Subject: global calibration stuff Date: Fri, 31 Oct 97 11:45:42 MST From: jhe@noao.edu (Jay Elias) To: tchester@ipac.caltech.edu, jhe@noao.edu CC: skrutski@north.phast.umass.edu, roc@ipac.caltech.edu Global Calibration Issues: There are two specifications where the overall accuracy of the calibration process is involved. These are 1. The requirement that the accuracy of reasonably bright sources is 0.05 magnitudes 2. The requirement that the survey be "uniform" to 0.04 magnitudes. =============== 1. Accuracy of individual sources. First of all, this should be recognized as an allowable 1-sigma uncertainty, not a 3-sigma uncertainty or 95% confidence limit. If it is intended to be one of the latter, then all paramaters associated with calibration must be tightened up. Since this is a 1-sigma error, it should also be recognized that there will be bright sources detected by the survey whose catalog magnitudes are in error by 0.15 mag or greater. They will be a small fraction of the total, but not a negligible number. There are five contributors to the magnitude uncertainties of an individual source: a. Photon noise. This is assumed to be negligible, since this requirement is for bright (but not saturated) sources. b. Extraction errors. These are errors due to pixel non-uniformity, difficulties in correcting to standard apertures, and other similar effects. Since any source is observed several times during a scan, this effect is reduced for the final measurement. It is known to be significant, though. I think best estimates for this with current survey parameters are ~0.02 - 0.03 mag. This error could be further reduced only by a major alternation of the survey parameters, such as rescanning the entire sky or halving the scan rate. c. Photometric residuals. If variable transmission, seeing, or other effects are causing temporal variation in the photometry, the measured magnitude will be in error. The size of this effect is determined by the residuals in the standard measurements; the manner in which standards are observed is supposed to ensure that these measured residuals are in fact representative of the variations that are occurring during the period the survey data are taken (or at least survey data that are used). The scan to scan overlaps provide an additional check on this. The maximum allowable residual is currently set to be 0.04 mag. This in fact include effect (b) to some extent. This is clearly the largest of the source of error, at least under poor conditions. d. Airmass correction errors. Observations are corrected to a standard airmass. What matters for this purpose is the difference in airmass between the object and the avarge for the standards for that night. This would normally be only a few tenths of an airmass, and would be ~0.5 airmass only in extreme cases (e.g. the poles). The uncertainty due to airmass correction uncertainty is thus only a fraction of the uncertain in the airmass correction. If one takes 0.02 mag/airmass as a plausible uncertainty, then the errors due to this effect will normally be <0.01 mag. e. Zero point errors. The uncertainty in zero-point on a given night is the avaerage residual for the standards divided by sqrt N, for N standards. For partial nights, the minimum allowable value for N is currently 3, so the worst zero-point error would be 0.04 mag * 0.577 = 0.023 mag. Another way to look at it is that the worst case combination of (b), (c), and (e) that is allowed is sqrt(4/3)*0.04 mag = 0.046, which basically meets the requirement of 0.05 mag. ===================== 2. Survey Uniformity Here I think one needs to be a bit more specific in defining this requirement. In particular, there are really several scales on which one worries about uniformity, and to illustrate I will consider two cases: a - 10-degree x 10 degrees. This is a scale on which one might be investigating large-scale structure. Plauisbly, such an area would contain ~1000 detected galaxies and one would therefore be interested in statistical effects almost to the 1% level. A photometric error of 0.01 magnitude implies a distance error of 0.5% or a volume density error of 1.5%. What are the potential sources of error in this area? Although the survey can cover roughly this area in a single night, in reality the survey observations during a night will take place over several non-continguous strips of sky. Thus a 10x10 degree area will likely be observed over several nights. There are several sources of error: a. Transmission fluctuations and zero-point error. Since the allowable photometric residuals are <0.04 mag, and since the observations on a single night most likely will take place on the time scale of the interval between standards, all the data on a single night could be systematically in error by ~0.04 mag. The added effect of zero-point error would allow errors in a night's data of up to 0.05 mag (1-sigma). These errors would be uncorrelated from night to night, so the effect of combining the data from several nights would be to reduce this effect overall by sqrt N. Thus the overall 1-sigma error would be <0.02 mag. It seems clear that uncertainties of ~0.01 mag would be common. b. Airmass correction errors. As noted above, these will normally be <0.01 mag. However, they will tend to be similar for all related scans and the airmass error may be correlated from night to night. Thus in an extreme case an error in airmass correction could lead to errors over a 10 x 10 degree area ~0.01 mag. c. Standard errors. There will be a tendency to use particular standards when doing survey work in particular parts of the sky. Again, the extreme case is one in which all the data come from nights where only three standards were measured and where the same three were always used. The overall error would then be the standard magnitude uncertainty/sqrt(3). For a conservative value for the standard magnitude error of 0.02, this would be 0.012 mag. Again, this is an extreme case. ------------- Overall, then, there are several effects that can produce uncertainties on this scale at the 0.01-0.02 mag level. Normally the effects will be smaller, and in case (b) and (c) quite a bit smaller. It is, however, clear that on this scale 1-sigma uncertainties of ~0.01 mag should be expected. If the 0.04 mag requirement is treated as an allowable 1-sigma error, it is clearly met in all circumstances. If it is treated as a 2- or 3-sigma requirement it will usually be met but could plausibly be exceeded at times. Since the primary contributor is effect (a), it should be possible to produce an estimate of the uncertainty. Note that this analysis does not address ways of improving uniformity by means of subsequent analysis. "Martinizing" might help, as would comparison of overlaps from different nights. The survey will provide enough data to check standard magnitudes and thus reduce effect (c). --------------- Very large scale uniformity. Consider now uniformity on the scale of tens of degrees. Under these circumstances, most of the effects consider above are reduced by a large factor -- perhaps almost 10. This does not, however, mean that one can be confident of measuring effects on this scale to tenths of a percent. At that level, various additional effects may be present, including the uniformity of the standards system between N and S, systematic extinction effects between N and S or winter and summer, the non-linear nature of real extinction, and probably others that haven't occurred to me yet. It would certainly be useful to try to understand the limitations of the survey on these scale, but we may not be able to do more than determine the point where we lose confidence in our ability to understand all the systematics. My guess is that this is somewhere between 0.5% and 1% but will confess freely that this only a guess. ----- Jay Elias