1. Shapelets shear measurement methods
&
Simulations
shapelets
Second-generation weak lensing pipeline.
By-products of weak lensing calibration.
Richard Massey (CalTech)
with
Jean-Paul Kneib, Alexie Leauthauld, Molly Peeples, Alexandre Refregier & Jason Rhodes

2. Simulated COSMOS images
Real
Simulated Subaru i’-band (& ACS I-band) COSMOS images made available by Molly Peeples.
Simulated galaxies and stars have realistic and precisely known properties.
Calibrate Alexie Leauthauld’s WL pipeline by comparing measured properies to true values.
Noise model can be as complicated as you like: not currently including problems #1 or #2,
but as soon as we have physical models for these, they can easily be added.

3. “Shapelets” image analysis method
Complete & orthogonal “shapelets” basis:
Can represent any object by fitting a (unique) weighted, linear sum of shapelet basis functions. Such a model parameterises all of the object’s shape information.
Useful parameterisation for COSMOS lensing:
Mathematically convenient basis for image analysis/manipulation. Simple combinations of coeffs give photometry, astrometry, shear, & morphology estimators. Can also deal analytically with PSF deconvolution, plus
Pixellisation
Noise correlated
between pixels 8 6 4 2 -2 -4 -6 -8 M
Truncation of high
spatial frequencies }
Problem #2? N

4. Interpretation of shapelet models
A shapelet decomposition splits each galaxy image into components with differing radial or rotational symmetries. Simple combinations of such coefficients yield estimators for galaxy concentration (radial), asymmetry/chirality (rotational) and shear (rotational).

5. How well do shapelets work?
Measurement of increasingly higher-order moments from simulated COSMOS ACS images.

6. How well do shapelets work?

7. Galaxy morphology estimators
Standard morphology diagnostics:
A shapelet decomposition parameterises all of an object’s shape information. So if we can measure slight deviations (shears) from ordinary morphologies, we should also be able to classify these standard categories! Concentration, asymmetry and clumpiness estimators for each object are simply derived from combinations of their shapelet coefficients.
Integrate within pixels
PSF deconvolution
Parameter-free approach:
Perform PCA on the shapelet catalogue of the entire COSMOS field, to determine the most important morphology components… keeping pixels ordered!
Kelly & McKay (2004)

8. I. Second-generation weak lensing pipeline
Conclusions
I. Second-generation weak lensing pipeline
Higher precision shear measurement method.
If we can figure out what causes “problem #2”, we can (probably) solve it
using shapelets.
II. By-products of our work (useful to you?)
Simulated Subaru i’ and ACS I-band images are available.
Shapelet catalogues of ACS data are available.
Morphology estimators for each galaxy.