S
1
Supplementary
Information
Bioinspired Nanophotonic Angle
-
independent and Ultralarge Light
Dispersion Allowing Simultaneous Near
-
infrared
-
spectroscop
y and Visible
-
imaging
Daniel
Assumpcao
1,
3
*
, Radwanul Hasan Siddique
1,2,*,ϯ
, Hyochul Kim
3
, Yeonsang Park
4,5
, Un
Jeong Kim
3
,
Young
-
Geun Roh
3
,
Y
ibing M
. Wang
1
,
Hyuck Choo
2,3, ϯ
1
Meta Vision
Lab, Samsung Advanced Institute of Technology (SAIT), Samsung
Semiconductor Inc., 2 N Lake Ave #2
4
0, Pasadena, CA, USA.
2
Department of Me
d
ical Engineering, California Institute of Technology, 1200 E.
California Blvd., MC 136
-
93, Pasadena, California 91125, USA.
3
Advanced Sensor
Lab, Device Research Center, Samsung Advanced Institute of
Technology
(SAIT), Suwon, 16678, Republic of Korea
.
4
Department of Physics, Chungnam National University, Daejeon 34134, Korea
5
Institute of Quantum Systems, Chungnam National University, Daejeon 34134, Korea
†Corresponding author. Email:
r.siddique@samsung.com
,
hyuck.choo@samsung.com
*These authors contributed equally to this work.
Contents
Supplementary
N
ote 1: Design optimization and simulations
Supplementary Note 2:
BioDE fabrication and surface characterization
Supplementary Note 3: Device characterization and performance testing
Figures
S1 to S10
Table
S1
Captions for Movies S1 to S3
S
2
Supplementary N
ote 1: Design optimization and simulations
1.1
FDTD simulations
3D o
ptical simulations of
BioDE device design and optimizations
were set up in the
FDTD Maxwellian solver Lumerical.
A large domain (5um x 5um) was simulated with periodic
boundary conditions.
The response of the structure with wavelengths ranging from 700
nm
to
900
nm was simulated.
The scattering element (nanoholes) were distributed across the substrate
in one
-
dimension randomly, and a no overlapping condition was enforced. The number of
scatterers was chosen such that the average density (given by the length
of the simulation divided
by the square root of the number of scatterers) was provided in the
Figure
2C.
The transmitted angular intensity distribution was calculated for each wavelength and the
dispersion was computed
from this distribution
.
The dispers
ion for each wavelength was fit to an
exponentially broadened Lorentzian due to the asymmetric response of the resonance with
respect to pixel location.
The
peak location was extracted with respect to the wavelength
from
the fit
. This peak location was t
he
n fit to Eqn. 1 to extract
λ
0
and
n
* for each structure. The
FWHM of the fit was considered for the calculation of the experimental resolution.
In order to calculate the efficiency, first the transmission was simulated for
the
BioDE.
T
he ratio of non
-
specu
lar power over total power versus the resonance angle was computed
using the far
-
field projection of the simulation data
to discount the specularly transmitted power
in the efficiency
. This ratio was then multiplied by the transmission to determine the eff
iciency.
1.2
Optimization of
scattering
and density of scatterers
In order to design the optimal distribution of scatterers in the scattering layer of the
BioDE for maximizing the dispersion efficiency and angle
-
independent performance, a simple
analytica
l model was developed. A random hole with radius
R
is
assumed to impart a phase shift,
θ
such that the near
-
field scalar response of a single nanohole can be written as:
퐴
ℎ
표푙푒
(
푟
⃗
)
=
{
푒
푖휃
−
1
,
|
푟
⃗
|
<
푅
0
,
|
푟
⃗
|
≥
푅
The random distribution of the holes can be w
ritten as a probability density function of the
position,
푃
(
푟
⃗
)
. Thus the full scalar near field when the random scattering structure is illuminated
by normal incident light can be written as:
퐴
(
푟
⃗
)
=
1
+
퐴
ℎ
표푙푒
(
푟
⃗
)
∗
푃
(
푟
⃗
)
Where,
∗
represents the convolution oper
ation. Based on this the resulting wave vector,
distribution of the scattered light,
푈
(
푘
⃗
⃗
)
can be computed using Fraunhofer diffraction theory:
푈
(
푘
⃗
⃗
)
=
ℱ
(
퐴
(
푟
⃗
)
)
=
훿
(
푘
⃗
⃗
)
+
ℱ
(
퐴
ℎ
표푙푒
(
푟
⃗
)
)
ℱ
(
푃
(
푟
⃗
)
)
As can be seen, distribution of scattered light contains two components:
specular term,
훿
(
푘
⃗
⃗
)
, and
scattered term,
ℱ
(
퐴
ℎ
표푙푒
(
푟
⃗
)
)
ℱ
(
푃
(
푟
⃗
)
)
.
This specular light passes through at the same angle as the
incident light and thus is non
-
scattered. This light contains positional information and is angle
dependent. This specular transmitted l
ight is beneficial for the work as the positional information
can be used to easily construct the incident image, allowing for simultaneous imaging. Therefore,
we focus to optimize the scattering of the high angle light
for
angle
-
independent
spectroscopy
To ensure angle independence, we would like the magnitude of
ℱ
(
퐴
푟표푑
(
푟
⃗
)
)
ℱ
(
푃
(
푟
⃗
)
)
to
be as independent of
푘
⃗
⃗
as possible.
ℱ
(
퐴
푟표푑
(
푟
⃗
)
)
is the Fourier transform of the near field
response of the hole. To ensure this is as independent of
푘
⃗
⃗
as possible, the hole
must scatter light
S
3
to wide angles which can be achieved through tailoring the diameter and thickness of the hole.
To maintain the subwavelength periodicity of 400 nm in the other direction, the hole diameter is
chosen to be 280 nm given the no
-
overlapping
condition. Based on FDTD simulations nanohole
diameter of 280 nm and thickness of 750 nm were chosen for wide angle scattering.
ℱ
(
푃
(
푟
⃗
)
)
corresponds to the Fourier transform of the probability distribution which is the characteristic
function of the distribut
ion. To ensure this is independent of
푘
⃗
⃗
as possible, a completely random
distribution of holes is used with no spatial correlation present among the neighboring holes.
Afterwards, the scattering efficiency of the scatterers was optimized through finding t
he
optimal density of random holes in the thin film as shown in
Figure
2B.
To do this, simulations
were performed of the BioDE devices with varying nanohole density and the efficiency was
calculated for each as described in SI 1.1.
A higher number of scatt
erers intuitively leads to a
higher probability of scattering and thus it is beneficial to increase the density. The total
scattering cross
-
section is proportional to the number of scatterers at low densities. However, at
higher densities, the amount of sc
attering decreases due to the subwavelength condition.
Intuitively, as the average inter
-
hole spacings decreases to subwavelength spacings, the holes
appear as a continuous thin film to incident light and thus do not scatter. Assuming a perfectly
ordered d
istribution with average distance
푑
and inner dielectric index
푛
, the condition for no
scattering for light at close to normal incidence can be derived as (see SI 1.5):
휆
≥
푛
·
푑
Although the above
-
mentioned equation is true for periodic design, the same
principle applies in
this case of the random distributions. Thus, these two factors work against each other, leading to
an optimum density of the nanostructures.
1.3 Resolution scaling analysis and methodology
We computed the diffraction limited resolut
ion of the BioDE and grating to analyze the
scaling of the resolution with respect to the focusing lens as shown in
Figure
2F. First, the
dispersion of the BioDE (Eq 1) can be derived from Eqn. 1:
푑휆
푑휃
=
휆
0
√
1
−
(
sin
휃
푛
∗
)
2
sin
휃
cos
휃
(
푛
∗
)
2
=
휆
0
2
휆
sin
휃
cos
휃
(
푛
∗
)
2
The minimum resolvable angle
푑휃
can be computed through
sin
휃
=
푥
푓
, where
x
is the
distance on the detector of the receiving pixel and
f
is the focal length of the lens. Thus,
푑휃
=
푑푥
cos
휃
∙
푓
, where
푑푥
is the minimum resolvable distance on the detector. Again,
푑푥
=
푅퐹
∙
푊
푝
,
where
푅퐹
is the resolution factor definining the number of pixels in the FWHM of the diffraction
limited focus and
푊
푝
is the width of a single pixel on the detector. Including all
the terms, we can
obtain the minimum pixel resolvable resolution of BioDE,
휕
휆
푝푖푥푒푙
.
However, BioDE also has
another contributing factor to its resolution that is the resolution of the underlying filter
resonance
,
휕
휆
푓푖푙푡푒푟
, which is independ
ent of the focal length and only dependent on the number
of layers in the DBR. The two factors were combined to get the total resolution of the
BioDE:
휕
휆
푡표푡푎푙
=
√
휕
휆
푝푖푥푒푙
2
+
휕
휆
푓푖푙푡푒푟
2
. This was computed for a variety of focal lengths,
assum
ing
휕
휆
푓푖푙푡푒푟
=
2
.
8
nm
(simulated average resolution of BioDE device)
,
푛
∗
= 1.75 (fit from
the simulation),
휆
=
800
nm,
휃
=
20°
,
푅퐹
= 2 (ideal value), and
푊
푝
=
1
.
22
μm
(width of the
S
4
pixels of a compact CMOS sensor)
to compute the ideal resolution of
the BioDE spectrometer in
these circumstances.
The same procedure was repeated for the equivalent grating spectrometer to determine its
minimum resolution. The dispersion is given by:
휆
(
휃
)
=
푑
sin
휃
Where,
d
is the period of the grating. Thus, we can ca
lculate the resolution factor for grating
structures in the following manner:
푑휆
푑휃
=
푑
cos
휃
휕
휆
푡표푡푎푙
=
푑휆
푑휃
푑휃
=
푑
∙
푑푥
푓
The same values of
푓
,
푊
푝
, and
푅퐹
were used to keep consistency.
1.4 Resolution comparison of miniature spectrometer with BioDE and standard grating
For developing the miniature spectrometer, the optical quality of the focusing lens will
determine the minimum diffraction limited spot. To analyze the resolution achievab
le with a
grating in the miniature spectrometer platform used in this work, the resolution of an ideal
grating in this platform was calculated. The grating’s period was set to 1.8 μm so that a
wavelength of 900 nm was still within the acceptance angle of 3
0°. A pixel factor of 10 pixels
was estimated by measuring the full
-
width
-
half
-
max of a diffraction limited spot in our miniature
setup when collimated broadband light is incident upon the detector. The pixel size of our
detector was 6 μm and the focal len
gth of the lens was 8 mm. By including these numbers in the
equations developed in the “Scaling Analysis” section 1.3, an ideal grating resolution is found to
be 13.5 nm.
For comparison, the ideal BioDE resolution achievable with this platform was calcul
ated
to be 0.7 nm, over an order of magnitude better. Moreover, since the BioDE fabricated in this
work has a filter
-
dependent resolution of 4.5 nm, it is seen that this resolution is unchanged even
in the compact platform, and is 3 times better than that
achievable with an optimal grating. It
could then be trivially improved up to 0.7nm resolution through adding additional layers to the
DBR.
1.5 Derivation of Subwavelength Limit for Scattering
When the average spacing of the nanostructures becomes small
compared to the wavelength,
intuitively the nanostructures begin to appear as a continuous film, and do not scatter incoming
light
The condition for scattering can be more rigorously calculated using diffraction theory. First
consider a 1D grating with spa
cing
d
. As any periodic structure can be broken down into a
convolution of a grating with the farfield response of the individual scatterer, the results derived
from the grating can be applied generally to any 1D periodic structure.
The electric field jus
t beyond the grating assuming an ideal grating can be written as:
퐴
(
푥
)
=
∑
훿
(
푚
푥
−
푚
∙
푑
)
Where
훿
is the dirac delta function. The k vectors in the x direction of the light making up the
resulting field can then be calculated as
(
1
)
:
S
5
푈
(
푘
푥
)
=
∫
퐴
(
푥
)
푒
−
푖
푘
푥
푥
푑푥
=
∑
훿
(
푘
푥
−
2
휋
푑
푚
)
푚
Thus we see that the resulting wave vectors of light beyond the grating are given by
푘
푥
=
2
휋
푑
푚
where m is an integer.
The grating will not scatter light if it only has the 0
th
diffraction order, i.e.
|m|=1 must lie outside the
light line. The k vector for light beyond the light line is given by:
푘
푥
≥
푛
2
휋
휆
Where
휆
the wavelength in free space and n is is the refractive index of the surrounding medium.
Thus we can conclude that the requirement for having no diffraction for l
ight initially at close to
normal incidence and thus no scattering is:
휆
≥
푛
·
푑
In this work, random distributions were considered as opposed to perfectly ordered structures
considered in this analysis. However, the core result still is maintained for rand
om distributions,
the difference being that the diffraction orders become blurred due to the randomness, leading to
a suppression, but not necessarily complete elimination of scattering at wavelengths above the
subwavelength limit
1.6 Limitations to the r
ange of BioDE
As discussed in the main text, a single BioDE element only had a resolution of around 30nm, but
through interleaving multiple at different angles we showed the range could be extended up to
200nm. This then begs the question how much further
the range could be extended beyond this
through interleaving further BioDEs at different angles. Although the ultimate limit of the
number of elements that can be interleaved on a single chip will be limited by the ability to
distinguish neighboring lines
from the angular resolution of the imaging system and detector, the
total range of the chip will be set by the width of the stop band of the DBR layer since all BioDE
units on the same chip share the same underlying DBR and the cavity resonances can only e
xist
within the stopband. For the materials and dimensions used in this work, we estimate a
maximum stop band of ~280 nm
(2)
, setting that as the maximum spectral range of a BioDE chip
given our material stack. This can be increased by using a material sta
ck in the DBR with a
larger index contrast (at the expense of a shorter range per BioDE element, and thus requiring a
larger number of interleaved units on a single chip, see Eq. 1).
Alternatively multiple sets of BioDE elements can be fabricated with ea
ch set containing a
different underlying DBR mirror layer at a slightly different angular offset, ensuring they are all
interleaved. The main cost of this will be additional fabrication steps to create the different sets
of BioDE elements. The limit of thi
s technique will be given by either the minimum resolvable
angle between successive BioDE elements or the limitations of the maximum geometric footprint
able to be integrated in the system. This minimum angle will be dependent on the properties of
the imag
ing system, and can be estimated from the minimum angular resolution of the imaging
system where the aperture size of the system is set by the size of area of the individual BioDE
elements. To get an order of magnitude estimate for the device dimensions us
ed in this work, we
will assume a circular aperture with the same area as our BioDE elements, thus enabling us to
calculate the minimum angular resolution via the Rayleigh criterion as
휃
푚푖푛
=
1
.
22
휆
/
퐷
(
3
)
where
퐷
is the diameter of the BioDE element. Given a BioDE element with an area of 500
μm x
500
μm provides
휃
푚푖푛
≈
0
.
1°
. Thus around 1000 BioDEs could in theory be interleave around
S
6
the 180
°
of angular range. Considering the limit set by the geometric footprin
t, given a small
aperture of 3 mm (so that it would be suitable for integration in cell phones), and given the
BioDE dimensions of 500 μm x 500
μm, a total of ~30 BioDE elements could in practice be fit.
This thus sets the practical limit on total number o
f BioDEs that could be integrated, leading to
an estimated total range of ~900
nm. In practice, covering such a wide range would require the
integration of different materials to operate at the different wavelengths, and numerically
removing the passband a
rtifacts from light being transmitted through BioDE elements at the
wrong wavelength, this calculation shows the ability of interleaving to extend a single BioDE
chips range to cover much larger spectral ranges.
Supplementary Note 2: BioDE fabrication an
d surface characterization
2.1
Fabrication process of BioDE
The fabrication of the BioDE was performed at Samsung nanofabrication facilities at
Suwon, South Korea. The fabrication flow of the BioDE is shown in
Figure
S
5
. The filter section
of BioDE consis
ted of two quarter wavelength stacks made of TiO
2
and SiO
2
and an inner cavity
of SiO
2
. The thickness of the two materials in the stack were 83 nm and 135 nm respectively so
that the stop band was centered at 800nm. The inner cavity thickness was varied us
ing a
grayscale lithography technique depending on the each block of BioDE in the interleaved
structure. The inner cavity thicknesses used were evenly spaced between 227 nm and 375
nm to
cover the wavelength range of 700
nm to 900
nm.
For the scattering l
ayer, air holes with diameters of
280
nm
and thicknesses of 750
nm
were etched into a 1
μm thick SiO
2
layer using e
-
beam lithography and reactive ion etching. The
mask of the nanostructure position was designed based on the simulation results. They were
po
sitioned randomly in one direction but had a subwavelength periodicity with a period of 400
nm along perpendicular dimension to ensure no scattering along that dimension.
Supplementary Note 3: Device characterization and performance testing
3.1
Benchtop
Optical Setup
Two different optical benchtop setups were used to characterize the BioDE’s
performance. The first setup uses a tunable laser to characterize the BioDE’s dispersion diagram
as shown in
Figure
S
6
A. A tunable laser in the 700nm to
900nm range (
Coherent Mira, USA) is
put
through a 5x beam expander (Thorlabs GBE05
-
B, USA) for illuminating the entire BioDE
sample. The transmitted light is then put through a custom k
-
space imaging setup consisting of a
4f relay (2 Thorlabs AL4532, USA), focusing len
s (Thorlabs
MVL4WA
, USA), and a CMOS
detector (Hamamatsu C11440
-
22CU, Japan).
The second setup was used to test the imaging and spectroscopy performance of the
BioDE (
Figure
S
6
B). The illumination path was changed to use a broadband source (Thorlabs
SLS201
, USA) with a 900 nm short pass filter (Thorlabs
FESH0900
, USA), and 450 nm long
pass filter (Thorlabs
FEL0450
, USA). A 700 nm long pass (Thorlabs FELH0700, USA) and
short pass (Thorlabs FESH07
00
, USA) filters were placed in the beam path to change t
he
illumination to either visible or NIR, respectively. In addition, a 785nm notch or bandpass filter
with 33nm bandwidth (Thorlabs
NF785
-
33
, USA) and an 850nm short pass filter (Thorlabs
FESH085
0
) were occasionally placed in the beam path for testing of t
he spectrometer
functionality. The illumination light was then placed through a diffuser (Thorlabs
ED1
-
C50
,
S
7
USA) and illuminated through an opaque sheet with a transparent imaging target cut into it. The
sheet used was a custom ordered photomask (Outputcit
y, Bandon, OR, USA). Finally, the same
optics as in the previous setup was used for imaging after adding an imaging lens (Thorlabs
TRH127
-
020
-
A
-
ML
, USA) in front of the BioDE.
The imaging lens, placed a focal length away
from the imaging target, transforms
the image into angular intensity incident on the BioDE. The
specular transmission of this angular intensity through the BioDE device is then mapped on
to the
CMOS
through the previously mentioned 4f relay and focusing lens k
-
space setup, reforming the
init
ial image with the additional streaks from the BioDE which correspond to the spectrum. This
permits the BioDE to measure both the image and the spectrum simultaneously.
3.2 BioDE experimental parameters extraction
To extract the BioDE characterization
parameters, the angular dispersion was measured
with the varying incident wavelength using the tunable laser setup (see SI 3.1) and the
parameters
λ
0
and
n
* were fit for each BioDE block using the same procedure as done for the
simulation data (see SI 1.1
). In order to calculate the efficiency, first the transmission was
measured using a transmission microscope of each BioDE blocks. The resolution and the
efficiency was calculated from the measured data as in the simulations (see SI 3.1).
3.3 Simulated v
s f
abricated
BioDE d
iscrepancy
There was a noticeable increase in both the average resolution (4.5 nm vs 2.5 nm) and
efficiency (6.6% vs 5%) between the fabricated and simulated BioDE. This is consistent with a
lower quality factor of the filter in the fab
ricated BioDE versus the simulated BioDE. To test this
hypothesis, the transmission of the filter without any nanostructures was measured and compared
to the simulated values (
Figure
S
7
). It is observed that the FWHM of the resonance of the
fabricated filt
er (~5 nm) is larger than the resolution of the simulated filter (~3nm), thus
confirming the hypothesis. There could be many possible reasons for this discrepancy in quality
factor including discrepancy in the refractive index profiles of the materials, su
rface roughness
leading to a decreased quality factor, and fabrication imperfections.
3.4
Image
reconstruction
a
lgorithm
To reconstruct the image,
post
-
processing was necessary to remove the distortions caused
by scattering. To achieve this, the point
-
spr
ead function (PSF) was measured by analyzing the
transmitted angular intensity through the BioDE when illuminated with collimated visible light
(400 nm
-
650 nm). The measured PSF was then used to deconvolve the raw image, utilizing the
Richardson
-
Lucy alg
orithm in MATLAB (refer to
Figure
S8). The process utilized 10 iterations
for optimal balance between deblurring
and avoiding ringing artifacts. Notably, the spatial
resolution of the visible image remains the same as the original CMOS image sensor pixel
resolution, which is 1.22 μm, even after the image processing. This applies to both of the
compact CMOS cameras u
sed in this study.
3.5 Spectrum reconstruction algorithm
The spectrum was extracted from the spectral region of the raw data through fitting the
raw data to an ideal model of the wavelength dependent scattering streaks of the BioDE (
Figure
S
8
A). When inci
dent light impinges on the BioDE, first, the incident light is scattered to
different angles depending on the orientation of the BioDE and the initial angle of the light.
Second, the light is filtered at that given angle depending on the light spectral con
tents.
S
8
Therefore, we model the scattered intensity distribution,
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
with respect to
the incident light angles
휃
푥
,
휃
푦
and the position
x, y
on the detector. We assumed that an ideal
BioDE scatters equally to all pixels along its random
axis angle. Hence,
푔
can be defined as:
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
=
훿
(
tan
−
1
푓
sin
휃
푦
−
푦
푓
sin
휃
푥
−
푥
−
휃
)
.
Where
푓
is the focal length of the focusing lens and
휃
is the angle at which the random
axis of BioDE is oriented. For a given image, the total scattered
intensity distribution can be
written as (
Figure
S7B):
푔
′
(
푥
,
푦
)
=
∫∫
훼
(
휃
푥
,
휃
푦
)
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
푑
휃
푥
푑
휃
푦
.
Where,
훼
(
휃
푥
,
휃
푦
)
is the intensity distribution of the image taken as an input parameter in the
model.
Next, we define the filtering effect
at different angles with the spectral intensity
퐼
(
휆
)
.
From Eqn. 1, it is known the only the resonance wavelength
휆
푅
(
휃
)
is transmitted at a given angle
휃
for the BioDE. Thus, we can define the spectral filtering function at a pixel location
x, y
as
(
Fi
gure
S7B):
푆
(
푥
,
푦
)
=
∫
퐼
(
휆
)
∙
훿
(
휆
푅
(
휃
푒푞
(
푥
,
푦
)
)
−
휆
)
푑휆
=
퐼
(
휆
푅
(
휃
푒푞
(
푥
,
푦
)
)
)
.
Where,
휃
푒푞
(
푥
,
푦
)
is the angle corresponding with the pixel location
푥
,
푦
for the optical system
that can be written as:
휃
푒푞
(
푥
,
푦
)
=
sin
−
1
√
푥
2
+
푦
2
푓
Finally, the full streak pattern for the BioDE can be computed through multiplying the spectral
filtering with the random scattering to obtain the final streak pattern (
Figure
S
9
B):
푆푃
(
푥
,
푦
)
=
푔
′
(
푥
,
푦
)
∙
푆
(
푥
,
푦
)
The same calculation was repeated for eac
h 8 BioDE blocks and then the intensity pattern was
summed together to obtain the final spectral streak pattern from the model.
Now, to calculate the spectrum from a measured streak pattern, the obtained model was fitted to
the raw data using a least squa
res fit method (LSQR) in MATLAB with a tolerance of 10
-
6
.
As mentioned above, an ideal BioDE was considered with an angle independent scattering and
transmission efficiency. In practice, however, a slight intensity variations versus angle is
observed sin
ce the scattering is completely random. In addition, higher angle light transmits less
efficiently through the filter than lower angle light due to Fresnel reflections. Moreover, the
transition from one BioDE to another versus wavelength cause additional e
rrors. Therefore, we
noticed jagged edges in the reconstructed spectrum as shown in
Figure
S
10
. In order to correct
this, a wavelength dependent calibration term was multiplied across the spectrum:
퐼
′
(
휆
)
=
푐
′
(
휆
)
퐼
(
휆
)
.
Where,
퐼
′
is the calibrated spectral int
ensity and
푐
′
is the calibration factor. To compute
푐
′
, the
spectrum measured using a high resolution commercial spectrometer was divided by the
spectrum
퐼
(
휆
)
measured by the BioDE for incident unfiltered light. This factor was then used to
compute the
spectrum with the filters inserted, showing good agreement with the measurement
with the reference spectrometer (
Figure
S
10
).
S
9
Since the calibration takes into account the non
-
constant scattering of the BioDE, it can
change depending on the incident angle
of light and thus the incident image of light. Therefore, a
separate calibration matrix of
푐
′
(
휆
)
for each incident angle was measured and used for each
image used. However, in a more general setting where the images cannot be known a priori, the
linearity
of the system can be exploited to compute an arbitrary calibration factor for an arbitrary
image as formulated below:
퐼
푠푖푛푔푙푒
−
푝표푖푛푡
(
휆
)
=
푓
(
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
)
,
퐼
′
(
휆
)
=
푐
(
휃
푥
,
휃
푦
,
휆
)
퐼
푠푖푛푔푙푒
−
푝표푖푛푡
(
휆
)
=
푐
(
휃
푥
,
휃
푦
,
휆
)
푓
(
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
)
.
퐼
(
휆
)
=
푓
(
푔
′
(
푥
,
푦
)
)
=
푓
(
∫∫
훼
(
휃
푥
,
휃
푦
)
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
푑
휃
푥
푑
휃
푦
)
=
∫∫
훼
(
휃
푥
,
휃
푦
)
푓
(
푔
(
휃
푥
,
휃
푦
,
푥
,
푦
)
)
푑
휃
푥
푑
휃
푦
=
∫∫
훼
(
휃
푥
,
휃
푦
)
퐼
′
(
휆
)
푐
(
휃
푥
,
휃
푦
,
휆
)
푑
휃
푥
푑
휃
푦
.
Finally
, using the definition of the calibration factor, the total calibration factor
푐
′
can
be
computed:
푐
′
(
휆
)
=
퐼
′
(
휆
)
퐼
(
휆
)
=
1
∫∫
훼
(
휃
푥
,
휃
푦
)
푐
(
휃
푥
,
휃
푦
,
휆
)
푑
휃
푥
푑
휃
푦
Thus, if pre
-
calibration is done to measure
푐
(
휃
푥
,
휃
푦
,
휆
)
, then
푐
′
(
휆
)
can be computed for any
arbitrary incident image using the BioDE.
3.6 Specular Transmission Algorithm
Modific
ation
Usually the incoming light will be scattering in nature which is accounted in our previous
algorithm. However, for the specular transmission measurements especially for the biosensing
experiment, the algorithm was slightly modified. Specular transmit
ted light leads to different
amounts of power being incident on different blocks of the BioDE creating a disjointed
spectrum. Therefore, the spectrum for each block was measured and calibrated individually for
specular transmission. The spectral range of e
ach block overlapped, the intensity of each block
was scaled so that the intensity of these overlap regions was equal between blocks. These
individual spectrums from each block was then stitched back together to get the full spectrum.
3.7 Low
-
a
ngle
reference s
pectrometer
m
easurement
For the low angle reference measurement in
Figure
4E, the same benchtop setup was
used except the BioDE was replaced with a custom fabricated metal aperture with an equal
aperture size of 1x2mm to avoid any vignetting art
ifacts in the signal. In addition, the detector
and focusing lens were replaced with a lens
-
fiber collimator (Thorlabs
F810SMA
-
780
, USA). A
500 μm
core fiber was used so that the acceptance angle of the lens
-
fiber interface was set to ±
0.4°. The fiber was then attached to a commercial NIR spectrometer (Ocean Optics Maya 2000,
USA).
3.8 Miniaturized spectrometer assembly
Figure 5A shows the assembl
y of the miniature spectrometer. A commercial CMOS
detector was used (Thorlabs DCC3260M, USA) as an imaging sensor. A singlet lens with a focal
length of 8 mm (Thorlabs AL108, USA) was attached to the detector and focused at infinity for
the focusing lens.
The BioDE was then added on top of the lens through an attachment ring
S
10
(Thorlabs
SM05RRC
, USA). An aperture (Thorlabs SM1D12D, USA) was added to the exterior
of the handheld spectrometer to limit the field of view to ± 15°.
To provide near field imaging /
spectroscopy, the aperture was replaced with a Hastings triplet lens (Thorlabs TRH127
-
020
-
A
-
ML, USA).
3.9 Biosensing experiment
DNA aptamers or oligo conjugated 25 nm Au nanorods were custom ordered from
Nanopartz, USA. Oligo Sequence was chosen to capt
ure specifically VEGF protein. The
sequence was
AuNP
-
polymer
-
5'
-
TGTGGGGGTGGACGGGC CGG GTA GA
-
3'
.
The Au
nanorod conjugated aptamers was obtained lyophilized and stored in Tris
-
EDTA (TE) buffer (10 mM
Tris
-
HCl, 1 mM EDTA, pH 7.4) at
-
20°C at a concentration
of 100 μM. For experiments, aptamer
conjugated Au nanorods was diluted in Tris
-
HCl buffer (pH 7.4) at a concentration of 1 μM.
Thereafter, a drop (10 μL) of the solution was added onto a thin film silicone to prepare the
plasmonic biosensor substrate.
VEG
F
was
obtained from Sigma Aldrich, USA. Stock solutions with
molecular concentration 1 μM were prepared in PBS buffer (pH 7.4) and stored at
-
20°C.
Prior to
use, the
VEGF solutions
were diluted to desired concentrations and 10 μL of each sample was added
t
o the substrates.
The samples were placed in a humidity chamber and left undisturbed for an hour
before the biosensing experiment.
The collimated NIR broadband light source previously used in the benchtop setup was
utilized to illuminate the plasmonic nano
particles biosensors. The specularly transmitted light
then was captured by the miniature spectrometer. The reconstructed transmission signal was then
fit with a low order polynomial to extract the resonance peak position. For the reference
measurement, th
e miniature spectrometer was replaced with the fiber collimator and commercial
spectrometer used in the benchtop reference measurements.
3.10
Discussion
on spatially
-
variable filtering to achieve simultaneous imaging and spectroscopy
As discussed in the
main text, a position dependent filter transmitting visible light in the
interior and NIR only in the exterior could be added on the detector as shown in
Figure
S
10
and
combined with the BioDE to achieve simultaneous visible imaging and NIR spectroscopy.
The
fabrication of this spatially
-
varying filter is outside the scope of this work. However, we have
computationally as well as experimentally emulated the filter configuration through separately
illuminating the imaging target with visible and NIR light (
450nm
–
900nm) or just NIR light
(700nm
–
900nm). The interior, imaging section of the visible/NIR image was then combined
with the exterior, spectral section of the NIR only image to form the image that would have been
taken with a position dependent filt
er. Also note that, alone NIR (700
-
900 nm) light can also be
adequate to capture both the image and spectrum. The handheld spectrometer measurements
were made only for NIR light illumination.
3.11 Table of compact spectrometers explanation
The values for
the range, resolution, and angle independence as indicated in Table S1 were
taken directly from the references in the literature.
The efficiency was taken from the literature when available. For certain references
including our design
, a max efficiency of
100% divided by the number of individual cells was
assumed. Note that in this context, efficiency is defined as the percent of incident light that is
received by the underlying detector.
The total optical throughput (etendue), was calculated through multi
plying the solid angle
of the input times the dimensions of the input aperture. For the devices with scalable input