Photometric CTE Correction
Introduction
Since 2003, the ACS Team has taken observations of 47 Tuc to quantify the dependece of stellar photometry on the number of parallel and serial transfers. The observations employ a specialized dither pattern that allows one to derive an analytical model that depends on the following parameters: stellar flux, background level, and the number of parallel transfers. Losses due to serial transfers are currently very small (< 2% at the edge of the chip and far from the amplifiers, where losses are the worst) and consistent with zero for the level of sky background usually achieved by GO observations (> a few electrons per pixel). In 2012, the original model was revisited and the assumption of a log-space linear relationship between the magnitude losses as a function of stellar flux (valid for the small CTE losses in pre-SM4 data) was shown to be an oversimplification of the CTE effects after ~10 years in space. This led to a new and improved model that also correctly accounts for the time-dependence of the derived coefficients (see ACS ISR 2012-05).
Recent Updates
Analysis of data from the Cycle 24 External CTE monitor program (CAL/ACS 14507, P.I. Chiaberge) show that the CTE trends are continuing according to the model presented in ACS ISR 2012-05. We derive new coefficients and provide an updated correction to be used for aperture photometry of ACS/WFC drizzled images taken after Servicing Mission 4. The updated correction allows an average photometric accuracy of better than 3% for stellar sources located at any distance from the amplifiers. In order to achieve the highest accuracy, the ACS Team has developed two tools for computing and applying the photometric CTE corrections.
Updated coefficients and accuracy
The target of the calibration program is a field ~7’ West off the core of the globular cluster 47 Tucanae. Images are taken using two different filters (F502N and F606W) and with a range of exposure times (between 30s and 400s), in order to sample at least five different background levels. For a more extensive description of both the characteristics of the datasets and the method for the data analysis we refer the user to ACS ISR 2012-05. In the following we summarize the main steps and the latest results.
For each epoch, filter and exposure time combination, stars are grouped in bins of stellar flux (in e-) measured in each “pair” of images (0,0 and 0,1). Each star is assigned to a particular flux bin based on the lowest flux measured in each “pair”. In most cases six bins are obtained. A non-weighted linear fit to the data is performed and the value of Δmag2000 (Δmag for 2000 pixel transfers) is derived from the slope of the linear regression.
These measurements are used to perform a global fit and derive the coefficients pi, qi, pi’, qi’, (i=1, 2) of the following model correction
\(\begin{equation} \begin{aligned} \Delta mag(Y_{tran},t,SKY,FLUX) = \Big[\big((p_1*log_{10}(FLUX)+p^{'}_{1})*t+ p_2*log_{10}(FLUX) +p^{'}_2\big)*log_{10}(SKY) \\+ (q_1 *log_{10}(FLUX) +q^{'}_1)*t + q_2 *log_{10}(FLUX) + q^{'}_2\Big] * Y_{tran}/2000 \end{aligned} \end{equation}\)
where t is the time the observation was executed (in modified Julian days, e.g. August 24, 2012 at 0h 0m 0s = MJD 56163.5), FLUX is the flux (in e-) measured within a 3-pixel aperture radius, SKY is the background level measured as close as possible to the star, and Ytran is the number of transfers. The CTE correction web-tool offers the option of using a 5-pixel aperture radius.
The values of the coefficients for a 3 pixel aperture radius derived using data from Cycle 17 through Cycle 24 are reported below:
| Coefficient | Error | Coefficient | Error |
|---|---|---|---|
| \(p_1 = 0\) | \(0\) | \(p_2 = 0.1412\) | \(2.473 \times 10^{-3}\) |
| \(q_1 = -2.837 \times10^{-5}\) | \(1.800 \times 10^{-6}\) | \(q_2 = 1.344\) | \(0.1015\) |
| \(p^{'}_1 = -1.043 \times 10^{-5}\) | \(1.443 \times 10^{-7}\) | \(p^{'}_2 = 0\) |
\(0\) |
| \(q^{'}_1 = 1.496 \times 10^{-4}\) | \(6.260 \times 10^{-6}\) | \(q^{'}_2 = -7.279\) | \(0.3529\) |
The values of the coefficients for a 5 pixel aperture radius derived using data from Cycle 17 through Cycle 24 are reported below:
| Coefficient | Error | Coefficient | Error |
|---|---|---|---|
| \(p_1 = 0\) | \(0\) | \(p_2 = 0.100\) | \(4.562 \times 10^{-3}\) |
| \(q_1 = -2.787 \times 10^{-5}\) | \(4.137 \times 10^{-6}\) | \(q_2 = 1.391\) | \(0.2357\) |
| \(p^{'}_{1} = -7.81 \times 10^{-6}\) | \(2.767 \times 10^{-7}\) | \(p^{'}_2 = 0\) |
\(0\) |
| \(q^{'}_{1} = 1.439 \times 10^{-4}\) | \(1.475 \times 10^{-5}\) | \(q^{'}_2 = -7.255\) | \(0.8398\) |
For a CTE correction cookbook, please refer to Chiaberge, M. ACS ISR 2012-05.
The updated formula was tested for different levels of background and stellar flux. Stars in the field range from ~100 to ~100,000e- (measured within 3 pixel aperture radius), depending on the exposure time. The global accuracy is better than 3% for all background levels. Note that the global accuracy is measured averaging out all stars in the calibration field. In Fig. 1, we show the magnitude loss for 2000 parallel transfers (Y axis of the detector), for stars of different fluxes. The average sky level of 40 e- was obtained with an exposure time of 400s and the F606W filter. This corresponds to a typical background level for science images. The black points are the losses measured when no CTE correction is performed (from photometry performed on DRZ files). The red points are obtained by correcting the photometry of stars on the DRZ files with the photometric correction formula. The blue points are derived using photometry on DRC files, i.e. corrected using the pixel-based CTE correction currently available in the MAST pipeline.
The formal accuracy of the beta correction for photometry performed using a 5-pixel aperture radius is also better than 3%. However, since the parameters were derived using data from three cycles only, it should be used with some care.
