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An optical metasurface planar camera
Amir Arbabi,
1
Ehsan Arbabi,
1
Seyedeh Mahsa Kamali,
1
Yu Horie,
1
Seunghoon Han,
1, 2
and Andrei Faraon
1,
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology,
1200 E. California Blvd., Pasadena, CA 91125, USA
2
Samsung Advanced Institute of Technology,
Samsung Electronics, Samsung-ro 130,
Suwon-si, Gyeonggi-do 443-803, South Korea
Abstract
Optical metasurfaces are 2D arrays of nano-scatterers that modify optical wavefronts at subwavelength
spatial resolution [1–5]. They are poised to revolutionize optical design by enabling complex low cost
systems where multiple metasurfaces are lithographically stacked on top of each other and are 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 an f-number of 0.9,
an angle-of-view larger than 60
×
60
, and operates at 850 nm wavelength with large transmission. The
camera exhibits high image quality, which indicates the potential of this technology to produce a paradigm
shift in future designs of imaging systems for microscopy, photography and computer vision.
faraon@caltech.edu
1
arXiv:1604.06160v1 [physics.optics] 21 Apr 2016
Optical systems such as cameras, spectrometers, and microscopes are conventionally made by
assembling discrete bulk optical components like lenses, gratings and filters. The optical compo-
nents are separately manufactured using cutting, polishing and grinding, and have to be manually
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 low-cost
miniature optical systems. As we show here, by using a camera as an example, metasurfaces enable
a vertical on-chip integration platform allowing implementation of optical systems by cascading
metasurface optical components and other planar optoelectronic devices like image sensors. In
this integration platform, multiple flat optical components are fabricated in different layers paral-
lel to the plane of the chip, and are lithographically aligned, thus forming a rigid optical system
and 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 [6]; however, the camera lenses are yet to be fully integrated with
the image sensor. The freedom in controlling the metasurface phase profiles has enabled imple-
mentation of spherical-aberration-free flat lenses that focus normally incident light to diffraction
limited spots (as schematically shown in Fig. 1a) [7–10]. Such lenses have been used in appli-
cations requiring focusing of an optical beam or collimating emission from an optical fiber or a
semiconductor laser [11]. However, as shown in Fig. 1b, 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 [12–14]. However, direct patterning of nano-structures on curved surfaces is challenging.
Although conformal metasurfaces might provide a solution [15], the resulting device would not be
flat. Another approach for correcting monochromatic aberrations of a metasurface lens is through
cascading and forming a metasurface doublet lens as schematically shown in Fig. 1c.
The doublet lens is composed of two metasurfaces behaving as polarization insensitive phase
plates which 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 holo-
graphic lenses, and it has been shown that such a combination can realize a fisheye lens with
significantly reduced monochromatic aberrations [16]. We used the ray tracing approach to opti-
mize the phase profiles of the two metasurfaces when they are separated by a 1-mm-thick fused
2
silica substrate. Simulation results of the focal plane spot for different incident angles (
θ
) are pre-
sented in Fig. 1d, showing nearly diffraction limited focusing by the doublet up to 30
incident
angle. The doublet lens has an input aperture diameter of 800
μ
m and a focal length of 717
μ
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 [10]. The metasurfaces are composed of hexagonal arrays of amorphous
silicon nano-posts with different diameters which rest on a glass substrate and are covered by the
SU-8 polymer. The nano-posts behave as truncated waveguides with circular cross sections sup-
porting Fabry-P
́
erot resonances [10, 15, 17]. The high refractive index between the nano-posts and
their surroundings leads to weak optical coupling among the nano-posts and allows for the imple-
mentation 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
π
phase coverage is achieved
with an average transmission over 96% (see Methods for details).
We fabricated the metasurfaces on both sides of a fused silica substrate by depositing amor-
phous 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 bot-
tom 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
(left: top view, right: oblique view).
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
φ
(
ρ
) =
(2
π/λ
)
ρ
2
+
f
2
,
ρ
: radial coordinate,
f
=717
μ
m: focal length,
D
=800
μ
m: aperture diameter) was also fabricated
3
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 Figs 3b and 3c, respectively (see Methods for details). The doublet lens
has a nearly diffraction limited focal spot for incident angles up to 30 degrees while the singlet
exhibits significant aberrations even at incident angles of a few degrees. As Figs 3b and 3c show,
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 to the
simulation results, which we attribute to a misalignment (estimated
2
μ
m along both
x
and
y
directions) between the top and bottom side patterns (see Fig. S1).
The focusing efficiency (ratio of the focused power to the incident power) for the metasurface
doublet lens is shown in Fig. 3d, and is
70% for normally incident light. The focusing efficiency
is polarization dependent, and its value for unpolarized light drops at the rate of
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 [10], undesired scattering due to the sidewall roughness of the
nano-posts, residual reflection at the air/SU-8 interfaces, and measurement artifacts (see Methods
for details). The focusing efficiency is lower for the transverse magnetic (TM) polarized light
compared with the transverse electric (TE) polarized light because of the excitation of some reso-
nances of the nano-posts with the axial component of the electric field of the incident light [15].
This also causes the slight difference between the TE and TM spot shapes for the 30
incident
light shown in Fig. 3b. We measured a focusing efficiency of
75% for the singlet, and did not
observe a detectable difference between the focal spots measured with TE and TM 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(
θ
)
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 [16]. Also, the specific
f
sin(
θ
)
fisheye distortion of
the image leads to a uniform brightness over the image plane [18].
We characterized the imaging performance of the metasurface doublet lens using the experi-
mental setup shown in Fig. 4a. A pattern printed on a letter-size paper was used as an object. The
object was placed
25 cm away from the metasurface doublet lens and was illuminated by an LED
(center wavelength: 850 nm, bandwidth: 40 nm, spectrum shown in Fig. S2). The image formed
by the doublet lens was magnified by
10
×
using an objective and a tube lens and captured by a
4
camera. A bandpass filter with 10 nm bandwidth (see Fig. S2 for the spectrum) was used to spec-
trally 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 Fig. S3 for an image taken with a higher NA objective). The modulation transfer functions
(MTFs), which represent the relative contrast of the image versus the spatial details of the object,
for the metasurface doublet and singlet lenses were computed using the measured focal spots (Figs
3b,c) and are shown in Figs 4d and 4e, respectively. Both the images and the MTFs shown in Figs
4b-d demonstrate the effectiveness of correction achieved by cascading two metasurfaces, and the
diffraction limited performance of the metasurface doublet lens over a wide field of view.
To further demonstrate the use of this technology in imaging applications, we realized a minia-
ture 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 Fig. S4).
The total dimensions of the camera (including the image sensor) are 1.6 mm
×
1.6 mm
×
1.7 mm.
The miniature camera was characterized using the setup shown in Fig. 4g and by imaging the
object shown in Fig. 4a which was illuminated by a filtered LED (center wavelength: 850 nm,
bandwidth: 10 nm, see Fig. S2 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 nonuniform sensitivity of the image sensor pixels to the 850 nm light due to the color 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 (which is
0.4
μ
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 pro-
portional to NA
2
); 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 im-
age space, and light is incident on the image sensor with the uniform angular distribution (see Fig.
S4), and thus removing the need for the variable incident angle correction in the image sensor.
The metasurface doublet lens suffers from chromatic aberrations that reduce the image quality
5
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 Figs 5a and 5b, respectively. See Fig. S5 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 illumina-
tions). For the imaging purpose, the fractional bandwidth of a metasurface lens is proportional to
λ/
(
f
NA
2
)
(see 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 sig-
nificant high frequency components, the unfavorable effect of chromatic aberration can to some
extent be corrected using Wiener deconvolution [19]. 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.
The miniature metasurface camera concept can be extended for color and hyperspectral imaging
by using a set of metasurfaces that are designed for different center 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 color filters with different
center wavelengths can be directly deposited on the correcting metasurface of each doublet lens,
and the color filter efficiency and crosstalk issues associated with small size color filters will
be avoided [20, 21]. Also, multiwavelength metasurface lenses which work at multiple discrete
wavelengths have been demonstrated [22, 23]. However, the multiwavelength metasurfaces exhibit
the same chromatic dispersion (i.e.
d
f/
d
λ
) and thus similar chromatic aberrations as the single
wavelength metasurface lenses. The amorphous silicon metasurfaces have negligible absorption
loss for wavelengths above 650 nm. For shorter wavelength, materials with lower absorption loss
such as polycrystalline silicon, gallium phosphide, or silicon nitride can be used [24].
The metasurface-enabled camera we reported here has a flat and thin form factor, exhibits
nearly diffraction limited performance over a large field of view, and can be monolithically man-
ufactured on top of image sensors using the high throughput microfabrication techniques used
in semiconductor industry. This work demonstrates a novel vertical on-chip integration architec-
ture for designing and manufacturing optical systems, which is enabled through high performance
6
metasurfaces. This architecture will enable low-cost realization of conventional optical systems
(e.g. spectrometers, 3D scanners, projectors, microscopes, etc.), as well as systems with novel
functionalities in a thin and planar form factor with immediate applications in medical imaging
and diagnostics, surveillance, and consumer electronics.
7
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 (Ze-
max OpticStudio, Zemax LLC). The phase profiles were defined as even order polynomials of the
radial coordinate
ρ
as
φ
(
ρ
) =
5
n
=1
a
n
(
ρ
R
)
2
n
,
(1)
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
445-
μ
m-thick cover glass of the CMOS image sensor, and was used in the implementation of the
miniature camera as shown in Figs 4f,g. The optimal values of the coefficients for the two doublet
lenses are listed in Tables S1 and S2, and the corresponding phase profiles are plotted in Fig.
S6. The phase profile for the spherical-aberration-free metasurface singlet is given by
φ
(
ρ
) =
(2
π/λ
)
ρ
2
+
f
2
, where
f
=717
μ
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, Figs 2b,c, and Fig. S1 were computed assuming the
metasurfaces operate as ideal phase masks (i.e. their phase profile is independent of the incident
angle). Incident light was modeled as a plane wave and optical waves passed though the metasur-
faces were propagated through the homogeneous regions (i.e. fused silica and air) using the plane
wave expansion technique [25]. The simulated focal plane intensity results 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
10% fractional bandwidth [10]. The simulated bandwidth-dependent modulation transfer
function of the metasurface doublet lens shown in Fig. 5b and Fig. S5 were obtained by taking the
Fourier transform of the simulated focal plane intensity distributions presented in Fig. 5a.
8
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 [26]. The simulations were performed at
λ
=
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 nano-posts are arranged in a hexagonal lattice with the lattice
constant of
a
=450 nm. For normal incidence, the array is non-diffractive in both SU-8 and fused
silica at wavelengths longer than
λ
=
n
SU
8
3
/
2
a
=
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
φ
(
ρ
)
and the relation be-
tween 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 minimize the transmission error defined as
E
=
|
t
(
d
)
exp(
)
|
, which is the difference between the nano-post transmission
t
(
d
)
and the de-
sired transmission
exp(
)
. The nano-posts diameters corresponding to low transmission, which
are highlighted in Fig. 2b, are automatically avoided in this selection process, as the low transmis-
sion 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 vapor 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
300-nm-
thick positive electron resist (ZEP-520A) was spin coated on the substrate and baked at 180
C for
5 min. Then a
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 aluminum oxide was deposited on the resist and was patterned by lifting-off the resist in a
solvent (Remover PG, MicroChem). The patterned aluminum 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
9
process. Next, the aluminum 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) which acts as a protective layer
for the metasurfaces during the processing of the substrate’s backside. A
2-
μ
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 UV 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 sub-
strate and aligned to the topside alignment marks using optical lithography. The focusing metasur-
face 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 pho-
toresist lift-off. To reduce the reflection at the interface between SU-8 and air, a
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
2.5% for every 5 nm error in the nano-post
diameters.
Measurement procedure and data analysis.
The measurement results shown in Figs 3b-e where
obtained using the experimental setup schematically shown in Fig. 3a. An 850 nm semiconductor
laser (Thorlabs L850P010, measured spectrum shown in Fig. S2) was coupled to a single mode
fiber. The fiber passed through a manual polarization controller and was connected to a fiber
collimation package (Thorlabs F220APC-780, 1/
e
2
beam diameter:
2.3 mm). The collimated
10
beam was passed through a linear polarizer (Thorlabs LPNIR050-MP) which 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
μ
m). A 100
×
objective lens (Olympus
UMPlanFl, NA=0.95) was used in measurements shown in Figs 3b-d, and a 50
×
objective lens
(Olympus LMPlanFl N, NA=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 Figs 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-
μ
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
500
μ
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
μ
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-
μ
m-diameter circular aperture formed by depositing
100 nm chrome on a
fused silica substrate and had a transmission of
94% (i.e. 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-
μ
m-diameter circle centered 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
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 incident
11
and corrected for the smaller effective input aperture (i.e. a
cos(
θ
)
factor). The measurement was
performed for transverse electric (TE, with electric field parallel to the doublet lens’s surface) and
transverse magnetic (TM, with magnetic field parallel to the doublet lens’s surface) polarizations
of the incident beam.
The images presented in Figs 4b,c were captured using the experimental setup schematically
shown in Fig. 4a. A pattern was printed on a letter-size paper (approximately 22 cm by 28 cm)
and used as an object. The object was placed in front of the metasurface lens at a distance of
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 Fig. S2). The images formed by the metasurface lenses were magnified by
approximately 10
×
using an objective lens (Olympus UMPlanFl, 10
×
, NA=0.3) and a tube lens
(Thorlabs AC254-200-B, focal length: 20 cm). A bandpass filter (Thorlabs FL850-10, center
wavelength: 850 nm, FWHM bandwidth: 10 nm) was placed between the objective lens and the
tube lens. The magnified images were captured using a camera (Photometrics CoolSNAP K4)
with pixel size of 7.4
μ
m. The images shown in Figs 5c,d and Fig. S3 were also captured using the
same setup but with different objective lenses (Olympus LMPlanFl, 20
×
, NA=0.4 for Figs 5c,d
and Olympus LMPlanFl N, 50
×
, NA=0.5 for Fig. S3).
The miniature camera schematically shown in Fig. 4f is composed of the metasurface doublet
lens II (with parameters listed in Table S2) and a low-cost color CMOS image sensor (OmniVision
OV5640, pixel size: 1.4
μ
m) with a cover glass thickness of 445
±
20
μ
m. An air gap of 220
μ
m
was set between the metasurface doublet lens and the image sensor to facilitate the assembly of
the camera.
The modulation transfer functions shown in Figs 4d,e were computed by taking the Fourier
transform of the measured focal plane intensity distributions shown in Figs 3b and 3c, respectively.
The dark noise of the camera was first subtracted from the recorded intensity distributions. The
diffraction limit curves shown in Figs 4d,e is the simulated modulation transfer function of a
diffraction limited lens (i.e. Fourier transform of a the diffraction limited Airy disk) with the
same focal length (
f
=717
μ
m) and aperture diameter (
D
=800
μ
m) as the metasurface doublet and
singlet lenses used in the measurements.
The image shown in Fig. 5e was obtained using Wiener deconvolution [19], and by filtering
12
the image shown in Fig. 5c by the Wiener filter
H(
ν
) =
MTF(
ν
)
MTF
2
(
ν
) + N(
ν
)
/
S(
ν
)
,
(2)
where
ν
is the spatial frequency,
MTF(
ν
)
is the on-axis modulation transfer function of the meta-
surface doublet lens for illumination with 40 nm FWHM bandwidth (shown in Fig. 5b), and
N(
ν
)
and
S(
ν
)
are the power spectral densities of the noise and the image, respectively. The noise was
assumed to be white (i.e. constant power spectral density), and
S(
ν
)
was assumed to be equal
to the power spectral density of an image formed with a diffraction limited imaging system with
NA=0.4 (i.e. the NA of the objective lens used for magnification in the experimental setup). The
signal to noise ratio was found as
250 by estimating the camera’s noise, and was used to set the
constant value for
N(
ν
)
.
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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. was supported by the DOE “Light-Material Interactions in Energy Conversion” Energy
Frontier Research Center funded by the US Department of Energy, Office of Science, Office of
Basic Energy Sciences under Award no. de-sc0001293. The device nanofabrication was per-
formed at the Kavli Nanoscience Institute at Caltech.
15
T
T
a
c
b
2
P
m
T
=0°
2.5°
0
1
Intensity (a.u.)
d
2
P
m
10°
20°
30°
0
1
Intensity (a.u.)
T
=0°
Fig. 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.
c
, and
d
, similar illustration and simulation results as presented in
a
and
b
but for a metasurface doublet lens corrected for monochromatic aberrations. Both lenses have
numerical aperture of 0.49 and the simulation wavelength is 850 nm. See Methods for details.
16
1
P
m
1
P
m
c
d
Top side
Bottom side
1 mm
ab
100
150
200
250
0
1
Diameter (nm)
|t|
2
‘
t /(2
S
)
1
t
Transmission (a.u.)
Fused silica
SU-8
Side view
Top view
Unit cell
amorphous
silicon
Fig. 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 and the phase of transmission coefficient 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 gray rectangles, are excluded from the 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
glass substrate, an aperture stop, and a field stop. The photographs of the top and bottom sides of an array
of doublet lenses are shown on the right.
d
, Scanning electron micrographs showing a top (left) and an
oblique view (right) of the amorphous silicon nano-posts composing the metasurfaces.
17
a
b
c
0
20
40
60
80
(QEWUKPIGHsEKGPE[ 
+PEKFGPVCPING FGITGG
TE
TM
10
02030
e
0
100
200
300
400
(QECNURQVNQECVKQP
P
O
+PEKFGPVCPING FGITGG
10
02030
T
=0°
10°
20°
30°
/GCUWTGF6/
/GCUWTGF6'
Simulated
2
P
m
0
1
+PVGPUKV[ CW
d
T
=0°
u
u
2
P
m
0
1
+PVGPUKV[ CW
Simulated
/GCUWTGF
Doublet lens
%COGTC
Tube lens
2QNCTK\GT
%QNNKOCVQT
2QNCTK\CVKQP
EQPVTQNNGT
.CUGT
T
100X
0#
\
x
[
x
[
x
[
Fig. 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 (
θ
). 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 (i.e. ignoring polarization dependence).
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.
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 and 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(
θ
)
curve,
where
f
=717
μ
m is the focal length of the metasurface doublet lens.
18
a
e
0
400
800
1200
MTF (a.u.)
0
0.5
1
Frequency (cycles/mm)
Diffraction limit
2.5°
d
0
400
800
1200
0
0.5
1
Frequency (cycles/mm)
MTF (a.u.)
Diffraction limit
20°
10°
30°
LED
25 cm
740 pixels
Filter
g
f
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
10X
0.3 NA
b
15°
30°
c
15°
30°
Fig. 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 (center 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. The insets show zoomed-in views of the images
at the locations indicated by the rectangles with the same outline colors which correspond to viewing
angles of 0
, 15
, and 30
.
d
, and
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
μ
m and focal length of 717
μ
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. The bandpass filter (center wavelength:
850 nm, FWHM bandwidth: 10 nm) placed in front of the LED reduces the chromatic aberration.
19
Deconvolved, FWHM: 40 nm
15°
Measured, FWHM: 10 nm
15°
0
10
20
40
FWHM (nm)
0
400
800
1200
0
0.5
1
Frequency (cycles/mm)
MTF (a.u.)
2
P
m
0 nm
10 nm
20 nm
a
40 nm
0
1
Intensity (a.u.)
bc
de
0
1
850
Wavelength (nm)
Power density (a.u.)
0.5
FWHM
T
T
=0°
T
=15°
FWHM:
Measured, FWHM: 40 nm
15°
x
z
y
x
y
Fig. 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 centered 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.
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). See Fig. S2 for the spectra. The images are captured using the setup shown in Fig.
4
a but with
a higher magnification objective (20
×
, 0.4 NA).
e
, Result of chromatic aberration correction for the image
shown in
d
. The insets in
c
-
e
show zoomed-in views of the images at the locations indicated by the
rectangles with the same outline colors corresponding to viewing angles of 0
(red border) and 15
(green
border). FWHM: full width at half maximum.
20
Note S1: Imaging bandwidth of metasurface lenses
Here we discuss the relation between the numerical aperture (NA), focal length and bandwidth of
a metasurface lens. We consider a metasurface lens with the focal length of
f
which is designed
for operation at the wavelength
λ
, and is placed at the distance
f
from an image sensor. The
metasurface lens focuses light with the wavelength of
λ
+ ∆
λ
to the distance of
f
f
from the
metasurface lens. Because of the phase jumps at the zone boundaries of the metasurface lens, the
fractional change in the focal length is equal to the fractional change in the wavelength [23], that
is
f
f
=
λ
λ
.
(3)
As
λ
increases the focal plane of the lens moves further away from the image sensor and the
size of the spot recorded by the image sensor increases. As a quantitative measure, we define the
bandwidth of the metasurface lens as the wavelength change
λ
that increases the diameter of
the recorded spot by a factor of
2
compared to its value at
λ
. With this definition, the distance
between the image sensor and the focal plane at the wavelength of
λ
+ ∆
λ
is equal to the Rayleigh
range
z
0
of the focused light (i.e.
f
=
z
0
). The Rayleigh range is given by
z
0
=
πw
2
0
λ
,
(4)
where
w
0
is the
1
/
e
2
focal spot radius and is inversely proportional to the NA of the metasurface
lens
w
0
=
λ
2
ln(2)NA
.
(5)
Therefore, the fractional bandwidth of the metasurface lens is given by
λ
λ
=
πw
2
0
λf
=
π
4ln(2)
λ
f
NA
2
,
(6)
and is proportional to
λ/
(
f
NA
2
)
.
21
a
b
2
P
m
0
1
Intensity (a.u.)
dx= 0
dy= 5
P
m
dx= 5
P
m
dy= 0
15°
-15°
T
=-30°
30°
dx= 0
dy= 0
Correcting
metasurface
Focusing
metasurface
dy
dx
T
x
z
x
y
Fig. S1
:
Effect of misalignment between the two metasurfaces
.
a
, Schematic illustration of the side
view (left) and the top view (right) of the metasurface doublet lens. The misalignments along
x
and
y
directions (d
x
and d
y
) are shown in the top view illustration.
b
, Simulated focal plane intensity of the
metasurface doublet lens for different misalignments between the metasurfaces and at several different
incident angles
θ
. The aperture and field stops are assumed to be aligned with the metasurfaces on their
corresponding sides.
22