Supporting Information
for
Adv. Optical Mater.
, DOI 10.1002/adom.202302241
Compact Mid-Infrared Spectrometer Using Continuously Variable Infrared Fi
lter and
Microbolometer Array for Simple and Fast Measurement of Molecular Mid-IR Spe
ctra
Taeyoon Jeon*, Amirhossein Nateghi, Changsoon Choi, Jack Jewell
and Axel Scherer
Compact Mid
-
Infrared Spectrometer using Continuously Variable Infrared Filter and
Microbolometer Array for Simple and Fast
Measurement
of Molecular Mid
-
IR Spectra
Taeyoon Jeon†*, Amirhossein Nateghi†, Changsoon
Choi†, Jack Jewell and Axel Scherer
Applied Physics and Materials Science, California Institute of Technology, Pasadena, California,
91125, USA
*Corresponding author, Email :
jty209@caltech.edu
†Equal contribution
Section 1
-
Manufacturing continuously variable mid
-
IR filter.
The substrate material for filter deposition is undoped silicon wafer, which is transparent on
mid
-
IR region. And anti
-
reflection coating is deposited on the back side of silicon wafer to
decrease the reflection loss from the silicon/air interface. DBR is
deposited on the surface of silicon
wafer with quarter wavelength thickness. BaF
2
is deposited by using thermal evaporator and Ge is
deposited with RF sputtering. After depositing DBR, two step photolithography has been done on
the one of DBR to make 3 um and 6 um thickness of spacer. Two DBRs are pressing against each
other and heated
on convection oven at 130 degree C to adhere each other. This makes
continuously variable air
-
cavity on between two DBRs
. Manufacturing procedure is described in
Figure S1
.
However, during the pressing and heating of two mirrors at high temperatures, the
non
-
uniform stress on the filter results in curvature on the lateral direction of the cavity length. The
pressing process is illustrated in
Figure S2
. Because two DBRs are pressing each other from 4
different tightening screws, the curvature in the lateral direction of the filter is generated as shown
in
Figure S2c
.
To determine whether the curvature originates from the wafer bonding process, we prepared a
Ge
-
cavity filter that can be grown in the deposition system, eliminating the need for wafer bonding.
As shown in
Figure S3
, after constructing the entire optical filter, we observed a straight
absorption line from the polypropylene sample. However, due to the higher Q
-
factor of the Ge
-
cavity filter compared to the air
-
cavity filter, the overall contrast is less than that of t
he air
-
cavity
filter.
Figure S1.
(a) Anti
-
reflection film coated on undoped silicon wafer. (b) Ge/BaF
2
DBR is deposited on the
surface of silicon. (c) Two SU
-
8 spacers with 3
μm
and 6
μm
thicknesses are deposited on the side
of wafer. (d) Two DBRs are attached each other.
Figure S2
.
The schematic diagram illustrates the bonding process of two DBRs. (a) Side view of how the two
DBRs are pressed against each other, with a carbon sheet used to protect the sample during the
pressing. (b) The top view provides a detailed depiction of the position of one DBR relative to
tightening screws. (c) The schematic demonstrates how the tightening of four screws produces
curvature in the lateral direction of the filter’s air
-
cavity regio
n, resulting in a curvy absorption
line.
Figure S3.
(a, b)
The schematic diagram
s
illustrate a continuously variable air
-
cavity filter
(a) and Ge
-
cavity
(b). (c, d)
The spectrometer captured absorption lines of polypropylene
from air
-
cavity filter (c)
and Ge
-
cavity filter (d). (e, f) Calculated transmittance spectra and Q
-
factor at the center
wavelength from air
-
cavity filter (e) and Ge
-
cavity filter (f).
Section 2
-
Refractive index of Ge and BaF2 in mid
-
IR region.
The refractive indices of Ge and BaF
2
thin films were measured using the J.A. Woollm IR
-
VASE Mark II spectroscopic ellipsometer at five different angles: 55°, 60°, 65°, 70°, and 75°. The
thickness of the native oxide (SiO
2
) on the Si wafer was predetermined and fixed in the model at
1.76 nm. The substrate used for film deposition was a 0.36 mm float
-
zone silicon wafer. As shown
in
Figure S
4
, the n
-
value of Ge in the LWIR region is approximately 4.2. When comparing the
refractive index of sputtered Ge to that of crystal Ge (4), it is observed t
hat sputtering Ge can be a
slightly higher refractive index, especially when the deposition conditions are in very low pressure.
(This Ge film was deposited on 5 mTorr pressure). The density (n
-
value of Ge film) can vary
depend on the pressure inside the s
puttering chamber. The extinction coefficient (k
-
value) of Ge
is zero in the LWIR region. For BaF
2
, the n
-
value is less than 1.4, and the k
-
value is zero up to 9
μm in LWIR region. The k
-
value of BaF
2
slightly increases as the wavelength increases. However
,
even up to 13 μm, the value of the extinction coefficient remains in the range of 10
-
4
order, which
makes it suitable for use in the LWIR region.
Figure S
4
.
(a, b) Graphs show the n
-
and k
-
values of sputtered Ge and evaporated BaF
2
, respectively. (c,d)
Tables present exact n
-
and k
-
values of Ge and BaF
2
at different wavelengths, respectively.
Section 3
–
SNR comparison between a single row and integration of 130 rows
To check the SNR increase after the integration of all the data
points, we calculated SNR
using the definition of the peak absorption signal (peak height) divided by the standard deviation
of the residual (baseline)
1
. Using this definition, we obtained an SNR of 9.5 from a single row of
data, and it increased to 44.8 when we integrated all the data points (130 rows). This changed SNR
value is depicted in
Figure S5
.
Figure S5a
shows
the
polypropylene transmittance spectrum from
a
single row of detector pixel
,
and
Figure S5b
depicts the spectrum obtained
from the integrat
ion
of 130 rows.
Figure S5
.
(a) Polypropylene transmittance spectrum from a single row of detector pixel
s with an SNR
value
of
9.5. (b) Polypropylene transmittance spectrum from the integration of 130 rows
with an
SNR
value is 44.8.
Section
4
–
Deconvolution of spectrum to find the original spectrum
(A) Developing deconvolution algorithm and find the amount of improvement on spectrum
The spectra from our compact spectrometer have been blurred due to optical conditions
such as some ranges of incident angle, lens abbreviation and surface scattering and so on. This
blurred spectrum can be restored from deconvolution process. To do the dec
onvolution, finding
the width of Gaussian kernel should be done first. Convolution can be performed first on the
spectra obtained from a high
-
resolution Fourier transform infrared (FTIR) spectrometer with a
resolution of 1 cm
-
1
and match with the spectra f
rom our spectrometer. This is to find the width of
Gaussian kernel for deconvolution. The transmittance spectra of PP using the high
-
resolution FTIR
(1 cm
-
1
) is shown in red plot on
Figure S
6
a
. The FTIR measured spectrum is then convolved with
a Gaussian function:
푓
(
푥
)
=
푒
−
푛
2
2
휎
2
where
n
is the number of data points and
휎
is the standard deviation. During the convolution
process, the standard deviation is divided by 2.35. The resulting convolved transmittance spectrum
when FWHM value is 17 cm
-
1
is shown in blue plot
Figure S
6
a
and this spectrum shows high
similarity with the spectra measured by our compact spectrometer (
Figure S
6
b
).
By using this FWHM values for gaussian function, deconvolution can be done to restore
the original signal. The Richardson
-
Lucy deconvolution algorithm
2
is used for the deconvolution
process. The iteration procedure based on the given blurred spectrum (
푑
푖
) and the spread function
which is a gaussian kernel (
푝
푖푗
), can be described like following equation:
푢
(
푡
+
1
)
=
푢
푗
(
푡
)
∑
푑
푖
푐
푖
푝
푖푗
푗
+
푟
×
푢
푗
(
푡
)
̈
where
푐
푖
=
∑
푝
푖푗
푢
푗
(
푡
)
푗
,
푡
is iteration number and
푟
is regularization parameter. The gaussian
kernel,
푝
푖푗
is determined by using the FWHM value of 17 cm
-
1
. The regularization parameter is
added to suppress the amplification of noise. The value,
푟
,is set to 3 nm. After 10 iterations, the
deconvolved spectrum (
푢
푗
) of the PP film becomes more distinguishable, as shown in red plot in
Figure S
7
. When compared to transmittance spectrum before deconvolution (blue curve), the
peaks are more prominent. Through the deconvolution process, the amount of improvement in
sharpness is comparable to transitioning from a blurring with a width of 17 cm
-
1
to a sharper state
with a width of 12 cm
-
1
. This comparison is made with respect to the intentionally blurred data
from 1 cm
-
1
-
resolution FTIR measurement shown in
Figure S
8
. This
sharpness improvement can
be further improved by optimizing the parameters for deconvolution and improve the optical
system.
Figure S
6
.
(a) The transmittance
spectra of PP film measured from 1 cm
-
1
-
resolution FTIR (red plot) and
convolved with Gaussian function with FWHM value of 17 cm
-
1
(blue plot). (b) The plot represents
the transmittance spectrum of PP measured using our compact spectrometer. This spectrum is
obtained by averaging the pixels at each wavelength. This spectrum shows similarity with blue
plot in (a).
Figure S
7
.
The transmittance spectra of PP film measured from our compact spectrometer. The blue plot
represents the spectrum before deconvolution, while the red plot represents the spectrum after
deconvolution process.
Figure S
8
.
The transmittance spectra of PP film measured from 1 cm
-
1
-
resolution FTIR and then convolved
with two different FWHM values of Gaussian functions. The blue plot represents the spectrum
convolved with 12 cm
-
1
FWHM value, while red plot represents the spectrum convolved with 17
cm
-
1
FWHM value. The difference observed is similar to the contrast between the spectra before
and after the deconvolution process, as depicted in
Figure S
7
.
(B) Comparison of transmittance spectra of PS, Methane and Acetone measured by our
spectrometer and 1 cm
-
1
-
resolution FTIR, convolved 12 cm
-
1
FWHM value.
The transmittance spectra of PS film, methane gas and acetone from our spectrometer and
following deconvolution can be compared with FTIR measured spectra, convolved with Gaussian
function which has 12 cm
-
1
FWHM values.
Figure S
9
a
-
c
show spectra of PS, methane, and
acetone from 1 cm
-
1
-
resolution FTIR. And
Figure S
9
d
-
f
show spectra after convolving with
Gaussian function of 12 cm
-
1
FWHM value. The value of 12 cm
-
1
is from Section
4
(A). As shown
compared with convolved spectra
from FTIR measurement, the spectra from our spectrometer
(
Figure S
9
g
-
i
) looks similar with convolved FTIR spectra.
Figure S
9
.
(a
-
c) The transmittance spectra of PS film (a), methane gas (b), and liquid acetone (c) that were
measured using a high
-
resolution FTIR spectrometer with a resolution of 1 cm
-
1
. (d
-
f) The
transmittance spectra of the same samples (PS film, methane gas, and acetone) after being
convolved with a Gaussian function. The FWHM value (12 cm
-
1
) of Gaussian function used for
convolution was obtained from Section 3A of Supporting Information. (g
-
i) The transmittance
spectra of the same samples (PS film, methane gas,
and acetone) that were measured using our
compact spectrometer following with deconvolution.
Section
5
-
Attenuated total reflection (ATR)
The ATR (Attenuated Total Reflection) method can be used to measure liquid samples without
requiring additional preparation. ATR utilizes an evanescent wave generated by total internal
reflection at the interface between a germanium (Ge) crystal and air, m
aking it a highly surface
-
sensitive measurement technique. In this experiment, a Ge crystal is employed for the ATR
experiment. Blackbody radiation is directed into the Ge crystal and undergoes multiple reflections
at the surface before eventually escaping
from the crystal. Each time the light is reflected, an
evanescent wave is generated in the air region to satisfy the boundary conditions. The electric field
of the transmitted light, E
t
, can be calculated using the following equation:
퐸
푡
=
퐸
푘푡
푒
−
휅푦
푒
푖
(
푘
푥
푥
−
푤푡
)
,
, where
휅
=
푘
0
√
푛
퐺푒
2
sin
2
휃
푖
−
푛
퐴푖푟
2
,
푘
푥
=
푛
1
푘
0
sin
휃
푖
.
Here, E
kt
represents the complex amplitude for the transmitted wave, k
0
is the wavenumber in
vaccum, n
Ge
is refractive index of Ge (4) and n
Air
is a refractive index of Air (1). The 1/e penetration
depth (
d
), which indicates the distance at which the amplitude of evanescent wave drops by a factor
of e, is given by
d
= 1/
휅
. For 9 μm wavelength of light and 45 degrees of incident angle, the 1/e
penetration depth is
541 nm.
Figure S
10
.
(a) The schematic shows the propagation of light inside of Ge crystal through total internal
reflection. (b) The wavevectors for incident, reflected and transmitted lights.
Section
6
-
Molecular spectra and corresponding images taken by 2D microbolometer
array (Molecular barcode)
Molecular transmittance information can be also visualized by 2D image. Because detector is
2D microbolometer array, molecular transmittance information can be represented as 2D image.
Figure S
1
1
shows transmittance spectra of four different molecules and corresponding images
from 2D microbolometer array. As shown in images, the absorption lines are captured on image
well. These images can be called molecular barcode, which can tell molecular info
rmation based
on the width, spacing and intensity of lines.
Figure S
1
1
.
(a
-
d) The transmittance spectra of PP film (a), PS film (b), methane gas (c), and liquid acetone (d)
that were measured using a compact spectrometer. (e
-
h) Molecular barcode images of PP film (e),
PS film (f), methane gas (g), and liquid acetone (h) taken
by 2D microbolometer array.
Section
7
–
The Effect of Incident Angle Range on Spectrometer Resolution
The transmittance spectrum of the Fabry
-
Perot filter can vary with the incident angle of
incoming light. If the incoming light is not fully collimated, then the filter’s transmittance peak
may broaden, potentially leading to lower resolution. To address th
is, we calculated the
transmittance peak shift at an incident angle of 5 degrees and determined the amount of peak shift
for different cavity gap values.
In this calculation, we set the center wavelength at 9 μm.
As shown
in
Figure S1
2
, the peak wavelength
can shift at a 5
-
degree incident angle compared to perfectly
collimated incoming light. Therefore, the collimation of the light
source is another crucial factor
in achieving high resolution in a spectrometer.