1. No category

the Tractor DECaLS Fin
Astronomical image reduction using
the Tractor
Dustin Lang
McWilliams Postdoc Fellow
Carnegie Mellon University
visiting University of Waterloo
UW / 2015-03-31
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Context the Tractor Examples Tricks
Astronomical image reduction
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Context the Tractor Examples Tricks
Astronomical image reduction
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Context the Tractor Examples Tricks
The Tractor – context
I
the traditional or algorithmic approach: estimators;
“arithmetic operations on the pixels”
m = f (pixels)
I
model-fitting approach: write down a scalar objective
function g and optimize it:
m = arg max g(pixels, µ)
µ
I
generative model-fitting: working in pixel space: g = −χ2
X model(µ)i − pixel 2
i
m = arg min
µ
σi
pixels i
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
What is the “center” of this source?
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
First smooth by a Gaussian the size of the PSF
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Find peak, and look at 3x3 window around the peak
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Find peak, and look at 3x3 window around the peak
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Fit columns as parabolas
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Fit columns as parabolas
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Fit columns as parabolas
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Peak lies along this locus
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Fit rows as parabolas
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Fit rows as parabolas
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Fit rows as parabolas
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Peak lies along this locus
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
Peak lies at the intersection
y
x
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Context the Tractor Examples Tricks
The Traditional, or Algorithmic, Approach
The essence:
I
Make some assumptions or approximations about the data
I
Come up with an estimator that would produce the right
answer if those assumptions held
I
Write an algorithm to implement that estimator
Remarks:
I
Works when the assumptions hold
I
Can be hard to find estimators
I
Usually single image
I
Tends to produce pipelines: measure A, set it in stone;
measure B, set it in stone; . . .
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Context the Tractor Examples Tricks
The Generative Modelling Approach
What is the “center” of this source?
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Context the Tractor Examples Tricks
The Generative Modelling Approach
What center does a model of this source need to have to best
match this image?
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Context the Tractor Examples Tricks
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
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Context the Tractor Examples Tricks
The Generative Modelling Approach
Optimize model parameters (eg, with linearized least squares)
d(Model)/dx
d(Model)/dy
d(Model)/dflux
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Context the Tractor Examples Tricks
The Generative Modelling Approach
Optimize model parameters (eg, with linearized least squares)
Image
Model
Residuals
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Context the Tractor Examples Tricks
The Generative Modelling Approach
Optimize model parameters (eg, with linearized least squares)
Image
Model
Residuals
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Context the Tractor Examples Tricks
The Generative Modelling Approach
Optimize model parameters (eg, with linearized least squares)
Image
Model
Residuals
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Context the Tractor Examples Tricks
The Generative Modelling Approach
Optimize model parameters (eg, with linearized least squares)
Image
Model
Residuals
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Context the Tractor Examples Tricks
The Generative Modelling Approach
The essence:
I
Assume we have calibration info about the image (eg, PSF
model)
I
Assume we can parameterize the appearance of sources
in our images
I
Seek maximum likelihood parameters: it’s an optimization
problem
Remarks:
I
Heuristics to get into the ballpark
I
In theory, very clean
I
In practice, optimization can be tough!
I
Enables iterative solution: fit sources with PSF held fixed;
then fit PSF with sources held fixed
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Context the Tractor Examples Tricks
What is the Tractor? (in a picture)
image calibration
catalog

· RA, Dec



· Mags


Galaxies:


· profile
Photometric, WCS, PSF, Sky
model image
· shape



Stars:




· motion
· variability
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Context the Tractor Examples Tricks
What is the Tractor? (in a picture)
image calibration
catalog

· RA, Dec



· Mags


Galaxies:


· profile
· shape



Stars:




· motion
Photometric, WCS, PSF, Sky
model image
-
observed image
=⇒ chi2
per-pixel error
· variability
likelihood
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Context the Tractor Examples Tricks
What is the Tractor? (in a picture)
image calibration
catalog

· RA, Dec



· Mags


Galaxies:


· profile
· shape



Stars:




· motion
Photometric, WCS, PSF, Sky
model image
-
observed image
=⇒ chi2
per-pixel error
N
· variability
likelihood
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Context the Tractor Examples Tricks
What is the Tractor? (in a picture)
image calibration
catalog

· RA, Dec



· Mags


Galaxies:


Photometric, WCS, PSF, Sky
model image
· profile
· shape



Stars:




· motion
-
observed image
=⇒ chi2
per-pixel error
N
· variability
priors
posterior
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Context the Tractor Examples Tricks
Benefits of the Tractor approach
I
handling multiple exposures, multiple bands, multiple
instruments is easy
I
handling masked pixels (cosmic rays, bleed trails) is easy
I
avoids deblending
I
possible to go back and re-fit calibration parameters
I
easy to add priors or external information
I
possible to sample
I
possible to use physical models
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Context the Tractor Examples Tricks
Example: Galaxy fitting
Image
dx
Model
dy
dflux
Residual
dre
de1
de2
ExpGalaxy at pixel (18.00, 18.00) with Flux: 500
shape EllipseE: re=1, e1=0, e2=0
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Context the Tractor Examples Tricks
Example: Galaxy fitting
Image
dx
Model
dy
dflux
Residual
dre
de1
de2
ExpGalaxy at pixel (18.30, 18.30) with Flux: 432.5
shape EllipseE: re=3.74, e1=0.07, e2=0.98
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Context the Tractor Examples Tricks
Example: Galaxy fitting
Image
dx
Model
dy
dflux
Residual
dre
de1
de2
ExpGalaxy at pixel (18.33, 18.32) with Flux: 441.7
shape EllipseE: re=3.85, e1=0.03, e2=0.46
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Context the Tractor Examples Tricks
Example: Galaxy fitting
Image
dx
Model
dy
dflux
Residual
dre
de1
de2
ExpGalaxy at pixel (19.27, 19.29) with Flux: 837.4
shape EllipseE: re=8.16, e1=0.002, e2=0.70
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Context the Tractor Examples Tricks
Example: Galaxy fitting
Image
dx
Model
dy
dflux
Residual
dre
de1
de2
ExpGalaxy at pixel (20.12, 20.06) with Flux: 1094.5
shape EllipseE: re=8.89, e1=-0.013, e2=0.54
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Context the Tractor Examples Tricks
Example: Galaxy fitting
Image
dx
Model
dy
dflux
Residual
dre
de1
de2
ExpGalaxy at pixel (19.91, 19.85) with Flux: 1082.7
shape EllipseE: re=8.92, e1=-0.018, e2=0.54
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Context the Tractor Examples Tricks
Example: Two galaxy fitting
Image
Model
Residual
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Context the Tractor Examples Tricks
Example: Two galaxy fitting
Image
Model
Residual
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Context the Tractor Examples Tricks
Example: Two galaxy fitting
Image
Model
Residual
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Context the Tractor Examples Tricks
Example: Two galaxy fitting
Image
Model
Residual
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Context the Tractor Examples Tricks
Example: Two galaxy fitting
Image
Model
Residual
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Context the Tractor Examples Tricks
Example: Two galaxy fitting
Image
Model
Residual
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Context the Tractor Examples Tricks
Example: Two galaxy sampling
skip
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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
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Context the Tractor Examples Tricks
e2 B
e1 B
e2 A
Example: Two galaxy sampling
e1 A
e2 A
e1 B
e2 B
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Context the Tractor Examples Tricks
radius B
flux B
radius A
Example: Two galaxy sampling
flux A
radius A
flux B
radius B
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Context the Tractor Examples Tricks
Example: Moving Source
Model with no proper motion
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Context the Tractor Examples Tricks
Example: Moving Source
Model with proper motion
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Context the Tractor Examples Tricks
Example: Moving Source
Model with proper motion
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Context the Tractor Examples Tricks
Example: Moving Source
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Context the Tractor Examples Tricks
Example: Forced photometry
SDSS
WISE
Model for one source
Full Model
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Context the Tractor Examples Tricks
Tricks
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I
I
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
1/s
approximations of galaxy profiles (Gs (r) ∝ e−kr )
lux / M lux = 6 / ξmax = 4 / badness = 4.64 × 10−6
lux / M lux = 6 / ξmax = 4 / badness = 4.64 × 10−6
intensity (relative to intensity at ξ = 1)
intensity (relative to intensity at ξ = 1)
8
6
4
2
100
10−1
10−2
10−3
10−4
0
0
2
4
6
dimensionless angular radius ξ
8
10−5
10−3
10−2
10−1
100
dimensionless angular radius ξ
101
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Context the Tractor Examples Tricks
Tricks
I
I
I
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
1/s
approximations of galaxy profiles (Gs (r) ∝ e−kr )
luv / M luv = 8 / ξmax = 8 / badness = 8.42 × 10−6
luv / M luv = 8 / ξmax = 8 / badness = 8.42 × 10−6
102
intensity (relative to intensity at ξ = 1)
intensity (relative to intensity at ξ = 1)
8
6
4
2
0
0
2
4
6
dimensionless angular radius ξ
8
101
100
10−1
10−2
10−3
10−3
10−2
10−1
100
dimensionless angular radius ξ
101
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Context the Tractor Examples Tricks
Convolution Trick #1
I
approximate galaxy profile as mixture of Gaussians
(galaxy shape and sky-to-pixel are affine transformations)
I
approximate PSF as mixture of Gaussians
I
→ convolution is analytic!
I
Npsf × Ngalaxy Gaussian components in the convolution
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Context the Tractor Examples Tricks
Convolution Trick #1
I
approximate galaxy profile as mixture of Gaussians
(galaxy shape and sky-to-pixel are affine transformations)
I
I
I
approximate PSF as mixture of Gaussians
→ convolution is analytic!
Npsf × Ngalaxy Gaussian components in the convolution
25
25
20
20
15
15
10
10
5
5
0
0
25
5
10
15
20
20
0
25 0
25
5
10
15
20
25
5
10
15
20
25
20
15
15
10
10
5
5
0
0
25 0
0
5
10
15
20
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Context the Tractor Examples Tricks
Convolution Trick #2
I
I
I
I
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
14
12
10
8
6
4
2
0
0
2
4
6
14
12
10
8
6
4
2
0
8 10 12 14 0
2
4
6
8 10 12 14
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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
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Survey Results
the DECam Legacy Survey (DECaLS)
29
LSST full
Depth (mag)
28
HSC
DES
26
g
r
i
g
r
z
i DECaLS
z
g
25
24
23
y
i
z
g
r
y
i
u
z
z
SDSS
g
22
u
r
y
i
21
20
0
u
LSST single
r
y
r
g
27
z
5000
10000
Area (square degrees)
15000
20000
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Survey Results
the DECam Legacy Survey (DECaLS)
What’s it for?
I Overlaps the SDSS/BOSS/eBOSS footprints: millions of
spectra (Dec −20 to +30)
I Galaxy and AGN feedback & evolution
I Milky Way halo & satellites
I Things we haven’t thought of . . .
90
60
lac
tic
Pla
ne
30
0
Ga
KIDS
ATLAS
120
150
180
210
240
270 −30 300
−60
ATLAS
330
0
30
KIDS
60
90
DES
−90
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Survey Results
the DECam Legacy Survey (DECaLS)
What’s it really for?
I Overlaps the SDSS/BOSS/eBOSS footprints: millions of
spectra (Dec −20 to +30)
I Galaxy and AGN feedback & evolution
I Milky Way halo & satellites
I Things we haven’t thought of . . .
I DESI targeting
90
60
Ga
la
ctic
Pla
ne
30
KIDS
0
ATLAS
120
150
180
210
240
270 −30 300
−60
−90
ATLAS
330
0
30
KIDS
60
90
DES
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
DECaLS observations
I
I
I
∼12 nights 2014B, 14 nights 2015A, 8 nights 2015B, . . .
Three-pass tiling: ideally 2 photometric and < 1.300 seeing
∼ CCD-sized dithers
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Survey Results
Applying the Tractor to DECaLS data
I
DECam Community Pipeline calibrated images
(with tweaked photometric & astrometric calibration)
I
PsfEx PSF models
I
SDSS catalogs for the bright end
I
SED-matched detections for the faint end
I
Run a brick at a time
(0.25 × 0.25 degrees; 3600 × 3600 pixels)
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Survey Results
Applying the Tractor to DECaLS data
SDSS
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
SDSS sources
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
New sources
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
Blobs
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
DECam Coadd
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
Model + Noise
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
Model
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
Residuals
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
Model
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
Model
DECam Coadd
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Survey Results
Applying the Tractor to DECaLS data
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Survey Results
Applying the Tractor to DECaLS data
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Survey Results
Applying the Tractor to DECaLS data
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Survey Results
Tractor catalog results
SDSS
3.0
stars
galaxies
2.5
r - z (mag)
2.0
1.5
1.0
0.5
0.0
0.5
0.5
0.0
0.5
1.0
g - r (mag)
1.5
2.0
2.5
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Survey Results
Tractor catalog results
DECaLS
3.0
stars
galaxies
faint
2.5
r - z (mag)
2.0
1.5
1.0
0.5
0.0
0.5
0.5
0.0
0.5
1.0
g - r (mag)
1.5
2.0
2.5
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Thanks!
Sample questions
I what about star/galaxy separation?
I what about brightness-dependent PSFs (“brighter–fatter”)?
I what was that SED-match detection thing you mentioned?
I can we see that two-galaxy sampling example?
I what’s DESI?
I what about cosmic rays, satellites, and transients?
I what about color gradients in galaxies?
I is linearized least squares the best you can do?
I could you run this using data from a very different
instrument?
I is the code public?
I can I run it on my images?
I will it ever run “out of the box” like SourceExtractor?
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Dark Energy Spectroscopic Instrument (DESI)
I
I
5000-fiber spectrograph, 3◦ FOV, on the 4-m Mayall
On-sky 2018, 5-year survey. 9k to 14k sq deg
I
I
I
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 > 2.1
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Dark Energy Spectroscopic Instrument (DESI)
BAO in many redshift slices to nail down the growth history
Before DESI
DESI
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WISE Satellite
I
Wide-field Infrared Survey Explorer
I
Mid-infrared: W1 (3.4µ), W2 (4.6µ), W3 (12µ), W4 (22µ)
I
Primary survey: 2010-2011; reactivated for more in 2014!
I
W1/W2 — median of 33 exposures all-sky
I
Scans from Ecliptic pole-to-pole — 5,000 exposures at the
poles
I
Pixel scale: 2.75 arcsec/pixel: (7 times bigger than SDSS)
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WISE photometry
SDSS
1984
WISE
1984
1982
1982
1980
1980
1978
1978
1976
1976
1974
1974
1972
1678 1680 16821684 1686 1688
1972
Model for one source
1984
Full Model
1984
1982
1982
1980
1980
1978
1978
1976
1976
1974
1974
1972
1678 1680 16821684 1686 1688
1678 1680 16821684 1686 1688
1972
1678 1680 16821684 1686 1688
(Targeted in BOSS W3 ancillary; quasar at z = 2.71)
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WISE Tractor photometry: depth
We measure sources below the WISE catalog
5-sigma threshold
Number of sources
106
105
104
103
102 10
W1 (Tractor)
W1 (WISE catalog)
12
14
16 18 20
W1 mag (Vega)
22
24
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WISE Tractor photometry: accuracy
Tractor W1 mag
The Tractor measurements are consistent
with the WISE catalog
10
11
12
13
14
15
16
17
1818 17 16 15 14 13 12 11 10
WISE W1 mag
10000
1000
100
10
1
0
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WISE Tractor photometry: depth
The Tractor measurements of faint objects
make sense astrophysically
Catalog matches
Tractor photometry
12
12
14
18
100
20
10
22
24
4
2 0 2 4 6
r - W1 (mag)
8
10
1
0
1000
16
r (mag)
16
r (mag)
14
1000
18
100
20
10
22
24
4
2 0 2 4 6
r - W1 (mag)
8
10
1
0
93
the Tractor DECaLS Fin
Multi-Band (SED-matched) Detection
I
Example: g,r,i measurements
I
Assume flat SED (“Vega”); estimate r flux
I
g flux is an estimate of r flux; rˆg = g
I
i flux is an estimate of r flux; rˆi = i
I
Three predictions of r flux, with Gaussian errors
I
→ inverse-variance weighting
I
Assume red spectrum (colors g − r = r − i = 1):
I
g flux is an estimate of r flux; rˆg = g ∗ 2.5
(with variance 2.52 larger)
I
i flux is an estimate of r flux; rˆi = i/2.5
(with variance 2.52 smaller)
94
the Tractor DECaLS Fin
SED-matched detection
95
the Tractor DECaLS Fin
SED-matched detection
96
the Tractor DECaLS Fin
SED-matched detection
97
the Tractor DECaLS Fin
SED-matched detection
98
the Tractor DECaLS Fin
SED-matched detection
99
the Tractor DECaLS Fin
SED-matched detection
100
the Tractor DECaLS Fin
SED-matched detection
101
the Tractor DECaLS Fin
SED-matched detection
102
the Tractor DECaLS Fin
SED-matched detection
103
the Tractor DECaLS Fin
SED-matched detection
104
the Tractor DECaLS Fin
SED-matched detection
2.0
1.5
Color-color space locations of strongest detections
Flat
Red
S1
S2
S3
S4
r-i
1.0
0.5
0.0
0.0
0.5
1.0
g-r
1.5
2.0
2.5
105
the Tractor DECaLS Fin
SED-matched detection
Strength of SED-matched detections
1.8
Red
Blue
1.6
Relative S/N vs Flat
1.4
1.2
1.0
0.8
0.6
0.4
1
0
1
2
SDSS catalog color (g-i)
3
4
106
the Tractor DECaLS Fin
SED-matched detection
107