Instrument Science Report NICMOS 2006-002
NICMOS Count Rate Dependent
Non-Linearity in G096 and G141
Ralph C. Bohlin, Adam Riess, & Roelof de Jong
January 2006
ABSTRACT
Since the discovery of the NICMOS count rate dependent non-linearity
documented in NICMOS ISR 2005-002, additional tests have been conducted to
further understand and quantify the effect. Long integrations of up to 25 minutes
exhibited the same level of non-linearity as the original 1-3 minute integrations.
Observations of the star P041C on high background from an internal flat field
lamp provides another measure of the wavelength dependence of the nonlinearity to compliment the measures based on pure hydrogen WD models.
1. Introduction
The count rate dependent non-linearity discovered by Bohlin, Lindler, & Riess
(2005, BLR) is characterized in more detail with new NICMOS grism data. In
Section 2, integration times of ~25 min that are typical of science observations
are compared with the shorter times of 1-3 min used by BLR. Section 3 is an
evaluation of the new data where the number of dither steps on the detector is
much less than the 15 steps used by BLR. Section 4 details the revised flat
fielding strategy, while Section 5 includes the new P041C data in a re-analysis
1
to update the BLR correction algorithm. Section 6 dispels worries that
persistence effects from previous observations can seriously affect the grism
data considered here. Section 7 presents typical results on the accuracy of the
final NICMOS spectrophotometric fluxes. In a companion ISR, de Jong, et al.
(2006, JBRB) present a similar study of the non-linearity effects for NICMOS
photometry.
2. Dependence of Count Rate on Integration Time
As summarized in Table 1, three stars were re-observed with integration times
of several minutes in order to better represent typical science observations of
faint targets. To fit within the total time available in each orbit, the number of
dither positions were reduced from the BLR standard of 15 positions. However,
the total range of the dithers in Y, perpendicular to the dispersion axis, was
maintained at 15 pixels, i.e. 3arcsec for the 0.2arcsec/px plate scale of NIC3.
Table 1. Observations with Long Integrations and
Fewer Dither Positions
Star
GD153
WD1057+719
WD1657+343
Rootname
n94a02
n9g501
n97u54
Obs-Date
2005Jul26
2005Jun13
2005Jul25
Dithers
3
2
4
Integ(min)
7.5
25.6
23.5
Normally, the grism spectroscopy from the NIC3 camera is derived from the
“CAL” files from the STScI NICMOS pipeline (see BLR). These CAL files
represent the best final values of the measurements in the 256x256 imaging
format, as corrected for cosmic ray hits. Also provided by the STScI NICMOS
pipeline are the intermediate readout IMA images that are the count rates for
each non-destructive read. Analysis of the IMA files reveals the evolution of the
differential count rates up to the full integration period. These average
differential count rates in each time step in the exposure sequence can be
derived from the difference in total counts in the adjacent images in the IMA
file. For the 0.8-1.2µm range of G096 where the non-linearity of BLR is the
2
largest, Figures 1-2 show the differential net count rates as a function of
cumulative integration time for the two brighter stars. WD1647+343 is so faint
that the weak, un-removed cosmic ray hits cause too much noise for its
analogous plot to be meaningful. The gross signal is the total response of all
pixels centered within one pixel of the spectral trace center-line. Because the
NICMOS detectors are subject to amplifier drift during an observation, the net
signal is defined by subtracting from the gross a background that is the median
signal within a strip lying 20 to 50 pixels below the spectrum.
Figure 1 - Count rate in each step of the sample sequence as a function
of cumulative integration time of the intermediate non-destructive
readouts for WD1057+719. Solid line and squares - 25.6 minute integration at
two dither positions per Table 1. Dotted and triangles - Original BLR
observation n8vj04 with 2.9min integrations at each of 15 dither positions.
The rate at each point is normalized to the average count rate of the last four
3
integrations.
Figures 1-2 demonstrate a scatter in the count rates that is larger for the first few
reads with small time steps. The fainter star WD1057+719 has more scatter than
the brighter GD153. The typical count rates converge within 1-2% of their
average after one minute of integration. The occasional high point can be caused
by cosmic ray hits, which are not removed.
Figure 2 - As in Figure 1 for GD153. The original observation n8u402 (triangles) has
one min integrations at each of 15 dither positions.
3. Spectrophotometric Repeatability
Figure 3 shows the broad and narrow band spectrophotometric repeatability for
the repeated observations of the five white dwarf (WD) stars, the two solar
4
analogs (P041C and P330E), and BD+17°4708. The journal of observations for
these seven stars appears in Tables 1-2. The WD stars include the three primary
standards G191B2B, GD71, and GD153 that determine the absolute sensitivity
of the grism modes (BLR), while the fainter two WD stars WD1057+719 and
WD1657+343 also have pure hydrogen NLTE model atmosphere calculations.
Residuals for the WD stars are computed relative to these models. (See Section
5 for more discussion). Residuals for the other three stars are relative to the first
NICMOS observation of each star, where these residuals are reduced by 1.414
for comparison with the WD residuals computed relative to the noise free
models.
Table 2. Repeat Observations with 15 Dither Positions
Star
Rootname
BD+17°4708 n8vj07
BD+17°4708 n94701
BD+17°4708 n94702
G191B2B
n8u405
G191B2B
n94a03
GD71
n8u401
GD71
n94a01
GD153
n8u402
P041C
n8u403
P041C
n9jj02-bef
P041C
n9jj02-aft
P330E
n8br01
P330E
n8u406
WD1057+719 n8vj04
WD1657+343 n8vj03
Obs-Date
Integ(s)
2004Jan10
2004Nov15
2004Nov25
2003Sep6
2005Mar1
2004Jan19
2005Feb28
2004Jun9
2004Jan19
2005Nov12
2005Nov12
2002May27
2004Jun19
2004Feb2
2004Jun6
32
10
10
104
104
56
64
56
72
12*
12*
56
96
176
152
* Before and after the lamp-on observations discussed in Section 5. Both have 5 dither
positions.
Except for the faintest star WD1657+343, the excellent NICMOS photometric
repeatability is demonstrated by average residuals of <1% with a typical rms
5
pixel-to-pixel scatter of ~1%. The observations with 3-5 dither positions do not
Figure 3 - Residuals for repeated observations vs. average signal. Upper panel:
Percent deviation from the WD model or from the original observation, as averaged
over 0.81-1.18µm for G096 (circles) or 1.15-1.90µm for G141 (squares).
Lower panel: Pixel-to-pixel rms scatter in the same wavelength intervals.
The number of dither positions is normally 15, while the integer inside
a few symbols indicates the number of dither positions when reduced below
the normal sequence of 15 steps. The two-dither spectra are too noisy to use
6
for constructing the merged WD1057+719 spectrum.
exhibit anomalous residuals, and the spectra are utilized in all the analyses with
weight equal to the 15-dither data. However, the observation of WD1057+719
with only two dither steps is anomalous, especially in the rms scatter of >1.5%
for both G096 and G141. Figure 4 illustrates the G096 residuals for
WD1057+719 along with GD153, which has a three dither observation. The
noise in the two-dither WD1057+719 data is much worse than the corresponding
15-dither observation, while the scatter of the three- and 15-dither GD153
spectra are comparable. The region below 0.92µm generally shows excess
scatter because of the strong, sharp features in the spectra, eg. GD153 shown in
Figure 5. These features arise in the interference filter used to delimit the
bandpass and are under sampled, i.e. there are large changes across the
wavelength coverage of a single pixel. Any actual spectral features from 0.8 to
0.92 are <<1%. Because of sub-pixel offsets in the sampling of the sharp
instrumental features in different observations, the flux calibration of the net
signal to a flux spectrum has pixel-to-pixel noise of a few percent and results in
generally larger rms values for G096 in comparison to G141.
Presumably, the cause of the excess noise in the two-dither observations is
caused by flat fielding errors. New flat fields may make two-dither data useful.
Observations with fewer dithers are more efficient. For example, the four-dither
observation of WD1657+343 achieves more than twice the efficiency of the 15dither observation set. The longer integration times more than compensate for
the increased residual flat fielding errors, because the rms values with a 4 inside
the plot symbols for WD1657+343 in Figure 3 lie below the 15-dither rms data
points. Until improved flat fields are available, the best compromise number of
dither steps is four or five.
7
Figure 4 - Residuals for repeated observations of WD1057+343 and GD153
in comparison to their pure hydrogen NLTE model atmospheres.
8
Figure 5 - Net spectrum for GD153 in instrumental response units.
The structure is caused by the blocking filter used to delimit the G096
bandpass. The strongest spectral feature in this region is Pγ at 1.0938µm with
a depth of ~5%. Under sampling of the structure is the worst below 0.92µm.
4. Modifications to the Spectral Extraction Technique
In the same orbit as the five-dither observations of P041C on 2005Nov12 in
Table 2, the same star was observed with the same dither, timing, and readout
pattern but with the flat field lamp turned on. The resulting background is ~10x
9
the peak stellar signal, in contrast to a background of ~1% of the peak with the
lamp off.
Figure 6 - Comparison of the net spectra for P041C with the lamp off (two heavy
solid lines) to the lamp on spectra (light lines) with the flat fields applied before
subtracting the background. The original reduction method of BLR with the flat
field applied after subtracting the background would be mostly off-scale in this
plot. The dotted line is for the standard wavelength dependent flat field method.
A better lamp-on spectrum (dashed line) is produced by applying the single G141
flat field, instead of the standard wavelength dependent data cube of flats per BLR
that is the proper method for data with low backgrounds. The best lamp-on spectrum
(thin solid line) is from an image with a scaled grism flat field subtracted, as
described in the text.
10
Figure 6 illustrates results for the net spectrum of the lamp-on data for various
flat-fielding strategies. For normal observations with low background, BLR
found a slight advantage to applying the flats after background subtraction.
For the high background case of the lamp-on data, this BLR method of applying
the wavelength dependent data cube of narrow band flats after background
subtraction produces deviations up to a factor of two from the lamp-off spectra
in Figure 6, while applying the flat data cube before background subtraction
(dotted line) yields a spectrum with some resemblance to the low background
spectra (heavy solid lines). Because of this improvement and because, in
principle, the flat field should be applied before background subtraction, the
default processing method for all spectral extractions is now to apply the flat
field before background subtraction. This change has little effect, in general, but
does reduce the pixel-to-pixel noise noticeably in WD1657+343.
However, most of the signal in the P041C lamp-on data is background with the
same spectral mix in all pixels; and a better flat should be a broadband flat that
is independent of spectral wavelength. These broadband flats are derived from
continuum illumination with the appropriate grating in the optical path. In
particular, applying the G141 grism flat before spectral extraction produces an
even better lamp-on spectrum in Figure 6 (dashed line).
Even though the grism flat produces a reasonable result, the differences between
the lamp-off and the dashed, lamp-on spectra are exquisitely sensitive to any
error in the normalization of the grism flat relative to the other flats used in the
normal lamp-off reduction. For example, the typical maximum differences of
~20 ADU/s near 1.7µm can be caused by an error of only 20/5270 = 0.4% in the
relative normalization of the two different flats applied in extracting the dashed
and thick solid line results at 1.7µm. The value of the total lamp-on signal at
1.7µm is 5270 ADU/s.
An even better flat field technique for high background grism data is to measure
the background well above and below the spectrum. These background values
can be used to scale the grism flat; and subtracting this scaled flat removes the
broadband signal contributions from each pixel. Then, the spectrum is extracted
using the normal procedures, including the wavelength dependent flat field data
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cube. This reduction technique is not so sensitive to the relative normalization of
the flats. If the subtraction of the scaled grism flat produces signals that are
~20ADU/s low in an extended region that covers both the spectrum and the
background region near1.7µm, then the second subtraction, i.e. of the spectral
background, compensates for the 20 ADU/s error in the first subtraction of the
global background image. This two step background subtraction procedure
produces the best estimate of the lamp-on spectrum shown as the thin solid line
in Figure 6.
5. NICMOS Non-linearity
The linearity measurements of BLR have better precision now because of better
flat fielding techniques, more stellar data, an improved STIS non-linearity
correction, and slightly improved fidelity of the pure hydrogen models for
WD1057+719 and WD1653+343. The analysis illustrated in figures 3-4 of BLR
is repeated, using all the currently available observations processed with the
improved techniques.
5.1 Comparison with STIS at 0.82-.97µm
The STIS charge transfer effect (CTE) correction has been revised for the
G750L mode that overlaps with NICMOS spectra. This G750L mode has a
raised background over the entire detector at the longest wavelengths due to
scattering in the CCD substrate. This extra background reduces the STIS CTE in
the 0.8-1µm NICMOS overlap range well below the CTE at the shorter
wavelengths (Goudfrooij & Bohlin 2006, in preparation). As a result of the
improved STIS calibration, the four faint stars that were excluded in the BLR
figure 3 are now included in the update of that figure shown as Figure 7 here.
BLR found these four stars to be systematically low by ~0.04, while in Figure 7
these stars with net count rates of 2-4/sec are now all within 0.02 of the linear
fit.
5.2 Non-Linearity vs. Wavelength
Figure 8 shows the various determinations of the non-linearity
12
as quantified by the b-value in Equation 4 of BLR:
Net(corr)=Net(obs)/{1-2b+b log(Net(obs)}
(1)
Figure 7 - As in figure 3 of BLR. The ratio of the NICMOS to the STIS fluxes in
their overlap region is well modeled by a linear function of the log of the NICMOS
count rate.
5.2.1 WD Stars with Fluxes Predicted by Models
The four thick circles at 0.825-0.975µm in Figure 8 are from the same analysis
as in Figure 7, except that the full STIS overlap region is divided into four
independent sub-regions. In comparison to figure 4 of BLR, the diamond and
triangle data points from WD1057+719 and WD1657+343 show less scatter
13
Figure 8 - The linearity correction, b, as in figure 4 of BLR, where the
diamonds and triangles are from comparison of pure hydrogen NLTE
models with observations of WD1057+719 and WD1657+343, respectively.
The squares are determinations of b from the P041C lamp-on data. The open
circles are the adopted linearity correction, where the thick circles are
determined from a comparison of 23 NICMOS observations with STIS in the
overlap region and have the smallest uncertainties.
because of an additional observation of WD1657+343 and because of improved
processing techniques. There are also small systematic shifts, because the NLTE
model predictions for the flux of these two stars require a small amount of
interstellar reddening to fit the far-UV STIS spectrophotometry. Because the
two models are normalized to the STIS fluxes in the visible, systematic
uncertainties increase with wavelength. Thus, the low values for WD1057+719
14
at the longer wavelengths in Figure 8 may be largely attributable to uncertainty
in the model combined with the ~1% uncertainty in broad bands for the single
NICMOS observation with G141. A 2% decrease in the ratio of observed/model
above 1.4µm would bring the WD1057+719 data points into agreement with
WD1657+343.
5.2.2 Internal Lamp plus P041C
The amount of non-linearity for small stellar signals on top of a large
background signal is expected to be less than the non-linearity for low
backgrounds, because the linearity correction is about the same for the
background and background+star. To verify and quantify this expectation, a one
orbit visit in program 10726 obtained spectra of the bright standard star P041C
with the flat field lamp 3 on. A set of b-values vs. wavelength can be derived
from this NICMOS data set. This determination of the linearity parameter is
independent of the STIS data and of the WD models used for the original BLR
method summarized above. Because the sky contribution is negligible compared
to this bright star and to lamp 3, the corrected count rate for the total lamp+star,
N(tot), should equal the corrected N(off) with the lamp off plus the corrected
lamp-on background N(lamp), which is typically ~90% of the total signal:
N(off )
N(lamp)
N(tot)
+
"
=0
1" 2b + b log N(off ) 1" 2b + b log N(lamp) 1" 2b + b log N(tot)
(2)
Multiplying by the product of the denominators and regrouping the terms with
the unknown b, Equation 2 becomes a quadratic:
!
P + Qb + Rb2 = 0
(3)
where the solution is
"Q + Q 2 " 4PR
b=
2R
!
(4)
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The other solution results in non-physical negative count rates. If
A = N(off), B = N(lamp), C = N(tot), D = log N(off)-2, E = log N(lamp)-2,
and F = log N(tot)-2, then P = A + B - C, Q = AE+AF+BD+BF-CD-CE, and
R = AEF+BDF-CDE. This solution is programmed in the IDL routine
lampbval.pro and plotted as the filled squares in Figure 8. The error bars in
Figure 8 are the rms scatter in the 15 pixel bins represented by the three sets of
small symbols.
The non-linearity coefficient, b, ranges from 7 to 0 with an uncertainty of ~1 at
the shorter wavelengths to ~2 %/dex at the longer wavelengths. Thus, the data
are consistent with no non-linearity longward of 1.5µm, although the companion
ISR (JBRB) shows even more non-linearity at all wavelengths for Nic1 and
Nic2 photometry than the open circles for Nic3 in Figure 8. To further reduce
the uncertainty in the b-values for Nic3, additional observations of
WD1057+719 and WD1657+343, along with a repeat of the P041C lamp-on
orbit, are required.
6. Count Rate Dependence on Illumination History
As a final check for electronic traps with long time constants for release of the
photoelectrons, the first integration after the lamp on observations is compared
to the last integration before the lamp was turned on. Both data sets are at the
same position on the detector and also at the same position as the last lamp-on
integration. There is a 40s interval between the end of the lamp-on exposure and
the beginning of the first G141 12s lamp-off integration. Figure 9 show that the
count rates of the five non-destructive reads following the ~10x brighter lampon observations are all within ~1% of the rates before the lamp illumination.
The analogous plot for the G096 integration that begins 76s after the last lampon integration is similar to Figure 9.
7. Results
After correcting for the non-linearity per Section 5 above and applying the flux
calibration, the NICMOS residuals with respect to the pure hydrogen NLTE
models are shown in Figure 10, which corresponds to the original BLR figure 6.
16
The residuals for the three bright primary standards are little changed, while
significant reductions of the flux errors for the fainter WD stars are achieved.
Now, there is no region as broad as 0.1µm where the residuals exceed 1%; and
the rms scatter for WD1657+343 is reduced by more than a factor of 2.5.
Figure 9 - As in Figure 1 for P041C. The first 12s integration following the
lamp-on observations n9jj02wtq (triangles) agrees to ~1% in count rate with the
last observation (n9jj02tuq - squares) before the lamp-on sequence. In this case, the
rates are normalized to the last integration of n9jj02tuq in order to verify that
there is no big overall difference in the rates of the two IMA data sets.
17
Figure 10 - Ratio of the merged G096+G141 fluxes to predicted flux for the five
stars with pure hydrogen NLTE models. The average and rms of the ratio
is written in each panel. The brighter primary standards in the bottom three panels
define the absolute sensitivities; and the average of these three ratios should be unity
at any wavelength. Compare with figure 6 of BLR to see the dramatic reduction of
the residuals for WD1657+343. Below ~0.92µm, there is often excess noise caused by
the undersampling of the sharp wavelength dependent NICMOS response function
illustrated in Figure 5.
18
Figure 11 - Scaled STIS (light lines) and NICMOS (heavy lines) fluxes with
NO correction for NICMOS non-linearity. NICMOS fluxes are too bright for
the bright Sloan standard BD+17°4708 and are too faint for the fainter
Landolt standard star SF1615+001A.
19
Figure 12 - As in Figure 11 after making the non-linearity correction to the
NICMOS fluxes per Equation 1, using the b-values plotted in Figure 8. Shortward
of ~0.92µm, there is excess noise in the NICMOS spectra due to undersampling
of the structure of the NICMOS response function shown in Figure 5. The agreement
of the two independent flux determinations often approaches ~1%.
20
Additional checks on the precision of the cross calibration of STIS and
NICMOS are shown in their overlap region in Figures 11-12. Figure 11
illustrates the NICMOS non-linearity problem where the NICMOS fluxes are
too bright for bright stars and too faint for fainter stars. Figure 12 demonstrates
the agreement of the fluxes to ~1% after the correcting the NICMOS data per
Equation 1.
REFERENCES
Bohlin, R., Lindler, D., & Riess, A. 2005, Instrument Science Report,
NICMOS 2005-002, (Baltimore: STScI), (BLR)
de Jong, R., Bergeron, E., Riess, A., & Bohlin, R. 2006, Instrument Science
Report, NICMOS 2006-001, (Baltimore: STScI), (JBRB)
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