Mid-Infrared
Sky Background and Absolute Photometric Calibration of the Spitzer Space Telescope Infrared Array Camera
B. Bhattacharya1, W. Glaccum1,
P.J. Lowrance1, W.P. Lee1, W.T. Reach1, J.
Surace1, S. Carey1, M. Lacy1, B. Nelson1,
G. G. Fazio2 and othersÉ
1Spitzer Science Center, Infrared Processing and Analysis
Center, MS 220-6, California Institute of Technology, Pasadena, CA 91125
2Harvard-Smithsonian Center for
Astrophysics, 60 Garden Street, Cambridge, MA 02138
;
Abstract
Since
its launch in late 2003, the Spitzer
Space Telescope Infrared Array Camera (IRAC) has routinely measured
mid-infrared sky brightness from 3.6 - 8.0 mm as part of the nominal operations calibration program. We present a summary of these
observations, including background measurements at the north ecliptic pole as
well as in the ecliptic plane.
Temporal and spatial variations are noted and compared with a
pre-launch, DIRBE-based background model.
We find that offsets between observations and predicted sky brightness
can be attributed both to instrument bias as well as inaccuracies in the
zodiacal background model. The
data are used to derive band-specific scale and offset factors that can be used
to convert measured photometric values to an absolute scale.
1. Introduction
The
mid-infrared background provides a measure of thermal emission within and
outside of the solar system. At
IRAC wavelengths, 3.6, 4.5, 5.8, and 8.0 mm,
(Fazio, et al., 2004), the primary contributor to background emission is
interplanetary dust ???emanating from comets (wtr, if so, need ref) as well
as ?? from asteroid collisions. In addition to targeted studies of this
dust (e.g., Grogan, 2005), calibration observations can be mined to determine
overall morphology and temporal variation of this background emission.
An
empirical zodiacal (zody) background model (Kelsall, 1998), based on
observations by the Diffuse Infrared Background Experiment (DIRBE) on the
Cosmic Background Explorer (COBE) spacecraft (Bennett, et al. 1993; Boggess, et
al., 1992), has been used as the basis for modeling sky background in Spitzer data.
The Spitzer model (Reach,
2000; Bhattacharya and Reach, 2004) is routinely used in the data reduction
pipeline to predict sky background at a given location; the astronomical
community also makes uses of this model through the Spitzer Observer Planning
Tool (SPOT).
In
this study, we consider observations at various ecliptic latitudes in
comparison to the zody model; offsets between observed and predicted sky
background are used to determine revised photometric calibration factors. Reach, et al, 2005, provided an
assessment of in-flight calibration accuracy using 3.6 – 8.0 mm measurements of standard calibration
stars. We supplement their results
by examining additional IRAC calibration datasets, including sky background and
flat field observations taken as part of the Spitzer nominal operation calibration plan from December
2003 through February 2006. In
Section 2, the calibration observations and data analysis techniques are
described. Section 3 discusses the Spitzer zody model. In Section 4,
observed temporal and spatial variations in the 8mm sky background are discussed in the context of the zody
model. The difference between
observed and modeled sky background is used as the basis for conversion of IRAC
photometric measurements to an absolute scale, as presented in Section 5. Finally, in Section 6 these conversion
factors are applied to a representative IRAC dataset from the Spitzer Legacy GOODS program.
2. Observations and Data Analysis
In
order to characterize the sky background level and pixel-to-pixel variability
of the four IRAC detectors, deep observations near the North Ecliptic Pole
(NEP), as well as in the ecliptic plane, are taken systematically as part of the
nominal operations calibration program.
The current cadence of these measurements places them at the beginning
and end of each instrument campaign, leading to a pair of observations taken a
week to 10 days apart each time IRAC is turned on. During the first year and a half of operations, sky darks
and flats were taken more frequently, every two to three days per
campaign. To mitigate thermal
load, the observatory is sequentially dedicated to operate of one of its three
instruments, cycling through IRAC, the Multiband Imaging Photometer for Spitzer (MIPS) (Rieke, et al., 2004) (Houck, et al., 2004)
and then the Infrared Spectrograph (IRS) (Houck, et al., 2004).
Spitzer nominal operations (NomOps) started approximately 90
days after launch its launch on August 25, 2003. The first 90 days (In-Orbit
Checkout or IOC) were spent characterizing the space-based performance of
detectors and observatory, and data from IOC are not included in this
study. The IRAC detectors have
demonstrated a high level of stability throughout NomOps, as shown in the
long-term datasets presented below.
All calibration data publicly available through the Spitzer archive tool, Leopard (http://ssc.spitzer.caltech.edu). Data are taken at all frametimes for
the sky background and dark monitor programs, and taken with 100 second
frametimes only for the flat field and zodiacal background monitoring programs,
all of which are described below. Ensemble
images of 256 x 256 pixels, with a scale factor of 1.22Ó/pixel, are used for
the sky background and flat field analysis, and individual, pipeline processed
frames of the same size and resolution are used here in the dark and zody
monitoring data. These four sets
of calibration data, over 30,000 ???Wen, what is total number of dceÕs??? frames in all, provides a valuable, fiducial
reference set for determining variations in the mid-IR background and
determining instrument characteristics.
2.1.
Sky Background
Background
removal is performed in the standard Spitzer pipeline for IRAC data to subtract thermal emission
from foreground sources such as interplanetary dust as well as to subtract
instrumental dark current.
Background observations are made in a region of the NEP that is relatively
free of mid-IR sources. To obtain
a more accurate measure of the sky background, instrumental bias is removed
using pre-launch, laboratory-based dark frame measurements.
The
standard sequence for obtaining background observations is to observe nine
positions in a 3x3 grid surrounding the observing location with 100 pixel step
sizes, as illustrated in Figure 1.
Table 1 summarizes the NEP observations available at the time of this
paper, including data from December 2003 through 2005 November at the coordinates
(l,b)
~ (125o,87o) J2000 ecliptic or (a, d) ~ (265o,+69o)
J2000 equatorial. Small positional
offsets are required from time to time to avoid bright sources because of the
relative rotation of the Pole as Spitzer
travels around the Sun. For mid-IR
background determination, we use the the 100s high dynamic range skydark data,
in which observations at 0.6 s and 12s are taken prior to the 100s frame. The first two frames are not included
as they are susceptible to the so-called First Frame Effect (FFE), a bias level
variation that is dependent on the time elapsed since the previous
readout. Figure 2a provides the averaged
(not medianed, as per wplee, 4/06)
value for observations at 3.6, 4.5, 5.8, and 8.0 mm of the NEP as part of the Spitzer sky dark calibration
program on days 98-800 of the mission, 2003-Dec-02 through 2005-Nov-02. The average value in DN for each AOR
(Astronomical Observation Request), pipeline calibrated to correct for
instrument bias and the FFE, is plotted here against heliocentric ecliptic
longitude of the spacecraft. The
top set of curves in each panel shows measured sky brightness, and the bottom
set provides a measure of the offset from our zodiacal background (zody) model,
which is described in detail in Section 4. The periodic variability in sky brightness as the spacecraft
samples different lines of sight while traveling around the Sun is clearly
apparent. To examine the role of
frametime on measured background, in Figure 2b, we also present 30-second HDR
sky dark observations at 3.6 and 8.0 mm. These shorter exposure datasets were
taken concurrently and at the same location as the 100sHDR darks listed in
Table 1.
change daynum and dates
with W-PL delivery of more sodb results, BB, 4/20
2.2. Sky
Flats
Need to verify inclusion
of skydark in header keyword FLATNORM Verify inclusion of
skydark in header keyword FLATNORM for both flats and skydarks
Flat
field calibration is performed to remove pixel-to-pixel variations in detector
response. A 256x256 array of
wavelength-dependent scale factors is applied to IRAC data to account for
individual pixel response. Because
the IRAC shutter is set to the open position for the duration of the mission,
flat field calibration files are derived from a deep set of observations taken
near the Ecliptic Plane, which is a region of high zodiacal background, at
locations that are relatively free of stars. A mean solar elongation of 100o is observed in each campaign within a
few degrees of the Plane. As shown
in table 2, the coordinates observed vary as a function of spacecraft
position. SpitzerÕs earth-trailing
orbit around the sun lags the earth by approximately 6o/year. The sequence of observations for flat
data acquisition include the default 0.6 and 12s frames taken to ameliorate the
FFE and 126 additional frames
obtained using a 14-point dither of a 3x3 map, with 120 pixel step sizes and
100s frametime, as shown in Figure 1b.
Since flat field data are obtained at solar elongation of 100o,
the observed
position varies over the course of a year, as shown in Table
2. Figure 4 shows observations at
3.6, 4.5, 5.8, and 8.0 mm in the Plane
as part of the Spitzer sky flat calibration program on days 98-903 of the
mission, 2003-Dec-01 through 2006-Feb-13. As in Figures 2 and 3, median value in DN for the data, as
well as zody model, is plotted against heliocentric ecliptic longitude of the
spacecraft. The skyflat ensemble
plotted here, have been pipeline calibrated to correct for instrument bias and
the FFE.
The pipeline also
subtracts the median value for nearest-in-time 100s skydark observation, but in
Figure 4, this value has been added back in, to provide a more accurate measure
of the sky background at the viewing position.
2.3.
Dark Monitoring
Within
an IRAC campaign, it is important to separate instrumental bias variations from
actual changes in the mi-IR background.
Sky background observations provide calibration datasets for background
removal in the data pipeline, but they are not taken with sufficient frequency
to provide data on bias variation.
During the first ten IRAC campaigns, through July 2004, a calibration
program was implemented to observe the NEP every 12 hours; typically these observations
were executed 14-18 times per campaign. The dark monitor program was
implemented to detect variations in dark current for all frametimes. ???IER
description & obs strategy here???
We present an analysis of the longer
100s observations are considered in the present work. These 100s dark monitor observations, which complement the
sky dark calibration program, observed the NEP position 162 times over the
course of 8 months, as outlined in Table 3.
If
instrumental bias remains constant over an IRAC campaign, observations should
reveal out only the changes in zodiacal background itself. Figure 4 illustrates
the variation in zody over the first 6 campaigns for all four IRAC bands. These observations are consisted with
the skydark data presented in Figure 2a. In addition, the color of the sky measurements should
remain constant over time. Figure 8b indicates the 3.6/8.0, 4.5/8.0, and
5.8/8.0 mm colors are consistent over
time in the dark monitor program.
This is discussed in further detail in Section 4.1, with an examination
of the zody color at both the NEP and in the Ecliptic Plane data, illustrated
in Figures 8 and 9. From these
data, bias levels have been determined to be constant throughout a campaign.
2.4.
Routine Background Monitoring
Initial
analysis of the dark monitoring calibration program, described in Section 2.3,
indicated the presence of temporal variations that were not predicted by the
zody model (Bhattacharya and Reach, 2004). In order to further verify that these variations were due to
secular drift in instrumental bias or a real deviation from the model, the dark
monitoring program was replaced by a routine background monitoring test that
took background measurements at various locations in the sky. Positions observed in addition to the
NEP included the South Ecliptic Pole (SEP) and latitudes of b =
+15o both earthward and anti-earthward, relative to the
spacecraft at solar elongations of 95o (verify). This test was implemented in campaigns
12-17 in August-December 2004.
Table 4 summarizes the viewing geometry and observing times.
2.5. Pipeline and off-pipeline analysis
The
datasets used in this study include sky background and sky flat observations
taken each campaign for use in calibrating concurrent science data as well as
observations designed to monitor long-term variability in the background level. Spitzer IRAC data are processed through
a datatype-specific software pipeline that calibrates observations for
instrumental response and variability as well as observational effects, as
discussed by Lowrance, et al., (2006, in preparation). A detailed description
of the reduction procedures used to convert from data from raw counts to
physical units (MJy/sr) is also available through the Spitzer website. The science products pipeline removes
electronic bias, corrects for wraparound, non-linear detector response and the
FFE. It also uses NEP sky
background levels from the relevant campaign for background subtraction,
applies a flat field scale factor to account for pixel-to-pixel variability,
and conversion from DN to physical units based on the latest calibration
factors (Reach et al., 2005), and finally performs pointing refinement. This level of processing results in a
set of basic calibrated data (BCD), with one .fits file generated per
spacecraft pointing and exposure time.
These files are of size 256 x 256 pixels (one IRAC field of view) with
data in units of MJy/sr. An AOR is
provided as a series of BCDÕs, usually at varying dither positions, that are
mosaiced together in the post-BCD pipeline (Lowrance, et al., 2006).
How large a border (2
pixels) around each flat field bcd is omitted when computing the
median? Is a border ignored
for the skydark medians, too?
Is this to avoid gradients induced by telescope optics/ scattered
light?
Two
of the datasets presented in this study, the dark and routine background
monitoring programs, do not provide routine calibration files for use in the
pipeline. These are available as
BCDÕs, and for these observations we have added back in the sky background
value (header keyword SDRKEPID provides the relevant skydark ensemble product
ID number), and returned to data number values by multiplying by the exposure
time and dividing by the absolute calibration factors presented by Reach, et
al., 2005. In addition, for
channels 3 and 4, an extended source photometric scale factor (dividing by 0.63
and 0.69, respectively) has been applied.
Flatfield ÒuncorrectingÓ is unnecessary as pixel-to-pixel variations are
not significant when working with aor medians.
Routine
calibration products are processed into a final ÒensembleÓ of size 2562
pixels, are available for the skydark and flat field observations. The skydark ensembles are already
provided in DN. Skyflat ensembles
are normalized to the median value in DN.
This value is listed in the header keyword FLATNORM and is applied as a
multiplicative scale factor to obtain measurements in data number.
3. The Spitzer
Zodiacal Background Model
The
mid-IR sky background is a superposition of thermal emission from the cosmic
infrared background (CIB), the interstellar medium (ISM), and the
interplanetary dust (IPD) (Kelsall, 1998). At temperatures of ~3K (Bennett, et al., 1993), the CIB
typically emits most strongly wavelengths near 100 mm. This background,
a remnant of the Big Bang and a signature of the early universe, contributes
negligibly to background in the IRAC wavebands. The interstellar medium is
warmer, at temperatures of ???, and most easily detected in the 12-25 mm range (Bennett, et al. 1993). A local contributor to the mid-IR
background, the zody emits at temperatures near 300K and dominates the IRAC
background at 3.6 – 8.0 mm.
The
zodiacal background is comprised of three major components, each of which
clearly exhibits large-scale structure.
As verified by DIRBE (Kelsall, et al., 1998) the zody is a superposition
of a smooth cloud, a circumsolar dust ring at ~1 AU, and dust bands associated
with certain asteroid families.
Resonant leading and trailing dust clumps have been identified in the
circumsolar dust ring by Dermott, et al., 1994, using the Infrared Astronomical
Satellite (IRAS) and recently by Grogan, et al, 2005, using Spitzer data.
Structures within the smooth cloud and asteroidal dust bands have also
been identified using the DIRBE experiment (Jayaraman, et al., 1999).
The
Spitzer model builds upon Kelsall, et
al., 1998 by modifying several parameters (specify) and introducing a
non-geocentric line of sight.
Using the spacecraftÕs position on a given day as defined by the
ephemeris file, offsets from the Earth are computed to define the current
location of the observatory as the point of origination for viewing a specified
location on the sky. Contributions
to infrared emissiosn along the line of sight, which is extended to 5AU from
the Sun, are computed from modeled spatial distributions of the dust components
contributing to the zodiacal background.
Thermal contribution from the ISM, which is significantly lower at IRAC
wavebands, is calculated using SchlagelÕs dust maps (need ref, further
details). The 3.6 - 8.0 mm signature of the CIB, though poorly
defined at this time, is expected to be below that of the ISM (need ref---wtr,
K-band recent results??).
Consequently, thermal emission from this component is not included in
our model. The CIB is an isotropic
background source, superimposed on the IPD and ISM contributions to the zody,
whose effects can be removed by subtracting the NEP sky from that at the
ecliptic plane, as shown in Figure 11 and discussed further in Section
4.2.
For
the observations presented in Figures 2, 3, 4, and 5, we have computed the
zodiacal background model, as seen in Figures 6a, 6c, and 7a (also need
darkmon, zodymon model bkds). The
biannual spike in the ISM in Figure 7a is due to the spacecraft crossing the
galactic plane. The Spitzer zody model can be accessed through the SPOT
interface, available at http://ssc.spitzer.caltech.edu.
4. Variations in the zodiacal background
4.1
Skydarks and dark monitor
In
order to determine whether variation from the zodiacal background model is
affected by exposure time, we present additional skydark observations taken
with a 30s frametime at the NEP in Figure 2b. Dark monitor observations, as described in Section 2.3, have
been taken to check for change within an individual campaign of background
levels; these files are not used by the IRAC pipeline for data calibration. The
analysis performed on dark monitor data for the results presented here has
involved restoring data to DN values, removing the flat field correction, and
adding back in the sky background. These data are similar in nature to the sky
background measurements but taken with greater frequency. The sky dark should provide a combined measurement of
instrumental noise and offsets as well as the background sky.
Discuss
residuals. Discuss extended source photometric correction (0.63, 0.69) in
channels 3, 4. Discuss
color correctionÉ.
4.2 CIB
Discuss
4.2 Flat Field
As
these data are taken near the ecliptic plane, their trending over time is an
indication of change of sky background value near the ecliptic. Figure 3 shows variability in the flat
field over the first 903 days of the nominal mission, through 2006-Feb-13. Discuss residuals
The
routine background monitoring program, as described in Section 2.4, was
designed as a followup to the dark monitoring program discussed above. These data have been processed through
the science pipeline to generate BCDÕs as with the dark monitoring datasets and
are also not used by the IRAC pipeline for data calibration. Processing of BCDÕs from this program
has involved the same steps used for handling the dark monitoring data. From days ___ through ___ of the
mission, the background was observed at twelve (verify) different
locations. The positions observed
in this program are listed in Table 1d, and the time variability in the sky
background at these positions is plotted in Figure 5. Discuss residuals.
4.4.
Instrument bias removal
If labdark removes bias, zody color vs. time should be constant
provide each bandÕs labdark value, explain how derived, include text to support:
Fig. 6: ground-based lab darks
Fig. 7: zody color vs. time
zody color varies some (quantify)—attribute to Òspace darkÓ needed (using labdark now) and to differences in IPD from predicted
IRACÕs
bias level may be affected by stochastic temperature fluctuations due to
4.4.
Instrument bias levels and temperature
IRACÕs
bias level may be affected by stochastic temperature fluctuations due to ___
(CFT, WTA-why do temps change?), time since last readout, as well as by
anneals. The effects annealing on dark current have become an important issue
in NomOps because of the presence of latent images left by bright sources. Since campaign 3 in early 2004, all
four detectors have been systematically annealed at the beginning of each
campaign, and channels 1 and 4 are also annealed after each downlink.
In
this section, we consider the roles of variations in IRAC cold footpad assembly
and the warm temperature electronics on the dark monitor data, which were taken
frequently in early NomOps; considered time since previous readout, and time
since last anneal on bias level.
4.4.a.
Thermal fluctuations
Thermal
fluctuations in the detector or telescope assembly can potentially introduce
changes in dark current. In order
to examine the effects of temperature effects, we have plotted warm temperature
assembly and the cold footpad temperature (details-describe where these are and
why these are best places to examine -- Glaccum) and fluctuations over several
campaigns to look for correlations with dark monitor measurements at the
NEP. As shown in Figure 12a,
temperature fluctuations after IRAC turns on and stabilizes are small, on the
order of one degree for the warm temperature assembly and a few hundredths of a
degree for the cold footpad. The
top panel in Figure 12a shows that variations in measured background are
unaffected by these small excursions in temperature, even in the 3.6 mm detector where zody signal is lowest and
thermal noise should consequently play a more significant role.
4.4.b.
Time since last readout
IsnÕt
this just the FFE?
4.4.c.
Time since last anneal
Campaign
8 time change w/ anneal
5) Deriving absolute
photometric measurements using IRAC
If labdark removes bias, zody color vs. time should be constant
5.1) correction_factor =
darkmon_dn_with_ffcorr – zody_model
First frame correct the raw dn and subtract the zody model from this. The residual is a measure of the actual difference of observed zody from model as well as a measure of the change in bias from that predicted by ffcorr.
Absolute photometric value = (your bcd) – correction_factor
(in MJy/sr)
5.2.1) Look at change in correction factor vs. time—should be roughly constant
Fig. 8: correction factor vs. time, NEP; show each band
Fig. 9: correction factor vs. time, ecliptic plane; show
each band
Table 5: band, correction factor, to use for abs photometry
6) Application: Analysis of sky bkd variations in pipeline processed
COSMOS/GOODS data
6.1) Look at variation of skydark mosaics over time
<skydarks mosaics> have skybkd subtracted; therefore bkd in mosaics should be close to zero
Fig 10: <skydark mosaics>
vs. time
Consider COSMOS/GOODS bkd plots, where variation is substantial (plot from HaoJing)
Fig 11: <COSMOS/GOODS skydark
mosaics> vs. time
6.2) How does applying correction factor affect this variation?
Wtr usually quotes nominal values of a factor of two over two months in ecliptic and a factor of 10-20% over a year at the pole
7) Conclusions
8. References
Bennett, C.L., et al., Scientific results from COBE, Adv. Sp. Res., vol.13, no. 12, 409-423, 1993.
Bhattacharya, B., and Reach, W.T., Zodiacal Background: Spitzer Observations vs. DIRBE-Based Model, BAAS 205, #56.06.
Boggess, N., et al., The COBE Mission – Its Design and Performance Two Years after Launch, ApJ, 397, 420-429, 1992.
Dermott, S.F., et al., A Circumsolar Ring of Astgeroidal Dust in Resonant Lock with the Earth, Nature, 369, 719-723, 1994.
Fazio G.G. , et al., The Infrared Array Camera (IRAC) for the Spitzer Space Telescope, ApJS, 154,10-17, 2004.
Grogan, K., et al., First Spitzer Observations of EarthÕs Resonant Rings,
Protostars and Planets V, 1286., p. 8462, 2005.
Houck, J.R., et al., The Infrared Spectrograph (IRS) on the Spitzer
Space Telescope, ApJS, 154, 18-24, 2004.
Jayaraman, S., Studying the Fine Structure and Temporal Variations of
the Zodiacal Clooud and Asteroidal Dust Bands Using the 3-Year Near-IR COBE-DIRBE
Data, NASA Technical Report, NASA/CR-1999-209246,
1999.
Kelsall, T., et al., The COBE Diffuse Infrared Background Experiment
Search for the cosmic Infrared Background. II Model of the Interplanetary Dust Cloud,Ó AJ, 508, 44073,
1994.
Lowrance, P.J., et al., IRAC Pipeline Description Paper, title/journal
TBD, 2006.
Reach, W.T., SIRTF Background Estimation Methods and Implementation, http://ssc.Spitzer.caltech.edu/documents/background/, 2000.
Reach, W.T., et al., Absolute Calibration fo the Infrared Array Camera
on the Spitzer Space Telescope, PASP,
117, 978-990, 2005.
Rieke, G.H., et al., The Multiband Imaging Photometer for Spitzer
(MIPS), ApJS, 154, 25-29, 2004.
SchlagelÉISM maps
Silverberg, R.F., et al., Proc. SPIE, 2019, 180, 1993—not in
ADS—replace w/ correct DIRBE instrument description paper.
Fig. 1a. Skydark Fig 1b. Skyflat aors
Fig. 2a—100s NEP sky darks – observations
Fig. 2b—30s NEP sky darks – observations and zody model
Fig. 3—100s ecliptic plane sky flats – observations and zody model
Fig. 4—dark monitor NEP observations
***make sure skydark has been added back in correctly in sodb retrievalÉthese plots should match skydarks in fig 2!!
Fig. 5—Zody monitoring observations
POLES:
Leading Blob, PLANE:
Trailing Blob, PLANE:
Leading Blob, +- 15degs from ecliptic plane
Trailing Blob, +- 15degs from ecliptic plane
Fig. 6a—100s NEP sky darks –zody model
Fig. 6b—100s NEP skydark residuals
Fig. 6c —30s NEP skydark models
Fig. 6d—30s NEP skydark residuals
Fig. 7a—100s ecliptic plane sky flats models
Fig. 7b—100s ecliptic plane sky flats – residuals
Fig 8 – 100s NEP sky dark colors
Fig 8b – 100s zody monitor NEP sky dark colors—if these plots match skydark colors, which they should, donÕt include
Fig 8c – 30s NEP sky dark colors
Fig 10 – 100s ecliptic plane sky flat colors
Fig 11. Ecliptic minus NEP
Fig 12a – instrument temperature and zody—ch4 only
Fig 12b – variation with time since last anneal- ch1 is easiest to see (low dn)
Fig 13 – ch4 variation w/ readout
Fig. 8:
correction factor vs. time, NEP; show each band
Fig. 9:
correction factor vs. time, ecliptic plane; show each band
Fig 10:
<skydark mosaics> vs. time
Fig 11:
<COSMOS/GOODS skydark mosaics> vs. time
Tables
Table 1: IRAC skydark observing times and positions