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28.2 Photometric Corrections
A number of corrections must be made to WFPC2 data to obtain the best possible photometry. Some of these, such as the corrections for UV throughput variability, are time dependent, and others, such as the correction for the geometric distortion of WFPC2 optics, are position dependent. Finally, some general corrections are needed as part of the analysis process, such as the aperture correction. We describe each class in turn.
28.2.1 Time-Dependent Corrections
The most important time-dependent correction is that for the contamination of the CCD windows, which affects primarily UV observations. Other time-dependent corrections are due to the change in operating temperature in April 1994 and to the variations of the PSF with focus position; the latter is also position-dependent (see "Aperture Correction" on page 28-13 for more information).
Contamination
Contaminants adhere to the cold CCD windows of the WFPC2. Although these typically have little effect upon the visible and near infrared performance of the cameras, the effect upon the UV is quite dramatic, and can reduce throughput by
about 30% after 30 days for the F160BW filter. These contaminants are largely removed during periodic warmings of the camera and fortunately, in between these decontaminations, the effect upon photometry is both linear and stable, and can be removed using values regularly measured in the WFPC2 calibration program. Table 28.2 shows the contamination rates measured for each detector and Table 28.3 provides decontamination dates up until August 1997. Updated lists are kept on the WFPC2 WWW pages.
Contamination is measured primarily from the bimonthly observations of the WFPC2 primary standard, the white dwarf GRW+70d5824; thus the contamination rates in Table 28.2 are directly applicable to blue objects. These observations have been supplemented, for the standard photometric filters, by observations of a stellar field in the globular cluster 
Cen (mean B-V ~ 0.7 mag); the contamination rates thus measured (in parentheses in Table 28.2) are generally in good agreement with those measured on GRW+70d5824. The Cen data also indicate a slightly higher contamination rate towards the center of each chip. For more details, see WFPC2 ISR 96-04. These results will be verified further with the analysis of UV observations of NGC 2100, a young globular cluster in the LMC.
The synphot package can be used to determine the effect of contamination on your observations. For example, the following command computes the expected countrate for a WF3, F218W observation taken 20 days (MJD=49835.0) after the April 8, 1995, decontamination, with the gain=7 setup:
sy> calcphot "wfpc2,3,f218w,a2d15,cont#49835.0" \
>>> spec="bb(8000)" form=counts
Removing the cont#49835.0 from the command will determine the countrate if no contamination was present. An 8000 K black body spectrum was chosen largely as a matter of simplicity-the correction values for contamination depend only on the filter chosen and do not reflect the source spectrum.
Contamination Rates (Fractional Loss per Month)
Note: Units for Contamination Rates previously given incorrectly as 'Fractional Loss per Day.'
Corrected on 24 Feb 2000.
Cool Down on April 23,1994
The temperature of the WFPC2 was lowered from -76 C to -88 C on April 23, 1994, in order to minimize the CTE problem. While this change increased the contamination rates (see above), it also improved the photometric throughput, especially in the UV, and greatly reduced the impact of warm pixels. Table 28.4 provides a partial list of corrections to Table 28.1 for the pre-cool down throughput. Including the MJD in a synphot calculation using up-to-date tables will automatically provide an estimate of PHOTFLAM corrected for this change.
Ratio Between Pre- and Post-Cool Down Throughput
PSF Variations
The point spread function (PSF) of the telescope varies with time, and these variations can affect photometry that relies on very small apertures and PSF fitting. Changes in focus are observed on an orbital timescale due to thermal breathing of the telescope and due to desorption, which causes a continual creeping of the focal position. This change has been about 0.7 µm per month until mid-1996, when it greatly slowed. Currently the focus drift is less than 0.3 µm per month. The effect of focus position on aperture photometry is described in WFPC2 ISR 97-01. About twice a year, the focal position of the telescope is moved by several microns to remove the effect of the desorption.
In addition, jitter, or pointing motion, can occasionally alter the effective PSF. The Observatory Monitoring System (OMS) files provide information on telescope jitter during observations (see Appendix C). These files are now regularly provided to the observer with the raw data. Observations taken after October 1994 have jitter files in the Archives. Limited requests for OMS files for observations prior to October 1994 can be handled by the STScI Help Desk (E-mail help@stsci.edu).
Recently, Remy et al. (1997) have been able to obtain high-quality photometry of well-exposed point sources by modeling the point spread function with TinyTim (Krist, 1995), and taking into account focus and jitter terms via a chi-squared minimization method. Similar results have been obtained using observed PSFs (Surdej et al., 1997), provided that the PSF used is less than 10" from the observed star and corresponds to a spectral energy distribution similar to that of the target. The WFPC2 PSF library was established to help users find suitable PSFs, if they exist, or carry out experiments with what is available. The PSF library is described in Wiggs et al. (1997) and can be found at the following URL:
http://www.stsci.edu/ftp/instrument_news/WFPC2/Wfpc2_psf/
wfpc2-psf-form.html
28.2.2 Position-Dependent Corrections
In this Section we discuss the CTE correction and the possibly related long vs. short anomaly, the geometric distortion, the gain differences between different chips, and the effect of pixel centering.
Charge Transfer Efficiency
Shortly after launch it was discovered that WFPC2 had a substantial charge transfer efficiency (CTE) problem: objects appeared to be about 10% fainter when observed at the top of the chip (y~800) compared to when they were observed at the bottom of the chip (y~0). The April 23, 1994, cool down reduced the CTE problem to about a 4% effect peak-to-peak (Holtzman et al., 1995b) for a typical observation. The effect appears to be smaller, or nonexistent, in the presence of a moderate background.
Extensive observations made during Cycles 5 and 6 gave a much better characterization of the CTE calibration, indicating that its effect can be 5% or more (peak-to-peak) for faint images. WFPC2 ISR 97-08 quantifies the CTE effect under various observational circumstances and gives empirical rules to correct for it. After these corrections, the residual CTE effect for well-exposed stars is estimated to be less than 2%.
The correction depends on the average background, the average counts over the chip, and the counts in the source itself. Assuming a 2 pixel aperture, the corrected counts are given by:
where X and Y are the coordinates of the star center in pixels, and X-CTE and Y-CTE are the percentile loss over 800 pixels in the x and y direction, respectively, given by:
and
Here, BKGblank is the mean number of counts in DN for a blank region of the sky. For more details and other correction formulae, see WFPC2 ISR 97-08.
Long vs. Short Anomaly (non-linearity)
A comparison of repeated images of the same stellar field indicates that the count rates for the faint stars are higher for longer exposures. This apparent non-linearity appears to be a function of total counts in each source, rather than of count rates, and may depend on the image background. The magnitude errors produced appear to be less than 1% for well-exposed stars (over 30,000 e-), but can rise to as much as 15% for faint stars (less than 300 e-).1 The effect is quantitatively similar to a loss of about 2 to 3 e- per pixel in an aperture with a radius of 2 to 5 pixels. Although there is no evidence that this apparent non-linearity is, strictly speaking, position-dependent, it may be closely related to the CTE loss, and thus the two are often studied together.
An extensive program of observations is planned for Cycle 7 to characterize this non-linearity more completely. A preliminary report, based on data from Cycles 4 and 5, is available at:
http://www.stsci.edu/ftp/instrument_news/WFPC2/Wfpc2_cte/
ctetop.html
Geometric Distortion
Geometric distortion near the edges of the chips results in a change of the surface area covered by each pixel. The flatfielding corrects for this distortion so that surface photometry is unaffected. However, integrated point-source photometry using a fixed aperture will be affected by 1 to 2% near the edges, with a maximum of about 4-5% in the corners. A correction image has been produced and is available from the Archive (f1k1552bu.r9h). The counts measured for a star centered at a given pixel position must be multiplied by the value of this image. A small residual effect, due to the fact that the aperture radius differs from the nominal size, depends on the aperture used and is generally well below 1%.
Gain Variation
The absolute sensitivities of the four chips differ somewhat. Flatfields have been determined using the gain=14 setup, normalized to 1.0 over the region [200:600,200:600]. However, most science observations are taken using the gain=7 setup. Because the gain ratio varies slightly from chip to chip, PHOTFLAM values will be affected. The count ratios for the different chips from Holtzman (1995b) are:
Pixel Centering
Small, sub-pixel variations in the quantum efficiency of the detector could affect the photometry. The position of star relative to the sub-pixel structure of the chip is estimated to have an effect of less than 1% on the photometry. At present there is no way to correct for this effect.
28.2.3 Other Photometric Corrections
Miscellaneous corrections that must be taken into account include: aperture corrections, color terms if transforming to non-WFPC2 filters, digitization noise and its impact on the estimate of the sky background, the effect of red leaks and charge traps, and the uncertainty of exposure times on short exposures taken with serial clocks on.
Aperture Correction
It is difficult to measure directly the total magnitude of a point source with the WFPC2 because of the extended wings of the PSF, scattered light, and the small pixel size. One would need to use an aperture far larger than is practical. A more accurate method is to measure the light within a smaller aperture and then apply an offset to determine the total magnitude. Typically, magnitudes will be measured in a small aperture well-suited to the data at hand-a radius of 2-4 pixels, with a background annulus of 10-15 pixels, has been found adequate for data without excessive crowding-and the results corrected to the aperture for which the zeropoint is known. The aperture correction can often be determined from the data themselves, by selecting a few well-exposed, isolated stars. If such are not available, encircled energies and aperture corrections have been tabulated by Holtzman et al. (1995a). If PSF fitting is used, then the aperture correction can be evaluated directly on the PSF profile used for the fitting.
For very small apertures (1-2 pixels), the aperture correction can be influenced by the HST focus position at the time of the observation. The secondary mirror of HST is known to drift secularly towards the primary and to move slightly on time scales of order of an orbit. The secular shift is corrected by biannual moves of the secondary mirror, but the net consequence of this motion is that WFPC2 can be out of focus by up to 3-4 µm of secondary mirror displacement at the time of any given observation. This condition affects the encircled energy at very small radii, and thus the aperture corrections, by up to 10% in flux (for 1 pixel aperture in the PC); see WFPC2 ISR 97-01 for more details. If the use of very small apertures is required-because of crowding, S/N requirements, or other reasons-users are strongly advised to determine the aperture correction from suitable stars in their images. If such are not available, an approximate aperture-focus correction can be obtained as described in WFPC2 ISR 97-01.
A standard aperture radius of 0."5 has been adopted by Holtzman et al. (1995b) (note that Holtzman et al. 1995a used a radius of 1."0). For historic consistency, the WFPC2 group at STScI and the synphot tasks in STSDAS refer all measurements to the total flux in a hypothetical infinite aperture. In order to avoid uncertain correction to such apertures, both in calibration and in science data, this infinite aperture is defined by an aperture correction of exactly 0.10 mag with respect to the standard 0."5 aperture. Equivalently, the total flux is defined as 1.096 times the flux in the standard aperture of 0."5 radius. In practice, this means that observers wishing to use our tables or the synphot zero points should:
- Correct the measured flux to a 0."5 radius aperture.
- Apply an additional aperture correction of -0.10 mag (equivalently, multiply the flux by 1.096).
- Determine the magnitude using the zeropoints given.
See also the example in "An Example of Photometry with WFPC2" on page 28-15.
Color Terms
In some cases it may be necessary to transform from the WFPC2 filter set to more conventional filters (e.g., Johnson UBV or Cousins RI) in order to make comparisons with other datasets. The accuracy of these transformations is determined by how closely the WFPC2 filter matches the conventional filter and by how closely the spectral type (e.g., color, metallicity, surface gravity) of the object matches the spectral type of the calibration observations. Accuracies of 1-2% are typical for many cases, but much larger uncertainties are possible for certain filters (e.g., F336W with a red leak, see below), and for certain spectral types (e.g., very blue stars). Transformations can be determined by using synphot, or by using the transformation coefficients in Holtzman et al. (1995b).
Digitization Noise
The minimum gain of the WFPC2 CCDs, 7 e-/ADU, is larger than the read noise of the chip. As a result, digitization can be a source of noise in WFPC2 images. This effect is particularly pernicious when attempting to determine sky values, because the measured values tend to cluster about a few integral values (dark subtraction and flatfielding cause the values to differ by slightly non-integral amounts). As a result, using a median filter to remove objects that fall within the background annulus in crowded fields, can cause a substantial systematic error, whose magnitude will depend on the annulus being measured. It is generally safer to use the mean, though care must then be taken to remove objects in the background annulus.
A more subtle effect is that some statistics programs assume Gaussian noise characteristics when computing properties such as the median and mode. Quantized noise can have surprising effects on these programs. The recommended strategies for sky determination are described in WFPC2 ISR 96-03.
Red Leaks
Several of the UV filters have substantial red leaks that can affect the photometry. For example, the U filter (F336W) has a transmission at 7500 Å that is only about a factor of 100 less than at the peak transmission at about 3500 Å. The increased sensitivity of the CCDs in the red, coupled with the fact that most sources are brighter in the red, makes this an important problem in many cases. The synphot tasks can be used to estimate this effect for any given source spectrum.
Charge Traps
There are about 30 macroscopic charge transfer traps, where as little as 20% of the electrons are transferred during each time step during the readout. These defects result in bad pixels, or in the worst cases, bad columns and should not be confused with microscopic charge traps which are believed to be the cause of the CTE problem. The traps result in dark tails just above the bad pixel, and bright tails for objects farther above the bad pixel that get clocked out through the defect during the readout. The tails can cause large errors in photometric and astrometric measurements. In a random field, about 1 out of 100 stars are likely to be affected. Using a program which interpolates over bad pixels or columns (e.g., wfixup or fixpix) to make a cosmetically better image can result in very large (e.g., tenths of magnitude) errors in the photometry in these rare cases. See also "Charge Traps" on page 26-22.
Exposure Times: Serial Clocks
The serial clocks option (i.e., the optional parameter CLOCKS = YES in the Phase II proposal instructions) is occasionally useful when an extremely bright star is in the field of view, in order to minimize the effects of bleeding. However, when using this option, the shutter open time can have errors of up to 0.25 second. The error in the exposure time occurs as a result of the manner in which the shutters are opened when CLOCKS=YES is specified. Header information can be used to correct this error. If the keyword SERIALS = ON is in the image header, then the serial clocks were employed. The error in the exposure time depends on the SHUTTER keyword. If the value of this keyword is "A", then the true exposure time is 0.125 second less than that given in the header. If instead the value is "B", then the true exposure time is 0.25 second less than the header value.
Users should also note that exposure times of non-integral lengths in seconds cannot be performed with the serial clocks on. Therefore, if a non-integral exposure time is specified in the proposal, it will be rounded to the nearest second. The header keywords will properly reflect this rounding, although the actual exposure time will still be short as discussed above.
28.2.4 An Example of Photometry with WFPC2
This example shows the steps involved in measuring the magnitude of the star #1461 (Harris et al., 1993) in the Cousins I passband. The image used for this example can be obtained from the HST Archive, or from the WWW at:
http://www.stsci.edu/ftp/instrument_news/WFPC2/Wfpc2_phot
This WWW directory contains the materials for WFPC2 ISR 95-04, A Demonstration Analysis Script for Performing Aperture Photometry. Table 28.5 shows the results from an analysis script similar to WFPC2 ISR 95-04, but including some of the corrections discussed above.
Images: u2g40o09t.c0h[1] and u2g40o0at.c0h[1]
Position: (315.37,191.16)
Filter: F814W
Exposure Time: 14 seconds
Date of observation: MJD - 49763.4
Magnitude of Star #1461 in Cen
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1
See Casertano (1997), and Trauger (1997).
stevens@stsci.edu
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reserved.
Last updated: 07/01/98 10:56:16