Improving H2RG Performance in SPHEREx Brassboard Model
Chi H. Nguyen
1
, Phillip Korngut
1
, C. Darren Dowell
2
, James Bock
1
,
2
, Jill Burnham
1
, Samuel Condon
1
, Walter Cook
1
,
Grigory Heaton
1
, Howard Hui
1
, Branislav Kecman
1
, Hiromasa Miyasaka
1
, Kenneth Manatt
2
, Hien T. Nguyen
2
,
Stephen Padin
1
, and Marco Viero
1
1
California Institute of Technology, Pasadena CA 91125, USA;
chnguyen@caltech.edu
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109, USA
Received 2024 July 16; revised 2024 November 18; accepted 2024 November 25; published 2025 January 15
Abstract
Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer is an upcoming
NASA satellite mission to study the physics of in
fl
ation, the history of galaxy formation, and the abundance of
biogenic ices in the Milky Way, obtaining the
fi
rst all-sky spectroscopic survey at infrared wavelengths
0.75
–
5.0
μ
m. The instrument implements HAWAII-2RG
(
H2RG
)
detectors and custom-built Video8 electronics
with multiple sampling features to optimize the H2RG noise performance, including nonsequential row reads,
voltage monitoring, multiple visits to optically dark reference pixels, as well as onboard slope
fi
tting and cosmic-
ray removal. We report here the performance of a single H2RG with the readout electronics. We focus on the
effectiveness of multiple reference samplings to reduce 1
/
f
noise most relevant to the galaxy formation analysis, in
particular the noise on large angular scales
k
<
0.13
[
pix
−
1
]
(
∼
5
′′
–
20
′′
)
where the imprints of galaxy clustering will
be measured. Our characterization con
fi
rms that increased sampling of reference pixels successfully reduces the 1
/
f
noise by
∼
50% at these scales. However, the effectiveness of multiple reference reads is limited by irreducible per-
pixel telegraph noise. Further noise reduction can be achieved by using optical pixels in addition to the reference
pixels to remove common-mode signal offsets in each channel. Additionally, we observe that the gain of optical
pixels is consistently
∼
90% that of the reference pixels, prompting additional correction steps in the data reduction
pipeline.
Uni
fi
ed Astronomy Thesaurus concepts:
Astronomical detectors
(
84
)
;
Near infrared astronomy
(
1093
)
;
Astronomical instrumentation
(
799
)
;
Space telescopes
(
1547
)
1. Introduction
The Spectro-Photometer for the History of the Universe,
Epoch of Reionization
(
EOR
)
, and Ices Explorer
(
SPHEREx
)
satellite will produce the
fi
rst all-sky infrared spectroscopic
survey between 0.75 and 5.0
μ
m with spectral resolving power
R
=
λ
/
δλ
between 35 and 130
(
O. Doré et al.
2014
,
2018
;
P. M. Korngut et al.
2018
; B. P. Crill et al.
2020
)
. SPHEREx
will map the entire sky to address three key science areas:
(
1
)
constraining the physics of cosmic in
fl
ation by constraining
non-Gaussianity in large-scale structure,
(
2
)
investigating the
history of galaxy formation using intensity mapping of the
extragalactic background light
(
EBL
)
, and
(
3
)
searching for the
signatures of water and other biogenic ices in the Milky Way.
SPHEREx combines two key technologies: HAWAII-2RG
(
H2RG
)
detectors and linear variable
fi
lters
(
LVFs
)
. H2RGs are
2048
×
2048 HgCdTe pixels hybridized to a silicon readout
integrated circuit
(
J. W. Beletic et al.
2008
)
. HxRG detectors
are used in current and upcoming space instruments, including
JWST NIRCam and NIRSpec
(
W. Posselt et al.
2004
;
L. G. Burriesci
2005
)
, the
Euclid
Near Infrared Spectrometer
and Photometer
(
N. Mauri et al.
2020
)
, and the Nancy Grace
Roman Space Telescope
(
B. Smith et al.
2016
; J. Gregory
Mosby et al.
2020
)
. LVFs mounted immediately in front of
each H2RG transmit different wavelengths row-wise across the
detector to perform spectroscopy while minimizing the size of
the instrument. Despite having been used on planetary missions
like on the
New Horizons
/
LEISA instrument
(
D. C. Reuter
et al.
2008
)
, LVFs have only been used in specialized
applications in astrophysics
—
for example, in CIBER-2
(
K. Takimoto et al.
2020
; C. H. Nguyen
2021
)
to study the
EBL at 0.5
–
2.5
μ
m. SPHEREx will scan the entire sky every
six months, producing four complete sky maps over a two-year
mission. During a six-month survey, the ecliptic poles are
readily observable by SPHEREx in most orbits, enabling high-
cadence observations to produce deep regions for the galaxy
formation study.
Among the SPHEREx three science themes, the EBL
intensity mapping places the most stringent requirement on
the SPHEREx large-scale noise requirement
(
5
′′
–
20
′′
)
. The
near-infrared EBL is imprinted with signals from galaxy
clustering, therefore making EBL an important observable to
constrain the history of galaxy formation tracing back to the
EOR
(
A. Cooray et al.
2004
)
. Previous studies found that the
large-scale EBL
fl
uctuations exceed expectation from galaxy
counts
(
for examples A. Kashlinsky et al.
2012
; M. Zemcov
et al.
2014
)
. The origins of the excess remain an active research
topic, with multiple candidates being proposed including
intrahalo light at
z
2
(
A. Cooray et al.
2012
; M. Zemcov
et al.
2014
; Y.-T. Cheng et al.
2021
)
, Population III stars
(
A. Kashlinsky et al.
2005
,
2018
)
, and primordial direct
collapse black holes at high
z
(
N. Cappelluti et al.
2013
; B. Yue
et al.
2013
)
. The main challenge of probing the EBL comes
from bright foregrounds, most predominantly the Zodiacal
light. The sky photon noise level on 5
′′
–
20
′′
scale is expected to
be
∼
4
[
pW m
−
2
sr
−
1
]
after mosaicking 100 observations. To
decompose the EBL
fl
uctuations, the correlated read noise of
our instrument needs to fall below this value.
The Astrophysical Journal Supplement Series,
276:43
(
12pp
)
, 2025 February
https:
//
doi.org
/
10.3847
/
1538-4365
/
ad97bd
© 2025. The Author
(
s
)
. Published by the American Astronomical Society.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 4.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
1
The SPHEREx readout electronics have undergone testing
on a prototype of the focal plane assembly, hereafter referred to
as the brassboard model
(
BBM
)
at Caltech. The BBM unit
consists of a single H2RG detector with 2.5
μ
m cutoff and a
SPHEREx LVF covering 0.75
–
1.12
μ
m. The detector and
fi
lter
are enclosed in a molybdenum housing thermally similar to the
fl
ight focal plane assembly. In this paper, we report the results
of the BBM test and its impact on the
fi
nal design of SPHEREx
readout electronics. In Section
2
, we brie
fl
y review SPHEREx
readout electronics and our sampling techniques. The BBM test
is presented in Section
3
, and the data reduction steps are
summarized in Section
4
, with highlights on the additional
corrections discovered from analysis of the laboratory data. We
report the main results in Section
5
, followed by a discussion of
the improvements in Section
6
.
2. SPHEREx Readout Strategy
2.1. Video8 Readout Electronics
The detectors are read in slow buffered 32-channel mode at
100 KHz, with 2048
×
64 pixels per channel. SPHEREx
incorporates custom readout electronics based on a Video8
Application Speci
fi
c Integrated Circuit with specialized
features. The readout electronics use a low-voltage power
supply, six identical readout boards
(
ROBs
)
, one for each
H2RG, and a central electronics board
(
CEB
)
. The CEB
provides the interface to the spacecraft. Each ROB provides
detector bias and control signals and reads out the detector with
four Video8 ampli
fi
ers. Each Video8 can multiplex eight
H2RG channels. The Video8 ampli
fi
es the H2RG outputs with
low noise and a differential input for environmental immunity.
Input switches to a reference to enable continuous monitoring
of ampli
fi
er drifts. We refer the interested readers to G. Heaton
et al.
(
2023
)
for a more detailed description of the Video8
design and characteristics.
To shift low-frequency noise to higher frequencies where
photon noise from foregrounds like Zodiacal light dominates,
we implement a nonsequential reading of the pixel rows
(
“
row
chopping
”
; G. Heaton et al.
2023
)
. To monitor the drift of the
Video8 during operation, we measure the Video8 output with
the input connected to a stable reference voltage 32 times
uniformly spaced across a frame. We refer to these measure-
ments as
“
phantom pixels
”
because, while not physical
components of the H2RG detector arrays, they are incorporated
in the data frames in the same manner as pixel elements. To
improve the channel-to-channel offset correction, we sample
the built-in H2RG reference pixels multiple times to reduce the
uncertainty of the signals. Lastly, to optimize the downlink
capability of the data, we opt not to telemeter all readout frames
and instead apply an algorithm to perform line
fi
tting
simultaneously to the sampling-up-the-ramp
(
SUR
)
process
(
M. Zemcov et al.
2016
)
. The SUR line
fi
tting also
fl
ags pixels
approaching saturation or those hit by transient events like
cosmic rays.
2.2. Onboard Photocurrent Estimates
During an exposure, we sample each H2RG detector
multiple times at a regular time interval using an SUR scheme
(
e.g., G. H. Rieke
2012
)
. The output of each pixel produces a
time stream that increases proportionally to the sky
fl
ux
arriving at a pixel. To reconstruct the
fl
ux or photocurrent, we
fi
t for the slope of the signal versus time. The offset of the line
fi
t has some diagnostic value
(
for example, well depth and
persistence
)
but is generally not recorded in
fl
ight data.
Transient events are identi
fi
ed by searching for sudden jumps
in the pixel temporal stream. We linearize pixels that are
saturated during an exposure by
fi
tting only the presaturated
ramp to reconstruct the
fl
ux.
Despite its advantages, SUR generates an enormous volume
of data because each exposure is broken up into many frames.
In particular, SPHEREx uses 113 s integration corresponding to
74 frames per exposure. While not a particular problem
for ground-based instruments, the data frames are too big to
be realistically downlinked during our mission. Instead,
SPHEREx uses a real-time SUR algorithm
(
M. Zemcov et al.
2016
)
to estimate the photocurrent as the detectors are sampled
on-orbit and only the photocurrent maps are downlinked. In
addition, the algorithm
fl
ags potential transient events and
saturating pixels
—
information that would otherwise be lost
without all readout frames.
2.3. Row Chopping
Previous studies have identi
fi
ed a number of noise sources in
the HxRG detector family
(
B. J. Rauscher
2015
)
. In particular,
we are concerned with frequency-dependent
(
hereafter 1
/
f
)
noise at low frequencies because it reduces the sensitivity of
our instrument to the sky
’
s large-scale structures in the EBL
survey. To mitigate the effect of 1
/
f
noise, we implement
a novel row-chopping technique where
N
skip
row
(
s
)
are
skipped during sampling, e.g., row 0 is followed by 0
+
N
skip
,
0
+
2
N
skip
, etc., to shift low-frequency noise from the detector
output
fi
eld effect transistors to small spatial scales on the sky.
Setting
N
skip
=
1 recovers the conventional sequential sam-
pling. The data are telemetered down in time order, then
rearranged to the correct positioning in ground data processing.
G. Heaton et al.
(
2023
)
presents an in-depth discussion in the
prediction and validation of the row-chopping technique. The
data presented in this paper use 32 rows skip, which is within
the range optimized by G. Heaton et al.
(
2023
)
.
2.4. Phantom Pixels for Video8 Drift
The Video8 input has a leakage current of
∼
4es
−
1
at 0
°
C
(
expected on-orbit operating temperature
)
, far higher than the
leakage current
(
dark current
)
of
∼
10
−
3
es
−
1
typical of H2RG.
Given SPHEREx integration time, this drift is nontrivial and
needs to be monitored and corrected for during image
construction. To monitor the drift during an exposure, a stable
DC reference signal is connected to the Video8 inputs and
measured four times before an H2RG pixel row is read. The
reference signal measurements are added to the beginning of
the pixel row data and are displayed as pixel elements in the
image
fi
les, but they do not represent a physical pixel, hence we
refer to them as
“
phantom
”
(
Figure
1
(
a
))
. The phantom pixel
data are processed by the same SUR algorithm as the H2RG
pixels, allowing correction for preampli
fi
er temperature drift
during data processing. This processing step also reduces the
impact of sources of 1
/
f
noise that are visible to the phantom
pixel measurements.
2.5. Multiple Sampling of Bias Reference
H2RG detectors are equipped with reference pixels on the
four outermost rows and columns. These pixels are electrically
analogous to the active pixels but are not light sensitive and are
2
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Nguyen et al.
intended to capture only the read noise features. In particular,
the H2RG is known to have column-wise residuals
(
or
“
pedestal
”
drift
)
associated with the readout multiplexing
(
B. J. Rauscher
2015
)
, which are imprinted in the top and
bottom reference rows. To improve the accuracy when
determining the channel offsets, we weave additional readings
of the reference pixels at equal intervals between readings of
active optical pixels. The weaving order is illustrated in
Figure
1
(
a
)
, which also includes the row-chopping scheme.
Once the rows are rearranged after the data are downlinked, the
additional readings of the reference pixels are appended after
the typical 2048 rows
(
Figure
1
(
b
))
.
3. Component Level Test
3.1. BBM
The BBM unit was tested in two modes:
(
1
)
optical mode
with an LVF covering 0.75
–
1.1
μ
m and
(
2
)
dark mode with an
anodized aluminum cover in place of the LVF. The optical
mode allowed characterization of the LVF spectral response as
well as persistence and nonlinearity. The BBM unit was
encased in an anodized light-tight aluminum box, which
provided interface to a Winston cone fed by two small
integrating spheres to provide uniform illumination for optical
test
(
Figure
2
)
. A cold shutter assembly was installed at the
entrance of the pair of integrating spheres. During testing, the
BBM was cooled to 40 K and the temperature was actively
controlled to better than 5 mK. The ROB was kept at room
temperature outside the cryostat. The cold and warm test
harnesses were identical to the
fl
ight version.
3.2. MUX Glow
We initially used only the cold shutter and the BBM optical
mode to collect dark data. However, we detected emission from
the multiplexors
(
MUX
)(
also known as MUX glow
)
along the
wire bond edge of the detector, in the fast direction of read, and
spanning 20 pixel rows. The glow intensity is stable in time and
location; therefore, we treat the affected pixels like an
exceptionally high dark current zone, at a factor of 2
–
5 times
the mean dark current of the unaffected pixels
(
Figure
3
)
. The
glow was re
fl
ected back into the detector by the bare LVF
mounting frame, illuminating
∼
20% of the total pixels on the
array. The re
fl
ection is a problem with the BBM housing
design only and is not present in the
fl
ight design. To eliminate
the MUX re
fl
ection, we added the dark mode where the LVF
was replaced with an anodized aluminum cover. To reduce the
MUX glow intensity, we sampled the gate bias, VBIASGATE,
between 2.14 and 2.45 V. Increasing the bias reduces the glow;
however, bias voltage above 2.36 V pushes the readout
electronics to the limit of its dynamical range, resulting in
erroneous pixel values. The wrong pixel readings skew the
inferred photocurrents and also result in higher rms slope noise,
as seen in Figure
3
. Therefore, the 2.30
–
2.36 V range was
selected for SPHEREx operation, and we
fi
xed the voltage bias
at 2.30 V for the data below. Previous studies
fi
nd a correlation
between increasing VBIASGATE and ampli
fi
er crosstalks
(
N. Bezawada et al.
2020
; E. M. George et al.
2020
)
,
particularly in unbuffered fast mode. Slow buffered readout
mode, as used in SPHEREx, is expected to reduce the crosstalk
signi
fi
cantly, therefore lessening the impact of a higher
VBIASGATE choice.
3.3. Data Sets
To study the effect of multiple visits to the reference pixels,
we set the number of visit
N
visit
=
1
–
32, or 8
–
256 reference
rows, and took 40 exposures at each setting. We
fi
xed the
number of row skip at 32 following G. Heaton et al.
(
2023
)
and
the integration time to be 113 s. The frame intervals increase
with
N
visit
, so higher
N
visit
results in fewer frames per exposure.
Additionally, to calculate the gain factor from analog digital
unit
(
ADU
)
to electron, we collected 6 exposures of a
broadband light source taken in the optical mode.
Figure 1.
(
a
)
Schematic of the row readout order. The
fi
rst row to be read is the
fi
rst active pixel row on the detector
(
row 5
)
. The active pixel rows are read with
N
skip
to allow for row chopping. The reference pixels are weaved between the active pixel rows independent of
N
skip
, and their spacing is calculated from the number of total
rows given the number of visits to the reference rows
N
visit
. The
fi
rst reference row is read after
M
rows, which is approximately half of the spacing between the
reference rows, e.g. given
N
visit
=
4 and
N
skip
=
32, the spacing is 64 rows. In the read order, the
fi
rst appearance of a reference row
(
row 1, read 1
)
is the 26th row,
and the last instance of a reference row
(
row 2048, read 4
)
is the 32nd to last.
(
b
)
Schematic of how the phantom and additional reference pixels are packaged in a
SPHEREx exposure. The phantom pixels span 128 columns, grouped into 32 column channels with 4 columns of pixels in width. The H2RG pixel rows
(
active
+
reference
)
are arranged by their physical location, while extra samplings of the reference pixels
(
if any
)
are appended after row 2048. The phantom pixels associated
with each row are also rearranged to follow the H2RG rows. In our data reduction pipeline, the phantom and reference pixels are trimmed postprocessing
so the
science data consist of only the active optical pixels.
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Nguyen et al.
4. Data Reduction
In Figures
4
and
5
, we summarize the steps to construct a
map and apply corrections for the Video8 drift and the
detector
’
s channel offset. The photocurrent map is
fi
rst
obtained by line
fi
tting all readout frames in an exposure. In
each pixel, we take the differences of subsequent readout
frames and de
fi
ne the standard deviation of all pair differences
as the pixel correlated double sampling
(
CDS
)
noise. To avoid
the effects of settling after a detector reset, we exclude the
fi
rst
two frames after the reset. We convert the units from
[
ADU
frame
−
1
]
to
[
es
−
1
]
using the conversion factors inferred from
the optical data
(
Appendix
A
)
.
4.1. Phantom and Reference Subtractions
After unit conversion, we estimate and subtract the channel-
wide
fl
uctuations in the Video8 and in the detector. To correct
for the drift in the Video8 integrators in each readout channel,
we estimate the mean slope of the phantom pixels row-wise,
then subtract this mean from the H2RG pixels on the same row.
To correct for the pedestal drifts in the H2RG channels, we
calculate the mean slope of all reference pixels in a given
channel, then subtract the mean from the active pixels in the
same channel. At each correction step, there is a small offset
between the odd and even columns because the H2RG and
Video8 each use a pair of independent integrators. This parity
propagates into a small rise in the noise power at pixel scale
(
k
1
)
, so odd and even columns are treated separately in the
corrections. More details are in Appendix
B
.
4.2. Reference Correction
α
Factor
We observed a systemic difference between the photocur-
rents and noises of the reference pixels and the optical pixels in
all dark data, suggesting that the reference pixels are not fully
analogous to the optical pixels. Our measurements can be
explained if the gain factor of the reference pixel is actually
∼
10% larger than that of the optical pixels. In other words, if
we assume the same gain factor for both pixel populations, the
channel-wise offset calculated from the reference pixels
amounts to only 90% the offset seen by the optical pixels.
To make the reference pixels more similar to the optical pixels,
Figure 2.
The BBM unit inside a black light-tight box. In this optical mode, a
Winston cone and two integrating spheres were used to increase light diffusion.
The spheres are off-the-shelf Newport 819D-GL-3 with an average re
fl
ection of
95%
–
99%. The Winston cone is 490 mm in length, with radii 11. 5mm at the
input
/
sphere port
(
top
)
and 70 mm at the output
/
detector port
(
bottom
)
. The
cone is gold coated inside for similar re
fl
ectance as the spheres, and its
curvature is designed to produce an F
/
3 beam to simulate SPHEREx light
cone. The BBM was cooled to 40 K in a two-stage cryostat with thermal
fl
uctuation
5 mK.
Figure 3.
(
a
)
Photocurrents of rows 5
–
20
(
Y
coordinates
=
5
–
20 in Figure
6
)
affected by the MUX glow
(
“
MUX pixels
”
)
; rows 2024
–
2044 well outside of
the MUX glow zones
(
“
non-MUX
”
)
, which measure only the dark current; and
the reference pixels.
(
b
)
The rms slope noise of the three populations
(
as
calculated in Section
4.5
)
. VBIASGATE
>
2.36 V pushes the electronics to its
dynamical limit and degrades the detector performance, re
fl
ected in the fast rise
in
(
b
)
, so we only operate in the 2.30
–
2.36 V range
(
blue shaded zone
)
.
Figure 4.
High-level summary of the image construction steps. The phantom
correction is unique to our application of the VIDEO8 drift monitoring.
Additionally, to make the reference pixels a better analogy to the optical pixels,
here we apply a multiplicative correction
α
to the reference pixels before
subtraction
(
middle step in the blue box; Section
4.2
)
.
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Nguyen et al.
we divided the values of the reference pixels by a best-
fi
t
correction factor
α
before applying the reference subtraction
(
Appendix
C
)
.
4.3. Channel Filtering with Optical Pixels
To fall below the photon noise level required by the EBL
science, we considered using all available pixels
(
instead of just
reference pixels
)
to estimate the mean channel offsets for the
deep
fi
eld data. We report in Section
5
the power spectra
obtained using this method
(
“
channel
fi
ltering
”
)
as the best-
case scenario. In practice, this
fi
ltering is not a straightforward
application on sky images because of the presence of sources as
well as diffuse emissions, most notably zodiacal light.
Additionally, the channel
fi
ltering can alter the spatial
fl
uctuations of diffuse emission, effectively mixing the power
at large angular scales into other scales.
4.4. Bad Pixel Flagging
To
fl
ag and remove bad pixels and transient events in each
exposure, we used 5
σ
clipping on the photocurrent and CDS
maps. We produced two types of masks:
(
1
)
a static mask of
pixels that were always bad
(
e.g., hot, unresponsive, excess
CDS noise
)
and
(
2
)
a transient mask for each exposure that
includes cosmic-ray hits and
“
snow ball
”
events
(
B. Hilb-
ert
2009
)
. The static mask consists of pixels that are
fl
agged as
bad in at least 70% of exposures and is common to all
exposures in a given data set. On average, the transient
fl
ags
remove an additional
0.5% of pixels in a 113 s exposure.
4.5. Noise Estimates
To extract noise maps from dark photocurrent maps, we took
the differences pair-wise to cancel out the dark current, then
divided by
2
.Wede
fi
ned the standard deviation of the noise
map as the rms SUR slope noise
(
hereafter slope noise
)
.To
study the 1
/
f
noise, we followed the power spectrum
convention used in G. Heaton et al.
(
2023
)
, assuming
fl
at sky
and small angles. We performed fast Fourier transform on the
noise map to build a 2D spectrum, then took the azimuthal
average power
P
(
k
)
[
e
2
s
−
2
]
where
k
is the angular wavenumber
in unit of pix
−
1
. The wavenumber is related to the sky angular
scale
θ
by SPHEREx platescale 6
¢
¢
.
2 such that
k
=
2
π
(
6
¢
¢
.
2
)
/
θ
.
The power spectra are reported in
P
(
k
)
/
k
, so white noise has a
fl
at spectrum, while excess above the horizontal line comes
from 1
/
f
read noise. In this convention, the photon noise limit 4
[
pW m
−
2
sr
−
1
]
translates to
∼
1.25
×
10
−
5
[
e
2
s
−
2
pix
]
at
0.75
μ
m after accounting for SPHEREx etendue and spectral
resolving power
R
=
41. If the photocurrent
fi
t is dominated by
pixel-to-pixel white noise, we expect that the noise power on
pixel scale
(
k
1
)
, the slope noise, and the CDS noise can be
related by
()
()
s
p
=
NPk
k
2
,1
RMS
pix
⎛
⎝
⎞
⎠
()
ss
=
N
T
6
,2
CDS
RMS
frame
exp
where
N
pix
[
pix
]
is the width of the active pixel area or 2040 for
H2RG,
T
exp
[
s
]
is integration time,
N
frame
is the number of
readout frames in
T
exp
,
σ
RMS
[
es
−
1
]
is slope noise, and
σ
CDS
[
e
]
is the equivalent CDS noise in
T
exp
seconds.
5. Results
In Table
1
, we report the array-averaged dark current, the
CDS noise, and the read noise rms. Our results are consistent
with typical H2RG performance
(
for example, R. Blank et al.
Figure 5.
Example production of constructing a dark exposure.
(
a
)
Slope map that includes phantom and H2RG photocurrent.
(
b
)
The phantom-corrected photocurrent
map where the Video8 drift is removed.
(
c
)
The reference-subtracted map where the channel offset is removed using the mean of reference pixels. A 4 pixel Gaussian
kernel is applied to the plots to better illustrate the noise on large spatial scales.
Table 1
Measured Dark Current and Read Noise
Parameters
Reference Subtraction
Reference with 10% Correction
Channel Filter
Unit
Average dark current
−
0.0045
±
0.0032
−
0.0019
±
0.0032
−
0.0045
±
0.0032
e s
−
1
Read noise rms
0.041
±
1.5
×
10
−
3
0.045
±
1.7
×
10
−
3
0.041
±
1.5
×
10
−
3
es
−
1
CDS noise
17.6
±
0.6
17.9
±
0.6
15.8
±
0.7
e
5
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)
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Nguyen et al.
2012
)
. To evaluate the effect of the channel-to-channel offset
correction, we compare the average dark current and noise
maps of the reference subtraction, the reference subtraction
with 10% correction, and the channel
fi
ltering for the case of
N
visit
=
4 in Figures
6
and
7
.
In Figure
8
, we present the mean 2D noise power spectra of
the reference-subtracted and the channel
fi
ltered maps. The
channel-wise features in Figure
6
(
a
)
translate into excess noises
concentrating along the
k
x
axis in the 2D spectra most
prominently at
k
<
0.05, whereas the channel
fi
ltering success-
fully removes the variations. We report the annular average 1D
spectra of all
N
visit
in Figure
9
, adding the case where no
correction was applied to highlight the overall improvement of
our reduction pipeline. The large-scale
k
modes are highlighted
by the green shaded region. We are particularly interested in
two
k
bins: the two-halo nonlinear galaxy clustering scales
k
<
0.03
(
Y.-T. Cheng & J. J. Bock
2022
)
, and the one-halo
linear clustering scales 0.03
k
0.13
(
M. Zemcov et al.
2014
; A. Cooray
2016
)
. The reference-subtracted spectra fall
just below the photon noise level at angular scales
0.03
k
0.13 but remain almost 1 order of magnitude above
the requirement at
k
<
0.03. Only the channel
fi
ltering spectra
come below the photon noise on the largest scales.
6. Limitation of the Reference Pixels
To better understand the correlation and trade-off of multiple
visits and gain correction, we examine in Figure
10
the noises
as functions of
N
visit
in three
k
groups:
k
<
0.03,
0.03
k
<
0.13, and the pixel-to-pixel scale
k
1. In addition
Figure 6.
Comparing different methods to correct for the channel-to-channel offset. Each dark current map here is coadded from 40
×
113 s exposures.
(
a
)
Conventional reference subtraction using only their mean as is.
(
b
)
The reference pixels are divided by 0.91 to account for the 10% difference from active pixels.
(
c
)
Instead of using only reference pixels, we use all pixels in a given channel to estimate the offset in this channel
fi
lter. This is the most effective at smoothing the
channel-wide features. The visible row banding is the low-frequency noise of the electronics, modulated by the row chopping to 1
/
N
skip
[
row
−
1
]
or 42.35 Hz for
N
skip
=
32. A 4 pixel Gaussian kernel is applied to the plots to aid visualization.
Figure 7.
The noise maps corresponding to the three correction cases in Figure
6
. We take the differences of the 40 exposures in Figure
6
pair-wise, divide by
2
,
then coadd.
(
a
)
Reference subtraction as is.
(
b
)
Reference subtraction with 10% correction.
(
c
)
Channel
fi
ltering. A small number of bad pixels including those affected
by transient events are masked in white. The low-frequency noise modulated by the row chopping is also visible here. A 4 pixel Gaussian kernel is applie
d to the plots
to aid visualization.
6
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)
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Nguyen et al.
to the as-is reference subtraction, we also add the case with
10% correction to the reference pixels. In the two cases of
reference subtraction, there is a clear correlation between
N
visit
and the noise reduction because we get better estimate of the
reference pixels with more samples. In the two large-scale bins,
we see an exponential-like drop going from
N
visit
=
1 to 4, but
the noise
fl
attens at well above the channel
fi
ltering level even
as we reach the maximum
N
visit
=
32 allowable by the readout
electronics. The channel
fi
ltering outperforms both reference
subtraction in
(
a
)
and
(
b
)
, although all three methods see higher
small-scale noises with higher
N
visit
.
Our results con
fi
rm that increased sampling of reference
pixels is advantageous in general but also highlight the
limitations in term of the correla
ted noise. First, the reference
pixels contain nonrandom 1
/
f
noises, as illustrated in
Figure
11
, and this noise cannot be removed by increasing
the number of sampling. This noise
fl
oor can be seen in
Figure
12
(
a
)
where the slope noise of the reference pixel
converges to a nonzero value at higher
N
visit
. The channel
offset inferred from the refer
ence pixels always contains a
noise bias, and the reference subtraction adds this bias to the
science data on 64-column scale. Consequently, the slope
noise of the optically active pixels converges as
N
visit
increases
(
Figure
12
(
b
))
,evenwhenchannel
fi
ltering was
applied. The 1
/
f
noise
fl
oor explains why
N
visit
?
4doesnot
result in signi
fi
cantly better large-scale noise reduction than
N
visit
∼
4.
The second trade-off is longer frame interval and fewer
samples up the ramp for higher
N
visit
(
assuming
fi
xed
integration time
)
, resulting in excess noise power at pixel
scales in Figure
10
(
c
)
. Given this penalty and that the slope
noise
fl
oor of the optically active pixels can be reached as early
as
N
visit
=
4, there is little motivation to increase reference pixel
sampling beyond 4. The equivalent CDS and slope noise
inferred from
P
k
/
k
using mean
k
1 power for
N
visit
=
4 are
12.68
[
e
]
and 0.032
[
es
−
1
]
(
Equations
(
1
)
,
(
2
))
. These values
Figure 8.
The 2D power spectra of the noise maps using
(
a
)
reference subtraction as is and
(
b
)
channel
fi
ltering. By spatially smoothing the data in the
x
-direction, the
latter removes the power concentrated on
k
x
0.05 modes.
Figure 9.
The 1D noise spectra of all
N
visit
. Multiple samplings of the reference pixels improve the large-scale noise, but the improvement is not as pronounced at
N
visit
>>
4, and the largest-scale noises still exceed the photon noise level
(
blue dashed line
)
unless the channel
fi
ltering is used.
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Nguyen et al.
are lower than the direct measurements in Table
1
, implying
that the photocurrent
fi
t is dominated by pixel-to-pixel white
noise with a small contribution from the correlated noise.
While multiple reference visits can provide acceptable
performance for two out of three SPHEREx science areas
(
redshift and ice surveys; B. P. Crill et al.
2020
)
, the channel
fi
ltering may still be needed on the deep
fi
eld data to meet the
read noise level for EBL observation, in particular on the
largest scale. However, we have to consider that this
fi
lter can
distort the spatial power spectrum of underlying diffuse
emissions like the zodiacal light and the diffuse Galactic light.
In addition to the channel
fi
ltering, we also consider coadding
and mosaicking to meet the noise requirement. During the
course of the survey, the array orientation rotates over time at
the ecliptic poles where we de
fi
ne to be the EBL deep
fi
elds.
The rotation means that the same sky area is imaged with
different and uncorrelated imprints of the channel-wise pattern
in Figure
7
; therefore, the excess channel-wise noise is
averaged down after multiple repeated observations. Prelimin-
ary study of the simulated sky data suggests that we can meet
the noise requirement using only the reference subtraction by
coadding and mosaicking at least six months of observations of
the ecliptic poles, which is well within the limit of the two-year
survey. The detail of this study is beyond the scope of this
paper and will be reported in a future publication of the EBL
analysis pipeline. However, this result assumes that the
fl
ight
noise is similar to the performance measured in our controlled
lab environment as reported here. We opt to keep the channel
Figure 10.
Noise powers as functions of
N
visit
at
(
a
)
k
<
0.03,
(
b
)
0.03
k
<
0.13, and
(
c
)
k
1. We see signi
fi
cant noise reduction on large scales in
(
a
)
and
(
b
)
up to
N
visit
=
4; however, further samplings do not offer as signi
fi
cant reduction. The channel
fi
ltering offers the most noise reduction on large scales. Meanwhile, the pixel-
to-pixel noises in
(
c
)
increase with higher
N
visit
in all three corrections.
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)
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Nguyen et al.
fi
ltering module available in the science analysis pipeline in
case this option is needed for
fl
ight data.
Acknowledgments
A portion of the research described here was conducted at
the Jet Propulsion Laboratory
(
JPL
)
, California Institute of
Technology. We acknowledge support from the SPHEREx
project under a contract from the NASA
/
JPL to the California
Institute of Technology. We thank R. Smith
(
Caltech
)
for
his feedback on the detector testing. This article and analysis
made use of the Astropy
(
Astropy Collaboration et al.
2013
,
2018
,
2022
)
, NumPy
(
C. R. Harris et al.
2020
)
, SciPy
(
P. Virtanen et al.
2020
)
, and Matplotlib
(
J. D. Hunter
2007
)
Python packages.
Appendix A
Gain Measurement
The raw photocurrent images are recorded in ADU per
frame
(
or sampling
)
. To convert the raw unit into electron per
second
[
es
−
1
]
, the images are multiplied by a conversion
factor
g
:
[]
[
]
()
=
g
--
S
e s
gS ADU frame .
A1
1
raw
1
The factor
g
is split into the frame interval
t
f
[
s frame
−
1
]
,
which is measured directly in the electronics, and the
gain
g
1
[
e ADU
−
1
]
:
()
=
ggt
.A2
f
1
To estimate
g
1
, we multiply the conversion factor for voltage
per ADU set by the electronics with the number of electrons
per voltage given by the manufacturer. This gain can also be
measured directly from the data, where we can re
fi
ne
g
1
to
subarray level. J. D. Garnett & W. J. Forrest
(
1993
)
link the
photon noise to the photocurrent in a SUR H2RG exposure:
()
()
()
s
=
+
-
g
g
S
T
N
N
6
5
11
1
,A3
2
int
2
2
⎡
⎣
⎢
⎤
⎦
⎥
where
σ
γ
is the standard deviation of the correlated noise map
in
[
es
−
1
]
,
S
γ
is the photocurrent in
[
es
−
1
]
,
T
int
is the total
integration time, and
N
is the number of samplings in
T
int
. The
term in the square brackets is constant for a
fi
xed integration
time. We call this term
b
, and Equation
(
A3
)
is then simply
()
s
=
g
g
Sb
.A4
2
Next,
S
γ
and
σ
γ
can be written in term of
S
raw
and
σ
raw
:
()
()
s
=
gt
gt S b
.A5
ff
1
raw
2
1
raw
This equation is rearranged into
()
()·
()
s
=
t
g
tS b
1
.A6
ff
raw
2
1
raw
⎡
⎣
⎢
⎤
⎦
⎥
S
raw
and
σ
raw
can be measured and
b
can be calculated for any
given integration time. The slope
[
1
/
g
1
]
is
fi
t by either
Figure 11.
The time series of a single reference pixel in an exposure at SPHEREx
fl
ight cadence, mean subtracted by the time-averaged count to highlight the
fl
uctuations around zero
(
thin gray
)
. When smoothed by a
fi
ve-frame kernel
(
thick black
)
to suppress the white noise, the time series exhibits clear low-frequency
nonrandom
fl
uctuations.
Figure 12.
Slope noise of the
(
a
)
reference pixels and
(
b
)
optically active pixels as functions of visits. The noises converge to nonzero values highlighting the limit of
using only the reference pixels to measure the channel offset.
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Nguyen et al.
modulating the input light source to obtain multiple
S
raw
levels
or by changing the integration time to get different
b
and
σ
raw
for the same source. In practice, the measured noise comprises
of photon and read noises
s
ss
=+
meas
2
read
2
raw
2
, both of which
vary with integration time. By
fi
xing the integration time, the
read noise term becomes a constant offset in Equation
(
A6
)
.
To measure the gain, we collected two exposures in the
optical mode with identical broadband illumination and 14 s
integration time. In the mean photocurrent map of two
exposures, the pixels are binned by their
S
raw
with binwidth
of 1
[
ADU s
−
1
]
. We excluded bad pixels and rejected bins with
fewer than 100 pixels. Next, we took the map difference and
divided by
2
to get the correlated noise map. The
σ
raw
of each
S
raw
bin was the standard deviation of the correlated noise in
the bin.
We calculated
g
1
at two spatial scales: array level assuming
all pixels are the same and quartile level by grouping every
eight channels read by a Video8 chip. The data and best-
fi
t
results are shown in Figure
13
for all four quartiles. In
Figure
14
, the results are plotted as percentage of the expected
g
1
highlighting that the measured
g
1
factors are 5%
–
8% higher
than expected. The factor reduced at the array level is
consistent with the mean of the four Video8-level factors. This
result suggests that there are measurable variations between the
Video8 chips, which are suppressed if
g
1
is probed on an array-
wide level. The quartile variations are not the detector
’
s
fl
at
fi
eld because the same variations are observed in subsequent
testings of the same electronics with different detectors. If not
accounted for, the variations propagate into other calibrations
like
fl
at
fi
elding. In Figure
15
, we present the original exposure
calibrated with the manufacturer
’
s
g
1
factor and the best-
fi
t
g
1
at Video8 level. The quartile pattern is effectively removed
using our best-
fi
t factors.
In theory, the gain factor can be estimated down to the
readout channel level provided a large number of exposures to
reduce the effect of the read noise. However, we did not have
suf
fi
cient data from the BBM detector to perform such
calculation for this paper. The science pipeline is built to
accommodate 32 gain factors per
fl
ight detector, currently
populated with measurements from the ground calibration and
will be revised with the in-orbit calibration data. The in-orbit
calibration data will also be used to study if there is signi
fi
cant
channel-wise gain variation between the reference and active
pixels
(
as observed at the array level in Appendix
C
)
, which
may potentially improve the reference subtraction. We do not
currently have a plan to measure the gain down to the single-
pixel level because the pixel-to-pixel gain variations will be
statistically less signi
fi
cant compared to other effects on the
same spatial scale
(
for example, how well we can constrain the
spectral response or
fl
at
fi
eld at the individual pixel level
)
.Asa
result, the per-pixel variations
(
after correction at the channel
level
)
will be folded into the end-to-end systematics.
Figure 14.
The best-
fi
t factors
g
1
[
e ADU
−
1
]
, presented as percentages of the expected
g
1
(
manufacturer
)
. We estimate the gain factors at two levels: array-wide and
quartile level by grouping every eight readout channels. While the array-wide gain is consistent with the mean of the quartile factors, the quartile f
actors can capture
the small variations between the Video8 chips.
Figure 13.
Fitting the gain factor using only the readout channels corresponding to Video8 number 1
–
4
(
a
)
–
(
d
)
. The data suggest that we need different corrections to
the
g
1
factor in each quartile, which match the visible differences in Figure
15
(
a
)
.
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)
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Nguyen et al.
Appendix B
2D Image Construction
We consider an H2RG pixel in readout channel
i
, at row
y
,
and column
x
. To handle the parity nature of the ampli
fi
ers, we
use index
k
for columns within a channel such that
0
k
(
w
channel
−
1
)
, and
k
is related to
x
by
()
()
=+ +
xik x iw
k
,.B1
0
channel
The SUR photocurrent of this pixel
I
yik
is decomposed into
()
=+ ++
II I SdI,
B2
yik
yi
i
yik
yik
8,
ped,
where
I
8,
yi
is the Video8 drift in channel
i
on row
y
,
I
ped,
i
is the
column offset residual from the detector ampli
fi
er 1
/
f noise,
S
yik
is the photocurrent in the H2RG pixels including dark
current, and
dI
yik
is the noise.
B.1. Phantom Correction
Each readout channel
i
has
M
phan
phantom pixels, with
indices 0
m
M
phan
. The phantom pixels do not contain the
S
yik
term. The temporal slope of a phantom pixel in row
y
,
P
yim
is decomposed into
()
=+
PI dP.
B3
yim
yi
yim
8,
To obtain the best drift estimate
̄
I
yi
8,
,a5
σ
clipping is applied to
all phantom pixels in channel
i
to exclude abnormal phantom
readings in each channel. Next,
P
yim
is averaged across
m
readings in channel
i
to obtain
̄
I
yi
8,
. The average phantom
current is subtracted from the H2RG pixel slopes in channel
i
row-wise:
̄
()
++=-
SI dIII
.B4
yik
i
yik
yik
yi
ped,
8,
B.2. Reference Correction
Reference pixels are designed to be insensitive to photons, or
S
yik
∼
0:
()
+=-
IdIII
.B5
iyikyikyi
ped,
8,
When estimating
̄
I
i
ped,
,a5
σ
clip is used to reject outliers and
the column references
(
columns 0
–
3 and 2044
–
2047
)
are
excluded. To correct for the ampli
fi
er parity, we calculate the
reference means in pair of
̄
I
i
ped, ,odd
and
̄
I
i
ped, ,even
.
The reference-subtracted photocurrent is then
̄ ̄
̄ ̄
()
+=-
-
-
SdII
II k
II k
odd
even
.B6
yik
yik
yik
yi
i
yi
i
8, ,odd
ped, ,odd
8, ,even
ped, ,even
⎧
⎨
⎩
Appendix C
Reference Pixel Correction
In each
N
visit
data set, we difference 40 phantom-corrected
(
but not reference-subtracted
)
maps pair-wise and divide by
2
to obtain 20 noise maps. In each noise map, we calculated two
quantities per channel:
(
1
)
i
the median noise
δ
I
opt,i
from
2040
×
64 optical pixels and
(
2
)
the median noise
δ
I
ref,i
from
8
N
visit
×
64 reference values. To relate these two populations,
we consider a simple linear model with no offset:
()
a
D=D
,C1
i
ref,i
opt,i
where
α
i
is 1 if the reference pixels are faithful analogs of the
optical pixels.
In Figure
16
, we plot
Δ
opt,i
versus
Δ
ref,i
from 20 difference
maps for one channel. If the two populations follow the same
gain factor
g
1
, the data points should follow the red dash
diagonal line. However, the best-
fi
t
α
i
is consistently less than
1 across different data sets, suggesting that the reference pixels
need a slightly larger gain factor when converting from ADU to
[
es
−
1
]
. This result holds for all channels.
In Figure
17
, we plot
α
i
for all channels. The channel values
are average from all
N
visit
sets. While the uncertainty of
estimating
Δ
optical
remains unchanged between different
N
visit
sets, the statistical error of
Δ
ref
decreases as
N
visit
increases. To
combine all
N
visit
data sets, we weigh the best-
fi
t
α
i
by the
inverse of their error bars
(
95% con
fi
dence interval
)
in the
average. The channel-to-channel variations are consistent with
the uncertainties of
α
i
; therefore, we adopt a single 32-channel-
averaged
̄
a
=
0.91 0.04
as our gain correction factor.
Figure 15.
Exposure of a broadband light source.
(
a
)
Using the expected gain factor inferred from manufacturer information, the
fi
rst
(
columns 0
–
511
)
and the last
quartiles
(
columns 1536
–
2047
)
are visibly different from the middle two.
(
b
)
The same exposure after applying the best-
fi
t gain factor in every quartile.
11
The Astrophysical Journal Supplement Series,
276:43
(
12pp
)
, 2025 February
Nguyen et al.