A short presentation on the data processing system used for MegaCam data (Elixir) and why we need Photometric Grid data.

Mar 2004 Grid Results - New processing (June 04)
Dec 2004 Grid Results - At different processing stages
05Bm02 reprocessed Grid Results - with different flat processing

Bottom Line on the New Elixir (June 04) - With the exception of the u* filter, which has an RMS scatter of 0.012 mag, the chip-to-chip variations in filter zeropoints are less than 0.01 mag RMS. For the colors, the color term RMS is close to 1%, with the exception of (i' - z') which has an RMS of 2%. The color term zeropoint variation for all filters is close to 0.01 mag. Given the intrinsic dispersion in SNe Ia, there will be little contribution to the scatter in their distances from chip-to-chip variations in MegaCam. That being said, there is definite structure in the variations, indicating that refinements of the grid analysis in Elixir, such as using larger photometric apertures to measure the grid images, are worth doing and could lower the chip-to-chip variations even more. The details of this analysis and the results are displayed below.

Observations - The observations consist of 13 exposures in each of the u*g'r'i'z' filters of a fairly dense star field. The 13 exposures consist of an unshifted reference image, 6 images shifted East, and 6 images shifted North. The 6 shifts are 100", 200", 400", 800", 1600", and 3200". This shifting places many stars on multiple chips allowing a measure of the chip-to-chip photometric variations, after accounting for exposure-to-exposure variations.

Photometry - Photometry was performed in three ways:

1. IRAF apphot aperture photometry using a findiso object list
2. DAOPHOT aperture photometry using a findiso object list
3. SExtractor aperture photometry using a high threshhold (50)

In every case we used an effective aperture radius of 25px to minimize image quality variation effects. Stars within 10pix of the image edges are removed as well as stars with obvious problems (mag gt 50, e.g.). For the SExtractor output, stars within 45pix of the image edges are removed as are stars with unusually low FWHMs (cosmic rays).

Star Matching - For the zeropoints, the stars are astrometrically matched using a modified version of CJP's program 'mscmatch' which transforms coordinates in each chip to overall mosaic coordinates (based on the distortion analysis of Christian Veillet). For the color terms, the stars are matched with 'colmatch' which is based on 'mscmatch'. These programs output matched pairs of magnitudes or colors from which delta mags or delta colors are computed and used to analyze the variation of zeropoints or color terms from chip-to-chip and from exposure-to-exposure. The grid sets have the pairs from all unique combinations of the unshifted and shifted images for the given filter or color. The unshifted i' image is used as the astrometric reference image for all star matching.

Sigma Clipping - It was discovered that the astrometric matching is not perfect and that the findiso object list produced the cleanest results with the fewest mis-matches. SExtractor results were improved by lowering the star density (by raising the detection threshhold). Even so, to prevent mis-matches from influencing the parameter fits, we use a 5 sigma cut on the delta mags/delta colors before performing the analysis. The values of the cuts are indicated in the fit logs and on the uncorrected raw data plots for the DAOPHOT and IRAF photometry fits (see below).

Analysis - The method used to perform the analysis defines the magnitude or color relative to chip 13 and then uses the differentials produced by the shifting to tie the entire system together. The differential system is then fit with a linear least-squares method to derive the parameters.

For the zeropoints we define the magnitude relative to chip 13 as follows:

(1) m(i,s) = m(13,s) + zp(i) + zexp(e),

where m(i,s) is the magnitude of star s on chip i, m(13,s) is the magnitude of star s on chip 13, zp(i) is the zeropoint of chip i (relative to chip 13), and zexp(e) is the transparency zeropoint of exposure e (relative to exposure 1, which I chose to always be the unshifted exposure). The differential then becomes:

(2) dm(ij,s) = m(i,s) - m(j,s) = ( zp(i) - zp(j) ) + ( zexp(e) - zexp(f) ),

where i and j are the two chip numbers (not neccessarily different) and e and f are the two exposure numbers (also not always different). We define the zp of chip 13 to be 0. and the zexp of exposure 1 to be 0., then all parameters are relative to these.

For the color terms we define the colors relative to chip 13 as follows:

(3) c(i,s) = czp(i) + c(13,s) * ct(i) + czexp(e),

where c(i,s) is the measured color of star s in chip i, czp(i) is the color zeropoint of chip i, c(13,s) is the color of star s in chip 13, ct(i) is the relative color term of chip i and czexp(e) is the color zeropoint for the given exposure. The differential then becomes:

(4) dc(ij,s) = c(i,s) - c(j,s) = ( czp(i) - czp(j) ) + c(13,s) * ( ct(i) - ct(j) ) + ( czexp(e) - czexp(f) ),

with i and j, and e and f as above. We estimate c(13,s) by assuming that the color terms are close to 1 and the zeropoints are small and taking the average of the two solutions provided by solving equation (3) above for c(13,s) and plugging in c(i,s) and c(j,s).

Results - This analysis produced coefficients (with errors) for each chip and each exposure and are listed below. We also plot the raw input data and the chip-by-chip data and fits. As a check, we also compare the coefficients derived from the three photometry methods by plotting them up with a different symbol for each method (see below). This is probably the best place to look to get an idea of the amount and form of the variations. Considerable structure is visible in the coefficients but with an RMS near or below our error-budget limit of 0.01 mag in both zeropoints and color terms. Nonetheless, as mentioned above, the consistent structure in the zeropoints especially indicate that by tuning Elixir these variations can be removed.

Consistency Checks - A few consistency checks bear mentioning. To check the influence of errors introduced by the most extreme shifted images, an analysis without these images was performed and the resulting coefficients were indistinguishable from the results using these images. For the color terms, we also reversed the color, (i' - r') instead of (r' - i'), and derived the expected coefficients to high accuracy. We also compared the raw input data for a given chip to the coefficents derived for that chip. We plotted the input data for that chip, computed it's mean offset and std deviation (after accounting for the exposure offset) and compared this with the computed zeropoint and error for the chip. In every case, the two values agreed to within the errors and no systematic trends were observed with positional shift, mosaic row, mosaic column, or filter.

It would also be good to check the repeatability of these measurements by analyzing another grid data set. I will attempt to get the reprocessed version of the Oct 2003 grid set to analyze.

Data Reduction - None, obviously for the raw version. For the twilight flattened set and the fully processed set, the data were Elixir-processed by J-CC. The aperture photometry data can be downloaded here.

Analysis - All photometry was done with DAOPHOT using a 25px radius aperture.

Comments - Without the fringe removal, the z' and i'-z' analysis is nearly useless: extremely noisy.

TODO -

1. Compare photometry with Eugene Mangier to determine if residual chip-to-chip variation is due to photometric method.
2. Acquire and analyze raw and fully processed versions of Dec04 grid data.