
34. Lalanne, P., Astilean, S., Chavel, P., Cambril, E. & Launois, H. Design and
fabrication of blazed binary diffractive elements with sampling periods
smaller than the structural cutoff.
J. Opt. Soc. Am. A
16,
1143–1156 (1999).
35. Zhan, A.
et al.
Low-contrast dielectric metasurface optics.
ACS Photonics
3,
209–214 (2016).
36. Ren, Y.
et al.
Orbital angular momentum-based space division multiplexing for
high-capacity underwater optical communications.
Sci. Rep.
6,
33306 (2016).
37. Born, M. & Wolf, E.
Principles of Optics
7th edn (Cambridge University Press,
1999).
38. Liu, V. & Fan, S. S
4
: a free electromagnetic solver for layered periodic structures.
Comput. Phys. Commun.
183,
2233–2244 (2012).
Acknowledgements
This work was supported by Samsung Electronics. A.A., E.A. and Y.H. were also
supported by DARPA. A.A. was also supported by National Science Foundation award
1512266. Y.H. was supported by a Japan Student Services Organization (JASSO)
fellowship. S.M.K., who was involved with the device fabrication, was supported by
the DOE ‘Light-Material Interactions in Energy Conversion’ Energy Frontier Research
Centre funded by the US Department of Energy, Office of Science, Office of Basic Energy
Sciences under Award no. DE-SC0001293. The device nanofabrication was performed
at the Kavli Nanoscience Institute at Caltech.
Author contributions
A.A. and A.F. conceived the experiment. A.A. designed and optimized the device with
suggestions from S.H. A.A., E.A., S.M.K. and Y.H. fabricated the sample. A.A. and E.A.
performed the measurements and analysed the data. A.A. and A.F. wrote the manuscript
with input from all authors.
Additional information
Supplementary Information
accompanies this paper at http://www.nature.com/
naturecommunications
Competing financial interests:
The authors declare no competing financial
interests.
Reprints and permission
information is available online at http://npg.nature.com/
reprintsandpermissions/
How to cite this article:
Arbabi, A.
et al.
Miniature optical planar camera based
on a wide-angle metasurface doublet corrected for monochromatic aberrations.
Nat. Commun.
7,
13682 doi: 10.1038/ncomms13682 (2016).
Publisher’s note:
Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
This work is licensed under a Creative Commons Attribution 4.0
International License. The images or other third party material in this
article are included in the article’s Creative Commons license, unless indicated otherwise
in the credit line; if the material is not included under the Creative Commons license,
users will need to obtain permission from the license holder to reproduce the material.
To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
r
The Author(s) 2016
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13682
ARTICLE
NATURE COMMUNICATIONS
| 7:13682 | DOI: 10.1038/ncomms13682 | www.nature.com/naturecommunications
9