Adaptive Moments
Adaptive moments are the second moments of the object intensity, measured using
a particular scheme designed to have near-optimal signal-to-noise ratio.
Moments are measured using a radial weight function interactively adapted to the
shape (ellipticity) and size of the object. This ellipticial weight function
has a signal-to-noise advantage over axially symmetric weight functions. In
principle there is an optimal (in terms of signal-to-noise) radial shape for
the weight function, which is related to the light profile of the object
itself. In practice a gaussian with size matched to that of the object is
used, and is nearly optimal. Details can be found in Bernstein & Jarvis (2002).
The outputs included in the SDSS data release are the following:
- The sum of the second moments in the CCD row and column direction:
mrr_cc = <col2> + <row2>
and its error mrr_cc_err.
The second moments are defined in the following way:
<col2>= sum[I(col,row) w(col,row) col2]/sum[I*w]
where I is the intensity of the object and w is the weight function.
- The ellipticity (polarization) components:
me1 = <col2> - <row2>)/mrr_cc
me2 = 2.*<col*row>/mrr_cc
and square root of the components of the covariance matrix:
me1e1err = sqrt( Var(e1) )
me1e2err = sign(Covar(e1,e2))*sqrt( abs( Covar(e1,e2) ) )
me2e2err = sqrt( Var(e2) )
- A fourth-order moment
mcr4 = <r4>/sigma4
where r2 = col2 + row2, and sigma is the size of the gaussian weight. No error is quoted on this quantity.
- These quantities are also measured for the PSF, reconstructed at the position
of the object. The names are the same with an appended
_psf. No errors are
quoted for PSF quantities. These PSF moments can be used to correct the
object shapes for smearing due to seeing and PSF anisotropy. See Bernstein &
Jarvis (2002) and Hirata & Seljak (2003) for details.
Last modified: Wed Feb 12 13:14:39 CST 2003
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