How accurate do we need to be?

During observation, a galaxy image isconvolved with a PSF: making it bigger

and changing its ellipticity

During data analysis, shear measurementmethods seek to undo these changes torecover the true shape

An imperfect shear measurement method may not measure (any of) these quantities well. It instead obtains an inaccurate measurement, denoted by a hat.

The process of shear measurementThe Forward Process

The Inverse…

…problem

where

STEP Obtain imperfect shear measurements

Generically expect things tobe easier for large galaxies

GREAT10star challenge

GREAT10galaxy challenge

But can’t compare true against measured shearfrom images containing a spatially varying signal,and still average over intrinsic galaxy shapes.

G08

Previous figures of merit

Quantifying shear measurement accuracy from a power spectrum

From imperfect shear measurementswith constant m and c

form 2-point correlation function

Fourier transform into power spectrum

whereAdditive systematics

whereBut if systematics vary spatially,

Multip

licat

ive sy

stemat

ics

Requirement on multiplicative systematics

Can break this down into separate requirementson accuracy of PSF modelling (G10star) and galaxy shape measurement (G10galaxy).

To ensure bias/error<1(Kitching et al. 2010)

Multip

licat

ive sy

stemat

ics

Constraints on dark energy parameter w

whereBut if systematics vary spatially,

Quantifying shear measurement accuracy from a power spectrum

From imperfect shear measurementswith constant m and c

form 2-point correlation function

Fourier transform into power spectrum

whereAdditive scatter systematics

G10 “ ”

Req’mt on additive scatter systematics

Can break this down into separate requirementson accuracy of PSF modelling (G10star) and galaxy shape measurement (G10galaxy).

To ensure bias/error<1(Amara & Refregier 2009)

But this depends strongly on l-range, z-binning.

Possible figures of meritwhereSTEP

G10

G08

Simple & direct to useful quantitiesCannot be used with variable shear field

Single numberBigger is betterOnly really sensitive to cCannot be used with variable shear field

better?

Single number sensitive to both m and cA(l) and M(l) can vary with scaleSystematics prob’ly positive definite anywayUgly absolute value not really a varianceNormalisation depends on assumed l-range

and similar

denominator

What bias/error is enough?

What bias/error is enough?