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Illumination variations: characerization and correction
Report
Version: 1.0
Date: 30 Dec 2011
Authors: OmegaCAM Consortium.
Introduction
Flat field observations can have a straylight component. The flatfielding operation does not distinguish between true variations in sensitivity and apparent ones, mimicked by gradients in this straylight. Gradients in straylight are called illumination variations. Illumination variations can be characterized a posteriori from the residuals in observed stellar magnitudes compared to their reference value. The corresponding procedure is called Illumination Correction.
Illumination Correction Model 1: global 2nd-order polynomial
- An algorithm has been implemented that solves simultaneously for illumination variations and chip-to-chip gain variations for 32 chips. It models the illumination variations as a second order polynomial. As input it takes 32 dithered observations of SA fields that place a star on all different chips. The data are flatfielded using a flatfield that is a combination of a twilight flat and a domeflat. The large scale variations are set by the twilight, the small scale by the domeflats. Figures 1-4 show the illumination modelling and resulting magnitude residuals for Sloan u,g,r,i. Table 1 lists the resulting residuals. We define an internal and external rms in the residuals. External is with respect to the stellar reference magnitude in the standard star catalog, which is SDSS DR7 photometry in this case. Internal is wrt the mean of the observed magnitudes per star. Table 2 list the polynomial description and gives links to the data in Astro-WISE.
| filter | rms internal | rms external |
|---|---|---|
| (mag) | (mag) | |
| u | 0.019 | 0.032 |
| g | 0.012 | 0.022 |
| r | 0.011 | 0.024 |
| i | 0.014 | 0.026 |
Table 1: Residual magnitudes in Sloan u,g,r,i filters left after global illumination correction. Input data are the 32 dithered observations on SA fields. The data are flatfielded using a flatfield that is a combination of a twilight flat and a domeflat. The large scale variations are set by the twilight, the small scales by the domeflats. We define an internal and external rms in residuals. External is with respect to the stellar reference magnitude in the standard star catalog (SDSS DR7 stellar photometry). Internal is wrt the mean of its observed magnitudes.
| band | data in Astro-WISE | coeff x*x | coeff x*y | coeff y*y |
|---|---|---|---|---|
| u | illumu | 1.61533894480598e-09 | 1.93208441084062e-10 | 1.46502463058307e-09 |
| g | illumg | 1.7019894901137e-09 | 3.3104022217857e-11 | 1.67043927858479e-09 |
| r | illumr | 1.54534631642476e-09 | 2.55003412514956e-11 | 1.38537472866354e-09 |
| i | illumi | 1.527014845765e-09 | 1.07778571149453e-10 | 1.13924080056116e-09 |
Table 2. An algorithm has been implemented that models the illumination variations as a second order polynomial. This table gives links to the illumination correction frames in Astro-WISE and the polynomial coefficients. x,y is in pixel units with x,y=0,0 at the mosaic center.
Fig1. Illumination correction derivation for OmegaCAM Sloan u. Input data is 32-dither observations of SA113. The magnitude residual after flatfielding are modeled with one 2D-polynomial + 32 ZPTs as free parameters. SDSS DR7 is used as standard star catalog. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. Bottom left: External magnitude residuals after illumination model has been applied. Bottom right: model with ZPT per chip subtracted.
Fig2. Illumination correction derivation for OmegaCAM Sloan g. Input data is 32-dither observations of SA113. The magnitude residual after flatfielding are modeled with one 2D-polynomial + 32 ZPTs as free parameters. SDSS DR7 is used as standard star catalog. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. Bottom left: External magnitude residuals after illumination model has been applied. Bottom right: model with ZPT per chip subtracted.
Fig3. Illumination correction derivation for OmegaCAM Sloan r. Input data is 32-dither observations of SA113. The magnitude residual after flatfielding are modeled with one 2D-polynomial + 32 ZPTs as free parameters. SDSS DR7 is used as standard star catalog. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. Bottom left: External magnitude residuals after illumination model has been applied. Bottom right: model with ZPT per chip subtracted.
Fig4. Illumination correction derivation for OmegaCAM Sloan i. Input data is 32-dither observations of SA113. The magnitude residual after flatfielding are modeled with one 2D-polynomial + 32 ZPTs as free parameters. SDSS DR7 is used as standard star catalog. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. Bottom left: External magnitude residuals after illumination model has been applied. Bottom right: model with ZPT per chip subtracted.
- The internal rms listed in Table 1 demonstrates that illumination variations are characterized to a precision between 1 and 2% over the whole mosaic. The magnitude residuals in Figures 1-4 demonstrate that remaining systematic effects over a single chip are < 1%. The exception are areas near CCD edges with a width of ~200 pixels which display offsets upto ~0.06mag. In addition a few localized regions (typical sizes less than ~12% of a chip area) are apparent where offset can be up to ~0.03mag.
- The robustness of the illumination correction is determined in two ways. First, illumination corrections derived from two different SA fields for Sloan r differ by less than 1% percent (see Figure 5). Second, the illumination correction derived from SA113 as applied to SA95 does not show any systematics in the residuals (Figure 6).
Figure 5: Ratio of illumination corrections in Sloan r as derived from two different SA fields. The color scaling
from black to white corresponds to ratio values of 0.994 to 1.006. Largest variations over a single chip amount
to < 1% min-to-max.
Figure 6: Illumination correction residuals for OmegaCAM Sloan r for polynome method. Left: residuals after applying to SA113 the polynome model derived from SA113. Right: residuals after applying to SA95 data the polyonome model derived from SA113. No systematic differences are seen.
Illumination Correction Model 2: local linear planes.
To address the localized systematic offsets in residuals for the global approach we applied a localized illumination correction. The input data is identical to the global approach. A zeropoint is determined per chip. Each chip is then split into bins, 32 for u and 50 for g, r and i. In each bin a plane (a + b*x + c*y) is fitted to the magnitude residuals. Figures 7-10 show the results and Table 3 lists the rms residuals.
Fig7. Illumination correction derivation for OmegaCAM Sloan u. The illumination variations are modelled per bin with a plane. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. The bins
are sometimes visible. Bottom left: External magnitude residuals after illumination model has been applied.
Bottom right: model with ZPT per chip subtracted.
Fig8. Illumination correction derivation for OmegaCAM Sloan g. The illumination variations are modelled per bin with a plane. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. The bins
are sometimes visible. Bottom left: External magnitude residuals after illumination model has been applied.
Bottom right: model with ZPT per chip subtracted.
Fig9. Illumination correction derivation for OmegaCAM Sloan r. The illumination variations are modelled per bin with a plane. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. The bins
are sometimes visible. Bottom left: External magnitude residuals after illumination model has been applied.
Bottom right: model with ZPT per chip subtracted.
Fig10. Illumination correction derivation for OmegaCAM Sloan i. The illumination variations are modelled per bin with a plane. Top left: magnitude residuals after flatfielding (ZPT per chip not subtracted). Top right: model. The bins
are sometimes visible. Bottom left: External magnitude residuals after illumination model has been applied.
Bottom right: model with ZPT per chip subtracted.
| filter | rms internal | rms external |
|---|---|---|
| (mag) | (mag) | |
| u | TBComputed | TBC |
| g | TBC | TBC |
| r | 0.009 | 0.020 |
| i | TBC | TBC |
Table 3: Residual magnitudes in Sloan u,g,r,i filters left after local illumination correction. Input data are the 32 dithered observations on SA fields. The data are flatfielded using a flatfield that is a combination of a twilight flat and a domeflat. The large scale variations are set by the twilight, the small scales by the domeflats. We define an internal and external rms in residuals. External is with respect to the stellar reference magnitude in the standard star catalog (SDSS DR7 stellar photometry). Internal is wrt the mean of its observed magnitudes.
Dependence on rotator angle
- The OmegaCAM commissioning reports give the rotator angle dependency of the illumination variation. The straylight patterns are not fully circularly symmetric and can change more irregularly than a simple rotation. Flat fields and illumination corrections, the latter being an correction on the flat field, must be derived in an internally consistent manner. Thus for optimal precision, the weekly twilight flatfields and dome flatfields have to be observed at the same position angle wrt to the telescope / sky / dome screen as those used in deriving the illumination correction.
* For domeflats this requirement is fullfilled. They are taken at identical rotator angle, position angle, altitude and azimuth.
- For twilightflats this requirement is not fullfilled. They are taken at identical position angle on the sky. However, rotator angle, altitude and azimuth vary. The flatfield illumination shows variations of maximum ~2% within a chip as a function of rotator angle (see Figure 11).
We have explored the effect for the r band quantitatively. Table 4 shows that the usage of internally inconsistent rotator angles in flatfielding and derivation of illumination correction has a negligible effect on rms of residuals. Figure 12 shows that locally systematic changes in the residuals of less than 0.02mag are observed.
| filter | rms internal | rms external | comments (all illum corrs derived from SA113 data-set) |
|---|---|---|---|
| (mag) | (mag) | ||
| r | 0.009 | 0.020 | binning model applied on same data-set (i.e. SA113) |
| r | 0.011 | 0.023 | binning model applied on SA95 data-set, SA95 reduced with same ff |
| r | 0.011 | 0.024 | binning model applied on SA95 reduced with tw. flat with rotator angle different by 70 degrees |
Table 4: Rms of residual magnitudes in the SLOAN r filter for 3 different datasets using a single illumination correction with local binning.
Figure 11. Ratio image of two raw twilight exposures in z. The two exposures differ by 180 degrees in the rotator angle (header keyword ABSROT). The variation in the ratio changes ~2% (bottom-to-peak) within a CCD.
Figure 12. Left: Illumination correction residuals for OmegaCAM Sloan r SA95 reduced with same twilight as used in derivation of illumination correction. Right: residuals when SA95 is reduced with a twilight
flat with a rotator angle (ABSROT) that differs by 70 degrees with the twilight used in deriving the illumination correction. Localized systematic differences amount to 0.02mag maximum.
Conclusions
- We have ~0.03 mag (rms) photometric precision or better in u, g,r,i using SDSS DR7 as reference catalog. The dedicated OmegaCAM secondary standards catalog is expected to improve on this photometric precision. This is supported by the 0.01-0.02 magnitude (rms) internal rms achieved currently.
- The goal to determine the illumination correction better than 1% for the amplitude over a single CCD is met over the whole mosaic.
- The irregular spatial distribution in the illumination variation can be corrected with a local fitting approach.
- The illumination variation in twilights has an irregular dependence on rotator angle. Applying inconsistent (i.e., different) rotator angles are applied in flatfielding and derivation of the illumination correction has a negligible effect in terms of rms residuals over the whole moasic. However, locally (i.e., at the sub-chip level) systematic effects at 2% or less can be expected.
- Twilights shall be observed at fixed rotator angle
