Astronomical image reduction using the Tractor
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1 the Tractor DECaLS Fin Astronomical image reduction using the Tractor Dustin Lang McWilliams Postdoc Fellow Carnegie Mellon University visiting University of Waterloo UW /
2 Astronomical image reduction 2
3 Astronomical image reduction 3
4 The Tractor context the traditional or algorithmic approach: estimators; arithmetic operations on the pixels m = f(pixels) model-fitting approach: write down a scalar objective function g and optimize it: m = arg max g(pixels, µ) µ generative model-fitting: working in pixel space: g = χ 2 ( model(µ)i pixel m = arg min i µ σ i pixels i ) 2 4
5 The Traditional, or Algorithmic, Approach What is the center of this source? 5
6 The Traditional, or Algorithmic, Approach First smooth by a Gaussian the size of the PSF 6
7 The Traditional, or Algorithmic, Approach Find peak, and look at 3x3 window around the peak 7
8 The Traditional, or Algorithmic, Approach Find peak, and look at 3x3 window around the peak y x 8
9 The Traditional, or Algorithmic, Approach Fit columns as parabolas y x 9
10 The Traditional, or Algorithmic, Approach Fit columns as parabolas y x 10
11 The Traditional, or Algorithmic, Approach Fit columns as parabolas y x 11
12 The Traditional, or Algorithmic, Approach Peak lies along this locus y x 12
13 The Traditional, or Algorithmic, Approach Fit rows as parabolas y x 13
14 The Traditional, or Algorithmic, Approach Fit rows as parabolas y x 14
15 The Traditional, or Algorithmic, Approach Fit rows as parabolas y x 15
16 The Traditional, or Algorithmic, Approach Peak lies along this locus y x 16
17 The Traditional, or Algorithmic, Approach Peak lies at the intersection y x 17
18 The Traditional, or Algorithmic, Approach The essence: Make some assumptions or approximations about the data Come up with an estimator that would produce the right answer if those assumptions held Write an algorithm to implement that estimator Remarks: Works when the assumptions hold Can be hard to find estimators Usually single image Tends to produce pipelines: measure A, set it in stone; measure B, set it in stone;... 18
19 The Generative Modelling Approach What is the center of this source? 19
20 The Generative Modelling Approach What center does a model of this source need to have to best match this image? 20
21 The Generative Modelling Approach Assume it s a point source; assume we have a model of the PSF. Use heuristics to initialize. Render initial model image Image Model Residuals 21
22 The Generative Modelling Approach Optimize model parameters (eg, with linearized least squares) d(model)/dx d(model)/dy d(model)/dflux 22
23 The Generative Modelling Approach Optimize model parameters (eg, with linearized least squares) Image Model Residuals 23
24 The Generative Modelling Approach Optimize model parameters (eg, with linearized least squares) Image Model Residuals 24
25 The Generative Modelling Approach Optimize model parameters (eg, with linearized least squares) Image Model Residuals 25
26 The Generative Modelling Approach Optimize model parameters (eg, with linearized least squares) Image Model Residuals 26
27 The Generative Modelling Approach The essence: Assume we have calibration info about the image (eg, PSF model) Assume we can parameterize the appearance of sources in our images Seek maximum likelihood parameters: it s an optimization problem Remarks: Heuristics to get into the ballpark In theory, very clean In practice, optimization can be tough! Enables iterative solution: fit sources with PSF held fixed; then fit PSF with sources held fixed 27
28 What is the Tractor? (in a picture) catalog RA, Dec Mags Galaxies: profile shape Stars: motion variability image calibration Photometric, WCS, PSF, Sky model image 28
29 What is the Tractor? (in a picture) catalog RA, Dec Mags Galaxies: profile shape Stars: motion variability image calibration Photometric, WCS, PSF, Sky model image - observed image per-pixel error = chi 2 likelihood 29
30 What is the Tractor? (in a picture) catalog RA, Dec Mags Galaxies: profile shape Stars: motion variability image calibration Photometric, WCS, PSF, Sky model image - observed image per-pixel error = chi 2 N likelihood 30
31 What is the Tractor? (in a picture) catalog RA, Dec Mags Galaxies: profile shape Stars: motion variability image calibration Photometric, WCS, PSF, Sky model image - observed image per-pixel error = chi 2 N priors posterior 31
32 Benefits of the Tractor approach handling multiple exposures, multiple bands, multiple instruments is easy handling masked pixels (cosmic rays, bleed trails) is easy avoids deblending possible to go back and re-fit calibration parameters easy to add priors or external information possible to sample possible to use physical models 32
33 Example: Galaxy fitting Image Model Residual dx dy dflux dre de1 de2 ExpGalaxy at pixel (18.00, 18.00) with Flux: 500 shape EllipseE: re=1, e1=0, e2=0 33
34 Example: Galaxy fitting Image Model Residual dx dy dflux dre de1 de2 ExpGalaxy at pixel (18.30, 18.30) with Flux: shape EllipseE: re=3.74, e1=0.07, e2=
35 Example: Galaxy fitting Image Model Residual dx dy dflux dre de1 de2 ExpGalaxy at pixel (18.33, 18.32) with Flux: shape EllipseE: re=3.85, e1=0.03, e2=
36 Example: Galaxy fitting Image Model Residual dx dy dflux dre de1 de2 ExpGalaxy at pixel (19.27, 19.29) with Flux: shape EllipseE: re=8.16, e1=0.002, e2=
37 Example: Galaxy fitting Image Model Residual dx dy dflux dre de1 de2 ExpGalaxy at pixel (20.12, 20.06) with Flux: shape EllipseE: re=8.89, e1=-0.013, e2=
38 Example: Galaxy fitting Image Model Residual dx dy dflux dre de1 de2 ExpGalaxy at pixel (19.91, 19.85) with Flux: shape EllipseE: re=8.92, e1=-0.018, e2=
39 Example: Two galaxy fitting Image Model Residual 39
40 Example: Two galaxy fitting Image Model Residual 40
41 Example: Two galaxy fitting Image Model Residual 41
42 Example: Two galaxy fitting Image Model Residual 42
43 Example: Two galaxy fitting Image Model Residual 43
44 Example: Two galaxy fitting Image Model Residual 44
45 Example: Two galaxy sampling skip 45
46 the Tractor DECaLS Fin Context the Tractor Examples Tricks s1 ee2 s1 ee1 s1 logre s1 Flux s1 y s1 x s0 ee2 s0 ee1 s0 logre s0 Flux s0 y Example: Two galaxy sampling s0 x s0 y s0 Flux s0 logre s0 ee1 s0 ee2 s1 x s1 y s1 Flux s1 logre s1 ee1 s1 ee2 46
47 Example: Two galaxy sampling e2 B e1 B e2 A e1 A e2 A e1 B e2 B 47
48 Example: Two galaxy sampling radius B flux B radius A flux A radius A flux B radius B 48
49 Example: Moving Source Model with no proper motion 49
50 Example: Moving Source Model with proper motion 50
51 Example: Moving Source Model with proper motion 51
52 Example: Moving Source 52
53 Example: Forced photometry SDSS WISE Model for one source Full Model 53
54 Tricks the Tractor DECaLS Fin Context the Tractor Examples Tricks central operation: render pixel models & derivatives galaxies: convolution of galaxy profile by PSF (can t do naive convolution) we use two tricks, both using Mixtures of Gaussians approximations of galaxy profiles (G s (r) e kr1/s ) lux / M lux = 6 / ξmax = 4 / badness = lux / M lux = 6 / ξmax = 4 / badness = intensity (relative to intensity at ξ = 1) intensity (relative to intensity at ξ = 1) dimensionless angular radius ξ dimensionless angular radius ξ 54
55 Tricks the Tractor DECaLS Fin Context the Tractor Examples Tricks central operation: render pixel models & derivatives galaxies: convolution of galaxy profile by PSF (can t do naive convolution) we use two tricks, both using Mixtures of Gaussians approximations of galaxy profiles (G s (r) e kr1/s ) luv / M luv = 8 / ξmax = 8 / badness = luv / M luv = 8 / ξmax = 8 / badness = intensity (relative to intensity at ξ = 1) intensity (relative to intensity at ξ = 1) dimensionless angular radius ξ dimensionless angular radius ξ 55
56 Convolution Trick #1 approximate galaxy profile as mixture of Gaussians (galaxy shape and sky-to-pixel are affine transformations) approximate PSF as mixture of Gaussians convolution is analytic! N psf N galaxy Gaussian components in the convolution 56
57 Convolution Trick #1 approximate galaxy profile as mixture of Gaussians (galaxy shape and sky-to-pixel are affine transformations) approximate PSF as mixture of Gaussians convolution is analytic! N psf N galaxy Gaussian components in the convolution
58 Convolution Trick #2 pixelized PSF model; take Fourier transform Gaussians have analytic Fourier transforms; F (g) = G evaluate F (galaxy) directly multiply and Inverse FFT to get the convolved profile
59 the Tractor DECaLS Fin Survey Results the DECam Legacy Survey (DECaLS) I I I A public imaging survey using DECam: 64 nights g,r,z over 6,000 square degrees About 2 mags deeper than SDSS (g 24.7, r 23.9, z 23) SDSS DECaLS 59
60 the Tractor DECaLS Fin Survey Results the DECam Legacy Survey (DECaLS) 29 Depth (mag) HSC g r i z y DES g r i DECaLS z y g r z 21 i z Area (square degrees) g SDSS r u LSST full g z LSST single g r i i z y r u y u 60
61 the Tractor DECaLS Fin Survey Results the DECam Legacy Survey (DECaLS) What s it for? Overlaps the SDSS/BOSS/eBOSS footprints: millions of spectra (Dec 20 to +30) Galaxy and AGN feedback & evolution Milky Way halo & satellites Things we haven t thought of KIDS 30 ATLAS ATLAS KIDS Galactic Plane DES 90 61
62 the Tractor DECaLS Fin Survey Results the DECam Legacy Survey (DECaLS) What s it really for? Overlaps the SDSS/BOSS/eBOSS footprints: millions of spectra (Dec 20 to +30) Galaxy and AGN feedback & evolution Milky Way halo & satellites Things we haven t thought of... DESI targeting KIDS 30 ATLAS ATLAS KIDS Galactic Plane DES 90 62
63 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 63
64 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 64
65 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 65
66 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 66
67 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 67
68 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 68
69 the Tractor DECaLS Fin Survey Results DECaLS observations 12 nights 2014B, 14 nights 2015A, 8 nights 2015B,... Three-pass tiling: ideally 2 photometric and < 1.3 seeing CCD-sized dithers 69
70 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data DECam Community Pipeline calibrated images (with tweaked photometric & astrometric calibration) PsfEx PSF models SDSS catalogs for the bright end SED-matched detections for the faint end Run a brick at a time ( degrees; pixels) 70
71 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data SDSS DECam Coadd 71
72 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data SDSS sources DECam Coadd 72
73 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data New sources DECam Coadd 73
74 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data Blobs DECam Coadd 74
75 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data DECam Coadd DECam Coadd 75
76 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data Model + Noise DECam Coadd 76
77 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data Model DECam Coadd 77
78 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data Residuals DECam Coadd 78
79 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data Model DECam Coadd 79
80 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data Model DECam Coadd 80
81 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data 81
82 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data 82
83 the Tractor DECaLS Fin Survey Results Applying the Tractor to DECaLS data 83
84 the Tractor DECaLS Fin Survey Results Tractor catalog results SDSS stars galaxies 2.0 r - z (mag) g - r (mag) 84
85 the Tractor DECaLS Fin Survey Results Tractor catalog results DECaLS stars galaxies faint r - z (mag) g - r (mag) 85
86 the Tractor DECaLS Fin Thanks! Sample questions what about star/galaxy separation? what about brightness-dependent PSFs ( brighter fatter )? what was that SED-match detection thing you mentioned? can we see that two-galaxy sampling example? what s DESI? what about cosmic rays, satellites, and transients? what about color gradients in galaxies? is linearized least squares the best you can do? could you run this using data from a very different instrument? is the code public? can I run it on my images? will it ever run out of the box like SourceExtractor? 86
![[0.4, 1] 18M Emission Line Galaxies (ELGs), z [0.](/docs-images/75/71865582/images/87-2.jpg "6, 1.6] 2M tracer QSOs, z < 2.1 plus 0.")
87 the Tractor DECaLS Fin Dark Energy Spectroscopic Instrument (DESI) 5000-fiber spectrograph, 3 FOV, on the 4-m Mayall On-sky 2018, 5-year survey. 9k to 14k sq deg 4M Luminous Red Galaxies (LRGs), z [0.4, 1] 18M Emission Line Galaxies (ELGs), z [0.6, 1.6] 2M tracer QSOs, z < 2.1 plus 0.7M Ly-α QSOs, z >
88 the Tractor DECaLS Fin Dark Energy Spectroscopic Instrument (DESI) BAO in many redshift slices to nail down the growth history Before DESI DESI 88
89 the Tractor DECaLS Fin WISE Satellite Wide-field Infrared Survey Explorer Mid-infrared: W1 (3.4µ), W2 (4.6µ), W3 (12µ), W4 (22µ) Primary survey: ; reactivated for more in 2014! W1/W2 median of 33 exposures all-sky Scans from Ecliptic pole-to-pole 5,000 exposures at the poles Pixel scale: 2.75 arcsec/pixel: (7 times bigger than SDSS) 89
90 the Tractor DECaLS Fin WISE photometry SDSS WISE Model for one source Full Model (Targeted in BOSS W3 ancillary; quasar at z = 2.71) 90
91 the Tractor DECaLS Fin WISE Tractor photometry: depth We measure sources below the WISE catalog 5-sigma threshold 10 6 Number of sources W1 (Tractor) W1 (WISE catalog) W1 mag (Vega) 91
92 the Tractor DECaLS Fin WISE Tractor photometry: accuracy The Tractor measurements are consistent with the WISE catalog Tractor W1 mag WISE W1 mag
93 the Tractor DECaLS Fin WISE Tractor photometry: depth The Tractor measurements of faint objects make sense astrophysically 12 Catalog matches 12 Tractor photometry r (mag) r - W1 (mag) r (mag) r - W1 (mag)
94 the Tractor DECaLS Fin Multi-Band (SED-matched) Detection Example: g,r,i measurements Assume flat SED ( Vega ); estimate r flux g flux is an estimate of r flux; ˆr g = g i flux is an estimate of r flux; ˆr i = i Three predictions of r flux, with Gaussian errors inverse-variance weighting Assume red spectrum (colors g r = r i = 1): g flux is an estimate of r flux; ˆr g = g 2.5 (with variance larger) i flux is an estimate of r flux; ˆr i = i/2.5 (with variance smaller) 94
95 the Tractor DECaLS Fin SED-matched detection 95
96 the Tractor DECaLS Fin SED-matched detection 96
97 the Tractor DECaLS Fin SED-matched detection 97
98 the Tractor DECaLS Fin SED-matched detection 98
99 the Tractor DECaLS Fin SED-matched detection 99
100 the Tractor DECaLS Fin SED-matched detection 100
101 the Tractor DECaLS Fin SED-matched detection 101
102 the Tractor DECaLS Fin SED-matched detection 102
103 the Tractor DECaLS Fin SED-matched detection 103
104 the Tractor DECaLS Fin SED-matched detection 104
105 the Tractor DECaLS Fin SED-matched detection Color-color space locations of strongest detections Flat Red S1 S2 S3 S4 r - i g - r 105
106 the Tractor DECaLS Fin SED-matched detection Red Blue Strength of SED-matched detections 1.4 Relative S/N vs Flat SDSS catalog color (g-i) 106
107 the Tractor DECaLS Fin SED-matched detection 107
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