Singlerun QA
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Singlerun QA quantities
Singlerun QA is the first place to look to understand in detail
the quality for a given run. This explanation of a run's QA page will
use an example run (chosen more or less at random), run 1478, rerun
40, which covers a part of strip 12 S. It can be reached from the summary
web site; clicking on the run number gets us to
http://das.sdss.org/imaging/QA/1478/40/qa/allrunQA147840.html.
Note that the top of the run's QA page indicates the versions of the
astrometric and photometric pipelines used to generate the data that
went into this analysis. The run's QA page gives statistics of a wide
variety of internal consistency statistics run on the data, with links
to specific postscript figures (and in some cases, tables of numbers)
giving the gory details. The tests carried out reflect specific
concerns and problems we've had with the data and pipelines thereof,
and therefore allow us to determine whether for these data, the
problem does not appear. This will become clear with the detailed
descriptions of the specific tests carried out.
An SDSS run is divided into six scanlines or camera columns, and
each camera column is divided into a long series of slightly
overlapping fields of 10x13 arcmin^{2}. Each field, in turn,
is made up of five frames, one in each of the SDSS filters,
u,g,r,i,z. There is a condensed version of the QA for the
run described below, but to understand it
requires familiarity with the basic tests of runQA, which we now
describe.
The tests that are carried out on each run fall into six broad
categories, which are listed in the table of contents in the beginning
of the run's QA page.
 Field Quality
Statistics tabulate the distribution of field qualities of
each camera column.
 Principal Color Distributions. The constancy
of the distribution of stars in colorcolor diagrams (the stellar
locus) allows a test of the photometric uniformity of the data.
 Background Brightness Analysis. Another check of the photometric uniformity
comes from comparing the sky brightness from one camera column to
another.
 PSF Photometry. There are several algorithms to determine the
brightnesses of stars; systematic differences between them are an
indication of possible problems in the determination of the
pointspread function.
 Relative Astrometry. The relative positions of
stars in the five passbands are checked for systematic offsets.
 Flatfield Errors. The principal colors of stars can be used to check for
systematic offsets as a function of position on each chip, due to
errors in the flatfield vector. Note that the signaltonoise ratio
for this analysis is usually poor for a single run; this analysis is
better done on a large group of runs
together.
Determining the overall quality of each field
The table lists the fractions of fields in each camera column with
each quality classification as defined on thesummaryQA page. In our example run, the
vast majority of fields are good or excellent. Tables of relevant
numbers are given for each camera column in links in the first column
of the table, and (in even more excruciating detail) in the link
labelled Here is the QAwizhard's Field Quality
Table.
The Principal Colors of the Stellar Locus
The distribution of ordinary stars in SDSS colorcolor space
follows a tight locus with distinctive features that can be used as
measures of the photometric calibration. In particular, one can use
various regions of these stellar loci that appear straight to define a
series of principal colors, whose median values should be
essentially constant over the survey (although they are weakly
metallicitydependent). See Helmi
et al (2003, ApJ, 586, 195) for an initial description of these
principal colors. These colors are defined after correcting for
foreground reddening a la Schlegel,
Finkbeiner, and Davis (1998); to a very good approximation, at the
flux limits of the SDSS, all stars are beyond the absorbing dust.
There are four such principal colors defined:
 The s color,
s=0.249u+0.794g0.555r+0.234 , which
is perpendicular to the stellar locus in the ug,
gr diagram.
 The w color,
w=0.227g+0.792r0.567i+0.050 , which is perpendicular
to the blue branch of the stellar locus in the ri vs. gr diagram.
 The x color,
x=0.707g0.707r0.983 , which is perpendicular to
the red branch of the stellar locus in the ri vs. gr diagram.
 The y color,
y=0.270r+0.800i0.534z+0.059 , which is
perpendicular to the stellar locus in the ri vs. iz
diagram.
Each of these colors has been offset to be zero over the full SDSS
survey. They have been normalized such that the error in the
principal colors is comparable to the error in a single band, assuming
the errors in each band are the same. These colors are measured for
every star brighter than r=19 (which are not flagged as having
problematic photometry). The statistics are plotted in a series of
figures labelled Click here for the main s color plot (and
similarly for w,
x,
and y).
They show the median and rms statistics in each bin, as a function of
field number, for each camera column. Here one can see at a glance
the extent to which the stellar locus is in agreement with the SDSS
global average (the lines in the top panel stay close to zero), and
whether there are specific fields or groups of fields that deviate.
One can also see whether the width of the stellar locus stays
constant. Also shown are the number of stars used in each bin for the
principal color determination (this is usually not flat, as the
density of stars changes with Galactic latitude). Finally, the rms
statistic in bins does not measure the number of extreme outliers from
the stellar locus, so also shown is the number of stars more than 2
sigma from the median s, w, x, and y values, on the blue side and red
side, respectively.
In addition, these statistics are all made available in the Field Quality Table , and also in links off
the flatfield error page linked at the bottom of the runQA page, and
are summarized in a series of tables, that look like this:

The x color

Quantity:  Median  MaxPC  Rms  Width  MaxWidth  Nall  NblueTail  NredTail 
col. 1  0.013*  0.026  0.009  0.041  1.28  30  1  0 
col. 2  0.008  0.028  0.011  0.042  1.30  28  1  0 
col. 3  0.015*  0.039  0.012  0.041  1.37  30  1  0 
col. 4  0.013*  0.032  0.011  0.041  1.41  28  1  0 
col. 5  0.014*  0.024  0.012  0.042  1.33  29  1  1 
col. 6  0.012*  0.017  0.008  0.040  1.38  30  1  0 
mean value  0.012*  0.028  0.011  0.041  1.345  29.167  1.000  0.167 
*Red entries are triggered by entry < 0.01 0 0.0 0.0 0 0 0 0
or entry > 0.01 0.04 0.02 0.08 1.75 100 30 30
Colorcolor and colormagnitude diagrams are given in links to each camera column,
showing exactly the stars that go into the definition of each primary
color.
The quantities listed, for each camera column, include:
 Median: The median value over all bins of the median
principal color. That is, it is the median of the values shown in the
top panel of the principal color figure.
The principal colors are supposed to be close to zero, so
This is the value you want to look for to see if there is some
systematic offset of the photometry of the whole camera column from the survey
as a whole.
 MaxPC: The largest deviation of the median principal color in a bin from
the median over all bins. That is, it is the most outlying point of
the values shown in the top panel of the principal color figure. Look
here for an indication of outlying frames with problematic photometry.
 Rms: The RMS scatter of the median PC color in each bin.
That is, it is the scatter around the mean of the values shown in the
top panel of the principal color figure. Look here for an indication
of varying photometric calibration along a run (caused, e.g., by
clouds).
 Width: The median value of the rms width of the principal
color in each bin. That is, it is the median of the values shown in
the second panel of the principal color figure. Typical values are
less than 0.05 magnitudes.
 MaxWidth: The maximum value of the rms width of the principal
color in each bin. That is, it is the maximum of the values shown in
the second panel of the principal color figure. Look here for signs
of a single frame with poor photometry.
 Nall (admittedly a confusing name): The median number of
stars which went into the determination of the principal color in each bin (i.e., the third
panel in the principal color figure). This median is not very
interesting, as the number of stars is a strong function of Galactic
latitude. Much more meaningful are:
 NblueTail and NredTail, which give the median number of
stars per bin which lie more than 2 sigma (on the blue and red sides,
respectively) of the median principal color. This is an indication of
possible problems with some small fraction of the photometry. This is
the median of the quantity shown in the lower two panels of the
principal color plot.
Too large a value of any of these quantities indicates a problem.
If any of these values is above a threshold, as indicated, it is shown
in red, so problems can be recognized at a
glance. If a problem is indicated, often the best way to proceed is
to look at the principal color plots. For example, in run 1478, the
Median x color is about 0.013 (i.e., 13 millimags) in most columns, a
bit above the nominal threshold of 0.01. The x
color plot does indeed show an offset in the x color of about 1%,
which seems to be a real calibration problem.
Background (Sky) Brightness Analysis
Another check of the uniformity of the photometric calibration, from
one camera column to another, is the uniformity of the sky brightness.
The sky brightness, measured on a framebyframe basis, changes with
time; here we calculate for each filter a
running median as a function of field over the six camera columns.
The plot http://das.sdss.org/imaging/QA/1478/40/qa/runQA147840sky.ps,
shows the deviations of each camera column from this median, in
units of magnitudes per square arcsecond.
Note that the bandpasses of the z chips differ slightly, one
from another; this effect is corrected for before taking the medians.
Thus the variation of the sky brightness with time has been taken out;
these curves should be quite flat (as indeed they are). In addition,
the median of each of these curves has also been taken out, so
each should hug zero.
Summary statistics are then given of the quantities in that figure,
including medians (i.e., the quantity taken out of the graphs above)
in the table Phot. Zeropoint Corr. for Flat
Sky, rms (Sky: RMS), and max
deviation (Sky: Max Dev)statistics. Note
that each of these tables links to the same figure for each of the
camera columns.
As this example shows, this is a very powerful statistic, and
checks for consistency of the internal photometric calibration and the
flatfields at the level of much better than a percent. It is
limited, however, by the presence of scattered light, especially in
the u band. An interesting scientific question is whether the sky
brightness is expected to differ at this level over the 2.5 degree
field of the camera.
PSF Photometry
Errors in the determination of the Point Spread Function (PSF) have
been one of the most pernicious in the development of the photometric
pipeline. The following tests allow us to determine how well the PSF
is calculated, by comparing different measures of the brightnesses of
stars.
In particular, the PSF magnitudes of stars (i.e., that determined
from a direct fit of the PSF model to the brightness, aperture
corrected to a large aperture; see the EDR paper) should agree with
the largeaperture (here, a diameter of 7.5 arcsec) magnitude itself.
This comparison can be carried out only for bright stars, for which
the noise from the sky is negligible. This is carried out for each
column of data for each filter, and there are plots
such as this example showing the difference between aperture and PSF
magnitude (for objects believed to be stars, brighter than 19th
magnitude, and with estimated PSF error less than 0.05, in each band
considered). Each star is shown as a point, with a running median per
field shown as a red line.
The Postage Stamp Pipeline, which determines the PSF in the first
place, indicates for each field the quality of its determination of
the PSF. There are certainly fields in which the PSF is known to be
poorly determined (usually in regions where the PSF is changing
rapidly with time; note the bottom panels give the rband seeing and
its derivative); changes in seeing of 0.2 arcsec/field are definitely
bad! These fields are flagged as having suspect PSF, and are
indicated as such with cyan or magenta lines in the plot. These fields
are not included in the summary statistics now described.
These summary statistics consist of:
 The maximum deviation in the median aperture  PSF magnitude per
field (i.e., the quantity plotted in red), in m(apert7)m(psf): Max Dev;
 The median value of the median PSF  aperture magnitude per
field, in m(apert7)m(psf): Med Off;
 The rms scatter of the median PSF  aperture magnitude per field,
in m(apert7)m(psf): RMS.
In run 1478, the median PSFaperture magnitude hugs zero impressively
well, with essentially no offset, and an rms scatter of 0.01 mag in u
and z, and substantially better in g, r, and i. Two chips (out of
30!), the uband in columns 2 and 5, are flagged red in their median
offset. As an aperture correction is made to make the PSF and
aperture magnitudes agree in the mean, this test is more a consistency
check than anything else.
In addition to the PSF, every object is fit to exponential or de
Vaucouleurs profile. The betterfitting of these two yields a
socalled `model magnitude'. This quantity is aperturecorrected to
force the model and PSF magnitudes of stars to agree. Of course, for
stars, the model scalesizes are close to zero, but this has really all
worked properly with the latest version of the photometric pipeline,
as described in detail in the SDSS
DR2 paper. The consistency of model and PSF magnitudes for stars
is is tested in the next series of plots and tables, m(mod)m(psf): Max Dev/Med Off/RMS.
Internal Tests of Astrometry
The astrometric calibration is applied to the rband, and then
propagated to each of the other bands in turn. One can ask, on a
starbystar basis, whether the calibrated positions are consistent.
This is shown in the last two sets of plots and tables. The
photometric pipeline measures a "velocity" for each object. This is
done with asteroids in mind: a mainbelt asteroid has an apparent
proper motion of a few arcseconds over the fiveminute interval
between the rband image and the gband image. Thus the astrometric
position of the asteroid varies linearly with filter (in the order,
riuzg). The pipeline fits a line to the positions of
every object; for all real stars, this line has a slope
consistent with zero. The scatter in this slope can be expressed as a
relative positional uncertainty between bands in arcseconds; these
tables collect the statistics for bright stars (r<19.0).
In particular, the plots
under bandtoband astrometric accuracy show the measured
distribution of this effective positional uncertainty (in the row and
column directions), shown both linearly (upper panels) and
logarithmically (middle panels; note the change in scale on the
xaxis). The median and sigma (as measured from the interquartile
range) are given for each panel. Note the pesky periodic peaks in the
upper histograms; those are an artifact of roundoff errors in the way
the data are stored.
The distribution is roughly Gaussian. One wants to look at
outliers in this plot, for example to look for asteroids in the outer
solar system. The T3 and T5 statistics shown in the figure give the
number of 3sigma and 5sigma outliers relative to the number expected
in a purely Gaussian distribution, respectively. T3 is typically
510, while T5 is meaningless for all but the very longest runs. But
note that the distribution cuts off completely at +/ 100
milliarcsec; the internal astrometry is very clean!
If the astrometric errors are estimated correctly, the distribution of
the measured errors divided by the errors estimated by
the imaging pipelines will
be a Gaussian with variance unity. This is tested in the lower panel,
Relative Astrometry by Field
(for blue and red stars separately). The distributions are not too
far off from Gaussian, and indeed have a variance significantly less
than unity, implying that the estimated astrometric errors are biased
somewhat high.
All these statistics are summarized in the table shown, for row
and column statistics separately. All quantities are shown in units
of milliarcseconds (except for the chisquared statistics, which of
course are unitless).
One can then study these statistics as a function of field. The astrometry
plot (here for column 1) shows the internal astrometric offsets
for each star brighter than r=19, together with median per field. The
statistics for these quantities (median over the fields, maximum, and
rms) are listed in the table. The maximum over a field are a few tens
of milliarcsec, with an rms of only a few milliarcsec.
Checks of the flat fields
Note that the results of these tests are given on a separate
flatfield QA page, as they are less useful on a runbyrun basis. Also given
on the run's flatfield QA page are links to the data files containing detailed
information on the principal colors.
The SDSS images are from a driftscan, thus the flat field is a
onedimensional vector for each chip, as a function of pixel column.
If this flat field is in error, the error will propagate into all
derived quantities, especially the photometry. The Principal Colors,
described above, can be used to check the
flat fields. The stellar principal colors are determined for each
camera column as a function of pixel column (in bins of 32 pixels).
Systematics as a function of pixel column are an indication of
flatfield problems. There are four principal colors, and five
flatfields; the equations are closed by including constraints from
the PT. The results of solving for the possible correction in each of
the u, g, r, i, and z flatfields is shown in a
series of flatfield
quality plots like this one). Again, these tend to be noisy for a
single run, especially in u (where we've been having the most trouble
with the flats). The largest problems in the flats tend to be at
their edges. This information is used a posteriori to improve the
SDSS flatfields themselves.
Summary Table
At both the top and the bottom of the runQA page, there is a link to a
summary
table, which condenses all this information further. The first
table is a repeat of the the
Phot. Zeropoint Corr. for Flat Sky, giving estimates from the sky levels
of any photometric offsets of each chip. A second such estimate is
given from the principal colors in the table
entitled Zeropoint Corrections to Fix Principal
Colors. Here, the four principal colors for each chip
(median'ed over the run) are solved for the five passbands, under the
(arbitrary) assumption that the offsets in g, r, and i (the three
highest S/N bands) add to zero. Remember, the principal colors are
defined to have zero mean over the full survey, and are normalized to
have errors comparable to the error in a single band. Because the
uband enters into the principal colors only through u, where it has a
coefficient of 1/4, this process tends to "push" the offsets to u;
there will often be offsets in u that are somewhat above spec as a
consequence.
Note that the links off these tables are dummies and do not lead anywhere.
Following that is a table with mean statistics over the run of
various additional quantities associated with the PSF determination
and the relative astrometry between bands. These of course are taken
simply from the detailed QA we have already seen.
Last modified: Fri Jun 23 14:06:37 BST 2006
