# Flux Calibration

### Introduction

The objective of the photometric calibration process is to tie the SDSS imaging data to an AB magnitude system, and specifically to the “natural system” of the 2.5m telescope defined by the photon-weighted effective wavelengths of each combination of SDSS filter, CCD response, telescope transmission, and atmospheric transmission at a reference airmass of 1.3 as measured at APO (see transmission curves for SDSS 2.5m telescope).

DR6 and earlier data releases used a multi-stage process to calibrate the imaging data, using secondary references observed using the Photometric Telescope (PT).

In DR7 and later the calibrations for SDSS-III involve two steps: determining the relative photometry over the entire survey, and fixing the zero points in each filter to match the DR6 photometry. In DR7, both the recommended and PT (pre-DR7) photometric calibrations were reported. However, for the extra imaging taken prior to DR8 no PT observations were made. In DR8 and later, we only release the best estimates of photometric calibration at the time of the data release.

Between DR8 and DR12, the photometric calibrations were based on the ubercalibration procedure described by Padmanabhan et al., 2008. “Ubercal” used overlapping SDSS observations, including a set of fast binned scans orthogonal to most of the other runs, to determine the zero points, airmass terms, and flat field vectors as a function of drift scan run and time within each run. This procedure achieved 1% relative calibration errors in griz, and 2% in the u-band. The errors were dominated by unmodeled atmospheric variations at Apache Point Observatory. A full description can be found in the DR12 version of this page.

In DR13, we use updated zero points and flat-field vectors from the “hypercalibration” procedure of Finkbeiner et al. (2015). This work calibrates the SDSS data to Pan-STARRS 1 (PS1) griz imaging. Using PS1 ties down a small number of SDSS runs without strong overlap within SDSS, but more generally better ties down the run-to-run variations much more accurately. Using PS1 leads to direct improvements in the zero points, airmass terms, and flat fields of the SDSS griz imaging. It cannot directly improve the zero points and airmass terms of the u-band, which is not observed by PS1. However, by estimating PS1 u-band magnitudes based on optical colors, it does improve the SDSS u-band flat field vectors. Overall, in griz the estimated errors are driven below a percent and a number of large outliers are fixed.

### Calibration Parameters

The key parameter of the calibration for users is the conversion from counts (more precisely, ADU) into nanomaggies. We express this conversion factor as a single number per object per band, NMGYPERCOUNT. However, naturally this parameter is derived from the current atmospheric extinction, airmass, and flat-field values based on the parameters of a full photometric calibration solution for each run.

To perform this solution, the flux calibration assumes that the calibrated magnitude of an object m is related to its instrumental magnitude m0 by:

m = m0 + a – k(t)*x + f(i)

where a (the a-term) is a zero point, k (the k-term) describes the atmospheric extinction as a function of airmass x, and f is the flat field as a function of CCD column i (note that the SDSS flat fields are 1 dimensional, due to drift scanning). The a-terms are defined per camera column per night per filter. The k-terms are defined per night per filter, with a fixed linear time dependence (see the hypercal paper for details),

k(t) = k + (dk/dt)(t-tref)

where the reference time is assumed to be 0700 UT, and the time dependence of the k-terms (dk/dt) is fixed to the values below. The flat fields are defined per “season”, defined below; these are a subset of the seasons defined in the ubercalibration used in DR8 through DR12. Note that the season boundaries are given in terms of non-science drift scan run numbers.

Filter dk/dt (mag/airmass/10hr)
u -0.012
g -0.007
r -0.010
i -0.012
z -0.022
Flat field Season Starting Run Starting MJD Comments
1 1 51075 19-Sep-1998
3 725 51251 13-Mar-1999
7 1869 51865 17-Nov-2000 (vacuum leak in Dec 2000)
10 2504 52144 23-Aug-2001 (after camera tear-down)
12 4069 52872 20-Aug-2003 (after summer shut-down)
13 4792 53243 26-Aug-2004 (after summer shut-down)
15 6245 53959 11-Aug-2006 (after summer shut-down)
17 8032 55090 16-Sep-2009 (SDSS-III yr 2, after summer shut-down)

### Photometric Calibration Flags

The photometric calibration status flags are detailed here; we describe their recommended usage here. Most users will want to restrict to data with PS1_UNPHOT set to zero. Very careful use may require PS1_CONTRAIL also set to zero. The DR8 through DR12 data releases used PHOTOMETRIC as the primary determinant of photometricity; this flag is unchanged in DR13 but indicates only how well the photometry was tied down in the DR8 through DR12 ubercalibration.

If a user needs to use unphotometric data for some reason, there are four flavors to be aware of. The first, and best, is UNPHOT_OVERLAP – in this case, the unphotometric data overlaps photometric data, allowing a determination of the zero-point (a-term) on a field-by-field basis. For such data, the fluxes of objects should be correct on average, although the data could have larger than normal scatter. The next two UNPHOT_EXTRAP_CLEAR and UNPHOT_EXTRAP_CLOUDY are set when the data are assumed to be unphotometric and do not overlap any photometric data. In these cases, the ubercal algorithm extrapolates the solution from a clear (UNPHOT_EXTRAP_CLEAR, if available) or cloudy (UNPHOT_EXTRAP_CLOUDY) part of the night. Note that this is an extrapolation under unphotometric conditions, and there is no guarantee made on the data quality. The final class is UNPHOT_DISJOINT; this is set if the data are both spatially and temporally disjoint from the any survey data. In this case, even if the data may be photometric, the calibrations are set to an arbitrary default value and could have significant errors. Users should NOT treat these data as being calibrated.

Hypercalibration has introduced several new flags. PS1_UNPHOT indicates that unphotometric conditions were revealed by the PS1 comparison. PS1_CONTRAIL indicates that a small patch of unphotometric conditions was identified. In both cases, if these bits are set, the PHOTOMETRIC bit is not set. PS1_PCOMP_MODEL indicates that the flat field residuals were determined for that individual run, camcol, and band, which requires enough photometric data; otherwise, a per-season flat field is used. PS1_LOW_RMS indicates a run for which the photometric residuals are unusually low (less than half the median of all runs).

### Conversion from SDSS ugriz magnitudes to AB ugriz magnitudes

The SDSS photometry is intended to be on the AB system (Oke & Gunn 1983), by which a magnitude 0 object should have the same counts as a source of Fν = 3631 Jy. However, this is known not to be exactly true, such that the photometric zeropoints are slightly off the AB standard. We continue to work to pin down these shifts. Our present estimate, based on comparison to the STIS standards of Bohlin, Dickinson, & Calzetti (2001) and confirmed by SDSS photometry and spectroscopy of fainter hot white dwarfs, is that the u band zeropoint is in error by 0.04 mag, uAB = uSDSS – 0.04 mag, and that g, r, and i are close to AB. The z band zeropoint is not as certain at this time, but there is mild evidence that it may be shifted by about 0.02 mag in the sense zAB = zSDSS + 0.02 mag.

The large shift in the u band was expected because the adopted magnitude of the SDSS standard BD+17 in Fukugita et al. (1996) was computed at zero airmass, thereby making the assumed u response bluer than that of the USNO system response.

These statements are certainly not precise to better than 0.01 mag; in addition, they depend on the system response of the SDSS 2.5-meter, which was measured by Doi et al. (2010) and found to differ somewhat from the curves used to estimate the offsets just mentioned, and to probably be a function of time. They estimate the u-g change due to these differences to be at the 0.01 to 0.02 mag level.

Note that our relative photometry across the sky is quite a bit better than these numbers would imply; repeat observations and simulations of the ubercal pipeline show that our calibrations are about 1% in gri and about 2% in u and z.

### Conversion from SDSS ugriz magnitudes to physical fluxes

As explained in the preceding section, the SDSS system is nearly an AB system. Assuming you know the correction from SDSS zeropoints to AB zeropoints (see above), you can turn the AB magnitudes into a flux density using the AB zeropoint flux density. The AB system is defined such that every filter has a zero-point flux density of 3631 Jy (1 Jy = 1 Jansky = 10-26 W Hz-1 m-2 = 10-23 erg s-1 Hz-1 cm-2).

To obtain a flux density from SDSS data, you need to work out f/f0 (e.g. from the asinh magnitudes in the photoObj files by using the inverse of the relations given on the magnitudes page). This number is then the also the object’s flux density, expressed as fraction of the AB zeropoint flux density. Therefore, the conversion to flux density is

S = 3631 Jy * f/f0

Then you need to apply the correction for the zeropoint offset between the SDSS system and the AB system. See the description of SDSS to AB conversion above.

### QA Figures

The QA figures available for ubercalibration in the DR8 through DR12 releases are not available for hypercalibration in DR13. Some QA figures can be found in Finkbeiner et al. (2015).