Instrument Science Report ACS 2008-02
A new geometric distortion
solution for the ACS/SBC
Jesús Maı́z Apellániz
Instituto de Astrofı́sica de Andalucı́a-CSIC
Colin Cox
Space Telescope Science Institute
31 March 2008
ABSTRACT
We have used ACS/SBC observations of two UV astrometric fields derived from ACS/HRC data to create a new
geometric distortion solution for the Solar Blind Channel. The new solution consists of three components: (a)
a filter-dependent linear part that takes into account the existence of three epoch ranges in the SBC alignment;
(b) the remaining 24 higher-order components of a 4th degree polynomial; and (c) a fine-correction look-up
table. Some of the previous solutions introduced possible errors of several pixels when producing mosaics due
to an incorrect orientation. That issue has been solved and the accuracy due to the solution itself (excluding
rotation) has been improved by an additional factor of 1.5-2.0. As a result, it is now possible to measure
positions of medium to high S/N stars with a relative astrometric accuracy of 3-4 mas.
Introduction
This Instrument Science Report is the second one in a series of three devoted to testing and improving
the astrometric accuracy of the ACS and STIS imaging detectors in the UV. In the first ISR (Maı́z Apellániz
2007) the accuracy of the ACS/HRC geometric distortion solution of Anderson and King (2004) was tested and
Copyryght 2008 The Association of Universities for Research in Astronomy. All Rights Reserved.
Instrument Science Report ACS 2008-02
the coordinates for two UV astrometric fields measured. In this ISR we use the previous work to develop and
test a new geometric distortion solution for the ACS/SBC. In the third one new geometric distortion solutions
for the STIS/NUV-MAMA and STIS/FUV-MAMA will be obtained.
The two astrometric fields presented in the previous ISR have typical relative uncertainties of 1 mas for
each star. The high accuracy is possible thanks to the excellent characteristics of the HRC CCD detector and
the stability of its environment. The accuracy for the geometric distortion solution for a MAMA detector is
expected to be lower because count-rate limitations impose severe restrictions on the maximum S/N per star
achievable in a reasonable number of orbits. Therefore, we will assume that the reference coordinates obtained
with HRC are exact.
Data
The data for the two fields in this ISR are described below.
NGC 604
NGC 604 is a Scaled OB Association (SOBA) in M33 located at a distance of 840 kpc that was first
observed with an HST imager by Drissen et al. (1993) using WFPC1. Subsequent HST imaging is described
in Hunter et al. (1996) (WFPC2), Maı́z Apellániz and Úbeda (2004) (WFPC2 and STIS/NUV-MAMA), and
Maı́z Apellániz et al. (2004) (WFPC2). It has ∼ 200 O+WR stars (Hunter et al. 1996) as well as several hundred
bright-B stars (Fig. 1), most of them located within 13′′ of the center of a low-extinction cavity (Maı́z Apellániz
et al. 2004). The brightest sources have NUV ST magnitudes of 14-15. HST UV images of NGC 604 can be
classified as moderately crowded.
Table 1. NGC 604 datasets.
F122M
j96y12gvq j9hn01weq
j96y12gwq j9hn01wfq
j96y12gxq j9hn01wgq
j96y12gyq j9hn01whq
j96y12hcq
j9hn02ibq
j96y12hdq
j9hn02icq
j96y12heq
j9hn02idq
j96y12hfq
j9hn02ieq
j9hn01vqq
j9hn02isq
j9hn01vrq
j9hn02itq
j9hn01vsq
j9hn02iuq
j9hn01vtq
j9hn02ivq
F150LP
j96y12gzq
j9hn01wiq
j96y12h1q j9hn01wkq
j96y12h3q j9hn01wmq
j96y12h5q j9hn01woq
j96y12hgq
j9hn02ifq
j96y12hiq
j9hn02ihq
j96y12hkq
j9hn02ijq
j96y12hmq
j9hn02ilq
j9hn01vuq
j9hn02iwq
j9hn01vwq
j9hn02iyq
j9hn01vyq
j9hn02j0q
j9hn01w6q
j9hn02j2q
F165LP
j96y12h0q j9hn01wjq
j96y12h2q j9hn01wlq
j96y12h4q j9hn01wnq
j96y12h6q j9hn01wpq
j96y12hhq
j9hn02igq
j96y12hjq
j9hn02iiq
j96y12hlq
j9hn02ikq
j96y12hnq j9hn02imq
j9hn01vvq
j9hn02ixq
j9hn01vxq
j9hn02izq
j9hn01vzq
j9hn02j1q
j9hn01w7q j9hn02j3q
The ACS/SBC NGC 604 images used in this ISR were acquired under two HST programs, GO 10419
(P.I.: R. Barbá) and CAL 10722, using three filters, F122M, F150LP, and F165LP (the rest of the SBC filters
could not be used due to the presence of FUV-bright objects). A total of 24 exposures/filter were obtained in
three different visits (8 exposures/filter/visit) with each visit having a different orientation. Dithering patterns
were used to shift the positions of the stars inside the detector (Fig. 1) with 3 exposures (one per filter) being
obtained at each point in the pattern. All the data were collected between 21 September and 1 October 2005.
The individual exposure times were 40/41 s, 30 s, and 30 s for F122M, F150LP, and F165LP, respectively. The
2
Instrument Science Report ACS 2008-02
F122M exposures were obtained in the SHADOW portion of the orbit to minimize the geocoronal background.
The used datasets are listed in Table 1.
Several hundred low-extinction early-type (O/B/WR) stars are visible in the SBC images, of which in a
typical F150LP frame ∼150 are bright enough to be used for the purposes of obtaining a geometric distortion
solution. The brightest stars in an individual frame have S/N of 35, 70, and 35 for F122M, F150LP, and F165LP,
respectively. The stars are not uniformly spread over the field because a SOBA is not spherically symmetric,
since their spatial distribution still reflects the original mass distribution in the parent molecular cloud.
NGC 6681
NGC 6681 is a Galactic globular cluster located at a distance of 9 kpc (Harris 1996). It has been repeatedly observed with HST, since it has been used for calibration purposes for a number of HST instruments,
including the four UV detectors on STIS and ACS. Its UV-bright population is quite different from NGC 604:
in the FUV the luminosity is dominated by several tens of white-dwarf containing systems, with the rest of the
stars in the cluster contributing only a small percentage of the measured flux. Therefore, the HST FUV images
of NGC 6681 are quite sparse, even at the center of the cluster. As we move towards longer wavelengths we
start to detect main sequence stars, blue stragglers, and horizontal branch stars and, as a result, U -band (e.g
HRC F330W) images are already severely crowded near the center of NGC 6681. The brightest UV stars in
NGC 6681 have NUV ST magnitudes of 15-16.
NGC 6681 has been observed with ACS/SBC using its six imaging filters (F122M, F115LP, F125LP,
F140LP, F150LP, and F165LP) under twelve calibration programs: 9010, 9020, 9023, 9024, 9027, 9563, 9565,
9655, 10047, 10373, 10736, and 11050. There are 8, 44, 65, 44, 57, and 44 datasets available for F122M,
F115LP, F125LP, F140LP, F150LP, and F165LP, respectively, yielding a total of 262 datasets available (Table 2). The observations span almost five years, from 27 May 2002 to 22 April 2007 (note that the last exposures were obtained after the failure of HRC and WFC). The exposure times are in the ranges 560-560 s,
35-120 s, 40-560 s, 47-180 s, 70-560 s, and 245-435 s for F122M, F115LP, F125LP, F140LP, F150LP, and
F165LP, respectively.
The appearance of a typical SBC NGC 6681 frame is quite different to an NGC 604 one because the
different nature and distance of the two objects combined with the exposure times in the two cases produce
different FUV count functions and spatial distributions. In a typical F150LP exposure one sees ∼40 moderately
bright (S/N ∼70) stellar systems uniformly scattered over the field plus 20-30 additional dimmer objects that
can also be used for geometric distortion purposes.
A comparison of the two fields
A typical exposure of each field is shown in Fig. 3. For the purpose of obtaining and testing a geometric
distortion solution one wishes to have as many stars as possible and to maximize the S/N of those objects. Also,
multiple exposures with dithering patterns and different orientations are desirable in order to populate as much
of the detector as possible.
With respect to the number of stars and their S/N both fields have different characteristics. NGC 604
has more stars per frame but NGC 6681 has more bright objects and with a more uniform detector coverage.
This makes NGC 6681 a better case to study the behavior of the linear components of the distortion (which
depend more on uniform coverage with bright stars) and NGC 604 a better case for the rest of the distortion
components (where number of objects per frame matters most).
3
Instrument Science Report ACS 2008-02
Regarding multiple patterns and exposures, both fields serve our purposes. NGC 6681 has the advantages
of having more exposures and of using all SBC filters while NGC 604 has the advantage of having all the data
taken within a short period of time. Therefore, NGC 604 seems more appropriate to derive the initial geometric
distortion while NGC 6681 is a better choice to study the filter and time dependencies.
Therefore, we conclude that both fields have advantages and disadvantages, so in this ISR we will use
both in order to obtain the best possible solution.
Table 2. NGC 6681 datasets.
F122M
j8c601sfq
j8c601sqq
j8c601ssq
j8c601swq
j9v606jzq
j9v606k0q
j9v606k1q
j9v606k2q
F115LP
j8c101v9q
j8c101viq
j8c803htq
j8c804wmq
j8eg01hbq
j8eg01hkq
j8eg02wbq
j8eg02wkq
j8eg03n3q
j8eg03ncq
j8ep01ufs
j8ep02uxq
j8ep03gkq
j8ep04lsq
j8ep05pnq
j8ep06hpq
j8ep07vgq
j8ep08meq
j8hv01m2q
j8hv02eyq
j8hv05cuq
j8hv06qtq
j8hv07p4q
j8hv08sjq
j8hv09yxq
j8hv10ckq
j8hv11a7q
j8hv12dxq
j8vb01okq
j8vb03egq
j8vb05zjq
j8vb07f1q
j95ua1k2q
j95ua2itq
j9i003lrq
j9i003lsq
j9i004jaq
j9i004jbq
j9v602jqq
j9v602jrq
F125LP
j8bu01k5q j8hv08skq
j8bu01k7q j8hv09yyq
j8bu01kaq
j8hv10clq
j8bu01kfq j8hv11a8q
j8bu01kiq j8hv12dyq
j8bu01klq
j8vb01olq
j8bu01koq j8vb03ehq
j8bu01ktq j8vb05zkq
j8bu01kwq j8vb07f2q
j8c101vaq j95ua1k3q
j8c101vhq
j95ua2iuq
j8c601rwq
j9i003ltq
j8c601s2q
j9i003luq
j8c601s4q
j9i004jcq
j8c601scq
j9i004jdq
j8c803huq
j9v602jsq
j8cg51wxq j9v602jtq
j8cg51x0q j9v603o9q
j8cg51x7q j9v603oaq
j8cg51xbq j9v607kiq
j8cg51xhq j9v607kjq
j8cg51xnq
j8cg51xrq
j8cg51xwq
j8cg51y1q
j8eg01hcq
j8eg01hjq
j8eg02wcq
j8eg02wjq
j8eg03n4q
j8eg03nbq
j8ep01ugs
j8ep02uyq
j8ep03glq
j8ep04ltq
j8ep05poq
j8ep06hqq
j8ep07vhq
j8ep08mfq
j8hv01m3q
F140LP
j8c101vbq
j8c101vgq
j8c803hvq
j8c804woq
j8eg01hdq
j8eg01hiq
j8eg02wdq
j8eg02wiq
j8eg03n5q
j8eg03naq
j8ep01uhs
j8ep02uzq
j8ep03gmq
j8ep04luq
j8ep05ppq
j8ep06hrq
j8ep07viq
j8ep08mgq
j8hv01m4q
j8hv02f0q
j8hv05cwq
j8hv06qvq
j8hv07p6q
j8hv08slq
j8hv09yzq
j8hv10cmq
j8hv11a9q
j8hv12dzq
j8vb01omq
j8vb03eiq
j8vb05zlq
j8vb07f3q
j95ua1k4q
j95ua2ivq
j9i003lvq
j9i003lwq
j9i004jeq
j9i004jfq
j9v602juq
j9v602jvq
4
F150LP
j8bu52t0q
j8vb07f4q
j8bu52t1q
j95ua1k5q
j8bu52t2q
j95ua2iwq
j8bu52taq
j9i003lxq
j8bu52tbq
j9i003lyq
j8bu52tdq
j9i004jgq
j8bu52teq
j9i004jhq
j8bu52umq j9v602jwq
j8bu52uoq
j9v602jxq
j8c101vcq
j9v603odq
j8c101vfq
j9v603oeq
j8c601sxq j9v607kmq
j8c601t6q
j9v607knq
j8c601t7q
j8c601t8q
j8c803hwq
j8c804wpq
j8eg01heq
j8eg01hhq
j8eg02weq
j8eg02whq
j8eg03n6q
j8eg03n9q
j8ep01uis
j8ep02v0q
j8ep03gnq
j8ep04lvq
j8ep05pqq
j8ep06hsq
j8ep07vjq
j8ep08mhq
j8hv01m5q
j8hv02f1q
j8hv05cxq
j8hv06qwq
j8hv07p7q
j8hv08smq
j8hv09z0q
j8hv10cnq
j8hv11aaq
F165LP
j8c101vdq
j8c101veq
j8c803hyq
j8c804wxq
j8eg01hfq
j8eg01hgq
j8eg02wfq
j8eg02wgq
j8eg03n7q
j8eg03n8q
j8ep01ujs
j8ep02v1q
j8ep03goq
j8ep04lwq
j8ep05prq
j8ep06htq
j8ep07vkq
j8ep08miq
j8hv01m6q
j8hv02f2q
j8hv05cyq
j8hv06qxq
j8hv07p8q
j8hv08snq
j8hv09z1q
j8hv10coq
j8hv11abq
j8hv12e1q
j8vb01ooq
j8vb03ekq
j8vb05znq
j8vb07f5q
j95ua1k6q
j95ua2ixq
j9i003lzq
j9i003m6q
j9i004jiq
j9i004jjq
j9v602jyq
j9v602jzq
Instrument Science Report ACS 2008-02
Figure 1: HRC F250W DRZ mosaic of the NGC 604 field with the SBC fields (in green) superimposed. The
stars in Table 3 in Maı́z Apellániz (2007) are marked with blue circles. The field is centered at 1h 34m 32.s 8696,
30◦ 47′ 9.′′ 787, has a size of 63.′′ 75 × 58.′′ 75, and the vertical direction is 49◦ East of North. The total exposure
time is 2288 s.
Technique
As previously mentioned, our goal is to use the positions of the UV sources in the astrometric fields
obtained by Maı́z Apellániz (2007) to build a new geometric distortion solution for ACS/SBC. The technique
is essentially the same that was used by Maı́z Apellániz and Úbeda (2004) to produce a geometric distortion
solution for STIS/NUV-MAMA. Both cases share one of the reference fields (NGC 604) but differ in the other
one (NGC 4214 for STIS/NUV-MAMA, NGC 6681 for ACS/SBC). One important difference between this
5
Instrument Science Report ACS 2008-02
Figure 2: HRC F250W DRZ mosaic of the NGC 6681 field with the F150LP SBC fields (in green) superimposed. The stars in Table 4 in Maı́z Apellániz (2007) are marked with blue circles. The field is centered at
18h 43m 12.s 7401, −32◦ 17′ 29.′′ 911, has a size of 50′′ × 50′′ , with North towards the top and East towards the
left. The total exposure time is 6260 s.
work and the previous one is the higher accuracy of the reference astrometric fields, given the better astrometric
quality of ACS/HRC with respect to WFPC2 (the reference instrument used by Maı́z Apellániz and Úbeda
2004) and the better S/N of the reference exposures. We should point out that this technique is different
from the one used in the calibration of other HST detectors such as ACS/HRC (Anderson and King 2004) or
6
Instrument Science Report ACS 2008-02
Figure 3: (left) 30 s F150LP SBC exposure of NGC 604. (right) 180 s F150LP exposure of NGC 6681. In both
cases the dynamic range shown goes from 0 to 10 counts.
ACS/WFC (Anderson and King 2006). In those cases no reference data is used but the detectors are purely
self-calibrated. The technique here has the disadvantage of depending on the accuracy of the reference data but
it has the advantages of its simplicity and of providing an automatic internal calibration between HST detectors
(i.e. the SBC geometric distortion solution is directly expressed in the same reference frame as the HRC one).
However, given the extensive tests done when obtaining the reference fields and the lower expected accuracy
of the SBC geometric distortion solution compared to that of the HRC, the mentioned possible disadvantage
should not be relevant here.
We start by definining a polynomial distortion solution of degree k using a notation similar to the standard
IDCTAB one of Hack and Cox (2000):
xC − xC,r =
i
k X
X
cx,i,j (xF − xF,r )j (yF − yF,r )i−j
(1)
i
k X
X
cy,i,j (xF − xF,r )j (yF − yF,r )i−j
(2)
i=0 j=0
yC − yC,r =
i=0 j=0
Here xF , yF are the coordinates in the distorted (or FLT) frame, xC , yC are the coordinates in the undistorted (or COR) frame, xF,r , yF,r and xC,r , yC,r are the reference coordinates in each frame, and cx,i,j , cy,i,j are
the polynomial coefficients. Following the previous geometric distortion solution, we will use xF,r = yF,r =
512.0 (IRAF/FITS convention1 ) = 511.0 (IDL convention2 ) even though the real center of the detector lies at
(512.5,512.5) using the IRAF/FITS convention or at (511.5,511.5) using the IDL convention.
It will be useful to express Eqns. 1 and 2 as:
1
2
The center of the lower left pixel is (1,1).
The center of the lower left pixel is (0,0).
7
Instrument Science Report ACS 2008-02
Ã
x − xr
y − yr
!
=
Ã
=
Ã
cx,0,0
cy,0,0
!
cx,0,0
cy,0,0
!
+
Ã
+
Ã
cx,1,1 cx,1,0
cy,1,1 cy,1,0
!Ã
xi − xi,r
yi − yi,r
!
+ ···
(3)
cos θ − sin θ
sin θ
cos θ
!Ã
1 s
0 1
!Ã
ex 0
0 ey
!Ã
xi − xi,r
yi − yi,r
!
+ ···
in order to separate the 6 linear terms from the non-linear ones and redefine the former. The first line of Eqn. 3
expresses the linear terms as two displacements (cx,0,0 and cy,0,0 ) and a simple 4-element matrix (cx,1,1 , cx,1,0 ,
cy,1,1 , and cy,1,0 ) applied to the relative FLT coordinate vector. The second line rewrites the 4-element matrix
as the product of three matrices which are a function of four quantities: the two expansion coefficients (ex and
ey ), the shear (s), and the rotation angle (θ). The ex ey sθ form is useful in the context of calculating geometric
distortions because, for a rigid detector and telescope ex , ey , and s are fixed, with θ depending on the orientation
(and the accuracy of its knowledge), and cx,0,0 and cy,0,0 on the pointing and the relative positioning effect of
the different optical systems.
The positions and counts of all sources above a certain S/N threshold were extracted from all the
NGC604 and NGC 6681 SBC datasets using JMAPHOT, the crowded-field photometry package described
in Maı́z Apellániz (2007) that uses PSF fitting. The ePSFs were initially built from TinyTim models, modified
by comparison with the real data (TinyTim PSFs for the SBC are more centrally peaked than the real ones),
and then adjusted individually for each frame. The extraction of point-source photometry for a MAMA detector (such as SBC) is easier than for a CCD (such as HRC) due to the absence of cosmic rays and read noise.
However, the latter effect coupled with the low dark current and sky background of the detector implies that
the total background is strongly quantized and must be measured assuming Poisson statistics. Also, one must
still account for cosmetic defects, such as the broken SBC anode that disables rows 599 to 605 (see subsection
4.5.3 in STScI 2007).
The positions of the FUV-bright sources detected in each SBC frame were then displaced, rotated, and
distorted according to the original header keywords in order to cross-identify them with the NUV-detected
astrometric field (in most cases an additional displacement was needed in order to account for the use of
different guide stars; such a displacement was calculated simply by binning the coordinates into boxes of
several pixels and finding the maximum in the 2-D histogram). Once the cross-identification was completed,
the coordinates in the reference astrometric field were rotated in the opposite sense using the orientation in
each SBC header in order to place them in the same undistorted, unrotated (COR) frame for each exposure. In
principle, the COR frame can have any plate scale. Here we will use the same value as for both the previous
SBC and HRC solutions, 0.′′ 025/pixel though we note that FLT SBC pixels are considerably larger than that.
Polynomial fittings to the geometric distortion for either the NGC 604 or the NGC 6681 datasets were
done using the MPCURVEFIT package developed by C. Markwardt3 . MPCURVEFIT provides multi-parameter
fitting with possible parameter restrictions using χ2 minimization. We wrote an IDL code that fits a polynomial
geometric distortion solution using either the simple matrix or the ex ey sθ forms to all the datasets in one of the
fields simultaneously. The code uses the MPCURVEFIT capabilities to (a) allow for independent values of the
linear terms for each of the frames while using common values values for the non-linear terms (following the
recommendation by Anderson and King 2004) or (b) force ex , ey , and s to be the same in all cases (as in a rigid
detector). It also allows for θ to be fixed or free for each frame.
3
http://cow.physics.wisc.edu/˜ craigm/idl/idl.html
8
Instrument Science Report ACS 2008-02
With the above mentioned code in hand the following steps were used to build the SBC geometric distortion solution:
1. An initial polynomial solution was derived from the 24 F150LP NGC 604 frames. The choice was made
based on the larger number of usable stars per frame, which is the most important requisite for deriving
accurate high-order coefficients.
• The values of ex , ey , s, and θ were fixed to be the same for all the frames. Several tests were done
allowing them to vary but the position residuals did not improve significantly.
• Polynomials of third, fourth, and fifth degree were tested. Residuals improved when going from
a third to a fourth degree polynomial but not (at least significantly) when going from a fourth
degree to a fifth degree polynomial, the same result that was obtained for the STIS/NUV-MAMA
by Maı́z Apellániz and Úbeda (2004). Therefore, we selected a fourth degree polynomial for the
final solution.
2. We detected significant trends in the position residuals as a function of detector location. Therefore, we
calculated two fine-correction look-up tables (one for x and one for y) by spatially smoothing the NGC
604 F150LP residuals with a σ = 25 pixel 2-D Gaussian.
3. In order to further analyze the behavior of the linear terms, an individual fit to each of the frames (using
all filters and both fields) was done fixing the non-linear terms to those previously derived and allowing
the six linear term to vary. With this new fit, the goal was to study filter-to-filter variations (overall
distortion and relative displacements) as well as possible temporal evolutions.
4. Based on the previous results, average linear parameters were obtained for each filter for three different
epoch ranges and the overall behavior of the new geometric distortion solution was studied. This is
discussed in the next section.
Results
Description of the geometric distortion solution
We show in Fig. 4 the results of the linear-terms fit for each individual dataset (step 3 in the previous
section) as a function of time. The NGC 6681 data in the ex , ey , and s plots show significant differences among
filters but little evidence for temporal evolution. The NGC 604 data correspond to a near-single epoch and
generally agree with the NGC 6681 results but with a larger dispersion. This is an expected effect, because
the NGC 604 frames have fewer bright stars (though more stars in total) than the NGC 6681 ones, leading to
a worse precision of the fit for the linear terms. Therefore, we decided to calculate independent ex , ey , and
s values for each filter by averaging the higher-quality NGC 6681 results (note also that the NGC 604 data
includes only half of the filters).
The behavior of θ in Fig. 4 is quite different. No large difference appears to exist between filters (at least
with the scale used) but instead three different epoch ranges are clearly defined by the datasets taken between
[a] 27 May 2002-15 October 2002, [b] 11 November 2002-7 September 2004, and [c] 5 April 2005-22 April
2007. The mean values for θ in each epoch range are 6.36461◦ , 6.26301◦ , and 5.43978◦ , respectively. The jump
of 0.10160◦ between the first two values is due to the FGS realignment that took place in 21 October 2002. The
second jump of 0.82323◦ had not previously been documented to my knowledge (though its consequences in
9
Instrument Science Report ACS 2008-02
NGC 6681 F122M
1.34875
NGC 6681 F115LP
NGC 6681 F125LP
6.25
NGC 6681 F140LP
NGC 6681 F150LP
1.34850
NGC 6681 F165LP
NGC 604 F122M
NGC 604 F150LP
ex
θ (CW degrees)
1.34825
NGC 604 F165LP
6.00
1.34800
NGC 6681 F122M
NGC 6681 F115LP
5.75
1.34775
NGC 6681 F125LP
NGC 6681 F140LP
NGC 6681 F150LP
NGC 6681 F165LP
1.34750
NGC 604 F122M
NGC 604 F150LP
5.50
NGC 604 F165LP
1.34725
2003
2004
2005
2006
2007
2003
2004
time (a)
2005
2006
2007
time (a)
1.1985
0.09825
NGC 6681 F122M
NGC 6681 F115LP
NGC 6681 F125LP
0.09800
1.1980
NGC 6681 F140LP
NGC 6681 F150LP
NGC 6681 F165LP
0.09775
NGC 604 F122M
NGC 604 F150LP
1.1975
NGC 604 F165LP
s
ey
0.09750
0.09725
NGC 6681 F122M
1.1970
NGC 6681 F115LP
0.09700
NGC 6681 F125LP
NGC 6681 F140LP
0.09675
NGC 6681 F150LP
NGC 6681 F165LP
1.1965
NGC 604 F122M
0.09650
NGC 604 F150LP
NGC 604 F165LP
0.09625
1.1960
2003
2004
2005
2006
2007
2003
time (a)
2004
2005
2006
2007
time (a)
Figure 4: (top left) θ, (top right) ex , (bottom left) ey , (bottom right) s fitted for each dataset as a function of
time.
recent data had indeed been observed, prompting an interpretation of a possible large mistake in the original
solution, which we later show not to be the case).
Given the findings above, the geometric distortion solution provided in this ISR has independent linear
terms for each filter and three epoch ranges. The values for the third epoch range are given in Table 3. In
order to obtain the values for the other two epoch ranges, one can apply the corresponding rotation to the
matrix components (last four rows). Table 1 also includes significant offsets (non-zero values of cx,0,0 and
cy,0,0 ), which are measured with respect to the reference filter, F150LP. The appearance of the linear part of the
distortion is shown in Fig. 5
10
Instrument Science Report ACS 2008-02
x (COR, arcseconds)
−20
20
−15
−10
−5
0
5
10
15
20
20
15
15
10
10
F115LP epoch range 1
5
F115LP epoch range 2
F122M epoch range 3
F115LP epoch range 3
0
0
F125LP epoch range 3
F140LP epoch range 3
F150LP epoch range 3
−5
y (COR, arcseconds)
y (COR, arcseconds)
5
−5
F165LP epoch range 3
−10
−10
−15
−15
−20
−20
−15
−10
−5
0
5
10
15
−20
20
x (COR, arcseconds)
Figure 5: Linear distortion for the three epoch ranges for the F115LP filter and for the third epoch range for all
filters. In each case the detector corners are shown in the COR frame.
As previously mentioned, a common non-linear part of the geometric solution is used for all epoch ranges
and filters. Its appearance is shown as a vector plot in Fig. 6 and the values for all the terms are plotted in Table
4. Additionally, a common fine-correction distortion is provided in the form of two tables, one for x and one
for y, and shown as another vector plot in Fig. 7 (note the different scale for the arrows in the two vector plots).
At the time of the writing of this Instrument Science Report the reference files can be obtained from the
URL http://www.stsci.edu/˜ jmaiz/research/sbc calibration/. The three IDCTAB files
11
Instrument Science Report ACS 2008-02
x (FLT, pixels)
250
500
750
1000
1000
1000
750
750
500
500
250
250
0
y (FLT, pixels)
y (FLT, pixels)
0
0
0
250
500
750
1000
x (FLT, pixels)
Figure 6: Non-linear polynomial (second to fourth degree) distortion for the SBC. The arrows indicate 10x the
correction in COR pixels for a uniform grid in the FLT frame.
sbc epoch1 idc.fits, sbc epoch2 idc.fits, and sbc epoch3 idc.fits correspond to each of
the epoch ranges. An additional IDCTAB file, sbc multidrizzle epoch3 idc.fits, is included for
its use with MULTIDRIZZLE for the third epoch range because that software currently introduces an additional
rotation of 0.12436◦ . Another file, sbc finecor.fits provides the fine correction tables in the form of two
1024x1024 images.
sbc multidrizzle epoch3 idc.fits has been tested for all three epochs and has been found to
12
Instrument Science Report ACS 2008-02
x (FLT, pixels)
250
500
750
1000
1000
1000
750
750
500
500
250
250
0
y (FLT, pixels)
y (FLT, pixels)
0
0
0
250
500
750
1000
x (FLT, pixels)
Figure 7: Fine-correction distortion for the SBC. The arrows indicate 100x the correction in COR pixels for a
uniform grid in the FLT frame. Note the different amplification of the correction between this figure and the
previous one.
provide good results in all cases. How can that be possible when we have found significant rotations between
epochs in our analysis? The explanation is the different source for the reference orientation angle. Throughout
this work we have used the header keyword ORIENTAT to establish the reference angle of the detector while
MULTIDRIZZLE uses an alternative keyword, PA V3. Calculation of ORIENTAT uses an angle derived from
whatever distortion solution was present at the observation time. This affected the results shown. The current
13
Instrument Science Report ACS 2008-02
software does not use this angle but works directly from the telescope orientation, a measurement which does
not depend on any detector calibration. So a retrospective analysis calculating angles in this way is not affected
by earlier angle errors.
Table 3. Filter-dependent linear components of the SBC geometric distortion solution (epoch range 3). The
units for the first two rows and the last four rows are arcsec and arcsec/pixel, respectively.
cx,0,0
cy,0,0
cx,1,0
cx,1,1
cy,1,0
cy,1,1
F122M
−0.1244769618
0.3248295486
0.0000570924
0.0335597545
0.0300954636
0.0031959272
F115LP
−0.1193522736
0.3208538294
0.0000545003
0.0335544460
0.0300879087
0.0031954215
F125LP
0.0420230441
−0.1043991596
0.0000638024
0.0335504301
0.0300744921
0.0031950392
F140LP
0.1080347523
−0.2835376561
0.0000620286
0.0335517004
0.0300717987
0.0031951603
F150LP
0.0000000000
0.0000000000
0.0000596686
0.0335521735
0.0300778355
0.0031952055
F165LP
0.0115486840
−0.0443877056
0.0000580447
0.0335507803
0.0300760400
0.0031950728
Table 4. Non-linear components of the SBC geometric distortion solution. The units for the second, third, and
fourth order components are are arcsec/pixel2 , arcsec/pixel3 , and arcsec/pixel4 , respectively.
order
20
21
22
30
31
32
33
40
41
42
43
44
x
1.25356810−07
3.95143110−07
−4.97866610−07
−1.35140210−10
−8.74295110−11
4.05654010−12
1.44850110−10
−9.21871710−13
−3.66608710−14
1.11590610−13
−2.92311110−14
4.92833010−13
y
3.15610610−07
4.49136310−08
−3.47077610−08
3.59122010−11
6.91775210−12
−2.23585010−10
4.24473310−12
−1.29050210−14
1.92724810−13
1.52355410−15
1.30512710−13
6.92819210−14
Testing the geometric distortion solution
Finally, we test the new geometric distortion solution by applying it to all of the datasets in Tables 1 and 2
and comparing the calculated positions with those in the reference astrometric fields. We consider two types
of test: a restricted one, in which only the displacement terms (cx,0,0 and cy,0,0 ) are allowed to vary, and a
semi-restricted one, in which θ is also allowed to change4 . As a comparison, we also tested the old geometric
distortion solution, available from the IDCTAB file r7q1154hj idc.fits.
In Table 5 we show the mean distance residuals between the reference and the corrected positions as a
function of test type, field, filter, and S/N. mins is defined as −2.5 log10 (counts). The following conclusions
were obtained:
4
Those tests are called restricted and semi-restricted in opposition to an unrestricted test, in which we would allow all linear terms
to vary.
14
Instrument Science Report ACS 2008-02
1.5
xCOR−xHRC (pixels), fine correction
xCOR−xHRC (pixels), no fine correction
1.5
1.0
0.5
0.0
−0.5
−1.0
−1.5
0
250
500
750
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
0
250
xFLT (pixels)
1.0
0.5
0.0
−0.5
−1.0
0
250
500
750
750
1000
750
1000
−0.5
−1.0
0
250
500
xFLT (pixels)
1.5
xCOR−xHRC (pixels), fine correction
xCOR−xHRC (pixels), no fine correction
1000
0.0
1.0
0.5
0.0
−0.5
−1.0
0
250
500
750
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
0
250
yFLT (pixels)
500
yFLT (pixels)
1.5
yCOR−yHRC (pixels), fine correction
1.5
yCOR−yHRC (pixels), no fine correction
750
0.5
−1.5
1000
1.5
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
1.0
xFLT (pixels)
−1.5
750
1.5
yCOR−yHRC (pixels), fine correction
yCOR−yHRC (pixels), no fine correction
1.5
−1.5
500
xFLT (pixels)
0
250
500
750
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
yFLT (pixels)
0
250
500
yFLT (pixels)
Figure 8: Residuals in x and y as a function of xi and yi for the NGC 604 F150LP data. The left column
shows the residuals without applying the fine-correction look-up table and the right column the residuals when
applying it. The lines plotted in red (left) and blue (right) are built by smoothing the data with a Gaussian with
σ = 20 pixels. The residuals were obtained leaving cx,0,0 , cy,0,0 , and θ free in the fit (semi-restricted test).
• When comparing bright stars (i.e. those with medium S/N) in the semi-restricted case, the new solution
yields residuals which are lower than those of the old solution by factors of 1.5-2.0. The new solution
has a typical accuracy of 3-4 mas.
• There are no significant differences between the restricted and semi-restricted cases for the new solution,
indicating that the orientation is well established there. The comparison for the old solution yields a
15
Instrument Science Report ACS 2008-02
1.5
xCOR−xHRC (pixels), fine correction
xCOR−xHRC (pixels), no fine correction
1.5
1.0
0.5
0.0
−0.5
−1.0
−1.5
0
250
500
750
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
0
250
xFLT (pixels)
1.0
0.5
0.0
−0.5
−1.0
0
250
500
750
750
1000
750
1000
−0.5
−1.0
0
250
500
xFLT (pixels)
1.5
xCOR−xHRC (pixels), fine correction
xCOR−xHRC (pixels), no fine correction
1000
0.0
1.0
0.5
0.0
−0.5
−1.0
0
250
500
750
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
0
250
yFLT (pixels)
500
yFLT (pixels)
1.5
yCOR−yHRC (pixels), fine correction
1.5
yCOR−yHRC (pixels), no fine correction
750
0.5
−1.5
1000
1.5
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
1.0
xFLT (pixels)
−1.5
750
1.5
yCOR−yHRC (pixels), fine correction
yCOR−yHRC (pixels), no fine correction
1.5
−1.5
500
xFLT (pixels)
0
250
500
750
1.0
0.5
0.0
−0.5
−1.0
−1.5
1000
yFLT (pixels)
0
250
500
yFLT (pixels)
Figure 9: Same as Fig. 8 for the NGC 6681 F115LP data.
factor of ∼2 improvement for NGC 604 due to the existence of a small deviation in the orientation. Such
a comparison would yield a much larger effect for NGC 6681 (and is not shown in Table 4) due to the
existence of three epoch ranges in the data. Once the right orientation is used, the typical accuracy for
bright stars of the old solution is 5-8 mas.
• Overall, the residuals for NGC 6681 are lower than for NGC 604. This effect may be caused by the use
of NGC 6681 for the determination of the linear terms and could indicate the existence of small temporal
variations in them, similar to those observed in other HST detectors. There are no large differences in
accuracy among filters.
16
Instrument Science Report ACS 2008-02
• The residuals for dim stars are significantly larger than for bright stars. This is an expected behavior
caused by the larger uncertainties produced by PSF fitting when the S/N is lower.
All of the results for the new geometric distortion solution in Table 5 are for the full geometric distortion
solution i.e.: filter- and epoch-dependent linear tems, fixed non-linear terms, and fine-correction distortion
tables. One aspect that was also tested was whether the fine-correction tables improved the distance residuals
for all filters and not only for F150LP, the one for which it was derived. This turned out to be indeed the
case: for all filters the addition of the tables reduced the distance residuals by factors of 1.2-1.5, thus being
a significant contribution to the improvement of the new solution. Furthermore, the use of the fine-correction
tables eliminated some obvious trends in the residual plots in Figs. 8 and 9. It is easy to see that the use of
the tables corrects the same structures seen in the NGC 604 F150LP and the NGC 6681 F115LP data, thus
pointing to the detector as the source of the distortion rather than the filters. It is also interesting to compare the
right columns in both figures: the NGC 6681 F115LP plots show no overall trend but some small quasi-linear
residual trends are observable in the NGC 604 F150LP case. This points in the direction previously mentioned:
it is likely that small variations in the linear terms are present and that some of the scatter in Fig. 4 is indeed
real.
Table 5. Mean distance residuals for the data with mins < −8.0 (medium S/N) and mins > −8.0 (low S/N) in
this ISR using the old and the new geometric distortion solutions. Results are given for both the semi-restricted
(cx,0,0 , cy,0,0 , and θ free) and restricted (cx,0,0 , cy,0,0 free) cases, with the exception of the old geometric
distortion NGC 6681 case, where the presence of datasets from epochs 1 and 2 lead to very large residuals. All
values shown correspond to the case with the fine-correction look-up table applied. Results are expressed in
output (COR) millipixels (1 mpx = 25 microarcseconds).
F122M
mS/N lS/N
semi-restricted
restricted
245
449
F115LP
mS/N lS/N
F125LP
F140LP
mS/N lS/N
mS/N lS/N
NGC 604
old
306
582
F150LP
mS/N lS/N
F165LP
mS/N lS/N
252
583
339
629
364
589
312
584
175
191
256
265
121
130
258
256
272
—
226
—
247
—
231
—
252
—
196
199
126
129
175
178
135
136
184
185
NGC 604
new
semi-restricted
restricted
202
205
280
279
semi-restricted
restricted
171
—
219
—
192
—
233
—
246
—
semi-restricted
restricted
126
129
166
165
129
135
178
187
154
156
17
NGC 6681
old
323
260
—
—
NGC 6681
new
320
139
324
140
Instrument Science Report ACS 2008-02
Conclusions
We have calculated a new geometric distortion solution for the ACS/SBC which consists of [a] a filterand epoch- dependent linear part, [b] a common non-linear polynomial part, and [c] a fine-correction look-up
table. Several tests have been conducted and it has been found that the current solution solves the orientation
issues for the SBC found in earlier solutions. Also, the new solution is more accurate than the previous one by
factors of 1.5-2.0 even after orientation issues are not considered. About half of the improvement is due to the
new polynomial terms and the other half to the introduction of a fine-correction table, which fixes the higherfrequency geometric distortion that had not been considered in the past. The limiting factors of the geometric
distortion solution seem to be two: the difficulty of observing stars with large S/N due to bright object limits
and the fact that SBC shows signs of having small time-dependent variations in the linear terms, just like HRC
and WFC.
We would like to thank Jay Anderson for the very useful discussions on the topic of HST geometric
distortion and for his help with this work. JMA also acknowledges the hospitality of Rice University, where
part of this work was carried out.
Bibliography
Anderson, J. and King, I. R. 2004, ACS Instrument Science Report 2004-15 (STScI: Baltimore)
Anderson, J. and King, I. R. 2006, ACS Instrument Science Report 2006-01 (STScI: Baltimore)
Drissen, L., Moffat, A. F. J., and Shara, M. M. 1993, AJ 105, 1400
Hack, W. and Cox, C. 2000, ACS Instrument Science Report 2000-11 (STScI: Baltimore)
Harris, W. E. 1996, AJ 112, 1487
Hunter, D. A., Baum, W. A., O’Neil, Jr., E. J., and Lynds, R. 1996, ApJ 456, 174
Maı́z Apellániz, J. 2007, ACS Instrument Science Report 2007-09 (STScI: Baltimore)
Maı́z Apellániz, J., Pérez, E., and Mas-Hesse, J. M. 2004, AJ 128, 1196
Maı́z Apellániz, J. and Úbeda, L. 2004, STIS Instrument Science Report 2004-01 (STScI: Baltimore)
STScI 2007, ACS Instrument Handbook, F. R. Boffi et al. (eds.)
18