| Document Number: VDF-SPE-IOA-00009-0001 Version 3 |
| Author: Mike Irwin |
Changes
The main changes from the previous versions of this document are: a slightly refined set of radii for the larger aperture sizes (the previous ones extended to an optimistically large final aperture which was similar size to the the background following algorithm ie. too big); a hopefully clearer definition of the aperture radii used; renaming and redefinition of the radius of the FWHM total flux estimator to avoid confusion with the aperture 3 flux; and additional descriptions of further header content mostly relating to derived Data Quality Control (DQC) information. Finally a note has been added describing the user-selectable parameters that determine how the software is run.
Preamble
The derived object catalogues are stored in multi-extension FITS files as FITS binary tables, one for each image extension with a dummy primary header unit. Each catalogue header contains a copy of the relevant telescope FITS header content in addition to detector-specific information.
Each detected object has an attached set of descriptors, forming the columns of the binary table and summarising derived position, shape and intensity information. During further processing stages ancilliary information such as the sky properties, seeing and so on are derived from the catalogues and stored in the FITS headers attached to each catalogue extension.
The catalogue format was derived from similar APM/SuperCOSMOS/INT WFC/CIRSI analysis which produced 32 4-byte parameters per detected object. This has been enhanced for WFCAM to an 80 4-byte parameter set to include extra parameters for flux estimation and error estimates.
The following tables cover the WFCAM standard and further processing
pipeline output catalogues, where for simplicity all derived parameters are
stored as floating point numbers even though some of them are more naturally
integers.
Columns content description
No. ¯ Isophotal flux...... ¯ Description
No. Name Description
1 Seq. no.
running number for ease of reference, in strict order of image detections
2 Isophotal flux
standard definition of summed flux within detection isophote, apart from
detection filter is used to define pixel connectivity and hence which
pixels to include. This helps to reduce edge effects for all isophotally
derived parameters.
3 X coord
intensity-weighted isophotal centre-of-gravity in X
4 Error in X estimate of centroid error
5 Y coord
intensity-weighted isophotal centre-of-gravity in Y
6 Error in Y estimate of centroid error
7 Gaussian sigma
these are derived from the three general intensity-weighted second moments
8 Ellipticity
the equivalence between them and a generalised elliptical Gaussian
9 Position angle
distribution is used to derive Gaussian sigma = (sa2+sb2)1/2
ellipticity = 1.0-sa/sb
position angle = angle of ellipse major axis wrt x axis
10 Areal profile 1
number of pixels above a series of threshold levels relative to local sky.
11 Areal profile 2
levels are set at T, 2T, 4T, 8T ... 128T where T is the threshold. These
12 Areal profile 3
can be thought of as a sort of poor man's radial profile. Note that for now
13 Areal profile 4
deblended, i.e. overlapping images, only the first areal profile is computed
14 Areal profile 5
and the rest are set to -1 flagging the difficulty of computing accurate
15 Areal profile 6
profiles.
16 Areal profile 7
17 Areal profile 8 for blended images this parameter is used to flag
the start of the sequence
of the deblended components by setting the first
in the sequence to 0
18 Peak height
in counts relative to local value of sky - also zeroth order aperture flux
19 Error in pkht
20 Aperture flux 1
These are a series of different radii soft-edged apertures designed to
adequately sample the curve-of-growth of the majority of images and to
provide fixed-sized aperture fluxes for all images. The scale size for
these apertures is selected by defining a scale radius » < FWHM >
for site+instrument. In the case of WFCAM this ``core'' radius (rcore) has
been fixed at 1.0 arcsec for convenience in inter-comparison with other
datasets. A 1.0 arcsec radius is equivalent to 2.5 pixels for non-interleaved
data, 5.0 pixels for 2x2 interleaved data, and 7.5 pixels for 3x3 interleaved
data. In » 1 arcsec seeing an rcore-radius aperture contains roughly
2/3 of the total flux of stellar images. [In general the rcore parameter
is user specifiable and hence is recorded in the output catalogue FITS
header.]
The aperture fluxes are sky-corrected integrals (summations) with a
soft-edge (ie. pro-rata flux division for boundary pixels). However,
for overlapping images they are more subtle than this since they are in
practice simultaneously fitted top-hat functions, to minimise the effects
of crowding. Images external to the blend are also flagged and not
included in the large radius summations.
21 Error in flux
22 Aperture flux 2
23 Error in flux
24 Aperture flux 3
Recommended if a single number is required to represent the flux for ALL
25 Error in flux images - this aperture has a radius of rcore.
26 Aperture flux 4
27 Error in flux
Starting with parameter 20 the radii are:
1/2× rcore, 1/Ö2× rcore, rcore, Ö2× rcore,
2× rcore,
2Ö2× rcore, 4× rcore, 5× rcore, 6× rcore, 7× rcore,
28 Aperture flux 5 8× rcore, 10× rcore, 12× rcore
29 Error in flux
30 Aperture flux 6 Note 4× rcore, ensures ~ 99% of PSF flux
31 Error in flux
32 Aperture flux 7 extras for generalised galaxy photometry further spaced
33 Error in flux
34 Aperture flux 8 in radius to ensure reasonable sampling further out.
35 Error in flux
36 Aperture flux 9
37 Error in flux
38 Aperture flux 10 Note these are all corrected for pixels from overlapping neighbouring images
39 Error in flux
40 Aperture flux 11
41 Error in flux
42 Aperture flux 12
43 Error in flux
44 Aperture flux 13 The biggest with radius 12× rcore ie. » 24
arcsec diameter
45 Error in flux
The aperture fluxes can be combined with later-derived aperture
corrections for general purpose photometry and together with parameter 18
(the peak flux) give a simple curve-of-growth measurement which forms
the basis of the morphological classification scheme
46 Petrosian radius rp as defined in Yasuda et al. 2001 AJ 112 1104
47 Kron radius rk as defined in Bertin and Arnouts 1996 A&A Supp 117 393
48 Hall radius rh image scale radius eg. Hall & Mackay 1984 MNRAS 210 979
49 Petrosian flux flux within circular aperture to k ×rp ; k = 2
50 Error in flux
51 Kron flux flux within circular aperture to k ×rk ; k = 2
52 Error in flux
53 Hall flux flux within circular aperture to k ×rh ; k = 5; alternative total flux
54 Error in flux
55 Error bit flag bit pattern listing various processing error flags
56 Sky level local interpolated sky level from background tracker
57 Sky rms local estimate of variation in sky level around image
58 Child/parent flag for parent or part of deblended deconstruct
(redundant since only deblended images are kept)
The following are accreted after standard catalog generation
59 RA
RA and Dec explicitly put in columns for overlay programs that cannot,
60 Dec
in general, understand astrometric solution coefficients - note r*4
storage precision accurate only to » 50mas. Astrometry can
be derived more precisely from WCS in header and XY in parameters 5 & 6
61 Classification
Flag indicating most probable morphological classification:
eg. -1 stellar, +1 non-stellar, 0 noise, -2 borderline stellar, -9 saturated
62 Statistic
An equivalent N(0,1) measure of how stellar-like an image is, used in
deriving parameter 61 in a `necessary but not sufficient' sense.
Derived mainly from the curve-of-growth of flux using the well-defined
stellar locus as a function of magnitude as a benchmark
(see Irwin et al. 1994 SPIE 5493 411 for more details).
From the further processing pipeline after deriving a suitable PSF
63 PSF flux fitted flux from PSF
64 Error in flux
65 X coord updated PSF-fitted X centre
66 Error in X coord
67 Y coord updated PSF-fitted Y centre
68 Error in Y coord
69 PSF fit c2 standard normalised variance of fit
70 nPSF no. of degrees of freedom for PSF fit
71 1D Sersic flux fitted flux for Sersic profile
72 Scale length scale factor of fit
73 Power index power law index of fit
74 Error in fit standard normalised variance of fit
75 nS1 no. of degrees of freedom for 1D Sersic fit
76 2D Sersic flux fitted flux for PSF-deconvolved 2D Sersic fit
77 Scale length scale factor of fit
78 Power index power law index of fit
79 Error in fit standard normalised variance of fit
80 nS2 no. of degrees of freedom for 1D Sersic fit
[For numerical stability the Sersic fits will use the previously derived x-y coordinates]
Note:- a more formal mathematical definition of many of these parameters,
together with a corresponding definition of the image processing steps
is given in the VDFS Data Reduction Library Design document
VIS-SPE-IOA-20000-0010, and references therein, available on
http://www.ast.cam.ac.uk/vdfs/docs/.
Although this particular document is specific to VISTA, the formalism is
generally applicable and the processing steps
and catalogue parameters are expected to be almost identical.
Derived catalogue FITS header contents
Examples of extra FITS header items derived from the catalogues or during catalogue creation, one set for each extension.
SKYLEVEL= 91.8 / Median sky brightness (counts/pixel)
An automatic 2D background-following algorithm is used to track and "remove" slowly varying background features such as image gradients etc.. The default scale size for background tracking (NBSIZE) is currently set to 64 pixels, coupled with a smidge of non-linear filtering this gives a background tracking scale of order 100 pixels. (A bilinear interpolator is used to generate pixel resolution background maps internally).
SKYNOISE= 6.0 / Pixel noise at sky level (counts)
Robust MAD estimator for noise scaled to equivalent Gaussian rms value ie. = MAD x 1.48 after removing large scale sky background variations. MAD = Median of the Absolute Deviations about the median
THRESHOL= 9.0 / Isophotal analysis threshold (counts)
User-selectable parameter, the default is to set this to 1.5 skynoise as a compromise between detecting close to the limit of the data and not being swamped by spurious sources. It is possible to push the data limit fainter but at the expense of a large increase in spurious sources. LSBG detection requires a more subtle add-on to the catalogue and could be added given suitable demand.
MINPIX = 4 / Minimum size for images (pixels)
User-selectable parameter, in conjunction with the threshold above this determines how deep and how small ``real'' images can be. This default precludes many of the few pixel-hit cosmic rays from being considered since ``real'' images must have 4 contiguous simply-connected pixels in the union of the detection filter and data domains. For more details on image detection and parametersiation see the papers in http://www.ast.cam.ac.uk/vdfs/publications.html .
CROWDED = 1 / Crowded field analysis flag (0 none, 1 active)
User-selectable parameter, detection algorithm tried to disentangle overlapping images or images supperposed on the ``slowly'' varying background of other large images (default) otherwise just straighforward isophotal detection.
RCORE = 3.50 / Core radius for default profile fit (pixels)
User-selectable parameter, aperture flux designed to match median seeing of survey data. It is straighforward to show that if rcore = FWHM then for typical profiles encountered the rcore flux estimate has between 80-90idealised perfectly known PSF model method.
SEEING = 2.95 / Average FWHM (pixels)
An average realistic FWHM estimated directly from the stellar images on the frame. Mutiply by pixel scale size to convert to arcsec (eg. *0.400 WFCAM; *0.333 INT WFC).
ELLIPTIC= 0.04 / Average stellar ellipticity (1-b/a)
A direct estimate of the average stellar ellipticity, useful for spotting trailed frames usw.. Should not average much above 0.15 for "normal" frames.
CLASSIFD= T / Classified
Has image morphological classifier been run ? if so an object classification flag and a stellarness index is included in the binary table columns.
SATURATE= 41593.8 / Average saturation level in frame
An estimate directly from saturated images on the frame at what level image saturation occurs, including sky. This varies from detector to detector depending on the relative gains applied to bring them to a uniform flatfield reponse etc..
Photometric Information
APCORPK = 2.812 / Stellar aperture correction - peak height APCOR1 = 0.635 / Stellar aperture correction - core1 flux APCOR2 = 0.114 / Stellar aperture correction - core2 flux APCOR3 = 0.028 / Stellar aperture correction - core3 flux APCOR4 = 0.000 / Stellar aperture correction - core4 flux APCOR5 = 0.000 / Stellar aperture correction - core5 flux APCOR6 = 0.000 / Stellar aperture correction - core6 flux APCOR7 = 0.000 / Stellar aperture correction - core7 flux
Aperture corrections in magnitudes needed to correct the assorted aperture-like
measures produced in the catalogues onto the equivalent of a total flux
stellar system. These constitute the components of a curve-of-growth analysis
contained within the catalogues with radii defined in the previous table; t
o be used in the sense that
| (1) |
The remaining information necessary for photometric calibration may also be included in the following keywords:-
PERCORR = -0.006 / Sky calibration correction (mags)
this is a correction based on the median dark sky recorded in science frames
compared to the median for all the detectors and as such is an ancillary correction
to the gain correction derived from the flatfield (usually twilight flats)
data. This correction is to be used in the same sense as before in that
| (2) |
MAGZPT = 22.10 / Photometric ZP (mags) for default extinction
Derived detector zero-point in the sense of what magnitude object gives a
total (corrected) flux of 1 count/s. These ZPs are appropriate for generating
magnitudes in the natural detector+filter system based on Vega,
see http://www.ast.cam.ac.uk/vdfs/docs/reports/
for more details on colour equations etc.. The
ZPs have been derived from a robust average of all photometric
standards observed on any particular set of frames, corrected for airmass
but assuming the default extinction values listed later.
For other airmass or other values of the extinction use
| (3) |
You can then make use of any of the assorted flux estimators to produce magnitudes via
| (4) |
Note that for the so-called total and isophotal flux options it is not possible to have a single-valued aperture correction
MAGZRR = 0.15 / Photometric ZP error (mags)
error in the zero point. If good photometric night this error will be at the level of a few percent. Values of 0.05 and above indicate correspondingly non-photometric night and worse. [Currently set to -1 for WFCAM data.]
EXTINCT = 0.05 / Default extinction in passband
for WFCAM these are currently set to a constant clear night level, which within the current measuring error is the same for all passbands. Note that the frame-by-frame derived ZP from 2MASS automatically corrects for extinction variations, assuming they are uniform across the field of view.
To compute approximate errors in the fluxes you can also use the following:-
| (5) |
where npixels is either the effective area ie. p*rcore2 for the ``core'' measures or the no. of pixels above the detection isophote ie. areal profile1; gain is the final overall detector system gain. (see http://www.ast.cam.ac.uk/vdfs/docs/reports/sv for values); flux is whichever measure you are using but note that for ``total'' this formula is not accurate since ``total'' fluxes are derived using a rather convoluted curve-of-growth technique; average skynoise can be obtained from the catalogue fits header.
Astrometric Information
For a description of the World Coordinate System (WCS) see Calabretta & Greisen 2002 A&A 395 1077 and Greisen & Calabretta 2002 A&A 395 1061.
CTYPE1 = 'RA---ZPN' / Zenithal polynomial projection CTYPE2 = 'DEC--ZPN' / Zenithal polynomial projection CRPIX1 = 2999.40 / Reference pixel X on axis 1 CRPIX2 = -940.32 / Reference pixel Y on axis 2 CRVAL1 = 112.45449231 / [deg] Right ascension at the reference pixel CRVAL2 = 30.07196251 / [deg] Declination at the reference pixel CRUNIT1 = 'deg ' / Unit of right ascension co-ordinates CRUNIT2 = 'deg ' / Unit of declination co-ordinates CD1_1 = -7.11999928E-08 / Transformation matrix element CD1_2 = 1.11427136E-04 / Transformation matrix element CD2_1 = 1.11433289E-04 / Transformation matrix element CD2_2 = -1.73270884E-07 / Transformation matrix element PV2_1 = 1.0 / Pol.coeff. for pixel -> celestial coord PV2_3 = -50.0 / Pol.coeff. for pixel -> celestial coord PROJP1 = 1.0 / Old style ZPN projection keyword r term PROJP3 = -50.0 / Old style ZPN projection keyword r**3 term NUMBRMS = 87 / Number of standards used STDCRMS = 0.089 / Astrometric fit error (arcsec)