1 E.Bertin (TERAPIX IAP) SkyMaker: Astronomical image simulations made easy 2 Theory in the VO 04/2008E.Bertin Astronomical image simulations made easy Motivation What is an astronomical image made of? Modelling the Point Spread Function Pixellation, noise and image artifacts Displaying realistic images Examples Implementation in the VO 3 Theory in the VO 04/2008E.Bertin SkyMaker terapix.iap.fr/soft/skymaker Originally written as an assessment tool for image analysis algorithms Source list as input Single pass FITS image as output Point-sources and simple galaxy models Accurate at the sub-pixel level. Fast ( sources/s) Multithreaded C code Applications TERAPIX: software testing & completeness checks Weak lensing (STEP program) N-body simulations & semi-analytical models (GalICS) Galaxy morphology (EFIGI program) Space projects (PrimE, Gaia, DUnE) Photometric redshift algorithms 4 Theory in the VO 04/2008E.Bertin Motivation Validate detection and measurement algorithms Source extraction Photometric redshift estimators Morphometric estimators Compare models to observations: take into account contributions from Projection effects Non-linear impact of noise on measurements Detection biases (Malmquist, Eddington) Adaptive measurements Contaminants Image artifacts Crowding (deblending) Non-uniform field coverage and image quality Prepare and support instrumental projects Exposure time calculators Public outreach Generate images from n-body simulations (on demand?) In the VO framework, image products may be easier to distribute and more user-friendly than the original source datasets 5 Theory in the VO 04/2008E.Bertin What is an astronomical image made of? Gaussian+Poisson noise: close to stationary may be correlated on small scales large scale gradients Gaussian+Poisson noise: close to stationary may be correlated on small scales large scale gradients S/N of sources between -6 and +100dB/pixel Image artifacts: Halos Detector blooming Diffraction spikes Cosmic-ray hits Image artifacts: Halos Detector blooming Diffraction spikes Cosmic-ray hits Faint sources: barely resolved contribute to the background Faint sources: barely resolved contribute to the background Unsaturated stars will be used to map the variable PSF Isophotal footprint of objects: from 1 to 10 9 pixels 6 Theory in the VO 04/2008E.Bertin Galaxy image selection effects Surface brightness limits (Driver et al. 2005) faint-end: detection threshold may generate a bias against face-on galaxies in some infrared surveys bright-end: detector saturation Size limit small-end: point-source/resolution threshold often reached in ground-based faint galaxy surveys large-end: background modeling scale Flux limit faint-limit: background-noise limit Environment The two-point correlation function must vanish at separations < galaxy size Faint objects cannot be detected too close to bright ones 7 Theory in the VO 04/2008E.Bertin Photometric biases Type-related The wings of early type galaxies are more shallow than those of late types higher Sersic index n a larger flux fraction may be missed (up to ~40%) k-corrections make spheroids vanish in the optical at high redshift Environment-related Profile overlaps in dense galaxy clusters Noise-related Eddington bias (1913): the strong 2 nd derivative of differential galaxy number counts artificially boost the counts, especially above the completeness limit (mostly unresolved sources) Close to the noise limit, detected sources stand preferably on positive noise peaks Below 5 accurate Monte-Carlo simulations may be needed to correct for this bias (Murdoch et al. 1973, see also Teerikorpi 2004) 8 Theory in the VO 04/2008E.Bertin The Point Spread Function Convolution of several components: Atmospheric blurring Motion blurring Instrumental vibrations Guiding errors Diffraction on the pupil Fourier optics Resolving power Aberrations Reflection/diffusion within the instrument Halos from refractive optics Micro-diffusion Within the detectors Intra-pixel response Charge diffusion Charge transfer 9 Theory in the VO 04/2008E.Bertin Atmospheric blurring For a long exposure made through an atmosphere whose turbulent structure follows a Kolmogorov model (see Roddier 1981), phase fluctuations on the pupil lead to the Modulation Transfer Function with r 0 is the Fried (1966) parameter, which is connected to the PSF Full-Width at Half Maximum 10 Theory in the VO 04/2008E.Bertin Diffraction and aberrations Pupil: Assume Fraunhofer diffraction The PSF is the Fourier transform of the auto- correlation of the pupil Central obscuration Spider arms Start from a complex pupil Aberrations are modeled as phase shifts over the pupil Quantified as ESO- Zernike polynomials Filters with large bandwidth would require complex pupils to be summed over wavelengths 11 Theory in the VO 04/2008E.Bertin Diffusion ( aureole ) Dominant beyond a few arcsec from the PSF center Well modeled by an 1/r 2 law (see, e.g. Racine 1996) Origin still somewhat controversal Roughness and micro-scratches in the optics Diffusion by atmospheric particles Diffusion within the detector Intensity is typically 16 mag/sq.arcsec 1 away from a star of magnitude 0. 12 Theory in the VO 04/2008E.Bertin Motion blurring and pixel footprint Trailing and jittering can be applied in Fourier space The PSF is eventually convolved by the intra-pixel response One may also provide external PSFs to SkyMaker 13 Theory in the VO 04/2008E.Bertin Undersampling and micro-dithering Undersampling effects are faithfully reproduced Possibility to simulate micro-dithering 14 Theory in the VO 04/2008E.Bertin Noise and Artifacts 15 Theory in the VO 04/2008E.Bertin Galaxies Sersic Bulge Exponential disk Adaptive limiting radius depends on galaxy surface brightness and background noise level 16 Theory in the VO 04/2008E.Bertin PrimE (H,K,L) simulation 17 Theory in the VO 04/2008E.Bertin DUnE (Stuff) 18 Theory in the VO 04/2008E.Bertin Space/ground-based image comparison g,r,i, 1.2m in space, 20 ming,r,i, 3.6m from ground, 1h 19 Theory in the VO 04/2008E.Bertin Galaxy morphometry on CFHTLS D1 deep-field Original (g,r,i)Re-simulated with perfect seeing 20 Theory in the VO 04/2008E.Bertin GalICS light cone (Blaizot et al. 2005) 21 Theory in the VO 04/2008E.Bertin N-body simulations Cattaneo et al Mare z=2.46 (courtesy C.Pichon) 22 Theory in the VO 04/2008E.Bertin Producing consistent colour images FITS images are encoded linearly: for an input flux F, the encoded pixel value is p F However, JPEG, PNG, TIFF images and the like (even analog video tapes) are implicitely gamma encoded, that is, what is stored in the file is roughly p F 1/ with 2.2 STIFF can do it for you! terapix.iap.fr/soft/stiff Charles Poynton 2003 23 Theory in the VO 04/2008E.Bertin A Virtual Telescope (G.Lemson) 24 Theory in the VO 04/2008E.Bertin Conclusion SkyMaker (and Stuff) ready to be used in a VO environment Possible improvements to SkyMaker Additional objects Additional artifacts PSF variability Support for alpha-delta through WCS XML/VOTable interface visit terapix.iap.fr