# JWST NIRCam Defocused Imaging: Photometric Stability Performance and How it
Can Sense Mirror Tilts

Everett Schlawin Steward Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA  Thomas Beatty  Department of Astronomy
University of Wisconsin
Madison, Madison, WI 53706  Brian Brooks  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Nikolay K. Nikolov  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Thomas P. Greene NASA Ames Research Center, Space Science
and Astrobiology Division, MS 245-6, Moffett Field, CA, 94035, USA  Néstor
Espinoza Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Department of Physics & Astronomy, Johns Hopkins
University, Baltimore, MD 2121818, USA  Kayli Glidic Steward Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA  Keith Baka  Anton Pannekoek Institute, University of
Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands  Eiichi Egami
Steward Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA  John Stansberry  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Martha Boyer  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Mario Gennaro  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Department of Physics and Astronomy
Johns Hopkins University
3400 North Charles Street, Baltimore, MD 21218, USA  Jarron Leisenring Steward
Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA  Bryan Hilbert  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Karl Misselt  Steward Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA  Doug Kelly  Steward Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA  Alicia Canipe  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Charles Beichman NASA Exoplanet Science Institute/IPAC
Jet Propulsion Laboratory, California Institute of Technology
1200 E California Blvd
Pasadena, CA 91125  Matteo Correnti  Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  J. Scott Knight  Ball Aerospace & technologies, Corp,
1600 Commerce Street, Boulder, CO 80301  Alden Jurling NASA Goddard Space
Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  Marshall D. Perrin
Space Telescope Science Institute
3700 San Martin Drive
Baltimore, MD 21218  Lee D. Feinberg  NASA Goddard Space Flight Center, 8800
Greenbelt Rd, Greenbelt, MD 20771, USA  Michael W. McElwain NASA Goddard Space
Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  Nicholas Bond
ADNET Systems, Inc./Code 550, NASA’s Goddard Space Flight Center, Greenbelt,
MD 20771  David Ciardi  NASA Exoplanet Science Institute/IPAC
Jet Propulsion Laboratory, California Institute of Technology
1200 E California Blvd
Pasadena, CA 91125  Sarah Kendrew  European Space Agency, Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore MD 21218  Marcia Rieke
Steward Observatory
933 North Cherry Avenue
Tucson, AZ 85721, USA

###### Abstract

We use JWST NIRCam short wavelength photometry to capture a transit lightcurve
of the exoplanet HAT-P-14 b to assess performance as part of instrument
commissioning. The short wavelength precision is 152 ppm per 27 second
integration as measured over the full time series compared to a theoretical
limit of 107 ppm, after corrections to spatially correlated 1/f noise.
Persistence effects from charge trapping are well fit by an exponential
function with short characteristic timescales, settling on the order of 5-15
minutes. The short wavelength defocused photometry is also uniquely well
suited to measure the realtime wavefront error of JWST. Analysis of the images
and reconstructed wavefront maps indicate that two different hexagonal primary
mirror segments exhibited “tilt events” where they changed orientation rapidly
in less than $\sim$1.4 seconds. In some cases, the magnitude and timing of the
flux jumps caused by tilt events can be accurately predicted with a telescope
model. These tilt events can be sensed by simultaneous longer-wavelength
NIRCam grism spectral images alone in the form of changes to the point spread
function, diagnosed from the FWHM. They can also be sensed with the FGS
instrument from difference images. Tilt events possibly from sudden releases
of stress in the backplane structure behind the mirrors were expected during
the commissioning period because they were found in ground-based testing. Tilt
events have shown signs of decreasing in frequency but have not disappeared
completely. The detectors exhibit some minor (less than 1%) deviations from
linear behavior in the first few groups of each integration, potentially
impacting absolute fluxes and transit depths on bright targets where only a
handful of groups are possible. Overall, the noise is within 50% of the
theoretical photon noise and read noise. This bodes well for high precision
measurements of transiting exoplanets and other time variable targets.

stars: atmospheres — stars: individual (HAT-P-14 (catalog )) — stars:
variables: general

††facilities: JWST(NIRCam), JWST(FGS), Palomar††software: astropy (Astropy
Collaboration et al., 2013), photutils v0.3 (Bradley et al., 2016), matplotlib
(Hunter, 2007), numpy (van der Walt et al., 2011), scipy (Virtanen et al.,
2020), starry (Luger et al., 2019), pynrc (Leisenring, 2019), webbpsf (Perrin
et al., 2014), pysiaf (Sahlmann et al., 2019) jwst (Bushouse et al., 2022)

##  1 Introduction

JWST will provide transformational new studies of exoplanet atmospheres with
its unprecedented view in the infrared (Ahrer et al., 2022; Greene et al.,
2016; Morley et al., 2017; Schlawin et al., 2018; Bean et al., 2018). The
NIRCam instrument’s imaging, coronagraphic and spectrographic modes are
providing powerful new insights into a range of astrophysical environments
from the Solar System to the most distant galaxies from 0.6 µm to 5.0 µm
(Rieke et al., 2005). The NIRCam instrument has two wavelength channels that
simultaneously observe the same field. NIRCam’s grism time series mode
produces simultaneous spectroscopy on the long wavelength channel and
photometry on the short wavelength channel. The long wavelength spectroscopy
employs a grism that enables spectroscopy from 2.4 to 5.0 µm at R=1100 to
1700, with the wavelength coverage determined by the filter selected on the
filter wheel (Greene et al., 2017). This wavelength range includes many
prominent features in exoplanet atmospheres including H2O, CH4, CO, CO2 and
NH3 (Greene et al., 2016). The molecular, atomic and ionic spectral features,
when detected in exoplanet atmospheres, can give clues about the formation of
planets, composition, dynamics, structure and cloud and haze composition (e.g.
Bitsch et al., 2021; Mordasini et al., 2016; Powell et al., 2019; Kempton et
al., 2017).

Given the small scale heights of planetary atmospheres ($\lesssim
10^{-3}R_{\odot}$) compared to their host star radii ($\sim 1R_{\odot}$) and
their low temperatures compared to their host star temperatures
($T_{p}^{4}/T_{*}^{4}\lesssim 10^{-2}$, where $T_{p}$ and $T_{*}$ are the
temperatures of the planet and star respectively), exoplanet transit
spectroscopy requires extreme precision. The largest signals from even the
most favorable planets are still very small. The ‘prominent’ 1.4 $\mu$m water
vapor feature strength varies from 100 ppm in the prototypical hot Jupiter HD
209458 b (Deming et al., 2013) down to less than 30 ppm for the super-Earth GJ
1214 b (Kreidberg et al., 2018). The most favorable CO2 signatures are
predicted to be 50 ppm and below in the temperate Earth-sized TRAPPIST-1 d and
e (Barstow & Irwin, 2016; Lustig-Yaeger et al., 2019). Lessons from previous
space telescopes such as Spitzer, Kepler and the Hubble Space Telescope (HST)
have taught us that many instrument systematics can be present including
intrapixel sensitivity, thermal breathing, charge trapping, and pointing
errors (Beichman et al., 2014).

Here we present the performance of the NIRCam short-wavelength time-series
photometry based on commissioning observations of the HAT-P-14 system. A
companion paper, Beatty et al. (2022) describes the simultaneous long-
wavelength grism spectroscopy. The light that enters NIRCam is split by a
dichroic beamsplitter so that the short wavelengths (0.6 to 2.3 µm) and long
wavelengths (2.4 to 5.0 µm) are directed to different channels’ optics and
detectors. The pupil wheel and filter wheel selections determine the
wavelength extents of the observations ( a short wavelength F210M filter
paired with the long wavelength filter F322W2 will cover approximately 1.99 to
2.23 µm on the short wavelength channel and 2.43 to 4.01 µm on the long
wavelength channel). The flight software is configured to run the detectors
with the same size subarrays and readout patterns so the two exposures are
commanded to be simultaneous to within one frame time. For the grism time
series mode, two short wavelength detectors (NRCA1 and NRCA3) centered on
nearly the same piece of sky as the long wavelength (NRCALONG) are read out by
detector electronics and downloaded from the observatory. Appendix A shows the
relative layouts of the detectors.111Also see https://jwst-
docs.stsci.edu/jwst-near-infrared-camera/nircam-instrumentation/nircam-
detector-overview for the detector layout (STScI, 2016).

When performing grism spectroscopy, the short wavelength channel can be
(currently) configured to use the Weak Lens +4 or Weak Lens +8 lens optics,
which are designed for mirror wavefront sensing (Greene et al., 2010). The
Weak Lens +4 and Weak Lens +8 lens optics are a subset of all defocusing
lenses, which also include Weak Lens -4 and Weak Lens -8. The Weak Lens +4 (on
the filter wheel) and Weak Lens +/- 8 (on the pupil wheel) can be used in
series simultaneously so that focuses of -8, -4, 0, +4 and +12 Peak-to-Valley
(P-V) waves can be configured (Greene et al., 2010). The lenses were tuned to
be sensitive to various spatial frequencies and levels of aberration in the
wavefront at 2.12 µm (Dean & Bowers, 2003; Perrin et al., 2016). The Weak Lens
+4 defocuses the light by 4.0 P-V units at 2.12 µm and results in a core PSF
of approximately 31 pixels and the Weak Lens +8 defocuses the light by 8.0 P-V
units at 2.12 µm and results in a core PSF of approximately 65 pixels.
Physically, the Weak Lens +8 defocuses the light by modifying the wavefront by
+8.0 waves P-V at 2.12 um at the exit pupil, where the positive convention is
that the phase at the edge of the wavefront leads the phase at the center of
the pupil. We assume that the equation for the phase in waves for the Weak
Lens +8 is $8*(r^{2}-0.5)$ where r is the exit pupil radius normalized to
unity at the edge and 0 in the center. This wavefront error displaces the best
focus along the chief ray.

The defocused PSF from a weak lens makes the short wavelength imaging very
sensitive to changes in the wavefront and it also spreads the light over more
pixels to decrease the rate of saturation for a given star brightness. While
not yet supported, there is also an active proposal to allow the use of the
Dispersed Hartmann Sensor (DHS) in the short wavelength channel instead of the
weak lenses. Utilizing the DHS in the short wavelength channel would allow
simultaneous spectroscopy across a large fraction of the full NIRCam
wavelength regime (Schlawin et al., 2017).

The target HAT-P-14 b (Torres et al., 2010) was selected for calibration
purposes because it has no strongly detectable atmospheric features and a flat
spectrum due to a high gravity (42 m s-2, calculated from Stassun et al.,
2017) and small atmospheric scale height (2$\times 10^{-4}$ R⊙). The 3.4 MJ
1.4 RJ 1600 K planet (Stassun et al., 2017; Southworth, 2012) orbits a
$K=8.85$, 6600 K F-type star with low chromospheric activity (Torres et al.,
2010). It was observed by JWST NIRSpec (Espinoza et al., 2022), NIRISS and
NIRCam to enable cross-instrument performance checks and to determine the
transit depths are consistent. The expected variations in the transmission
spectrum are 16 ppm, assuming a typical atmosphere that exhibits atmospheric
features that are equivalent to 0.9 atmospheric scale heights (Wakeford et
al., 2019), so the differences across wavelengths are expected to be about as
large as the theoretical ideal photon noise $\sim$9 ppm for these
observations. One option to characterize stability is to observe a known
quiescent star and verify that the lightcurves are flat with time. However, in
the event that the lightcurve is not perfectly flat, disentangling the
measured precision from the baseline trend curves is challenging. Any de-
trending done to the data, such as a Gaussian process regression, can remove
trends but could also remove astrophysical signal on a time variable source.
Therefore, we observed a known transiting planet with a known ephemeris to
determine the ability of JWST to measure the transit depth. While the target
was chosen to have no significant atmospheric signal (no significant change in
transit depth with wavelength), it still has a transit depth of 6480 $\pm$ 240
ppm (Torres et al., 2010) or about 0.6% which is readily detectable.

Figure 1: The Weak Lens +8 PSF spreads the light over a large region, which
reduces the chance of saturation and reduces intra-pixel sensitivity. The Weak
Lens +8 was designed for retrieving the primary mirror state and thus phase
retrieval with the Weak Lens enables real-time monitoring of the mirror
wavefront error. The above image is near the middle of a 2048$\times$128
SUBGRISM128 subarray with the F210M filter, a 27.0 second long integration
time on HAT-P-14 with a plate scale of about 31 mas /px. The background
subtraction annulus as shown as concentric circles and is the inner radius is
the same as the source aperture used for photometry. The subarray position was
adjusted downward after HAT-P-14 b commissioning to better center the
hexagonal PSF on the subarray.

Section 2 describes the observations during commissioning and how they were
analyzed. Section 3 describes systematic effects in the data including mirror
tilt events, tilt timescales, the charge trapping ramp and observed non-
linearity. Section 4 describes the noise performance, pointing performance and
time accuracy as measured from in-flight data and the transit depth precision
when accounting for contamination from a background source. We present our
conclusions in Section 5.

Table 1: Summary of Key Times During Observation

UT start time | Integration Number | Description
---|---|---
(YYYY-mm-ddThh:mm:ss) |  |
2022-05-02T06:43:04 | 1 | Exposure Start
2022-05-02T09:21:34 | 344 | Transit Start (Contact 1)
2022-05-02T10:10:01 | 449 | HGA Move
2022-05-02T10:30:20 | 492 | Transit Midpoint
2022-05-02T10:30:41 | 493 | Tilt Event 1
2022-05-02T11:23:19 | 607 | Tilt Event 2
2022-05-02T11:39:05 | 641 | Transit End (Contact 4)
2022-05-02T12:43:25 | 780 | Exposure End

Note. — Times are in Coordinated Universal Time. The barycentric dynamical
times are approximately 4.63 minutes later. Integration numbers are given for
1-based counting

##  2 Observations and Image Processing

###  2.1 Observation Description

We observed the hot Jupiter HAT-P-14 b to test the instrument performance and
verify that the NIRCam Grism Time Series mode was suitable for science. The
planet was selected to have a short duration transit (2.3 hr), high brightness
that enables high precision, low stellar activity and high planet surface
gravity to have a small atmospheric signal. The short duration requirement was
selected to minimize the needed observing time but has the flip side of
preferring targets with near-grazing transits (high impact parameters).
HAT-P-14 b’s impact parameter is 0.91 (Fukui et al., 2016), so fitting the
limb darkening without the planet crossing through the stellar mid-point can
complicate the transit depth measurement and stellar models may be preferred
for the limb darkening law, as described in Section 4.1. The observation
exposure started at 2022-05-02T06:43 UTC, which was the earliest start time
allowed by the Astronomy Proposal Tool (APT) special requirements to ensure a
long baseline before transit ingress. The lightcurve was observation 1 of
Commissioning Program ID 1442, which is available on the Barbara A. Mikulski
Archive for Space Telescopes (MAST). Table 1 lists key times during the
observations.

The exposure duration was 6 hours, which enabled 2.6 hours of stabilization
time before planet ingress. The SW channel was configured with the Weak Lens+8
pupil, F210M filter which covers approximately 1.9 to 2.2 $\mu$m. This was
paired with the GRISMR pupil and F322W2 filter on the long wavelength channel,
discussed in Beatty et al. (2022). The exposure setup was a single exposure
with the BRIGHT2 readout pattern, 20 groups integrated up the ramp and 780
integrations for a 2048$\times$128 subarray (SUBGRISM128) with 4 output
amplifier channels. NIRCam readout electronics sample non-destructive reads
(ie. frames) to create a ramp and then reset the detector at the end of an
integration. Detector groups are a set of 1 or more detector image frames
where the frames have been either averaged or skipped by onboard electronics
and the average frame (ie. a group) is downloaded from the spacecraft. The
averaging or else skipping of frames between groups is done to reduce the data
volume on some observations. Observations when more than one frame is averaged
or skipped per group reduce the data volume as compared to saving every frame
per integration. In BRIGHT2, there are 2 frames (ie. detector samples)
averaged per group and zero frames skipped. This resulted in a frame time of
0.67597 seconds, a group time of 1.35194 seconds and a cadence of 27.72001
seconds per integration for 780 integrations.

The 6 hour observation was continuous with no interruptions. Pointing
performance was extremely stable as discussed in Section 4.3 below. There was
one high gain antenna (HGA) move during the exposure but no interruptions or
pauses to the integrations in the 6 hour exposure. This allows detector charge
trapping effects to approach a steady state, unlike with HST where each
satellite orbit around Earth results in a new charge trapping ramp effect
approximately every 90 minutes (e.g. Berta et al., 2012).

The point spread function (PSF) with the Weak Lens+8 pupil is shown in Figure
1. The Weak Lens +8 (along with the -8 wave and +4 wave lenses) is designed to
measure the optical path differences of the primary mirror surface. It was
enabled as an option in the grism time series and imaging time series modes to
spread out the light over more pixels and also reduce the saturation on bright
targets. Having the light spread out over more pixels reduces the intrapixel
sensitivity, which strongly affected Spitzer Space Telescope lightcurves
because the PSF was highly undersampled (Ingalls et al., 2016). It also allows
realtime monitoring of the mirror surface along with the long wavelength grism
spectroscopy, discussed in Section 3.1. We note that the full extent of the
PSF is asymmetrically truncated by the subarray. This will be mitigated in
Cycle 1 science observations because an update was made to better center the
subarray position. Even with better centering, the SUBGRISM128 subarray
truncates some of the wings of the PSF. In other words, the commissioning
observations (Figure 1) had the PSF is asymmetrically truncated and in science
observations it will be still truncated in the wings but more symmetrically.
Fortunately, JWST pointing is so stable (to be discussed in Section 4.3) that
there were no impacts from the PSF truncation on the lightcurve and zero-
padding the image for wavefront analysis resulted in high quality wavefront
phase retrievals (to be discussed in Section 3.1).

Figure 2: The default rateints product for integration number 83 with no extra
corrections (top) has large pre-amplifier offsets (rectangular-shaped offsets)
and 1/f noise (horizontal banding). A row-by-row, odd/even by amplifier
(ROEBA) correction, described in Section 2.2 uses background pixels to reduce
the pre-amplifier offset and 1/f noise. The background pixels are the ones
outside of the dashed black circle that has a radius of 201 pixels.

###  2.2 Data Analysis from Uncalibrated Data to Rates Per integration

We begin with the uncal data (also known as “MAST level 1 uncalibrated”, “User
Data Product Stage 0 Fully-Populated FITS file” or Data Processing Level 1b).
We then run Stage 1 of the Calwebb STScI pipeline (Bushouse et al., 2022) with
some modifications described below, to produce a rateints file which contains
the counts in DN/s for each integration.

We started with the STScI JWST Detector 1 Stage 1 pipeline version 1.6.0 and
the Calibration Reference Data System (CRDS) context jwst_0822.pmap to convert
the raw data values to signal slopes (DN/s) per integration. The Detector
Stage 1 pipeline begins by scaling the groups (which doesn’t affect NIRCam
readout modes), initializing the data quality flags, flagging saturated pixels
and then subtracting a superbias. When examining the superbias subtraction, we
note that every 4 integrations has a bias offset structure due to the fast
frame resets that reset pixels across the whole detector to ensure that charge
doesn’t migrate into the subarray. For this SUBGRISM128 subarray, the fast
frame reset occurs every 4 integrations. However, accounting for the different
superbias every 4 integrations resulted in very little change to the
lightcurve so we used a single superbias subtraction for all integrations.

Normally, detector stage 1 processing then does a reference pixel correction
step. The reference pixels are light-insensitive pixels that share the same
electronic noise sources as the regular light-sensitive pixels and thus allow
efficient subtraction of common-mode noise sources. Normally, the bottom and
side reference pixels are used to mitigate odd/even column effects, pre-
amplifier resets and 1/f noise. However, the SUBGRISM128 subarray for the
short-wavelength time series mode has no reference pixels along the top or
bottom detector rows.222The SW subarray is designed to be centered on the
defocused PSF when the same source is centered near the Y=34 long wavelength
pixel on the LW subarray. See section A for a diagram. The relative positions
of the short and long wavelength detectors when projected on the sky result in
the weak lens +8 image being centered at Y= 167.5 in 1-based counting absolute
coordinates on the short wavelength detector. The subarray position was
adjusted to better center the PSF after HAT-P-14 was observed. Thus, the
reference pixel step does not correct for large pre-amplifier offsets and
smaller odd/even offsets. We instead replace the reference pixel step with a
similar step that uses background instead of reference pixels to remove many
of the same effects.

We use a shorthand for this modified reference pixel step ROEBA, which stands
for row-by-row, odd/even by amplifier correction, which lists the steps in
reverse order. First, we select one of the four amplifiers for correction at a
time. In this case a block pixels from 1 to 512, 513 to 1024, 1025 to 1536 or
1537 to 2048 pixels in the X direction and the entire 128 pixel tall subarray
in the Y direction. For this correction, it is necessary to define a
background region to use as a proxy for reference pixels that has minimal
contamination from bright sources. We select all pixels that are more than 201
pixels away from the central PSF as shown in Figure 2. We then apply a slow-
read correction, which subtracts the median odd count level in the background
region from all odd numbered columns and the median even count level from in
the background region from all even numbered columns. This removes the pre-
amplifier offsets. We then calculate the row-by-row median count level from
the background region and subtract this from all pixels in that row. This
largely removes the longer time scale (low frequency) components of the 1/f
noise (e.g. Schlawin et al., 2020). The resulting correction from ROEBA shown
in Figure 2 (bottom) has substantially smaller pre-amplifier reset offsets in
each amplifier as well as less 1/f noise banding along the horizontal
direction. We note that the ROEBA method uses many more pixels across the
horizontal fast-read direction than the side reference pixels on the detector
so it can improve results even when reference pixels are available in a
subarray. Another advantage of the ROEBA correction is that many fewer pixels
are erroneously marked as jumps at the jump detection step (described below).
One assumption in the ROEBA step is that it relies on a clean background
region and could potentially over-subtract when there is faint scattered light
or background sources so inspection for neighboring sources and faint emission
is necessary before applying it to all NIRCam data.

We next apply the non-linearity correction with default parameters. The result
of the bias subtraction and ROEBA step is that the signal level is close to 0
DN at the background before applying the linearity correction step. The stage
1 pipeline normally has a dark current subtraction step after non-linearity
correction, but dark current on the NIRCam short wavelength detectors is less
than 0.05 e-/sec and there is currently too much signal from cosmic rays and
persistence to measure well and subtract on these detectors. We next run the
jump step correction with a threshold of 6 sigma. Without the ROEBA
correction, many pixels are erroneously flagged as “jumps” (e.g. cosmic rays)
because the pre-amplifier offsets and 1/f noise can appear as jumps in signal
from one detector group to another. With the ROEBA correction, we note that
these erroneous jumps are much less frequent and instead the jump step flags
true outliers such as cosmic rays. One exception where the jump step does not
flag a cosmic ray perfectly is the outer radii of ‘snowball“ events (Rigby et
al., 2022), as shown in Figure 2 near X=737,Y=101. Here, only the brighter
portions of the snowball are flagged with the jump detection algorithm used in
the analysis for this paper. As the final step of stage 1, we run the ramp fit
step with default parameters to calculate a count rate per pixel in Data
Numbers (DN) per second. There is another gain scaling step for NIRSpec data
but it does not affect the NIRCam data presented in this paper.

###  2.3 Photometric Extraction

We next use aperture photometry with photutils (Bradley et al., 2016) to
measure the flux for each integration to derive a flux as a function of time.
We fit the central peak of the PSF with a Gaussian and used this to determine
the aperture center for each integration. We use a circular source aperture
with a radius of 81 pixels, and the mean background rate from a background
annulus with an inner radius of 81 and an outer radius of 101 pixels. These
pixels were found to produce the minimum lightcurve scatter from an aperture
size grid search. Although the ROEBA step described above largely removes the
background, we found that the additional background annulus subtraction
improved the precision, likely because of residual 1/f not removed by ROEBA.
We found the same level of noise whether we did aperture centering or kept the
apertures fixed, with the exception of better photometry during the HGA move
affecting one integration to compensate for the small amount of image motion
within that one integration. We normalize the flux time series to a value near
1.0 (1000 parts per thousand, ppt) for lightcurve fitting and noise analysis,
which we describe in Section 4.1.

##  3 Lightcurve Systematics

The lightcurves overall exhibited very low level systematic errors, which we
describe in this section. There were changes to the PSF due to “tilt” events
as discussed in Section 3.1 through 3.3, an exponential ramp discussed in
Section 3.4 and some evidence for non-linearity discussed in Section 3.5.

###  3.1 Tilt Events

We originally noticed a large jump in the long wavelength time series (Beatty
et al., 2022) but also found one at the same time at some aperture sizes in
the short wavelength and a smaller jump later in the time series. The jumps in
flux correspond to changes in the mirror surface, known as “tilt events”
(Rigby et al., 2022). These were first noticed by choosing an arbitrary
reference image (in this case the rate from the 6th integration) and dividing
the rate from all other integrations by it. Figure 3 shows three example ratio
images from 1) before the tilt events, 2) after the first tilt event and 3)
after the second tilt event. The tilt events show up as clear wave patterns in
these differential images due to changes in the mirror surface. The short
wavelength Weak Lens +8 defocused PSF is part of the wavefront sensing tools
aboard JWST and is thus highly sensitive to changes in the mirror surface.

Figure 3: Weak Lens Ratio Images before and after both Tilt Events (top) and
Phase retrieval, oriented as if looking down at the mirror surface from the
secondary mirror (bottom plots).  Figure 4: The jump in flux caused by the C6
tilt event is wavelength dependent. The black point and blue points with error
bars show the measured flux jump size for the short wavelength (SW) aperture
of 2.4″ and LW aperture of 0.630″, respectively. Our current model (green
circle) correctly predicts the SW channel’s jump with a 2.4″ aperture but
under-predicts the LW 0.63″ jump size (orange curve) for the grism spectrum,
especially at 2.5 to 3.0 µm.

We used a non-linear optimization based phase retrieval algorithm (Fienup,
1982, 1993) based on the algorithmic differentiation (Jurling & Fienup, 2014).
The coherent propagation model used a flexibly sampled discrete Fourier
transform (Jurling et al., 2018). We used a bias and gain invariant error
metric (Thurman & Fienup, 2009) as the cost function. The phase retrieval
model was initialized using the wavefront and pupil data calculated from the
JWST optical model for the nearest available field point, the NRCA3-FP2MIMF
multi-instrument multi-field point. Because PSF data were only available with
the +8 wave weak lens, this was a single image phase retrieval problem. We
configured the model with 128 pixels across the array storing the pupil and
256 pixels across the cropped and padded image. Because of the band-pass of
the F210M filter used for imaging, we used a broadband point-spread function
model (Fienup, 1999; Jurling et al., 2018). We ran the phase retrieval
optimization in two steps.

In the first step we used the first image in the time series to establish a
starting point. We sequentially estimated image position (using a sub-pixel
cross correlation method (Guizar-Sicairos et al., 2008)), global low order
Zernike aberrations, segment level piston, and tip/tilt errors (1st order
segment Zernike aberrations). Finally, we performed joint estimation over a
smoothly interpolated low resolution grid in wavefront and amplitude. With a
single image the ability to distinguish between phase and amplitude errors in
this last step is limited.

In the second step, we begin from the reference point established by the first
phase retrieval. In this case the optimization was done jointly over global
and segment Zernike aberrations without sequential bootstrapping. This
facilitates change detection by requiring the pupil amplitude and higher order
wavefront variation to be the same throughout the time series, but still
allowing low order and segment wavefront changes through time.

The phase retrieval results are shown in Figure 3 and it is clear that the C6
mirror segment changed orientation (tilted) at event 1 and that the C1 mirror
segment tilted at event 2. In event 1, the wavefront over C6 changed by 18 nm
RMS (evaluated over the segment) compared to the initial wavefront, and in
event 2, C1 changed by 26 nm (again evaluated over the segment). These changes
are much smaller than the wavelength of the light, so both the individual
segments and the overall telescope remain diffraction limited.

As shown in Figure 4, the C6 event produced a larger change with a magnitude
that varies from 200 ppm to 1000 ppm across the 2.4 µm to 4.0 µm wavelength
range for the long wavelength and 254 $\pm$ 22 ppm in the short wavelength
photometry using an aperture radius of 79 pixels or 2.45 arcsec. Using the
wavefront phase retrieval described in this section above (Jurling & Fienup,
2014) for the optical path differences, we make a prediction for the magnitude
of the flux jump by comparing the enboxed or encircled energy before and after
the jumps. We use enboxed energy for the long wavelength spectroscopic
extraction box and encircled energy for the short wavelength photometry. The
short wavelength (SW) model prediction of 260 ppm is very close to the
measured 254 $\pm$ 22 ppm for the large aperture used in the short wavelength
time series. The long wavelength (LW) jump model prediction under-predicts the
jump size from 2.5 to 3.5 $\mu$m but agrees from 2.7 to 4.1 $\mu$m. Some of
the difference between the model and measurement could be the difference
between an imaging and dispersed PSF and how they are extracted. Preliminary
models with a dispersed LW grism image can reproduce the 1000 ppm change at
2.5 $\mu$m.

###  3.2 Ways to Detect Tilt Events

Figure 5: The lightcurves exhibited jumps most noticeably in the long
wavelength spectroscopy, shown here as a broadband time series (plot A). These
jumps (marked as dash-dot vertical lines) can be detected in a variety of
ways. Apertures placed on the short wavelength weak lens (WL) PSF are highly
sensitive to mirror tilts on mirrors C6 and C1 (plot B). The time series are
shown on a group-by-group difference image (points in blue and orange, plot B)
as well as on the full jump-corrected integration (solid blue and orange
lines, plot B). The FGS instrument can also sense mirror tilts by a dot
product of a difference images, as defined in Equation 1 (plot C). The FWHM of
the long wavelength spectroscopy can also be used to sense mirror tilts (plot
D). The HGA move (vertical dotted line) also can create spikes in some tilt
statistics. The apertures used to sense the C6 and C1 mirror1 tilts (right
plot) are the ones used to generate the time series in plot B.

It is possible to quantitatively measure tilt events in addition to visually
inspecting the differential images or doing the phase retrieval shown in
Figure 3. The mirror changes can be evaluated with photometric apertures on
key parts of mirror surfaces, such as in Figure 5 (right plot). The time
series of these apertures can cleanly sense the two tilt events like step
functions as shown in Figure 5 (left second from the top). We also calculate
this photometry on the difference between pairs of adjacent detector groups to
assess the mirror changes at a higher time cadence (colored points in Figure
5).

The NIRCam grism time series and time series imaging modes are the only modes
currently supported that allows simultaneous high cadence wavefront sensing
along with the time series. In some time series modes such as the NIRSpec
Bright Object Time Series (Birkmann et al., 2022) or MIRI low resolution time
series (Kendrew et al., 2015), defocused imaging is not currently available
for real-time wavefront sensing of the primary mirrors, so other measures are
desirable to sense tilt events. NIRISS Single Object Slitless mode (SOSS)
(Doyon et al., 2012) has a de-focusing lens so this mode has some analogous
capabilities as the short wavelength weak lens.

We explored some ways to sense tilt events with the NIRCam grism time series
spectroscopy and the fine guidance sensor (FGS) fine guide data streams (Doyon
et al., 2012). We experimented with a few different statistics for the FGS
images. We found that the flux from the telemetry stream333See the
SA_ZFGINSTCT keyword https://jwst-docs.stsci.edu/methods-and-roadmaps/jwst-
time-series-observations/jwst-time-series-observations-noise-sources, (STScI,
2016) can sense the first tilt event (C6) but could not easily reveal the
second tilt event (C1). In addition, the first tilt event (C6) could be
detected with a dot product with the average PSF or the $3\times 3$ pixel flux
of the time series but the second tilt event from the C1 mirror was harder to
pull out of the noise. The FWHM of the FGS 8$\times$8 images also shows step-
like changes with the two tilt events but at low signal to noise. We found
that principal component analysis (PCA) could reveal evidence of both tilt
events but is also not easily distinguishable above the noise.

The noise-weighted “differential dot product” was most effective in detecting
tilt events with FGS.

$D_{i}\equiv\left((\vec{A_{i}}-\vec{R})/\vec{V}\right)\cdot\left(\vec{M}-\vec{R}\right),$
(1)

where $D_{i}$ is the differential dot product of 8$\times$8 images reshaped to
64-pixel linear vectors. In the expression, $\vec{A_{i}}$ is a single FGS cal
data image, $\vec{R}$ is a reference image after the tilt event, $\vec{V}$ is
the variance image, and $\vec{M}$ is a reference image before the tilt. This
method did use prior information about the timing of tilt events from NIRCam
data to find the average image from before the tilt $\vec{M}$ and the average
image after the tilt $\vec{R}$, but it may be possible to iteravely scan the
time series to determine $\vec{M}$ and $\vec{R}$ from FGS alone. This
statistic essentially magnifies the differences between the shape of the PSF
before and after the tilt event and weights by the noise. Figure 5 shows that
both tilt events can be sensed with FGS using a dot product, where the
$\vec{M}$ and $\vec{R}$ are chosen for the first tilt event (C6) and second
tilt event (C1).

Additionally, the full width at half maximum (FWHM, bottom left plot in Figure
5) of the long wavelength grism PSF is sensitive to tilt events because the
PSF changes with the mirror tilt. Thus, even when weak lens imaging is not
available, the FGS images and science instrument FWHM can be used in all time
series modes to give clues about tilt events. However, Equation 1 requires
some knowledge of the timing to find $\vec{M}$ and $\vec{R}$ unless they can
be found iteratively. Therefore, a more general-purpose indicator of tilt
events may be the FWHM of science data, which can be tracked in all time
series observations.

Tilt events are hypothesized to be structural microdynamics in the telescope
that may occur when stresses in the backplane structure behind the mirrors are
suddenly relaxed. As these stresses are released, the frequency of tilt events
is expected to decrease in time. Regular wavefront measurements indicate that
they are less frequent in the transition from commissioning to science
observations in July 2022 than earlier in commissioning. However, tilt events
were common even 4.5 months between launch and these observations, and similar
tilt events may occur during Cycle 1 science observations.

###  3.3 Tilt Timescale

The mirror changes appear to be step functions in Figure 5, so the change
happens on a timescale faster than the 27 second cadence of integrations. We
inspect the mirror changes at a higher cadence (but noisier) time series by
calculating the mirror tilt specific photometry on the group-by-group
difference images, which have a cadence of 1.351 seconds. In this analysis,
adjacent points are thus anti-correlated because they share a detector group
so if one sample is anomalously high, the next one will be anomalously low. As
shown in Figure 6, there is a rapid change that takes 2 sampling durations of
1.351 seconds each to go from low to high or high to low, or in other words
one sample between the low and high values. There are two causes for the
intermediate sample: 1) the tilt timescale is between 1.351 and 2.702 seconds
and 2) the timescale is shorter than 1.351 seconds and occurs midway through
the group. We consider the first scenario less likely as it would require some
fine-tuning to cause a tophat-like disturbance between these two time
intervals that shows little sign of change in the PSF beyond 2.702 seconds. We
therefore expect that the timescale is faster than the shortest measurable
time with the NIRCam photometry which is the 1.351 second group time. We also
note that these observations used the BRIGHT2 mode, which includes two frames
within a group so the tilt could happen between these two frames within a
group or within one of the frames. We do not see any discontinuities within
the image that would indicate a change within the frame, but the PSF only
covers a fraction of the field of view so it is not a strong constraint.

Figure 6: Mirror photometry on the pairwise-subtracted images, zoomed in on
events. We use the same apertures as shown in Figure 5 to sense the tilts on
the C1 and C6 primary mirror segments. These two happen on a timescale as fast
or faster than the 1.351 second time between BRIGHT2 detector groups, which
contain 2 frames each. For the C1 tilt event, the jump likely happened in the
middle of a detector group so it has a sample between the low and high flux
values.

###  3.4 Charge Trapping Ramp

The HST WFC3 IR detector, which is an earlier generation HgCdTe detector,
exhibits ramps with an exponential settling behavior (e.g. Berta et al., 2012;
Zhou et al., 2017). Ground-based laboratory tests showed likely negligible
effects for typical JWST detectors (e.g. Schlawin et al., 2021). However, the
NRCA3 short wavelength detector exhibits the most persistent charge and likely
charge trap density of the 10 NIRCam detectors that are used in flight
(Leisenring et al., 2016). NRCA3 is the same detector used for the short
wavelength component of the grism time-series observations when the long
wavelength filter is selected to be F277W, F322W2, F356W.444https://jwst-
docs.stsci.edu/jwst-near-infrared-camera/nircam-operations/nircam-target-
acquisition/nircam-grism-time-series-target-acquisition The NRCA1 detector
that is paired with the F444W filter, had about half the accumulated counts
from charge trap release as the NRCA3 detector in ground based tests
(Leisenring et al., 2016), so it is expected to have a smaller amplitude
exponential ramp.

We fit an exponential model to the charge trapping behavior, as is common with
HST charge trapping ramps (e.g. Berta et al., 2012) and show the results in
Figure 7. We first correct the small 260 ppm jump in the lightcurve using a
wavefront model described in Section 3.1. We fit the lightcurve with the
following planet and systematics model:

$f(t)=\left(A+Bx^{\prime}+Cx^{\prime
2}\right)\left(1-R\exp{(x-x_{0})/\tau}\right)f_{a}(t),$ (2)

where A, B and C are coefficients in the quadratic baseline trend and
normalization, $x$ is barycentric time, $R$ is the exponential amplitude,
$x_{0}$ is the exposure start time, $f_{a}(x)$ is the astrophysical limb
darkened lightcurve (starry, Luger et al., 2019), with a 4 parameter
polynomial limb darkening law from ExoCTK and $x^{\prime}$ is the normalized
time,

$x^{\prime}=\frac{x-x_{med}}{x_{max}-x_{min}},$ (3)

where $x_{med}$ is the median time, $x_{max}$ is the maximum time and
$x_{min}$ is the minimum time. We fit the lightcurves by fixing $C=0$ (ie. a
linear fit) and also letting it be a free parameter (ie a quadratic fit). As
will be shown in Section 4.2, significant correlated errors are seen in the
residuals if a linear baseline trend is adopted instead of a quadratic trend.

We find an exponential amplitude $R$ of 731 ppm and an exponential time $\tau$
of 5.1 minutes for a linear trend and $R$ of 656 ppm and $\tau=$15 of minutes
for a quadratic trend. The normalization and polynomial trend constants for
the quadratic trend are A=${1000.24\pm 0.01}$ parts per thousand (ppt),
B=${-0.911\pm 0.03}$ ppt and C=${0.80\pm 0.14}$ ppt. In absolute units, this
corresponds to a slope of -0.15 ppt/hr and derivate of the slope of 0.022
(ppt/hr2). We note that initially, we fit the baseline and exponential start
to just the initial part of the lightcurve and found an order-of-magnitude
exponential settling timescale of 11 minutes (Rigby et al., 2022). The 5.1 and
15 minutes minutes came from a MCMC Bayesian fit to the full lightcurve with a
linear and quadratic baseline respectively, whereas the 11 minutes comes from
least squared minimization of the first 300 points (before planet ingress) and
has a steeper linear slope. We have not determined the cause of the long
timescale trend, but note a that different linear trends were seen on the NRS1
and NRS2 detectors (Espinoza et al., 2022) so it may be detector-related. The
quadratic slope and exponential ramp terms in Equation 3 are correlated and
thus the change in slope is fit with a different exponential settling time. We
also looked through the previous JWST activities and found that NIRCam’s
previous use was 37 hours before for wavefront sensing. NIRCam detectors
remained in idle reset mode for those 37 hours so it is unlikely any long
timescale traps were filled and are being released to create the downward
slope seen in the data.

Figure 7: The lightcurve settling behavior is very fast with a fitted settling
timescale of 5-15 minutes but is somewhat degenerate with the time series
baseline.

###  3.5 Non-Linearity Effects

The H2RG detectors used in the near infrared instruments on JWST are never
strictly linear at any well filling fraction, ranging from sub-percent non-
linearity to tens of percent at 98% the hard saturation value (e.g. Canipe et
al., 2017). However, they become increasingly non-linear as the detector
approaches full well capacity and saturation (e.g. Plazas et al., 2017).
Correction polynomials are applied by the CalWebb JWST pipeline (Bushouse et
al., 2022) to linearize the counts as function of counts (DN). A different but
analogous method has been shown that linearity corrections are possible even
up to high well filling fractions ($\sim$97% Canipe et al., 2017).

We assessed the difference between pairs of groups up the ramp to look for
evidence of non-linearity. The stellar flux is highly stable within a 27
second long integration so it is expected that a linearity-corrected ramp
should have a constant difference between each successive group. We find
however that the first 4 group differences and the last 9 have a higher rate
of flux than the middle 6 group differences, as shown in Figure 8. The early
higher fluxes may be related to the release of trapped charge (e.g. Smith et
al., 2008; Leisenring et al., 2016) or a type of reset anomaly (Rauscher et
al., 2007). We do not perform a dark current subtraction, as discussed in
Section 2.2. However, the dark current is less than 0.05 e-/sec on the short
wavelength NIRCam detectors, and the 1% change in the differential samplings
(shown in Figure 8) on top of a representative rate of 400 e-/s would require
4 $e^{-}$/s of dark current. So the reset anomaly seen here may be different
from the anomaly seen on other H2RG devices (Rauscher et al., 2007).

Exoplanet time series observations with a small number of groups ($\lesssim
5$) could have an absolute photometric flux offsets but also systematic
differences in the transit depth as compared to observations with many groups
($\gtrsim 5$). This is because the non-linearity effects can change the
response of the detector to a differential signal (ie. a non-constant
derivative of count rate as a function of signal in e-/s/Mjy). With the
observed 1% change in signal from group 2-1 to group 4-3 in Figure 8, a 2%
deep transit of a hot Jupiter could have a measured transit depth of up to
$\sim$ 1% $\times$ 2% $\times$ 1/4 = 50 ppm deeper if just using group 2 and
1. This difference is below the measurement noise for a single transit of
HAT-P-14 b using only group 2 - 1 but could be assessed on a brighter target.
There is also a possibility of reciprocity failure with HgCdTe detectors that
can cause systematic changes in transit depth (Biesiadzinski et al., 2011;
Schlawin et al., 2021).

Figure 8: The difference in counts between groups up the ramp is not constant
across an integration, as would be expected after linearity correction curves
are applied. The violin-shaped points are the distributions of fluxes as
calculated by the pairwise difference image of two detector groups, using all
of the out-of-transit integrations . The median flux from all out-of-transit
integrations is shown as a short horizontal line. Future observations with
just 2 or 3 total groups may exhibit absolute flux differences and transit
depth differences due to this non-linearity soon after detector reset.

##  4 Lightcurve Performance

Figure 9: Lightcurve and residuals before and after corrections for an
exponential ramp and jump from the first tilt event. The blue symbols with
error bars are the fluxes for each integration at a cadence of 27.7 seconds,
while the orange symbols are 8 minute long time-integrated bins that aid in
viewing smaller-level changes. Red symbols are outlier points not used in the
fitting.

###  4.1 Lightcurve Fitting

We fit the lightcurve with a transit model to determine the lightcurve
performance, discussed in Section 4.2 and the timing accuracy, discussed in
Section 4.5. We remove a 260 ppm jump in the F210M (2.1 µm) time series due to
a tilt event using a wavefront model of the optics discussed in Section 3.1,
allow a quadratic trend with time and fit an exponential settling ramp
discussed in Section 3.4. We use the integration mid-times in the barycentric
reference frame and barycentric dynamical time standard int_mid_BJD_TDB
included in the INT_TIMES extension of the JWST data products.

We fit the corrected lightcurve with a starry transit lightcurve model (Luger
et al., 2019), an exponential ramp, a quadratic trend in time and the 260 ppm
jump correction. The planet’s near-grazing impact parameter (0.91 Fukui et
al., 2016)) means that the planet does not traverse near the stellar midpoint
and fitting the limb darkening parameters as free parameters can lead to large
uncertainties in the planet’s radius. We fix the limb darkening law to a 6600
K, [Fe/H]=0.11, $\log{g}$ = 4.25 (Stassun et al., 2017) ATLAS9 model (Kurucz,
2017) calculated with ExoCTK for the F210M filter for $\mu>0.05$ where $\mu$
is the cosine of the angle between the line of signt and the emergent
intensity (e.g. Kipping, 2013) for a 4 parameter non-linear law. We use the
starry lightcurve model, which uses a polynomial limb darkening law (Agol et
al., 2020), so we fit the intensity function from a 4 parameter nonlinear law
with a 6 parameter polynomial limb darkening law, which has been shown to be
accurate to $\lesssim 0.5$ ppm differences in flux (Agol et al., 2020). We
start with priors centered on the values from Bonomo et al. (2017) for the
period, inclination, eccentricity and argument of pericenter, but widened
these in case of systematic errors to 83.5 $\pm 0.3^{\circ}$, $e$=0.1071 $\pm$
0.01 and $\omega$=106.1 $\pm 5^{\circ}$. We use the ephemeris from publicly
vailable TESS data and a wide a/R∗ of 8.9 $\pm$ 1.0 centered on the value from
Stassun et al. (2017). The resulting lightcurve fits and resiuals are shown in
Figure 9. We show a model fit that does not account for two of the systematics
to better illustrate them as well as another that accounts for them (the
charge trap ramp and tilt event jump).

###  4.2 Photometric Performance

After fitting the lightcurve with a transit model that includes a jump
correction from a phase retrieval, an exponential charge trapping ramp and
quadratic baseline described in Section 4.1, we analyze the statistical
properties of the residuals. We include all points that are not marked as
outliers (all points within 5 $\sigma$ of the best fit model) which includes
775 out of 780 total integrations. The standard deviation (scatter) in all of
the non-outlier residuals is 152 ppm, compared to a theoretical limit of 107
ppm from photon and read noise. Thus, the measured noise is 42% larger than
the theoretical limit, some of which could be due to 1/f noise (Schlawin et
al., 2020). Even after ROEBA subtraction, there remains higher frequency
(shorter timescale than the 5.24 ms row read time) noise. We note that the
background annulus subtraction reduced the standard deviation of out-of-
transit flux in the lightcurve by 37% over skipping the background annulus
subtraction so there is likely residual 1/f noise. We next assess time-
correlations in the data by binning the residuals.

A key metric in the performance of the NIRCam photometry is how well the noise
scales as a function of bin size. This commonly is presented in the form of an
Allan Variance plot (e.g. Pont et al., 2006; Croll et al., 2011). In this
plot, the photometric scatter is computed as a standard deviation as a
function of bin size. In the case where each time sample is independent, the
noise drops as $1/\sqrt{N}$ and this is plotted as “white noise scaling”. When
the measured photometric scatter begins to diverge from the $1/\sqrt{N}$ power
law, this is a sign that the time samples are correlated and time-dependent
systematics are present.

Figure 10 (left) shows that the noise falls with $1/\sqrt{N}$. Thus, no noise
floor is measurable down to the 20 ppm level, but 1/f noise limits the
precision in our current analysis to 42% above the theoretical limit. It may
be possible to optimize the aperture to a hexagonal aperture, but previous
tests with a circular annulus had little difference in noise performance on
simulated data. For this Allan variance analysis, we have removed the first
tilt event from the lightcurve using a model discussed in Section 3.1, a
quadratic trend with time and an exponential settling ramp discussed in
Section 3.4. For comparison, we also calculated an Allan variance curve when
the baseline trend was fit with a linear polynomial instead of a quadratic
polynomial in time. In this curve, the noise begins to grow near 5 minutes
where the noise is about 60 ppm. Thus, there is some curvature to the
lightcurve either related to instrument or astrophysical trends.

Figure 10: The lightcurve errors per bin drop nearly as $1/\sqrt{N}$ for $N$
time points, after correcting for the exponential startup, quadratic trend and
transit (left plot curve). Thus, the noise is largely independent for each
integration. If we only include a linear baseline trend to fit the lightcurves
(right), there is excess noise beginning for bin sizes around 4 minutes. The
precision before time binning is about 42% worse than the ideal limit of
photon and read noise, likely because of 1/f noise correlations between pixels
within each frame.

The measured 20 ppm lightcurve scatter at a time bin size of 30 minutes can be
compared to the state-of-the-art best precision lightcurves from space-based
photometers. For the brightest targets observed by Kepler, the precision was
measured to be $\sim$15 ppm (Jenkins et al., 2010). For the bright exoplanet
system 55 Cnc, the precision with TESS was 10 ppm for 30 minutes (Meier Valdés
et al., 2022) and for CHEOPS the precision achievable on a 1.6 hour eclipse
observed 41 times using only out-of-eclipse data was 3 ppm (Demory et al.,
2022), which would scale to 3 ppm * sqrt(1.6 hours/0.5 hours * 41 eclipses
/2)=20 ppm for 30 minutes. The scaling uses the relative time of the eclipse
and the half hour benchmark, 41 separate eclipse events that were averaged and
finally a factor of 2 accounting for the fact that the out-of-transit to in-
transit ratio adds another factor of sqrt(2) in noise. Elsewhere, the
instrumental noise on hour-long timescales for CHEOPS is reported to be 15 to
80 ppm (Maxted et al., 2022). In the JWST photometry presented in this work,
precision is limited by photon counting statistics, so brighter sources with
more photons per minute will be needed to assess what is the highest possible
precision as compared to the state-of-the-art performance.

###  4.3 Pointing Performance

Target acquisition was successful and placed the target at X=1060.7 px,
Y=167.5 px on the NRCA3 detector in full frame 1-based Data Management System
coordinates. Pointing was stable to 0.01 pixels (0.3 mas) in the X direction
and 0.009 px (0.3 mas) in the Y direction. Some of the higher frequency jitter
is thus averaged over the 27 second long integrations. Thus, JWST attitude
control provides incredible pointing stability at the 10-2 pixel level and
this produces no noticeable changes in flux with position and jitter, likely
constituting a negligible part of the error budget. The guide star has an FGS
magnitude of 15.3 and we expect similarly high precision pointing performance
for guide stars from magnitude 12.5 to 15.5. Under the HgCdTe crosshatching
structures on the NIRCam ALONG/A5 detector, 2 mas pointing was expected to
produce 6 ppm changes of flux, so 0.3 mas jitter is likely to matter at the
single digit ppm level and flux changes at this level cannot be measured for
the HAT-P-14 target.

###  4.4 High Gain Antenna Move

JWST high gain antenna moves maintain pointing at the designated ground
stations on Earth’s Deep Space Network. While high gain antenna moves should
happen during slews or between exposures, the moves are permitted to occur
after 10,000 s during long time series observations with JWST. We had a high
gain antenna adjustment at 2022-05-02T10:10:01 UTC, which was measurable with
the Fine Guidance Sensor and NIRCam short wavelength time series centroids. As
shown in Figure 11, the pointing change from the HGA move settles very quickly
in less than 0.5 minutes. Furthermore, the position was returned back to the
original pointing to within 1 mas. The data around an HGA move can be
discarded and in the case of weak lens photometry that is spread over many
pixels, only produced a transient 500 ppm change in flux. Thus, HGA moves are
not expected to cause significant issues to most time series observations as
long as the Fine Guide mode does not lose a guide star from its subarray.

Figure 11: The High Gain Antenna moves are unlikely to have a big impact on
time series observations. The HGA move only affects about 0.5 minutes of data,
which is mostly corrected by shifting the aperture but could be excluded from
the lightcurve if it is an outlier. The normalized flux changes by a maximum
of about 0.5 parts per thousand (ppt). The plate scale of NIRCam’s Short
Wavelength detector is 31 mas/px

.

###  4.5 Timing Accuracy

We find a transit center time of 2022-05-02T10:34:55 +/- 7 seconds BJDTDB,
which is consistent (within 1.7 $\sigma$) with a prediction from the TESS
ephemeris of 2022-05-02T10:36:35.1 +/- 60 seconds BJDTDB. Other planets with
higher precision ephemerides will test JWST timing to higher accuracy. There
is also a dedicated GO program program identification number 1666 (PI Poshak
Gandhi) that will use a double white dwarf binary and is expected to calibrate
the absolute timing of an exposure to the 100 ms level.

###  4.6 HAT-P-14 B Contamination

The HAT-P-14 system was observed from the ground with Palomar adaptive optics
(AO) on 2021-08-08 UTC to assess the contamination and dilution of the transit
depth and find any unknown companions. No companions were detected with a
contrast less than $\Delta$mag = 7.0 within 0.5″. The nearby stellar companion
HAT-P-14 B (Ngo et al., 2015) was also imaged with Palomar AO to better
constrain the infrared colors and contamination on the transit depth. The
separation is 0.85″ at a position angle of 264 degrees, which is well within
the 2.5″ source aperture used in the lightcurves of the central (hexagonal)
portion of the PSF shown in Figure 1. With the Palomar AO imaging, we find a
delta K magnitude between the HAT-P-14 A and B of $\Delta$K=4.99, which is a
similar wavelength to this JWST F210M photometry. The JWST target acquisition
image shown in Figure 12 shows both HAT-P-14 A and HAT-P-14 B. Using the
target acquisition image, we find that the contrast is $\Delta$ MagF335M=5.03
$\pm$ 0.05 for the F335M filter (3.35 µm) and the separation is 0.83″. This
contrast is a similar to $K$ band, as expected for the Raleigh Jeans limit for
long wavelengths.

Using webbpsf, we simulate the overlap of two Weak Lens +8 PSFs for a 81 pixel
aperture and estimate the transit depth dilution. We use the flight wavefront
optical path difference evaluated at a time of 2022-05-02T10:30 UTC using
webbpsf and perform aperture photometry on the simulated PSFs of HAT-P-14 A
and HAT-P-14 B separately. For the F210M filter at 2.1 µm, we find that
HAT-P-14 B should dilute the fitted 6540 $\pm$ 22 ppm transit depth by 59 ppm
for an undiluted transit depth 6599 $\pm$ 22 ppm. This is within 3.2 $\sigma$
of the long wavelength F322W2 broadband result of 6670 ppm, but with
independent fitting methods and priors on orbital parameters and limb
darkening. This is also consistent with the NIRSpec time series broadband fit
with 6627 $\pm$ 8 ppm with an independent analysis (Espinoza et al., 2022),
with different priors on orbital parameters and limb darkening. We do not
expect the atmosphere to contribute much more than 15 ppm as described in
Section 1 for 0.9 atmospheric scale heights, but atmospheric gases could
contribute at 1.5$\sigma$ level for 2 atmospheric scale heights of absorption.

Figure 12: Long Wavelength Target Acquisition centered near HAT-P-14 A with a
faint ($\Delta$mag=5) stellar companion HAT-P-14 B (upper left) at 860 mas
separation that dilutes the transit depth.

##  5 Conclusions

Transiting exoplanet science and other time-variability studies will benefit
from JWST high precision time series photometry using the defocused photometry
that is collected simultaneously with the grism time series mode. Here, we
present performance results from the hot Jupiter HAT-P-14 b that was observed
to commission the instruments with a known flat transmission spectrum signal.
We detect the planet transit at high precision and find that the transit depth
is consistent with the NIRSpec result to within 28 ppm $\pm$ 20 ppm as
expected for this relatively high gravity planet.

The weak lens time series is particularly informative about small changes in
the PSF as a result of wavefront variations, and we found two clear tilt
events where two different hexagonal primary mirror segments quickly changed
orientation with a timescale $\lesssim 1.4$ seconds. Difference images clearly
show the tilt events associated with specific mirror segments. These tilt
events can cause jumps in time series’ signal levels but can be predicted
effectively for short wavelengths using a wavefront model. We also show how
tilt events can be sensed with other instrument modes that do not use
defocusing optics. FGS differential images and the FWHM of the PSF can both
reveal tilt events as step functions and will be good metrics to assess mirror
stability.

The NRCA3 detector exhibited a charge trapping persistence ramp that is
similar in shape to the ones seen on HST, but it settles out quickly on a 5-15
minutes decay timescale with an amplitude of 660 to 700 ppm and does not have
a big impact on the time series.

The overall precision is very high and has a low scatter over the residuals of
152 ppm compared to the photon and read noise value of 107 ppm per 27 second
integration, so it is only 41% above the theoretical limit for this quiescent
F-type $K$=8.85 star. Some of this excess noise may be due to residual 1/f
noise not corrected by the row-by-row subtraction. The noise bins down
approximately with the square root of the number of points in a time bin,
indicating that systematic noise is minimal after the exponential and jump
corrections and a quadratic polynomial as a function of time. Overall, the
prospects are good for high precision time series measurements of exoplanets
and other astrophysical phenomena. Defoucsed photometric monitoring will be
valuable for measuring mirror tilt events and mitigating their impact on high
precision measurements.

## acknowledgements

Funding for E Schlawin is provided by NASA’s Goddard Space Flight Center. T
Greene acknowledges funding from the JWST project via NASA WBS
411672.05.05.02.02. This research has made use of the SIMBAD database,
operated at CDS, Strasbourg, France; and NASA’s Astrophysics Data System
Bibliographic Services. Part of the research was carried out at the Jet
Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration (80NM0018D0004). We
respectfully acknowledge the University of Arizona is on the land and
territories of Indigenous peoples. Today, Arizona is home to 22 federally
recognized tribes, with Tucson being home to the O’odham and the Yaqui.
Committed to diversity and inclusion, the University strives to build
sustainable relationships with sovereign Native Nations and Indigenous
communities through education offerings, partnerships, and community service.
Thank you to Eddie Bergeron for sharing analysis on detecting tilt events with
FGS.

##  Appendix A Subarray Positions

To help orient JWST users on the subarrays and relative positions of the short
wavelength and long wavelength detector images, we provide diagrams of the
locations as measured by in-flight data. Figure 13 displays the relative
locations, in telescope coordinates, of the NIRCam LW grism trace (dashed
lines) and the NIRCam SW hexagonal PSF (green hexagon) from the +8 wave
defocused pupil element (Weak Lens +8), which are observed simultaneously.
There is a small amount of refraction with the grism so there is a vertical
offset between the two positions as placed in the same coordinate system. The
edges of the full frame images for the A1 (short wavelength), A3 (short
wavelength) and A5 (long wavelength) detectors are all shown as dotted lines
while the edges of the SUBGRISM128 subarrays for the same 3 detectors are
shown as solid lines. The positions here are shown for Cycle 1 after
commissioning where small (8-10 SW px) tweaks were made to better-center the
A1 and A3 subarrays on the hexagonal PSF. The reference pixels on JWST NIRCam
detectors are at the full frame boundaries, so the relative positions of the
both SUBGRISM64 and SUBGRISM128 subarrays necessitate excluding the bottom 4
reference pixel rows on the short wavelength NRCA1 and NRCA3 detectors.
Significant improvements in performance can be made if background pixels are
used in the same manner as reference pixels to correct for amplifier offsets
and 1/f noise, as discussed in Section 2.2.

Figure 13: The NIRCam SW and LW channels observe approximately the same region
of the sky simultaneously, however the overlap of detectors is not exact. The
relative position of the SW defocused weak lens image (green hexagon) is shown
compared to the LW grism F322W2 (top figure) and F444W (bottom figure) central
traces (brown dashed lines). The SW SUBGRISM128 subarrays on the A1 and A3
detectors (blue solid lines) are aligned to capture light from the hexagonal
+8 wave PSF while the the LW SUBGRISM128 subarray (solid red line) is aligned
to capture light from the LW grism trace and surrounding background area. The
full frame detector boundaries (dotted lines) are where the 4 reference pixels
are located, so the bottom references are included with the LW SUBGRISM128
subarray (solid red line) but no bottom reference pixels are available in the
A1 and A3 SUBGRISM128 subarrays (solid blue lines). All positions are shown in
V2 and V3 Telescope coordinate system using pysiaf (Sahlmann et al., 2019)
after 8-10 SW pixel adjustments were made to the A1 and A3 subarrays following
HAT-P-14 commissioning observations to better center the A1 and A3 subarrays
on the hexagonal PSF.

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