T. Jarrett, IPAC
(980602)
revised: 980622
We first noticed what appeared to be a -45 deg bias in the galaxy position angle parameter when we generated summary analysis plots for the RTB extended source results. See Summary of GALWORKS Results for combined RTBs .... At first, we suspected a bug in the code. But after looking at numerous images and plots and finding no apparent problems, we then concluded that the effect was caused primarily by the convolution of the PSF with the galaxy profile. See Source of Biases In Position Angle Determinations For 2MASS Galaxies . {As fate would have it, the bias appears to be caused by both a PSF bias and a systematic in the code. We will not know for sure until we can reprocess the northern RTB data in the coming weeks. Note: the northern RTB 971116n has been reprocessed with he p.a. bug fix; see gifs below }
The previous analysis was performed on northern 2MASS data. The southern data provides a means to test our hypothesis that the bias is caused primarily by the PSF. Why? Because the southern camera is effectively inverted along the Y-axis with respect to the nothern camera. Thus we expect to see the PSF bias along +45 deg for the south. The southern PSF does indeed align along +45 deg for large fraction of the scans (as indicated by analysis of the frame PSF; also see gif below showing PSF orientation for northern and southern data ). So in turn we expect to see the galaxy p.a. bias along +45 deg (as opposed to -45 for the north). However, analysis of data taken on 980319s (including the cluster ABELL 3558) revealed that the southern bias in p.a. was in fact aligned along -45 deg, the same as the north (the plots below will demonstrate the bias). This immediately tells us that the PSF bias is not the dominent (or at least not the only) component of the total p.a. bias. After again looking at the code and examining several southern galaxy and PSF images (including scans with "round" PSFs and scans with elliptical psfs), the "smoking gun" was found. It turns out to be a 1/2 pixel bias in the galaxy positions when determining the elliptical fit parameters (this position offset occurs no other place in GALWORKS). This position bias produces a -45 deg bias in the p.a., exactly the same direction as the real PSF bias in the NORTH, but orthogonal to the PSF bias in the south. More details on the nature of this bias and the algorithm itself is given at the end of this doc.
Since this bug was only recently discovered (yesterday), we have only limited data (the southern scans containing ABELL 3558) to compare BEFORE and AFTER the fix. Once the northern RTB's have been rerun with the latest 2MAPPS code (v. 2.1), the p.a. analysis can be performed in full. ( Note: northern 971116n has been reprocessed with the results given below ). Nevertheless, the following plots show the BEFORE/AFTER results for p.a. for a subset of galaxies amongst the 900 or so ABELL 3558 cluster galaxies from 980319s (scans 087 to 094). The systematic bias in the p.a. presumably due to the position bias bug (see above) is clearly seen. The "after fix" images look more uniform, but do suggest a bias at +50 deg or so, probably due the the aforementioned PSF bias.
Caution!!! Here 0 degrees position angle refers to the westward direction, with north representing +90 degrees.
Notice that the PSF tilt is orthogonal between the northern data and the southern data -- this reflects the actual orientation on the sky between the two cameras (i.e., one is "upside down").
(dark blue=J, green=H, red=Ks; cyan = super J+H+K)
"after fix", note the bias at +45 to +65, probably due to the PSF.
Notice the -50 deg p.a. bias in the "before fix" image. For the "after fix" image, the bias is greatly reduced, but with a hint of a p.a. bias at +50 or +60 deg (probably due to the PSF).
"after fix", note the slight bias at +45 to +65, probably due to the PSF.
"after fix", note the slight bias at +45 to +75, probably due to the PSF.
Ellipse Fitting Algorithm
GALWORKS determines the 2-D elliptical shape of galaxies using the 3-sigma isophot. The isophot is isolated by constructing vectors, vertex anchored to the center of the galaxy, with linear interpolation between pixels to estimate the radius (length of vector) corresponding to the 3-sigma isophot. A "mask" image is generated from this operation -- it respresents the isophot, with fixed values corresponding to the 3-sigma level, a different set of values corresponding to 'insided' the isophot and finally zeros for outside the isophot. The mask image is then fed to routine "twod_ellip" that determines the best fit ellipse to the mask (i.e., to the 3-sigma isophot).
Summary:
1. Construct radial vectors, vertex anchored to object center, covering the entire area of the object.
2. For each vector, determine radius at which the 3-sigma level occurs. Use linear interpolation for inter-pixel values.
3. Construct isophot mask image. Image has three sets of values:
ul>
a. 3-sigma isophot itself
b. inside of 3-sigma isophot
c. outside of 3-sigma isophot.
The additional information (b and c, above) is necessary to 'clean up' the isophot itself -- in some cases the isophot has a width larger than 1 pixel due to the method (using angular vectors). With three pieces of information in the mask, the isophot can be stripped to a width of one-pixel. This is crucial to accurate determination of the axil ratio (preliminary tests suggest our accuracy is about 0.025 or less with this method).
4. Determine best fit ellipse to the 3-sigma isophot represented by the mask image.
Algor:
For each combination of b/a and phi, input location of 3-sigma isophot -- get the population of semi-major axis values for each 3-sigma location.
Minimize the output semi-major axis population:
A more robust minimization of the chi-square is to use the mean and st. deviation of the population of semi-major axis point:
This algor has the advantage of being both robust and fast (it is a 'one-pass' algorithm).
