1. Shears from shapelets
Konrad Kuijken
Leiden

2. Shapelets
Direct modelling of PSF and sources as Gaussians x polynomials (QHO!)
Effects of shear, PSF &c analytic
Model sources as PSF  elliptical galaxy:
PSF  [1+1 S1+2 S2+…]  C
where C = c0 S00 + c2 S20 + c4 S40 + …
2 fit model to pixel values: straightforward

3. Shapelets PRO: CON Shapelet coeffs replace pixels (compression)
Error propagation simple
Simple combinations of coeffs. mimic weighted moments
Can be extended to flexions
CON
Galaxies are not Gaussian!

4. Choices Fixed order (N=8) for all sources
Ellipticity modelled with 1st order operators
Size  determined by Gauss fit to each source (quantized harmonically)
Centroids adjusted to zero 10,01 terms
PSF: all stars fitted with same , coeffs. interpolated quadratically over image
Shear estimator is <i> (without 1-2)

5. Next: 1. Sech-shapelets Gaussian  poly Sech  poly
(radial orders 0,2,4,6,8,10)

6. Gaussian vs sech parent (N=8):= =

7. Next 2: Non-linear ellipticity terms
Calculate the shapelet coeffs of a sheared round shapelet, fit to 4th order in ellipticity
Sheared n=0,m=0
n=2
n=4
n=6
n=8
n=0 e=

8. Sheared n=2,m=0
n=2
n=4
n=6
n=8
n=0 e=

9. Sheared n=4,m=0
n=2
n=4
n=6
n=8
n=0 e=

10. Sheared n=6,m=0
n=2
n=4
n=6
n=8
n=0 e=

11. Sheared n=8,m=0
n=2
n=4
n=6
n=8
n=0 e=

12. STEP4
Konrad Kuijken
Leiden

14. KiDS
Konrad Kuijken
Leiden