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Shear Measurement Review

Shear Measurement Review. Bluffer’s guide Shear measurement pipeline Shear estimation methods KSB, Shapelets, Model fitting STEP, GREAT08 PSF uncertainties Propagation of PSF errors PCA Cross-correlation Bluffer’s guide test. Shear Measurement Review. Bluffer’s guide

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Shear Measurement Review

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  1. Shear Measurement Review • Bluffer’s guide • Shear measurement pipeline • Shear estimation methods • KSB, Shapelets, Model fitting • STEP, GREAT08 • PSF uncertainties • Propagation of PSF errors • PCA • Cross-correlation • Bluffer’s guide test

  2. Shear Measurement Review • Bluffer’s guide • Shear measurement pipeline • Shear estimation methods • KSB, Shapelets, Model fitting • STEP, GREAT08 • PSF uncertainties • Propagation of PSF errors • PCA • Cross-correlation • Bluffer’s guide test

  3. Bluffer’s Guide to Shear MeasurementCan you say these phrases with confidence? • ‘The shear responsivity depends on the galaxy ellipticity distribution’ • ‘P gamma has to be averaged over galaxies with similar properties’ • ‘If the wrong galaxy profile is assumed, the shear is biased’ • ‘You should definitely participate in GREAT08 ‘ • ‘Shear systematics depend on the square of the PSF size’ • ‘PSF PCA technique allows a larger effective star density’ • ‘Cross correlation between images averages out random PSF shear biases’

  4. Shear Measurement Review • Bluffer’s guide • Shear measurement pipeline • Shear estimation methods • KSB, Shapelets, Model fitting • STEP, GREAT08 • PSF uncertainties • Propagation of PSF errors • PCA • Cross-correlation • Bluffer’s guide test

  5. Typical galaxy used for cosmic shear analysis Typical star Used for finding Convolution kernel

  6. Typical image

  7. Example: The DES pipeline Overview 1. Measure PSF at star positions DB DB 2. Interpolate PSF DB DB 3. Measure shears DB DB

  8. Example: The DES pipeline 1. Measure PSF at star positions Object catalogue From coadds All S/N>5 Single Boolean per object 1a. Identify Stars DB DB Star catalogue PSF coefs (per star) Images Noise images 1b. Get PSF coefficients DB DB

  9. Example: The DES pipeline 1. Measure PSF at star positions Object catalogue From coadds All S/N>5 Single Boolean per object 1a. Identify Stars DB DB Star catalogue PSF coefs (per star) Images Noise images 1b. Get PSF coefficients DB DB Shapelets 30 floating point #s 120 Bytes per star

  10. Example: The DES pipeline 2. Interpolate PSF – step (a) PSF coefs (per star) (all exposures) 2a. PSF Interpolator Step 1 PSF(space,time) DB DB

  11. Example: The DES pipeline 2. Interpolate PSF – step (a) PSF coefs (per star) (all exposures) 2a. PSF Interpolator Step 1 PSF(space,time) DB DB ~20 PCA components (3rd order polynomial per 62 chips) ~80 kB per PCA compt

  12. Example: The DES pipeline 2. Interpolate PSF – step (b) PSF(space,time) DB Parameters of PSF Interpolation 2b. PSF Interpolator Step 2 DB PSF coefs (per star) DB

  13. Example: The DES pipeline 2. Interpolate PSF – step (b) PSF(space,time) DB Parameters of PSF Interpolation 2b. PSF Interpolator Step 2 DB PSF coefs (per star) DB PCA 3rd order polynomial 62 x ~1.2 kB

  14. Example: The DES pipeline 3. Shear measurement Object catalogue All S/N>5 DB Shears per object Best Per filter Per exposure Errors on above Flags on the above Images Noise images DB 3. Shear measurement DB Parameters of PSF Interpolation DB

  15. Example: The DES pipeline 3. Shear measurement Object catalogue All S/N>5 DB Shears per object Best Per filter Per exposure Errors on above Flags on the above Images Noise images DB 3. Shear measurement DB Parameters of PSF Interpolation DB We may want e.g. flexions too

  16. Example: The DES pipeline Overview 1. Measure PSF at star positions DB DB 2. Interpolate PSF DB DB 3. Measure shears DB DB

  17. Shear Measurement Review • Bluffer’s guide • Shear measurement pipeline • Shear estimation methods • STEP, GREAT08 • KSB, Shapelets, Model fitting • PSF uncertainties • Propagation of PSF errors • PCA • Cross-correlation • Bluffer’s guide test

  18. Shear TEsting Programme (STEP) • Started July 2004 • Is the shear estimation problem solved or not? • Series of international blind competitions • Start with simple simulated data (STEP1) • Make simulations increasingly realistic • Real data • Current status: • STEP 1: simplistic galaxy shapes (Heymans et al 2005) • STEP 2: more realistic galaxies (Massey et al 2006) • STEP 3: difficult (space telescope) kernel (2007) • STEP 4: back to basics See Konrad’s Edinburgh DUEL talk

  19. Accuracy on g -20% 20% STEP1 Results → Existing results are reliable The future requires 0.0003 Heymans et al 2005 -0.2 0.2

  20. STEP1 Results - Dirty laundry Require 0.0003 0 Accuracy on g Average -0.0010 -0.005 High noise Low noise ~ noise level of image

  21. PASCAL Challenge

  22. Gravitational Lensing Galaxies seen through dark matter distribution analogous to Streetlamps seen through your bathroom window

  23. Cosmic Lensing gi~0.2 Real data: gi~0.03

  24. Atmosphere and Telescope Convolution with kernel Real data: Kernel size ~ Galaxy size

  25. Pixelisation Sum light in each square Real data: Pixel size ~ Kernel size /2

  26. Noise Mostly Poisson. Some Gaussian and bad pixels. Uncertainty on total light ~ 5 per cent

  27. GREAT08 Data ~10 000 images divided into ~10 sets One galaxy per image Kernel is given One shear per set Noise is Poisson ~100 000 000 images Divided into ~1000 sets

  28. GREAT08 Results You submit g1, g2 for each set of images

  29. GREAT08 Timeline • ~8 Feb 2008 GREAT08 Handbook public • Feb 2008 Produce simulations • Mar 2008 Internal analysis of simulations • ~ May 2008 Release simulations • Leaderboard starts containing best internal results • ~ Nov 2008 Competition deadline • ~ Dec 2008 Workshop; Release final report • Input shears public www.great08challenge.info

  30. tbc Going to astro-ph this week… Please advertise to your computer science and statistics colleagues

  31. GREAT08 Summary • 100 million images • 1 galaxy per image • De-noise, de-convolve, average → shear • gi ~ 0.03 to accuracy 0.0003 → Q~1000 → Win!

  32. Shear Measurement Review • Bluffer’s guide • Shear measurement pipeline • Shear estimation methods • STEP, GREAT08 • KSB, Shapelets, Model fitting • PSF uncertainties • Propagation of PSF errors • PCA • Cross-correlation • Bluffer’s guide test

  33. Quadrupole moments: the simplest possible shear measurement method

  34. Effect of shear on quadrupole moments

  35. Ellipticity |ϵ| = (a-b)/(a+b) from quadrupole moments Nasty noise properties Please correct this using the paper provided!! (Taylor expand for small g) Update after talk: better to start from reversed version of the above eqn (swap e^u with e^l and change “g” to “-g”. Then get e^l = e^u + g - ( (e_1^u2-e_2^u2) g_1 + e_1^u e_2^u g_2 ) – i ( (e_2^u2-e_1^u2) g_2 + e_1^u e_2^2 g_1) + O(g^2) Use <e_1^u> = <e_2^u> =0 so <e^u>=0 and assume symmetry <e_1^u2>=<e_2^u2> and <e_1^u e_2^u> =0 Where So ϵli can be treated as a noisy estimate of gi e.g. see Bartelmann & Schneider 1999 review p59+, Bonnet & Mellier 1995, Seitz & Schneider 1997

  36. Ellipticity ||=(a2-b2)/(a2+b2)from quadrupole moments

  37. Ellipticity ||=(a2-b2)/(a2+b2)from quadrupole moments Taylor expand and use Please check this Using the paper provided Depends on properties of galaxies Shear responsivity e.g. see Bartelmann & Schneider 1999 review p59+, Schneider & Seitz 1995

  38. KSB:As above, with weight function Herein lies significant complications The last two are the same in the case W(x,y)=1

  39. Why do weighted quadrupole moments?

  40. The KSB shear responsivity Kaiser, Squires & Broadhurst 1995, Luppino & Kaiser 1997, Hoekstra et al. 1998

  41. Improvements beyond KSB • Bernstein & Jarvis • Mandelbaum et al. • Kaiser 2000 • …

  42. Shapelets • Laguerre polynomials • Polynomial times Gaussian • Nice QM formalism • Lensing distortion has simple effect • psf convolution can be removed by matrix multiplication Massey & Refregier 2004

  43. Shapelets • Three main approaches • Refregier, Bacon, Massey • Use shapelet model to make perfect image. Measure Qij from this • Bernstein, Nakajima, Jarvis • Shear “circular” shapelet model to match the image • Kuijken • Shear exactly circular shapelet model to match image Massey & Refregier 2004

  44. Shapelets • Pros: • - Compact basis set • - Shearing and convolution v fast • Cons: • - QM formalism blindingly seductive • Gaussian envelope not well matched to galaxies or psf • .. see “Sechlets” poster.. • Three main approaches • Refregier, Bacon, Massey • Use shapelet model to make perfect image. Measure Qij from this • Bernstein, Nakajima, Jarvis • Shear “circular” shapelet model to match the image • Kuijken • Shear exactly circular shapelet model to match image

  45. Model fitting • Sheared shapelets (Nakajima & Bernstein; Kuijken) • Sums of Gaussians (Voigt & Bridle in prep) • de Vaucouleurs profiles (see Kitching talk) • Arbitrary radial profile (Irwin & Shmakova 2005) • …

  46. Is there a bias on gwhen fit 1 elliptical Gaussian?

  47. Modelling the galaxy with a single Gaussian: Simulated galaxy Model Exponential e=0.2 Gaussian • PSF perfectly known • Best-fit Gaussian to exponential found by minimising the Χ2 between the images with respect to the 6 model parameters: x0,y0,e,phi,a,A • No noise added to data! Voigt & Bridle in prep

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