Shears from shapelets Konrad Kuijken Leiden.

Slides:

Advertisements

Similar presentations

Antony Lewis Institute of Astronomy, Cambridge

Advertisements

These figures correspond to the image using shear =10 pixels And 2D convolution was done in order to get the images Using R=0 y0 Using R=1 y1.

1 Curve-Fitting Spline Interpolation. 2 Curve Fitting Regression Linear Regression Polynomial Regression Multiple Linear Regression Non-linear Regression.

Curve-Fitting Interpolation

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 29 Numerical Integration.

Interpolation Used to estimate values between data points difference from regression - goes through data points no error in data points.

ECIV 301 Programming & Graphics Numerical Methods for Engineers REVIEW III.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 181 Interpolation Chapter 18 Estimation of intermediate.

LSST and the Dark Sector: Image processing challenges Tony Tyson University of California, Davis ADASS September 25, 2007.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 181 Interpolation.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 21 CURVE FITTING Chapter 18 Function Interpolation and Approximation.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 171 Least.

CISE-301: Numerical Methods Topic 1: Introduction to Numerical Methods and Taylor Series Lectures 1-4: KFUPM.

Thomas Kitching Bayesian Shape Measurement and Galaxy Model Fitting Thomas Kitching Lance Miller, Catherine Heymans, Alan Heavens, Ludo Van Waerbeke Miller.

A Rapid Stereo Matching Algorithm Based on Disparity Interpolation Gang Yao Yong Liu Bangjun Lei Dong Ren Institute of Intelligent Vision and Image Information.

MA2213 Lecture 4 Numerical Integration. Introduction Definition is the limit of Riemann sums I(f)

STEP2 simulated images Richard Massey with Molly Peeples, Will High, Catherine Heymans, etc. etc.

Weak Lensing 3 Tom Kitching. Introduction Scope of the lecture Power Spectra of weak lensing Statistics.

CISE-301: Numerical Methods Topic 1: Introduction to Numerical Methods and Taylor Series Lectures 1-4: KFUPM CISE301_Topic1.

Physics 114: Exam 2 Review Lectures 11-16

WFC3 SOC, October 04, 2007 WFC3 Grisms Results from TV2 2D Simulations Harald Kuntschner, Jeremy Walsh, Martin Kümmel ST-ECF.

Geographic Information Science

6.1 Polynomial Functions.

6. Introduction to Spectral method. Finite difference method – approximate a function locally using lower order interpolating polynomials. Spectral method.

Spectral Extraction of Extended Sources Using Wavelet Interpolation Paul Barrett, Linda Dressel, STIS Calibration Group 2005 October 26.

Weak Lensing 2 Tom Kitching. Recap Lensing useful for Dark energy Dark Matter Lots of surveys covering 100’s or 1000’s of square degrees coming online.

Shapelets analysis of weak lensing surveys Joel Bergé (CEA Saclay) with Richard Massey (Caltech) Alexandre Refregier (CEA Saclay) Joel Bergé (CEA Saclay)

Conversion of Stackfit to LSST software stack Status as of Feb 20, 2012.

DES Cluster Simulations and the ClusterSTEP Project M.S.S. Gill (OSU / CBPF / SLAC) In collaboration with: J. Young, T.Eifler, M.Jarvis, P.Melchior and.

OWLS Pipeline Status Report STEP 2007 Workshop, JPL Mon, Aug 20, 2007 MSS Gill, J.Young, P. Martini, K. Honscheid, D. Weinberg, C. Kochanek + OWLS Team.

5.7 Completing the Square Ch. 6 Notes Page 38 P38 6.1: Polynomial Functions.

STEP4 Konrad Kuijken Leiden. Back to basics? STEP1,2,3 –‘end-to-end’ tests for constant-shear images –What causes discrepancies? Selection bias PSF modelling.

Gravitational Lensing

August 23, 2007JPL WL from space meeting1 Shear measurements in simulated SNAP images with realistic PSFs Håkon Dahle, Stephanie Jouvel, Jean-Paul Kneib,

" Fitting methods with direct convolution for shear measurements." STEP Workshop August 2007 M. Shmakova.

Measuring shear using… Kaiser, Squires & Broadhurst (1995) Luppino & Kaiser (1997)

Extending linear models by transformation (section 3.4 in text) (lectures 3&4 on amlbook.com)

In conclusion the intensity level of the CCD is linear up to the saturation limit, but there is a spilling of charges well before the saturation if.

Measuring Cosmic Shear Sarah Bridle Dept of Physics & Astronomy, UCL What is cosmic shear? Why is it hard to measure? The international competition Overview.

Section 4.1 Polynomial Functions and Modeling Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Global predictors of regression fidelity A single number to characterize the overall quality of the surrogate. Equivalence measures –Coefficient of multiple.

NON LINEAR FUNCTION Quadratic Function.

Higher-Degree Polynomial Functions and Graphs

STEP: THE SHEAR TESTING PROGRAMME

General Features of Fitting Methods

Curve-Fitting Spline Interpolation

Lecture 5 Polynomial Approximation

Interpolation Estimation of intermediate values between precise data points. The most common method is: Although there is one and only one nth-order.

Shapelets shear measurement methods

Closed-form Algorithms in Hybrid Positioning: Myths and Misconceptions

Polynomial Functions and Modeling

Regression-Based Prediction for Artifacts in JPEG-Compressed Images

OWLS Pipeline Status Report

MATH 2140 Numerical Methods

1. Use the quadratic formula to find all real zeros of the second-degree polynomial

Basics of Photometry.

NUMERICAL INTEGRATION

Linear regression Fitting a straight line to observations.

Graphing Techniques.

OWLS Pipeline Status Report

Turning to the Masters: Motion Capturing Cartoons

NUMERICAL INTEGRATION

Nonlinear Fitting.

CISE-301: Numerical Methods Topic 1: Introduction to Numerical Methods and Taylor Series Lectures 1-4: KFUPM CISE301_Topic1.

Numerical Integration

Approximation of Functions

Uncertainty Propagation

Approximation of Functions

Presentation transcript:

Shears from shapelets Konrad Kuijken Leiden

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

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!

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)

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

Gaussian vs sech parent (N=8): = .7 1 1.3 = .2 .3 .4 .5

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=-0.7 .. +0.7

Sheared n=2,m=0 n=2 n=4 n=6 n=8 n=0 e=-0.7 .. +0.7

Sheared n=4,m=0 n=2 n=4 n=6 n=8 n=0 e=-0.7 .. +0.7

Sheared n=6,m=0 n=2 n=4 n=6 n=8 n=0 e=-0.7 .. +0.7

Sheared n=8,m=0 n=2 n=4 n=6 n=8 n=0 e=-0.7 .. +0.7

STEP4 Konrad Kuijken Leiden

KiDS Konrad Kuijken Leiden