Toward a Multi-Wavelength Geometric Distortion …ciency, noise properties, and different geometric...

Instrument Science Report WFPC2 2003-002

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Toward a Multi-WavelengthGeometric Distortion Solution

for WFPC2.

V.Kozhurina-Platais, J.Anderson, A. M.KoekemoerJuly 1, 2003

ABSTRACT

The goal of an astrometric calibration of HST WFPC2 is to obtain a coordinate systemfree of distortion at the level of precision of 1 mas. So far such calibration has been doneonly for the wide bandpass F555W filter. The inner calibration field of ω Cen exposedthrough filters F300W, F555W and F814W has been used to examine the geometric distor-tion of WFPC2 as a function of wavelength. The improved PSF-fitting technique by Ander-son and King has been used to obtain the working sets of x,y coordinates for stars inassorted HST WFPC2 frames with the globular cluster ω Cen in these three band-passes.We used a bicubic polynomial model to derive geometric distortions in the F300W andF814W filters relative to the distortion-free coordinates in the F555W filter. For each filter,four sets of distortion corrections, corresponding to each of the four WFPC2 chips, havebeen optimized independently. The main conclusion of this study is that the difference inthe amount of distortion in the F300W filter is about 3% higher than in the F555W but inthe F814W filter it is about 1% smaller than in the F555W. Tables with distortion coeffi-cients are also presented.

Introduction.

Why is the geometric distortion in the CCD mosaic images a concern to the user ofthe Hubble Space Telescope’s WFPC2, if the majority of studies based on WFPC2 obser-vations are dealing with photometry anyway? To answer this question, two cases could beidentified for which the geometric distortion properties of the CCD mosaic play a crucialrole: 1) image resampling and stacking to enhance the spatial resolution and deepen thelimiting magnitude; 2) high precision astrometry to derive the precise proper motions andparallaxes for some exotic and very faint objects, for which groundbased astrometry is notfeasible. Thus the goal of astrometric calibration of HST WFPC2 is not only to obtain a


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world coordinate system (WCS) free of distortion down to the level of precision of 1 mas,but also to obtain a contiguous and seamless image over the FOV of the entire CCDmosaic. To achieve this goal, coordinates of individual CCD chips must be translated intothe WCS and fluxes stacked up, employing point spread function fitting. If the knowledgeof the PSF across the whole CCD mosaic frame, precise CCD mosaic metrology, and adistortion-free WCS are neglected, image re-sampling and stacking will produce anunwanted blurring of the objects of scientific interest. The geometric distortion of theCCD mosaic is a complicated issue, since each individual CCD chip in the mosaic is notonly a separate detector but also is integrated with its own corrective optics and thereforeconsists of individual properties: slightly different quantum efficiency, charge transfer effi-ciency, noise properties, and different geometric distortion within individual CCD chips,as described by Platais et al. (2002), and by Anderson and King (2003) . In the case ofWFPC2, apart from distortion within individual CCD chips, there is also the expectationof some amount of global distortion stemming from the HST aberrated primary mirrorand secondary - the Optical Telescope Assembly (OTA) (see Casertano, S., in HST DataHandbook, 1997), which affects all four WFPC2 chips in the same fashion and could berepresented by a single polynomial model. It is expected, however, that the contribution ofthe global distortion to the individual geometric chip solutions is at the level ~ 1mas.

The geometric distortion of HST WFPC2 has received repeated attention in terms ofastrometric calibrations, e.g. Gilmozzi et al.(1995), Trauger et al.(1995), Holtzman etal.(1995), Casertano and Wiggs (2001), Kozhurina-Platais et al.(2002), Anderson andKing (2003).

Gilmozzi et al.(1995) solved the geometric solution using third order Legendre poly-nomials for all four chips of WF/PC and WFPC2. Once the distortion correction wasdetermined, the resulting residuals of the four chips, transformed into one meta-chip coor-dinate system, were fitted to find the offsets, rotation and scale for each of four chips. Thedistortion derived from WFPC2 images ranges from a tenth of a pixel in the center of eachchip, up to 2-3 pixels at the edges of each chip. Some changes in plate scale were seenbetween the different filters for WFPC2. The amount of scale change is very similar towhat was derived in this study.

To calculate the geometric distortions of WFPC2, Holtzman et al. (1995) used theGilmozzi formalism i.e. general cubic distortion representation given by a third orderpolynomial, under the assumption that the distortion is zero at pixel location (400,400),i.e. symmetrical around this point. The scale and orientation of the center of the PC werechosen to define the global corrected result of the articulated fold mirror (AFM) motion.The global solution was used to derive the relative scale of each chip for the chip centerand relative rotations of each chip relative to the PC. The RMS of the fit was < 0.25 PCpixels, corresponding to ~ 10 mas, slightly larger than the accuracy of measurement in theWF cameras. The solved cubic distortion terms were very similar in all four cameras.


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Trauger et al. (1995) extended and superseded Holtzman’s geometric distortion solu-tion by considering the wavelength dependence in the optical distortion, especially atFUV wavelengths. The WFPC2’s wavelength-dependent geometric distortions were com-puted by analysing the results of ray tracing, where the coefficients were represented as aquadratic interpolation function of the refractive index n of the MgF2 field-flattenerlenses. The correction of geometric transformations provided by Trauger are accurate towithin 0.1 pixel RMS (or 4 mas) over the field-of-view of the CCD.

Casertano and Wiggs (2001) attempted to improve the geometric solution for WFPC2,using data which were specifically designed to provide a good sampling in all regions ofthe field-of-view, using the Holtzman formalism and global solution to derive the coeffi-cients of the geometric distortion for the F555W filter. This geometric solution forWFPC2 showed small systematic residuals, especially in WF cameras. The recorded RMSof the residuals are 1.2 mas in the WF cameras and under 4 mas in the PC.

Kozhurina-Platais et al. (2002) have expanded the analysis of the distortion for anothertwo band-passes, F300W and F814W, employing the Holtzman formalism with Caser-tano’s modification. The derived geometric distortion solutions did not fully representdistortions in the F300W and F814W filters since the chosen data set of observations werenot rotated with respect to each other to find the non-perpendicularity of coordinates axes- the skew parameter. However, the derived solution provided clues about the scalechange from filter to filter and, within the uncertainties, confirmed the values of the previ-ously found distortion coefficients.

The early attempts to measure the amount of the geometric distortion provide fairlyprecise sets of distortion coefficients, although each of them failed to detect the skew term,which actually is responsible for a ~0.25 pix residual distortion (Anderson and King2003). Using the inner calibration field of ω Centauri consisting of 80 exposures throughF555W, Anderson and King (2003) derived a new, substantially improved, geometricsolution for WFPC2. A large data set at various orientations and offsets allowed them tosolve for the non-perpendicularity of the coordinate axes (skew terms), and achieve anaccuracy for the geometric solution close to 0.01 pixels in WF cameras and 0.02 pixels inthe PC.

In this study we use the ’astrometric standard field’ (Anderson and King 2003) to cal-culate the amount of geometric distortion in the F300W and F814W filters. Thus we haveexpanded the analysis of geometric distortion of WFPC2 as a function of wavelength foranother two filters, F814W and F300W, and also established the plate scale and skewparameters.

Data Set and Reduction

The first step in the analysis of the geometric distortion is to measure the position foreach star in each chip of each exposure. It is a well known fact that the PSF of HSTWFPC2 is under-sampled and variable over the CCD chips and because of that, the images


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may suffer from systematic errors, i.e. the position of a star depends on its location onthe chip.

While Casertano et al. (2001) were able to measure the position of stars in F555Wwith errors of 0.25 pixels, Kozhurina-Platais (2002) improved the measurement of posi-tion to 0.05, 0.06 and 0.08 pixels for the F555W, F814W, F300W filters respectively, usingthe analytical PSF fitting technique IRAF/PSF/ALLSTARS (Stetson 1987, Stetson et al,1990). The accuracy of stellar positions for under-sampled images depends critically onderiving the highest precision PSF. Anderson and King (2000) developed a new conceptof an ‘effective PSF’. Whereas most previous PSF models used an analytical function toapproximate the instrumental PSF, which must be integrated over pixels to be comparedwith the image data. The approach of the effective-PSF can be summarized as follows:

1. it is completely empirical - no analytical function is approximated;

2. the effective PSF is derived from observed pixel values;

3. the effective PSF is fitted to the pixel values by simple evaluation and scalingwithout any integration.

The spatial variation of the PSF was solved for nine fiducial PSFs placed at extremepoints in the images so as to interpolate the locally appropriate PSF to any place on thechip. The spatially variable effective-PSF model approach has reduced the systematicerror (the pixel-phase error) to the level of 0.002 pixel for all regions of the chip. Thus therandom error in measurement for a typical star is 0.02 pixel in each coordinate.

The WFPC2’s wavelength-dependent geometric distortions have been computed froma series of overlapping images of the globular cluster ω Cen, taken in three WFPC2 band-passes - F300W, F555W and F814W -over a single five hour period in June 13, 1997. Theexposures were 100 sec for F555W and F814W, and 160 sec for F300W. Each set of the

F300W, F555W and F814W images consists of two central pointings at α=13h27m11s.8

and δ=-47o29’54."7 with a 0."25 shift and four outer pointing pairs with 35" offsets (with

an offset of 0."25 in each pair), the orientation of each of the pointings were similar to one

another and ranged from 244o.68 to 244o.71 , as shown schematically in Fig.1.


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Figure 1: The schematic illustration of the observation of ω Centauri taken June 13,1997. Each set of the F300W, F555W and F814W images consists of two central pointings

with a 0."25 shift and four outer pointing pairs with 35" shifts (with an offset of 0."25 in

each pair). The orientation ranges from 244o.68 to 244o71.


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Thus, the position and instrumental magnitude of each star on each image was mea-sured using the effective-PSF approach. If a star was identified in both F555W andF814W, we attempted to measure it also in the F300W filter. A linear transformation wasperformed to cross-identify stars in various frames of nearly the same pointing. The resid-uals after a linear transformation of distortion corrected coordinates in F555W and, forexample, the F300W filter, using the Anderson and King (2003) coefficients, are shown inFig. 2. It is obvious that, at least in the WF cameras, there is some unaccounted residualdistortion, apparently arising from positions in F300W with a varying amplitude andphase from chip to chip.

Figure 2: The residuals between the ’astrometric flat field’ (F555W positions correctedfor geometric distortion) and star positions in the F300W filter, after applying only a lin-ear transformation. As can be seen , there is varying amplitude - from 0.01 to 0.05 pixels -and phase for each WFPC2 chip. The panels from top to bottom represent the WFPC2camera chips: PC, WF2, WF3, WF4 .


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The Geometric Distortion Model.

As mentioned by Anderson and King (2003), in order to solve for the distortion cor-rection of HST images, it would be much easier to have prior knowledge of the positionsof all stars in a distortion-free system. Then, the residuals between observed and distortionfree relative positions of the stars would be the distortion. At the time of this writing theAnderson and King (2003) solution does provide such distortion free coordinates for theF555W filter at the precision level of 0.02 pixel. Thus, the geometric-distortion correctedpositions in the F555W filter were chosen as an ’astrometric flat field’ at each of thenearly identical pointings for F814W and F300W. Then, the positions in the filters F300Wand F814W were reduced into this astrometric flat field using a third-order polynomialmodel. In other words, the improved distortion coefficients are directly obtained as termsof a bicubic polynomial which transforms the distorted pixel coordinates x and y ofF300W and F814W for each of the WFPC2 chips into geometrically corrected coordinatesXg ,Yg in the F555W filter. The transformation operates on a single 800 x 800 CCD

image. However, the positions x,y have been normalized over the range (50:800) exclud-ing the pyramid edges (Baggett, S. et al. 2002) and adopting the center of our solution at(425,425) with scale factor of 375. Thus, the positions x,y are normalized in the same wayas by Anderson and King (2003), i.e.

X=(x-425)/375 and Y=(y-425)/375.

The final solution is represented as a third - order polynomial (Anderson and King 2003):

Xg=a1 + a2X + a3Y + a4X2 + a5XY + a6Y2X + a7X3+ a8X2Y + a9XY2 + a10Y3

Yg=b1+ b2X + b3Y + b4X2 + b5XY + b6Y2X + b7X3 + b8X2Y + b9XY2 + b10Y3 (1)

where the sets of coefficients a and b are obtained for each of the WFPC2 CCD chips byleast squares.

For each of the ten overlapping F300W/F555W and F814W/F555W pairs, and foreach chip, independent solutions were calculated using the least squares minimizationof the third-order polynomial. These ten sets of newly derived coefficients were each aver-aged and the standard deviation of the coefficients calculated. As illustrated by Fig. 3,after applying the newly derived bicubic-polynomial, the residuals are essentially flat .


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Figure 3: The residuals between the ’astrometric flat field’ (after correcting F555W posi-tions for geometric distortion using a standard Anderson-King solution) and star positionsin the F300W filter, applying the bicubic polynomial transformation. As can be seen, theresiduals no longer have systematics as a function of coordinates. The panels from top tobottom represent the WFPC2 camera chips: PC, WF2, WF3, WF4.

The early geometric distortion solutions as mentioned above failed to find the non-per-pendicularity of coordinates axes - the skew parameter - because;

1. the data sets which were used all had the same orientation, i.e. the shifts betweenof exposures are parallel;

2. external information about the size of the absolute offsets was used to solve forthe linear terms including the scale;


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3. the meta-chip nature of the early geometric distortion solution tends to propagateerrors from the PC (which is most affected by skew distortion) into the solution forthe WF cameras.

Thus, the principal difference from the earlier distortion solutions is to establish theskew terms. The skew term was estimated directly, using an astrometric flat field in theF555W filter which was possible owing to the large variety of HST roll angles. Thederived values of skew terms (the b2 term in the third-order polynomial equation) in the

filters F300W and F814W are provided in Table s1 and 2, which are in good agreementwith the Anderson and King solution for F555W within the error of the skew terms.

WFPC2 Geometric Distortion for F300W and F814W

Holtzman et al. (1995) point out that there should be a small but perceptible differencein the amount of expected distortion as a function of wavelength. Our distortion solutionsin the filters F300W and F814W (Tables 1,2) do show differences with respect to theAnderson and King distortion correction in filter F555W. Each set of our mean distortioncoefficients is based on 10 individual geometric solutions, derived from a least-squaresminimization. The required corrections to account for the cubic distortion are given inTables 1 and 2 (coefficients a4-a10 and b2-b10) .

In Fig. 4 we present the difference in the distortion correction between the filtersF555W and F300W. They clearly indicate a larger amount of distortion in F300W, espe-cially at the corners of chips. An average increase of distortion in the F300W filter is ~3%or 0.18 PC pixels and 0.25 WF camera pixels. Another way to look at the distortion solu-tion in F555W and F300W is to plot the differences in the coefficients themselves. Theyshow the contribution of each term in pixels to the total distortion. The differencesbetween the actual coefficients (Fig. 5) indicate large errors in the PC coefficients andnearly zero differences as opposed to small errors and distinctive behavior of the WF cam-era coefficient differences (e.g., compare a7,a8,a9). Larger errors in the PC distortion

coefficients can be explained by the smaller number of stars and poorer centering preci-sion in the filter F300W.

Instrument Science R

eport WFPC

2 2003-00210

Table 1. The bicubic-polynomial terms for the F300W filter.

Table 2. The bicubic-polynomial terms for the F814 filter.

aPC σ aWF2 σ aWF3 σ aWF4 σ bPC σ bWF2 σ bWF3 σ bWF4 σ

1 0.374 0.047 0.149 0.010 -0.142 0.014 -0.072 0.012 0.267 0.021 -0.164 0.014 -0.113 0.011 0.174 0.014

2 374.690 0.091 374.742 0.009 374.745 0.009 374.738 0.015 0.480 0.069 0.042 0.010 -0.028 0.008 0.048 0.006

3 0.055 0.032 0.001 0.009 0.006 0.008 -0.027 0.009 374.576 0.101 374.673 0.010 374.706 0.013 374.773 0.012

4 -0.547 0.035 -0.687 0.009 -0.363 0.005 -0.469 0.007 -0.298 0.113 -0.043 0.006 -0.019 0.005 -0.078 0.005

5 -0.255 0.035 -0.394 0.008 -0.299 0.007 -0.386 0.010 -0.265 0.051 -0.592 0.011 -0.419 0.005 -0.489 0.006

6 -0.235 0.078 -0.098 0.007 0.015 0.008 -0.079 0.005 -0.479 0.052 -0.453 0.018 -0.335 0.006 -0.386 0.008

7 -1.937 0.139 -1.837 0.019 -1.838 0.011 -1.874 0.022 -0.079 0.126 0.006 0.015 0.007 0.008 -0.028 0.008

8 0.003 0.067 0.034 0.016 0.003 0.013 0.054 0.012 -1.913 0.113 -1.877 0.024 -1.891 0.014 -1.950 0.014

9 -1.909 0.056 -1.869 0.010 -1.875 0.015 -1.936 0.009 -0.021 0.083 0.040 0.016 0.016 0.008 0.049 0.018

10 -0.039 0.064 0.001 0.007 0.021 0.012 -0.011 0.017 -1.863 0.148 -1.773 0.018 -1.846 0.016 -1.852 0.014

aPC σ aWF2 σ aWF3 σ aWF4 σ bPC σ bWF2 σ bWF3 σ bWF4 σ

1 -0.029 0.009 0.075 0.009 0.081 0.003 0.046 0.006 0.048 0.007 0.075 0.004 0.055 0.008 -0.015 0.006

2 375.159 0.017 375.164 0.007 375.122 0.004 375.150 0.004 0.428 0.016 0.049 0.004 -0.037 0.004 0.066 0.004

3 0.002 0.014 -0.009 0.004 -0.011 0.002 -0.010 0.003 375.189 0.018 375.128 0.003 375.124 0.007 375.205 0.004

4 -0.526 0.009 -0.636 0.005 -0.344 0.002 -0.494 0.003 -0.281 0.005 -0.032 0.003 -0.018 0.002 -0.055 0.002

5 -0.264 0.008 -0.407 0.003 -0.365 0.004 -0.404 0.003 -0.305 0.008 -0.566 0.003 -0.401 0.003 -0.485 0.002

6 -0.253 0.009 -0.092 0.003 0.009 0.002 -0.059 0.002 -0.465 0.007 -0.439 0.004 -0.371 0.002 -0.408 0.003

7 -1.891 0.019 -1.769 0.005 -1.805 0.006 -1.832 0.004 -0.011 0.015 0.003 0.006 0.003 0.006 -0.013 0.003

8 0.005 0.013 0.027 0.004 0.005 0.005 0.017 0.005 -1.912 0.017 -1.809 0.005 -1.834 0.005 -1.858 0.004

9 -1.895 0.013 -1.806 0.004 -1.822 0.005 -1.853 0.005 0.014 0.017 0.017 0.005 0.009 0.003 0.029 0.006

10 0.004 0.016 0.016 0.004 0.018 0.004 0.000 0.003 -1.917 0.018 -1.735 0.007 -1.799 0.005 -1.837 0.006


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Figure 4: Differences in the distortion correction in the sense "F555W-F300W". The sizeof the longest arrows are 0.18 pixel for the PC (in PC pixels) and ~ 0.25 pixel for WF cam-eras (in WF pixels). The panel corresponds to PC -upper right; WF2 - upper left; WF3 -lower left; and WF4 - lower right. The size of the residuals are scaled by a factor of 300.


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Figure 5: Direct differences between the coefficients of the geometric distortion polyno-mial for F300W in each of the WFPC2 chips in the sense "F555W-F300W". The differ-ence appears to be negligible except for the PC, which can be explained by larger randomerrors due to the smaller number of stars observed through the PC camera. From top tobottom are PC,WF2,WF3,WF4 respectively.

On the other hand, the cubic distortion is essentially identical in the F555W and F814Wfilters. This is illustrated by Fig. 6 which shows the differences in cubic distortion in thesense F555W-F814W. The longest vector is only 0.04 PC pixels or 2 mas and 0.05 WFpixels for the WF cameras, which is comparable with the image centroid precision.


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Figure 6: Differences in the distortion correction in the sense "F555W-F814W". Thesmall amount of these differences along with a fairly random pattern changing from chipto chip indicate that the differences are very small, if any. The size of the longest arrow is0.04 PC pixels for the PC, and ~0.05 pixels for the WF cameras. The size of the residualsare scaled by a factor of 300. The panels are the same as shown in Figure 4.


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Practical Application of the Distortion Coefficients.

The application of the derived distortion coefficients is straight forward. To correct forgeometric distortion of the measured raw coordinates x and y on a chip, the equation (1)should be used, employing the coefficients from Table 1 or Table 2. The measured rawcoordinates should be normalized as X=(x-425 )/375 and Y=(y-425)/375. The correctedcoordinates Xg, Yg are nominally in the F555W system which should be shifted back to

the natural system of the detector, with its proper orientation and scale, specifically,

X= Xg- 425 and Y=Yg- 425.

The constant terms a1 and b1 are random offsets (or zeropoints) between any two frames

and can be ignored. The linear coefffcients a2 and b3 represent the plate scale.

The plate scale variation with filter has been discussed by Trauger et al. (1995) usingcalculations based on ray tracing through the optics of a model (not actual) camera. Herewe present the plate scale (relative to F555W) as derived from our solution for F300W andF814W:

The mean scale factor is in good agreement with predictions by Trauger et al. (1995).For the F300W and F814W filters the predictions are 0.99805 and 1.00025, respectively.The findings by Anderson and King (2003) from a much larger observational data setprovide the plate scale - 0.99953 and 1.00036 for the F300W and F814W filters,respectively.

A linear solution of the post-corrected positions in F300W-F555W and F814W-F555W produced RMS values of 0.04 and 0.02 pixels for the F300W and F814W filtersrespectively.

Conclusions.

The precision of the geometric distortion solution for the WFPC2 cameras is depen-dent on 1) the centering technique in measuring star positions and 2) how the solution isperformed. Solving the geometric distortion for each WFPC2 chip independently ratherthan deriving a meta-chip solution excludes the error propagation from one chip to thesolution for another chip. The improved cubic distortion for F555W by Anderson andKing (2003) and the newly derived cubic distortion for F814W and F300W have shown aclear correlation in the amount of geometric distortion as a function of wavelength. The

Filter PC WF2 WF3 WF4 Mean

F300W 0.99917 0.99931 0.99932 0.99930 0.99928

F814W 1.00042 1.00044 1.00033 1.00040 1.00040


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amount of distortion in the F300W filter is about 3% higher than in F555W, but distortionin the F814W filter is about 1% smaller than in F555W. Therefore, for practical purposes itis safe to adopt the same distortion coefficients for both F555W and F814W, but not forthe F300W filter. We also were able to establish the scale plate and skew parameter (non-perpendicularity of X and Y axes) for the F300W and F814W filters which are in goodagreement with previous findings by Trauger et al. (1995) and by Anderson and King(2003).

Recommendations.

The expanded analysis of geometric distortion of WFPC2 as a function of wavelengthfor two filters, F814 and F300W, indicates the importance of astrometric calibration atwavelengths shorter than about 400 nanometers. It is expected that the amount of distor-tion in the FUV F255W filter with respect to F555W will be higher by a factor of 5% butthis must be established from observations which are proposed for Cycle 12 . The plannedcubic distortion measurements in F255W will allow us to linearly interpolate the cubicdistortion from the near infrared wide bandpass F814W filter through the UV filters. Thederived geometric distortion cooefficients can then used for: 1) stacking of images (e.g.with dithered offsets) using STSDAS/DRIZZLE; 2) as a starting point in calibrating theACS astrometric properties; 3) general users of the archival WFPC2 observations, in par-ticular, proper motion work.

Acknowledgements.

We are grateful to B.Whitmore and S. Casertano for support and interest in this study.V.K.-P. thanks Ronald Gilliand and Imants Platais for helpful comments and suggestionsat various stages of this projects. V.K.-P. is indebted to Susan Rose , Megan Sosey andInge Heyer for help with Frame Maker.

References

Anderson, J., King, I., 2002, PASP, 112, 1360

Anderson, J., King, I., 2003, PASP, 115, 113

Baggett, S., McMaster, M., et al. 2002, in HST WFPC2 Data Handbook, v.4.0, ed.B.Mobaster, (Baltimore, STScI).

Casertano, S., et al., 1997, WFPC2 Instrument Overview, in HST Data Handbook,

24-1, (Baltimore, STScI)


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Casertano, S., Wiggs, M., 2001, in WFPC2 Instrument Science Report, 2001-10, (Bal-timore, STScI)

Holtzman, J., Hester, J.J., Casertano, S., Trauger, et.al. 1995, PASP, 107, 156

Gilmozzi, R., Ewald, S., Kinney, E., 1995, in WFPC2 Instrument Science Report, 95-02, (Baltimore, STScI)

Kozhurina-Platais, V., Casertano, S., Koekemoer, A., 2002, in HST Calibration Work-shop, (Baltimore, STScI), ed. Arribas, S., Koekemoer, A., Whitmore, B.

Platais, I., Kozhurina-Platais, V., Girard, T., et al. 2002, AJ, 124, 601-611

Stetson, P.B. 1987, PASP, 99,191

Stetson, P.B., Davis, L.E., Crabtree, D.R. 1990, in ASP Conf. Ser. 8, CCDs in Astron-omy, ed. G.H. Jacoby, 289

Trauger, T.T., Vaughan, A.H., Evans, R.W., Moddy, D.D., 1995, in Calibrating HubbleSpace Telescope: Post Servicing Mission. (Baltimore, STScI), ed.Koratkar, A.,Leitherer, C.

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