Instrument Science Report STIS 96-015
ON-ORBIT FLAT FIELDS AND
ABSOLUTE CALIBRATION OF STIS
R. C. Bohlin, D. J. Lindler, S. Baum
January 1996
ABSTRACT
The Space Telescope Imaging Spectrograph (STIS) is a second generation HST instrument
with three 2-dimensional detectors: a far-UV CsI MAMA, a near-UV CsTe MAMA, and a
visible/near-IR CCD. STIS will obtain science data in both imaging and several spectroscopic modes, so that flat field corrections and absolute photometric calibrations are
required for many different instrumental configurations. The basic calibration philosophy
is to obtain the bulk of the flat field data from the internal calibration sources, while the
deviation of the internal lamps from the external OTA illumination at the focal plane (i.e.
“vignetting”) will be measured by external sources in selected modes. Some of these external sources will be standard stars and will also define the absolute photometric sensitivity
with the required ~1% internal consistency for all supported science modes and grating
settings.
1. INTRODUCTION
For a general overview of STIS, see Kimble (1995), Baum, et al. (1995), and Lindler
(1995). The calibration requirement in the STIS CEI Specification, Part 2 for the high frequency, pixel-to-pixel flats is to obtain a S/N of 100 per resolution element. The biggest
problem with obtaining these high S/N flats is the global count rate limitation of 300,000
counts/s for the STIS MAMAs. The MAMA detectors can be operated in a high resolution
mode with 2048x2048 pixels, while the default format is 1024x1024 pixels. Unless otherwise noted, a pixel will mean the default 1024x1024 pixel size. The MAMA resolution
element is 2x2 default pixels; so for the best case of uniform illumination with 0.3
counts/s per pixel, the minimum time to get 10,000 counts per resolution element or 2500
counts in each pixel is 2.3 hours.
The procedure to obtain MAMA flats in the laboratory is discussed by Ebbets
(1994,1995a,1995b,1995c), who tabulates the required flat field calibrations. On orbit, the
CCD flats will be determined from independent integrations. However, to avoid excessive
1
exposure time with the internal lamps, most MAMA flats are “manufactured” to indirectly
determine the flat field correction file (see 2.2.3). Our expectation is that the high frequency pixel-to-pixel P flats change slowly with wavelength. A grid of measured, P flats
with 10% spacing in wavelength means that any intermediate wavelength is within 5% of
a flat. If the wavelength of a required flat is within 5% of the wavelength of an existing P
flat, then the assumption is that an adequate (<1% added uncertainty) flat can be interpolated from the bracketing flats or that the nearest flat in wavelength is adequate. Table 1
lists the STIS spectral modes that require flats; and Table 2 lists the STIS camera modes
requiring flats. The difference #TOT-#PFLAT in Table 1 is the number of MAMA configurations that use manufactured P flats, rather than measured flats.
Table 1. STIS Spectral Modes and Flat Field Requirements
DET
MODEa
WL-RANGE
CsI
1.1 G140L
1150-1700
1.2 G140M
1150-1700
1.3 E140M
1150-1700
1.4 E140H
1150-1700
1.7X3 X140M
1150-1700
1.7X4 X140H
1150-1700
2.1 G230L
1650-3100
2.2 G230M
1650-3100
2.3 E230M
CsTe
CCD
Å/expb
#TOTc
#PRIMEc
#PFLATc
#STARc
1
1
0
0
18
12
4
2
1
1
0
0
11
3
0
0
1
1
0
0
11
3
0
0
1
1
0
0
90
23
19
6
2
1650-3100
800
6
2
0
0
2.4 E230H
1650-3100
267
26
6
0
0
2.7X3 X230M
1650-3100
800
2
2
0
0
2.7X4 X230H
1650-3100
267
6
6
0
0
2.1B G230LB
1750-3000
1
1
1
1
2.2B G230MB
1650-3100
12
11
12
1 ck
3.1 G430L
3050-5550
1
1
1
1
3.2 G430M
3050-5550
286
15
10
15
1 ck
4.1 G750L
5500-11200
4500
2
2
2
2
4.2 G750M
5500-11000
572
16
11
16
1 ck
totals
154
93
57
11
55
210
210
150
a. G-First order grating. E-Echelle grating. X-Cross dispersed grating.
b. Wavelength range per grating setting for the cases of #PRIME>1.
2
c. #TOT is the total number of allowed grating position settings, each of which require an L flat
measurement.
#PRIME is the number of steps to get complete spectral coverage with 10% overlap between
steps.
#PFLAT is the number of positions at which initial high frequency P flat field data will be
obtained with the internal lamps.
#STAR is the number of settings to be calibrated with a standard star at 10-20 positions along
slit.
The ck indicates a check of the vignetting assumptions.
Table 2. STIS Camera Modes Require 15 Flat Fields
DET
MODE
FILTER
BANDPASSa
COMMENT
CsI
1.6
25 MAMA
1150-1700
clear
F25LYA
1216,85
L-α
F25SRF2
1280-1700
SrF2 longpass
F25QTZ
1450-1700
Quartz longpass
25 MAMA
1150-3150
clear
F25SRF2
1280-3150
rejects L-α
F25QTZ
1450-3150
Quartz longpass
F25CN182
1820,350
medium bandwidth
F25CN270
2700,350
medium bandwidth
F25CIII
1909,70
CIII]
F25MGII
2800,70
MgII
50CCD
2000-10000
clear
F28X50LP
5500-10000
optical longpass
F28X50OII
3740,80
[OII]
F28X50OIII
5007,5
[OIII]
CsTe
CCD
2.6
3.6,4.6
a. Bandpass is in the form of a range of wavelengths for broad
filters and in the form of center, width for narrower filters.
2. PIPELINE CALIBRATION FILE REQUIREMENTS
2.1 Overview
The general strategy for STIS flat field and flux calibrations is to separate the process into
4 parts, which can be produced and updated asychronously over time. The four files that
comprise these calibrations are:
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2.1.1 LFLTFILE and PFLTFILE
The pixel-to-pixel flat, P or PFLTFILE, corrects the detector net response R for the high
frequency non-uniformities and leaves the low and intermediate scale instrumental sensitivity variations unchanged. After application of the P flat calibration, the residual lower
frequency sensitivity variations across the detectors are removed by the calibration image
L, which is stored in a CDBS file named LFLTFILE. Both files are normalized to unity;
and the product PL should have a S/N=100 per resolution element, i.e. S/N=50 per pixel in
the default 1024x1024 MAMA format.
If the internal krypton, deuterium, and tungsten lamps emit a pure continuum and provide
a perfect simulation of the OTA illumination at the focal plane, then the response to these
lamps RL can fully determine both L and P. The high frequency variation P and the lower
frequency variation L of the flat field are separated to save lamp lifetime. L is a heavily
smoothed version of RL and is measured for each grating setting with a short exposure of
only S/N~10 per resolution element. The P flats require long exposures; but our assumption is that P flats need be measured for only a small fraction of the grating settings, eg.
with a spacing of ~10% in wavelength. See 2.2 for the algorithms that precisely define L
and P.
2.1.2 DFLTFILE
One delta flat, D, with high S/N=100 per-pixel accounts for potential changes on approximately a monthly time scale for each MAMA detector. D=1 for the CCD modes and at
time zero when initial L and P flats are determined. These two delta flats are wavelength
and mode independent and account for possible internal gain changes in the microchannel
plates inside the two MAMA tubes. Thus, the fully corrected count rate image RC is
Rc = R/PDL,
(1)
where R is the net instrumental response in counts/s, corrected in the pipeline for rate nonlinearities and detector dark response.
2.1.3 PHOTTAB
After correction of a data image R by the P, D, and L flats, all pixels in imaging modes are
reduced to the same absolute sensitivity, while the spectroscopic modes have the same
sensitivity everywhere along the slit direction. For example for a slitless spectrum of a
point source, the variation of absolute sensitivity with wavelength is independent of position along the slit direction in the focal plane. This absolute sensitivity, S, will be derived
from observations of standard stars and is just one number for imaging or a 1-D vector for
spectroscopic modes. Therefore, the final calibrated pipeline output image is
F = Rc/(AS) = R/(ASPDL),
4
(2)
where the flux, F, for point sources centered between the slit jaws is in the HST standard
unit of erg s-1 cm-2 Å-1 and A is the aperture transmission for a point source relative to
A=1 for a large aperture. If the aperture width varies along the slit, then A must be a function of location along the slit. Since there are some wavelength regions of low sensitivity
where F should be set to zero, the inverse sensitivity (1/S) will be computed for use in the
pipeline. Details and transformations to surface brightness are discussed below in 2.2.5.
The total calibration image 1/(ASPDL) should be calculated “on the fly” in the pipeline in
order to avoid frequent redeliveries of a big file for every mode, since the small files S and
L may change more often than the big P file and since there is only one big file D for each
MAMA.
2.2 Details, Details
2.2.1 Vignetting
Since the response to the calibration lamps RL determines the L and P flats, which correct
for all of the STIS optical and detector relative sensitivity variations, any deviation of the
lamp illumination from the OTA illumination as a function wavelength, λ, and of position
(p,q) in the focal plane must be measured by an external source. This vignetting, V(p,q,λ),
in the lamp illumination should be nearly unity everywhere because of the clever design of
the cal lamp optical system and the precise polish and parallel construction of the slit jaws.
In order to avoid small scale variations >1% in the lamp spectrum along the slit, the smallscale polish on the slit jaws must be constant to 1% of the slit width; eg. a 0.5” slit is 140
microns wide at the focal plane, and the slit jaws must be smooth on the 1.4 micron scale
when averaged over the MAMA resolution element of 14 microns (0.05”), as projected to
the focal plane. To measure the lamp vignetting V and also account for any smooth largescale variation of the slit width or of any neutral density (ND) filters along a slit, a standard star is observed at ~15 positions along the slit in the focal plane. Observations of the
star should be slitless or in a wide slit, in order to avoid any uncertainty due to miscentering, jitter, or variation of the PSF along the slit. For a slit with one axis in the focal plane
along the p direction near the center q position, q-cent, V for a spectroscopic mode
reduces to a function of 2 parameters
R L ( p i, λ )/R L ( λ )
V ( p i, λ ) = ----------------------------------------,
R * ( p i, λ )/R * ( λ )
(3)
where RL(λ) is the 1-D spectrum of the lamp RL(pi,λ) averaged at the ~15 positions pi of
the star along the slit and R*(λ) is the similarly averaged stellar spectrum. The value of
RL(pi,λ) at each position is an extraction from the lamp image with an artificial slit of 3-4
5
pixels tall. The continuous function V=V(p,λ) needed to correct the lamp images is a
smooth 2-D fit to the measured V(pi,λ) at the ~15 pi discrete positions. The lab calibration
results may help set the exact number of stellar positions in the range 10-20 needed to
properly sample the vignetting along a slit. The V for a second slit lying at the same position in the focal plane will be the same as for the measured slit, if both slits have a uniform
width and ND transmission along their lengths, i.e. provided the only difference is a constant width ratio. If the relative lamp illumination along the slit is constant over time at all
wavelengths, then V is independent of mode and requires infrequent determinations. The
vignetting should be measured in the .1 modes to get full wavelength coverage with one
spectrum; however, the cal lamps are too bright for the MAMAs in wide slits. Perhaps, the
best approach is to measure V with 0.5 or 2.0” slits at two extreme wavelength settings in
the .2 modes with the hope of confirming the expectation that V should be independent of
wavelength, i.e. V(p,λ)=V(p).
The x.7 slits are orthogonal to the x.1 and x.2 slits and sample the vignetting V(q,λ) at pcent along the orthogonal axis, q, in the focal plane. However, the widest 0.2” slit may be
too narrow; or the cal lamps may be too bright on the MAMAs in all of the 1.7x3, 1.7x4,
2.7x3, and 2.7x4 modes. If the 0.2” slit is uniform enough, the V(q,λ) can be fully characterized down to 1650Å with the CCD detector for the tungsten lamps and for the
deuterium lamp in mode 2.1B. The star trail technique of Appendix A could eliminate the
need for measuring V for these x.7 slits, as well as for the problematic 45° tilted slits.
If V(p,λ)=1 or V(p,λ)=V(q,λ), then the full V(p,q,λ) that is needed for the imaging modes
might be assumed to be azimuthally symmetric on the CCD. Otherwise, a star must be
stepped over the full field to measure V for imaging modes; or more clever observations of
astronomical fields or streak earth flats might suffice (Cox et al. 1987). In general, the cal
lamps are too bright for the MAMA imaging modes. See section 2.2.2 for more discussion
of V and L for MAMA imaging mode.
2.2.2 LFLTFILE
The application of the L flats in the pipeline corrects for the low and intermediate frequency relative-response variations in the STIS images. After dividing the observed image
by the L, P, and D flats, the absolute flux calibration or diffuse surface brightness calibration should be the same for sources located anywhere in the field of view. The L flats are
derived primarily from images of the calibration lamps with their smooth continuum in the
dispersion direction, as corrected by the smoothly varying illumination function V along
the slit. The following steps describe the transformation of continuum lamp images RL
into the L flats that are required for each grating setting.
a) Compute the product image of the L and P flats that is normalized to unity and corrected
for any vignetting.
6
LP = {RL/RL(λ)}/V,
(4)
where RL(λ) is the 1-D average spectrum of the lamp spectrum collapsed along the slit
direction. Here, RL(λ) is the full average over all of the 1024 pixels that are illuminated,
rather than over the ~15 pi discrete positions used above to measure V. The division by
RL(λ) removes the cal lamp signature from the flats in the dispersion direction, just as the
division by V removes the lamp signature along the slit. For imaging modes, RL(λ) is
replaced by the average of the central ~100x100 pixel region of the flat image.
b) Remove the high frequency P flat variations from the product LP by rebinning and
filtering.
L = <LP> = <RL/RL(λ)>/V,
(5)
where the < > indicates a 21x21 median filter followed by a rebinning over 4x4 pixels to a
256x256 pixel image. The median filter smoothing eliminates data spikes and residuals of
emission lines in the lamp spectra. If the slit jaws are parallel, then the STIS optics should
be good enough to maintain constant image quality along the slit; and the technique of
dividing the lamp images by the average spectrum RL(λ) should remove the effects of any
emission lines in the lamp spectra well enough to recover full L flats under the emission
lines. However, the pixelization of the image probably prevents the recovery of P flats
under the edges of emission lines (cf. section 2.2.3).
Since the detector relative QE variations from center to edge may be greater than the typical pixel-to-pixel P flat variation, a finer grid in wavelength would be needed to predict the
large scale L flat variations to the same ~1% accuracy as the P flats with their 10% wavelength spacing. Therefore, an L flat should be measured for every STIS filter in the x.6
modes and every long slit grating setting in the x.1, x.2, and x.7 modes. However, since
these flats are smoothed versions of the images, the S/N requirement per resolution element is only 10, which reduces exposure times by 100 relative to the P flat observations.
The wavelength of a pixel at the end of the long slit in the x.7X3 modes is less than 2%
from the wavelength illuminating the same pixel in the x.3 modes, if the alignment of the
slit with the echelle orders is within the tolerance discussed in 2.2.3.
The Kr and D2 lamps are too bright for the broadband imaging filters on the MAMAs.
Therefore, external targets (Cox et al. 1987) may be required, eg. earth, moon, or a nebula
stepped around in the field of view to separate the scene lumpiness from the detector nonuniformities. External sources do not require a separate determination of the lamp vignetting. Other possibilities are the UV tail of the tungsten lamps, the ND filters that cover the
full field, or the Pt-Ne wavelength cal lamp at 10 milli-amp.
If the lamp V is near unity or has simplifying symmetries and if the filters are spatially
uniform, then the best way to get L flats for the imaging modes is to integrate the measured set of medium resolution L flats over the filter bandpass in the same way as the
7
camera mode P flats are determined from medium resolution P flats (see below). If the
lamp vignetting is asymmetric, then V must be measured by stepping a star over the entire
field of view on something like a 15x15 grid. After a correction for absolute sensitivity in
the wavelength direction, the medium resolution L flats are properly normalized along
both axes, except for the lamp vignetting. If the low or intermediate frequency variations
depend strongly on wavelength within the bandpass of a broadband observation, these L
flats will have large uncertainties regardless of the shape of the source spectrum that is
used to derive the L flat.
The L flat images can be stored and used in the pipeline as the tiny 256x256 binned versions. Bi-linear interpolation is used to resample the L flats, as needed for combination
with the larger format P and D flats, eg. the product image LP assumes that the 256x256 L
image is resampled to the pixel scale of P.
If the detectors are stable and the external stimulus is a high fidelity imitation of the OTA,
then any L flats generated in the lab calibrations should be appropriate for reduction of science data obtained on orbit.
On orbit monitoring for changes in L flats will be derived from the monthly D flat data and
any routinely obtained P flat monitoring. Except for the (unlikely?) event that the normalized lamp vignetting V changes with time, any smooth change in lamp output with
wavelength will not effect the L flats, since the mean spectrum is divided out.
2.2.3 PFLTFILE
From Eq. 4 and 5,
R L /R L ( λ )
P=LP/L=LP/<LP> = ------------------------------- .
<R L /R L ( λ )>
(6)
All images used to derive MAMA P flats will be obtained in hi-res 2048x2048 format,
since pipeline access to hi-res flats is required to properly flat field echelle spectra, where
the Doppler shift of the spacecraft orbital velocity of ~7 km/s can move the spectrum by
two resolution elements (8 hi-res pixels) on the MAMAs. The resampling of the 256x256
denominator image must be to the 2048x2048 size needed in Eq. 6. These measured P flats
can be rebinned to 1024x1024 for all cases except manufacturing of echelle mode flats.
Since the P flats are derived by dividing the original image RL by the average lamp spectrum and by a smoothed version of itself, both the emission lines and the low order
components of the flat field down to the scale of the smoothing length are removed from
the pixel-to-pixel flats. However, the pixelization of the image probably prevents the
recovery of P flats under emission lines; and the safest assumption is to consider the flats
indeterminate for pixels near the discontinuities of the slit edges for any contaminating
8
lines. Whether a P flat with a 10% difference in wavelength is close enough to define the
flats under contaminating emission lines or whether additional S/N=100 lamp exposures
are required must be determined experimentally.
In principle, pixel-to-pixel flats, P, can be obtained directly for each grating setting by
using the internal continuum lamps to illuminate a long slit for the spectroscopic first
order modes and for the cross disperser in the echelle modes. The lamps are too bright for
the broad filters in the camera modes. The cross-dispersed images in modes 1.7X3, 1.7X4,
2.7X3, and 2.7X4 provide echelle flats for the corresponding echelle spectroscopy modes
1.3, 1.4, 2.3, and 2.4, because the echelle orders lie nearly along the slit and perpendicular
to the dispersion in the x.7 modes, where the wavelength along the long slit is constant at
the value of the center wavelength of the echelle order. In the worst cases of the 1.3 and
2.3 echelle modes, the center to edge coverage in one order is <1% of the center wavelength. An additional 1% wavelength shift between the positions of the same wavelength
in the x.7 and x.3 modes would be caused by a misalignment of the x.7 long slits with the
echelle spectra by one order at the end of the slit.
Because of the long integration time of 2.3 hours minimum and 5-10 hours typically that is
needed to obtain MAMA flats of S/N=100 per resolution element, most of the required
flats cannot be obtained directly. Instead, for advance planning, the P flat values for each
pixel are assumed to be accurate to ~1%, if obtained at a wavelength within 5% of the
required wavelength. For the 1.2 G140M mode, P flats must be measured or manufactured
for the allowed 12 prime and 6 intermediate grating settings over the central wavelength
range of 1173 to 1714Å (Clampin 1995b). The wavelength assignment of any pixel in any
of these 18 MSM settings would be within 4.9% of flats measured at central wavelengths
of 1229, 1352, 1487, and 1635Å. The standard central wavelength settings of 1222, 1335,
1470, and 1640Å are close enough to these optimum wavelengths to avoid defining new
MSM settings. However, since the Kr cal lamp for band 1 has a SrF2 blocking filter, alternate techniques based on thermal vac data to be obtained in mid-1996 must be developed
to define STIS flats shortward of ~1280Å. Similarly, the 23 P flats for the 2.2 G230M
mode should be adequately determined by internal lamp images in the standard central
wavelength settings of 1769, 1933, 2176, 2419, 2659, and 2977, which are close to the
optimum 5.3% spacing of 1776, 1970, 2184, 2421, 2684, and 2976, except for the 1970Å
optimum case. Whether this baseline set of P flat measurements are too few, too many, or
just right must be answered by laboratory and inflight data analysis. In particular, since
cathodes near their long wavelength cutoffs are known to be more lumpy in response than
at the wavelength of their peak sensitivity, the longest wavelength flats at 1714Å for 1.2
and at 3134Å for 2.2 should be checked for agreement with the standard flat at 5% shorter
wavelength at least once in the lab or on orbit. Some investigation is also required to determine whether the unmeasured P flats are best derived by interpolation or from the nearest
neighbor in wavelength. These medium resolution flats could also be used to determine P
flats for the remaining MAMA modes. However because the dispersion directions are
9
orthogonal, a few corners of the x.7 cross dispersed P flats would have to be made from
flats measured at wavelengths differing by up to ~10%. Because the count rates from the
Kr and D2 lamps vary with wavelength by ~2 orders of magnitude in the 1.1 and 2.1
modes (MacFeely 1994) and because the Kr spectrum has too many lines to be very useful
below ~1250Å, the 1.1 and 2.1 mode P flats must be manufactured from the medium resolution data. Conceptually, even the imaging mode flats could be made by integrating the
medium resolution P flat grid over the wide filter bandpasses for each pixel and by choosing the nearest neighbor P flat for the narrow and medium width filters. Whether the 11 P
flats for the echelle modes 1.7 and 2.7 or the 11 flats for the imaging modes 1.6 and 2.6 are
obtained from the internal lamps, are also manufactured from medium resolution flats, or
are derived from earth streak flat data, depends on laboratory confirmation of the validity
of the manufacturing technique, how the lab and flight flats agree, STIS lamp operational
behavior, internal calibration capabilites when STIS is not the prime instrument, and the
stability of the various MAMA P flats. Laboratory data that will address some of these
questions should be obtained by early 1996. Since the exposure times are short for all of
the CCD modes, direct observation of the lamps will be used to derive all 2.xB, 3.x and
4.x P flats specified in Tables 1 and 2.
A minor complication in the manufacturing of P flats from the .2 modes is the lack of data
under the fiducial bars of the .05-2” long science slits. These bars of .4 and .86” length
comprise only 5% of the image area, which will be flagged as unflatted in the data quality
array for science observations that are made before full flats become available. For 1.1 and
2.1 mode observations, slight differences in grating alignment cause flagging of <5% of
the science data. If commanding is available, the P flat integrations could be divided with
half the time spent at a position that is offset in both axes to get full coverage of the
MAMAs under the emission lines and fiducial bars
Variability of the P flats in orbit will be routinely checked at one wavelength by the D flats
(2.2.4). If any changes are wavelength dependent, the long integration times make updates
prohibitive on time scales of much shorter than one year. Perhaps, checks at some wavelengths other than the D flat wavelength should be done on an annual time scale,
depending on how much the D flats change and on ancilliary evidence regarding MAMA
stability.
2.2.4 DFLTFILE
Because internal gain changes in the microchannel plates inside the MAMA tubes are
anticipated on relatively short time scales, the flat field correction will be monitored
monthly at one wavelength setting with very high S/N. Since this type of detector instability should be wavelength independent, the baseline plan is to measure these delta flats (D
flats) for the DFLTFILE pipeline correction at a S/N=100 per pixel and apply the correction to every P flat for the MAMAs. This S/N is twice the S/N of the P flats in order avoid
10
additional noise in the corrected STIS images. Lamp integrations times will be a minimum
of 10 hours; and therefore, a wavelength region with nearly constant count rate over each
MAMA is required. For example, the medium resolution central wavelengths at 1335 or
1470Å for the 1.2 CsI band and at 2176, 2419, or 2659Å for the 2.2 CsTe band have nearly
uniform count rates; and the choice for each band should have the fewest contaminating
emission lines. The two designated D flat positions should also have the initial P flat
upgraded to D flat S/N to minimize noise in the ratio of D=current/original, which is
applied to every MAMA image. If there are lamp illumination or L flat changes from original to current epoch, then the low and intermediate variations must be removed from the
D flats in the same way as for the P flats.
2.2.5 PHOTTAB
As defined above, the P, D, and L flats are unaffected by changes in the onboard cal lamps,
so that the reduced count rate images Rc=R/PDL have the same sensitivity everywhere in
the field of view. Since L is defined for slitless spectroscopy of point sources where A=1,
the absolute calibration of STIS images is reduced to a one dimensional problem akin to
FOS or GHRS. If the absolute flux of a point source must be measured through a slit, then
the transmission A of the slit at the location of the star must be known, and the source
must be precisely centered on the slit. For FOS, spline nodes are fit to the log of the sensitivity, which is the ratio of the extracted 1-D stellar spectrum to the standard star flux
(Bohlin, Lindler, & Keyes 1995). The spline fits should also be appropriate for STIS calibrations but should require few nodes, since the L and P flats should remove all the high
and intermediate frequency sensitivity variations. If the MAMA is nearly aligned with the
slits, then the high frequency orthogonal MAMA artifacts must be removed from RL(λ) in
order to divide by the smooth average lamp spectrum and retain all high and intermediate
frequency variations in the product LP of Eq. 4. One solution is to fit RL(λ) with a polynomial after masking the emission lines. The value of RL(λ) in the lines could be recovered
by scaling the fit to the peak over the width of each contaminating line. If the contamination is minimal, this fitting technique might be preferable in general. For example, the
bumps and dips in Figure 2 with about 0.5% height and ~50 pixel width would require less
effort to remove with the L flat than with the sensitivity S.
The measure of STIS response to a point source R(λ) is the sum of the count rates above
background over all pixels in Rc that lie along the slit and that contribute to the signal from
the star. The R(λ) is extracted at every pixel in the dispersion direction. For imaging mode,
R(λ) is the sum of the count rates in all pixels that contribute to the stellar signal. The
STIS sensitivity for each grating setting is
S = R(λ)/(AF),
(7)
where F is the known flux for the standard star (Bohlin 1995) and where the aperture cor-
11
rection, A, accounts for the loss in transmission through smaller slits (cf. Bohlin & Colina
1995). Since the total count rate at each wavelength does not depend on the PSF, S is the
relevent pipeline calibration per pixel in the image, as well as for the extracted spectrum as
long as no significant fraction (>1%) of the stellar signal is lost in faint wings. Observations of the standard stars should be done slitless or in wide slits where A=1 in order to
avoid any uncertainty due to miscentering or jitter. For imaging, A is also unity. Once the
values of A and S are established from observations of standard stars, Eq. 7 is used by the
pipeline to produce the flux images, F, in erg cm-2 s-1 Å-1 for all observations.
For the medium dispersion modes, the absolute calibrations of the intermediate grating
settings are derived by interpolation of the measured sensitivities at the primary positions
(1.2p1-1.2p12 and 2.2p1-2.2p19). To achieve this goal, the function S at each primary
position is broken into two parts: an absolute sensitivity Sc at the center of the detector and
a relative calibration as a function of detector pixel position Sr, where S = Sc Sr and Sr=1
at the center wavelength. The Sc part is a smooth function of wavelength and can be interpolated to ~1% accuracy for grating settings at any arbitrary center wavelength. The Sr
part is a family of smooth functions vs. pixel position on the detector, where there is one
smooth function for each primary grating setting. The smooth function Sr needed for the
arbitrary center wavelength can be linearly interpolated from the two primary position Sr
functions that are nearest to the arbitrary center wavelength. See Robinson (1994) for an
example of the use of this technique for GHRS.
For the echelle modes, the absolute calibration S is defined as a function of the central
wavelength for each order and is a one dimensional vector with a constant value to apply
to the image along the orders. The echelle ripple is the correction in the dispersion direction relative to the center of the order (Lindler 1994) and will NOT be removed until after
the spectrum is extracted into a flux vs. wavelength vector. For mode 1.4, the coverage is
sparse with only 3 primary and 8 intermediate settings, so each of the 11 positions will
require a separate calibration observation of a standard star or internal lamp. For 2.4, the 6
primary plus 20 intermediate settings may be dense enough to avoid absolute calibration
observations for some of the intermediate settings by applying a modeling technique that
is analogous to the medium resolution method.
If the internal lamps are stable over time to ~1%, absolute calibration Sa for mode a can be
determined from a previously calibrated mode b at the same wavelength without need to
expend HST integration time on external standard stars.
Rc ( a )
S a θ a = S b θ b = -------------Rc ( b )
(8)
where θa and θb are the widths of the respective clear slits and the ratio is just the relative
12
response to the same stable lamp, as corrected for any difference in the P, D, and L flats.
The Rc at both the a and b positions in Eq. 8 are averages over the respective slit lengths.
Since Sa and Sb are smooth spline functions, low S/N images suffice. However, the lamp
output is fixed and there is not enough dynamic range in the slit selection to directly relate
the x.1 calibration to the x.4 modes without long integration times. For example, the sensitivity difference between the 1.1 and the 1.4 modes is over 200x.
For an extended source with continuum emission, the surface brightness, I(contin), in erg
cm-2 s-1 Å-1 arcsec-2 is computed from the calibrated flux image by dividing by the solid
angle Ω(slit) seen by each pixel, which is the pixel height times the width of the slit, both
in arcsec; the width seen is the actual width/cos(45) for the tilted slits.
I(contin) = F A/Ω(slit)
(9)
For an extended source with line emission, the surface brightness, I(line), in erg cm-2 s-1
arcsec-2 is computed by dividing the calibrated flux image by the solid angle of each pixel
Ω(px) and multiplying by the dispersion in Å/px, since the response in any pixel does not
depend on the entrance slit width as long as the slit is wider than the 0.024” pixel size.
I(line) = F A(Å/px)/Ω(px)
(10)
The aperture transmission, A, that appears in Eq. 2 for the flux F must be removed for the
computation of I, because the energy lost from the PSF in a narrow slit is returned from
neighboring nebulosity for a uniform diffuse source (cf. Bohlin 1993). These three calibration constants, A, Ω(slit), and Ω(px), for diffuse sources should be placed in the header of
the flux calibrated spectroscopic data image. The dispersion in Å/px should also be specified in the header, especially if the sampling interval for the extracted flux vector is not
exactly one pixel. For images without dispersion, divide the flux image F by the pixel size
in arcsec2 to get I. Table 3 is from Table 2.4 of Kimble (1995, and private comm. for the
updates and correction).
13
Table 3. STIS Plate Scales
Modea
arcsec/px
(along dispersion)
arcsec/px
(cross-dispersion)
1.1,2.1,1.6,2.6
.0244
.0244
1.2,2.2
.0306
.0290
1.3,2.3
.0358,.0332
.0290
1.4,2.4
.0466
.0290
3.1,4.1,3.6,4.6
.050
.050
3.2,4.2
.054
.050
2.1B
.050
.050
2.2B
.061
.050
a. STIS IDT nomenclature for modes. See Table 1 for translation to STScI names.
Modes 1.1 and 2.1 cover the full UV range of 1150-3100Å and provide the best monitors
for both lamp changes and for changes in UV sensitivity over time. If the lamps are stable,
changes in STIS sensitivity in a few narrow wavelength regions are monitored with the
monthly D flats and less frequently obtained P flat data. However, one star from a set of 45 STIS standard stars should be observed in the x.1 modes ~4 times per year to firmly
establish and maintain the absolute calibration, to provide complete wavelength monitoring for changes, and to obtain photometric repeatability statistics through the widest slits
that are commonly used for science observations.
3. SUMMARY OF EXISTING LAB FLAT FIELD DATA
Three MAMA flats with uniform illumination of the CsTe prototype STF2 have been
obtained as part of the detector subassembly testing and are summarized in Table 4. After
rotating the images to correct a one deg alignment offset of the MAMA with respect to the
dispersion direction, adding two bands of zeros at the locations of the .4” and .86” (17 and
36 px) fiducial bars near the top and bottom of the field of view, and then rectifying for an
emission line with a 3 deg tilt with respect to the dispersion, an example of the 1800Å
image is shown in Figure 1 and should be a good fidelity simulation of a rectified STIS
image of the cal lamp spectrum. Three different width emission lines are simulated: 2”
(83px at 1800Å), 0.5” (21 px at 2200Å), and 0.05” (2 px at 2800Å). The instrumental resolution is simulated by smoothing the emission lines and the fiducials with a Gaussian of
2.5 px FWHM. The extracted average spectra RL(λ) shown in Figure 2 must be transformed back to the unrotated and unrectified image coordinates in order to derive flats for
the original 1024x1024 image according to Eq. 4. In order to avoid artifacts in the derived
L flats, the regions of the fiducials and the emission line edges must be interpolated from
14
the median of 21 pixels of data on either side. The derived L flats and the differences
among them are shown in Figure 3. Since actual data exist at the locations of the introduced artifacts, the accuracy of the computed L flat from the simulation can be
quantatively evaluated under the emission lines. An example of the ratios of the derived L
flats to the actual L flats appears in Figure 4, where the errors at the position of the lower
fiducial bar approach ~2%. A sample 1800Å P flat appears in Figure 5, while the ratio of
the 2800 to the 1800Å P flat is shown in Figure 6.
Table 4. STF2 Flat Field Observations
Data Set
Exposure Time
(seconds)
Wavelength
(Angstroms)
Date
STF2_HIRES_FLAT_79000_180_031295.DAT
79,000
1800
3/12/95
STF2_HIRES_FLAT_54000_220_031195.DAT
54,000
2200
3/11/95
STF2_HIRES_FLAT_79000_280_031395.DAT
79,000
2800
3/13/95
The statistics of the flat field variations with wavelength are in Table 5.
Table 5. Flat Field Statistics in the Three Images
1800Å
2200Å
2800Å
Actual Sigma (%)
2.59
2.68
2.88
Minumum
0.93
0.94
0.93
Maximum
1.07
1.07
1.09
Poission statistics (%)
0.47
0.38
0.41
Actual Sigma (%)
1.48
1.45
1.47
Minimum
0.51
0.64
0.64
Maximum
1.14
1.15
1.15
Poission statistics (%)
1.88
1.51
1.64
Actual Sigma (%)
33.4
32.7
33.5
Mimimum
0.17
0.14
0.24
Maximum
2.45
2.65
2.46
L FLATS (256X256 PX)
P FLATS (512x512 px)
P FLATS (204x2048 px)
Since the expected variation from counting statistics is always less than the actual RMS
variations, the true detector performance on the bench has been measured. The three low
frequency flats show 13-16% variation over the detector from regions of minimum to max15
imum sensitivity. The high frequency P flats for the 512x512 images have an RMS
variation per resolution element of 1.5%, while the 2048x2048 mode flats have an RMS of
33%. Because of systematics in the MAMA electronics, the variations in the 2048x2048
mode flats are much worse than the 512x512 variations.
One important question is: Can a flat taken at one wavelength be used to correct data taken
at a nearby wavelength? Table 6 summarizes the statistics for the ratios of the flats.
Table 6. Statistics for the Ratio of Flat Fields Taken at Different Wavelengths
2200/1800
2800/2200
2800/1800
Sigma (%)
1.00
1.76
2.20
Minimum
0.99
0.96
0.97
Maximum
1.04
1.03
1.05
a (%)
Sigma
0.64
0.62
0.71
b (%)
Sigma
0.21
0.27
0.35
a (%)
Sigma
2.84
2.77
2.78
b (%)
Sigma
1.50
1.65
1.23
L FLATS (256X256 px)
P FLATS (512x512 px)
P FLATS (2048x2048 px)
a. Includes contribution of counting statistic errors
b. Counting statistic error contribution removed.
Table 6 demonstrates that the low frequency L flats for each of the three wavelengths are
not appropriate for correcting the other two wavelengths (also see Figure 3). The RMS
deviations from unity for the ratios are significantly larger than the fraction of a percent
scatter expected from the counting statistics. Therefore, a low frequency L flat must be
measured at most primary central wavelengths for band 2.
The ratios of the high frequency P flats in Table 6 show RMS deviations from unity of less
than ~0.3% per resolution element. However, isolated spots (Figure 6) show local deviations of 1-2%, which indicates that a single high frequency flat is insufficient for all
wavelengths of band 2. However, the six P flats that are baselined for band 2 in section
2.2.3 may be adequate to achieve flat fielding to 1% per resolution element.
4. CALIBRATION OBSERVATIONS AND EXPOSURE TIMES
Since the flat field exposures are INTERNALS and do not consume HST prime pointed
observation time, the requirement for a few hundred hours of MAMA integration time on
observations of the internal lamps can be achieved in a few months with a duty cycle of
16
~10 hours per 24 hour day. The specified internal lamp lifetime is 2500 hours.
Because of uncertainty in the cal lamp output flux and degradation rates, exposure times
and total program time accounting will not be done until after STIS thermal vac testing in
mid-1996. In the event that lamps drift badly, some typical exposure time will be estimated for L flat determinations with stars trailed along the slits.
17
APPENDIX A: TILTED 45° SLITS
The tilted slits are not supported for cycle 7 but may be calibrated for later HST cycles.
For the first order x.1 and x.2 modes, there are 4 slits tilted at +-45° from the dispersion
direction to alleviate spacecraft roll constraints, especially in the ecliptic for planets (Kimble 1995, Clampin 1995a). There are only 2 choices of slit width and both choices have a
width change along the slit, viz. 0.05 and 0.2” for one slit and 0.6 and 2” widths for the
other. In the x.1 modes, the wavelength shifts corresponding to the 12.4” offsets at the
edges of the field of view exceed 10% of the central wavelengths. However, the P flats for
the tilted slits in MAMA modes 1.1, 1.2, 2.1, and 2.2 should be manufactured adequately
from the measured x.2 flats for the orthogonal science slits, since these medium resolution
P flats are a set with a 10% wavelength interval at every pixel, which means that every
pixel has a measured flat within 5% of any wavelength.
Table 7 contains the summary of requirements for full flat field calibration of all allowed
configurations of the tilted slits with the first order gratings. Since the totals for these
peculiar modes are comparable to the complete list for all other spectroscopic modes in
Table 1, a phased implementation of calibrations for subsets of the Table 7 modes is
advisable.
Table 7. STIS Flat Field Requirements for Each 45° Tilted Slits
DET
MODE
WL-RANGE
#TOT
#PFLAT
#STAR
CsI
1.1 G140L
1150-1700
1
0
0
1.2 G140M
1150-1700
18
0
2
2.1 G230L
1650-3100
1
0
0
2.2 G230M
1650-3100
23
0
2
2.1B G230LB
1750-3000
1
1
1
2.2B G230MB
1650-3100
12
12
0
3.1 G430L
3050-5550
1
1
1
3.2 G430M
3050-5550
15
15
0
4.1 G750L
5500-11200
2
2
2
4.2 G750M
5500-11000
16
16
0
totals, each tilt
90
47
8
totals, both tilts
180
94
16
CsTe
CCD
Notes to Table 7:
Summary of allowed configurations for the plus and minus 45° tilted slit pairs
(cf. Table 1).
18
#TOT is the total number of allowed grating position settings.
#PFLAT is the number of positions that initial high frequency P flat field data will be
obtained with the internal lamps.
#STAR is the number of settings to be calibrated with a standard star at 10-20 positions
along slit.
A handle on the vignetting for each of the plus and minus 45° slits can be obtained for the
0.6-2” slits at the wavelength extremes of the 1.2 or 2.2 grating range in the same way as
for the normal science slits. (See section 2.2.1).
The measurement of the L flats for the 45° slits is not possible with the Kr or D2 lamps in
the 1.1 and 2.1 modes because of the 300,000 counts/s global count rate limit. In addition,
cal lamp spectra through the tilted slits show both dark stripes due to bars where the size
changes and also a bright streak due to overlapping spectra from the failsafe “safety” apertures. Can the x.1 L flats be manufactured from the dense grid of L flats from the x.2
modes for all 3 slit orientations? Since the purpose of the L flat is to remove instrumental
differences in response in the spatial direction along the slit and intermediate scale fluctuations in sensitivity in the dispersion direction, the requirement is that any difference in
center to edge response to the lamp along the slit is the same to <1% for any differential
shift in wavelength at the slit ends. The offset from the center to where the 35.7” long, 45°
tilt slits intersect the edge of the 24.9” field of view is 12.4”. The shift in Angstroms at the
ends of the 45° slits is (px/arcsec) (Å/px) 12.4” = (Å/px) 510, since the arcsec/px=0.024.
These shifts are listed in Table 8 for the relevant MAMA modes. For cases with the same
vignetting function, manufacturing of L flats could be investigated.
Table 8. Center to Edge Wavelength Shifts for the 45° Tilted Slits
Mode
1.1
2.1
1.2
2.2
Å/px
0.60
1.58
.054
.087
Å Shift
310
810
28
44
For the 1.1 and 2.1 tilted-slit and x.7 cross-dispersed L flats, an alternative calibration
technique of trailing a star along the slit direction could provide the required L flat data
without the need for a separate determination of V. For observations of a point source, the
local count rate limit of 50 cts/s applies. To get 100 counts per pixel at the peak response
requires 2 sec per pixel, and the whole observation of the 1024 pixels along the slit
requires about 2000 s for a calibration star of the proper brightness. The trail rate is 24.9/
2000 = 0.012”/s and must be constant to 1% on the ~10 px = 20 s time scale for L flat
determination. If the jitter file can be synchronized with the trailed data to ~0.1 s, then the
illumination variations caused by jitter could be removed on the 0.024” pixel scale.
19
5. REFERENCES
•
Baum, S., Clampin, M., Hartig, G., Hodge, P., and Kinney, E. 1995, STIS Instrument
Mini-Handbook.
•
Bohlin, R. C. 1993, in Proc Conf. Calibrating HST, p234; also 1994, CAL/SCS-002.
•
Bohlin, R. C. 1993, FOS Instrument Science Report, CAL/FOS-106.
•
Bohlin, R. C. 1995, STScI Instrument Science Report on Standard Calibration
Sources, CAL/SCS-006.
•
Bohlin, R. C., & Colina L. 1995, FOS Instrument Science Report, CAL/FOS-136.
•
Bohlin, R. C., Lindler, D. J., & Keyes, C. D. 1995, FOS Instrument Science Report,
CAL/FOS-144.
•
Clampin, M. 1995a, STIS Instrument Science Report, STIS-008.
•
Clampin, M. 1995b, STIS Instrument Science Report, STIS-009.
•
Cox, C. R., Bohlin, R. C., Griffiths, R. E., & Kelsall, T. 1987, Standard Astronomical
Sources for HST: 6. Spatially Flat Fields, STScI.
•
Ebbets, D. 1994, Ball Systems Engineering Report, STIS-CAL-003.
•
Ebbets, D. 1995a, Ball Systems Engineering Report, STIS-CAL-010.
•
Ebbets, D. 1995b, Ball Systems Engineering Report, STIS-CAL-011.
•
Ebbets, D. 1995c, “Prelaunch Calibration Plan for STIS, AV-03”, Ball.
•
Kimble, R. 1995, “STIS GTO Observers’ Handbook, Rev. A”, GSFC, 5/22/95.
•
Lindler, D. J. 1995, STIS Science Data Management and Analysis Software Requirments Document”, version 1.0.
•
MacFeely, K. 1994, Ball Systems Engineering Report, OPT-115B.
•
Robinson, R. D. 1993, in Proc Conf. Calibrating HST, p291.
20
6. FIGURE CAPTIONS
Fig. 1 - Sample MAMA STF2 image at 1800 Angstroms with simulated fiducial bars
(black horizontal stripes near the top and bottom) and emission line (vertical white stripe).
The image is normalized to unity by dividing by the mean count rate of ~16000 and is
geometrically rectified to correct for simulated alignment offsets of the MAMA with
respect to the dispersion direction and for simulated tilt of the slits with respect to the dispersion. The rectified image is inserted into a larger image of zeroes to avoid loss of any
data. The wedge of black (zeroes) at the top and bottom are from the simulated difference
of one degree between the dispersion direction and the MAMA, while the four degree
wedges of black on the sides are caused by an additional three degrees of tilt of the slit
with respect to the dispersion direction.
Fig. 2 - The normalized spectra RL(λ) from the three rectified images after averaging in
the direction perpendicular to the dispersion. The original pixel scale has been preserved
in order to divide the original spectral images by their averages. The spectra have been linearly extrapolated in the wavelength range where the spatial coverage is not complete. The
fine scale pixel-to-pixel noise is <<1%, as required, since the offset between the spatial
direction and the MAMA columns removes most of the signature of the detector from
RL(λ). If the long slits are aligned with the detector, then some smoothing of RL(λ) is necessary (see section 2.2.5).
Fig. 3 - MAMA STF2 low frequency flats for three wavelengths derived according to our
algorithm by dividing by the average RL(λ) from Figure 2, binning the raw flat field (HiRes) data to 1024x1024 pixels, filtering with a 21x21 median filter, and binning to
256x256 pixels. The top three images show the computed low frequency flats scaled from
0.93 (black) to 1.07 (white), while the bottom three images show ratios of the low frequency flats with the same intensity scale.
Fig. 4 - The ratio of the derived L flat at 1800Å to the actual L flat. The slit causes an error
of <1%, because the slit edges contaminate regions that are only the 2.5 pixel width of the
STIS resolution. For the fiducial bars, errors approach 2% occasionally, because of the
regions without data are 17 or 36 pixels wide. The narrower lower slit is closer to edge,
where the smoothing is ineffectual, and shows larger errors in interpolating the L flat
across the region of missing data.
Fig. 5 - The 1800Å high frequency flat scaled from .95 black to 1.05 white. The regions of
the slit edges and fiducial bars that lack measured data are set to unity.
Fig. 6 - The ratio of the 2800 and 1800Å high frequency P flats scaled from .98 black to
1.02 white.
21