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Reference image selectionfor difference imaging analysis
Leo HuckvaleJodrell Bank Centre for Astrophysics
University of Manchester, UK
Supervisor: Eamonn Kerins
Difference imaging analysis
RTi
Variable
From a set of images:
● Choose a reference, R
● Convolve to match seeing
of target, T
via kernel, k● Subtract images
➔ Only true variables remain
...ideallyOther residuals
In practice: other residuals due to badly matched PSFs
Di=R⊗k i−T i
R⊗k i
Difference imaging analysis
Kernel is a sum of some basis functions:
Convolution kernel derived by least-squares:
k=∑n
an k n
∑i
D i2=∑
i
((R⊗k )i−T i)2
Kernel derived from bright stars across whole image
Reference image selection
Reference image is crucial
➔ Common factor in every difference image
Di=(R⊗k i)−T i
Reference image selection
Undersampled data:
PSFs sampled below spatial Nyquist limit
i.e. FWHM < 2.5 pixels
Problematic for DIA
(see Wozniak 2008)
Reference image selection
VVV data frequently undersamples the PSF
Seeing typically between 2 and 3 pixels
Reference image selection
For VVV Science Verification data:
● A stack of all images in the dataset can perform better as a reference image
● Stacked image has worst seeing but high S/N
Usual equation must be flipped:
Di=R−(T i⊗k i)
Reference image selection
● Reference selection is usually done manually
● For large datasets we need an algorithm
● Reference image selection has potential for big improvements to photometry
Reference image selection
VVV has a narrow range in which to get DIA right:
● High background
● Low saturation
● Undersampling
Reference image selection
Our approach:
● Simulate a 2D Gaussian PSF on a pixel grid like the kernel mesh used in DIA
● Defines a simple metric space:● “Stellar flux” (Gaussian integral)● Background flux per pixel● Seeing in pixels
Reference image selection
Figure-of-Merit
A single quantifier for reference image suitability
FOM ∝(∏i H iN i)
1
∑i
∣N i∣
H i
N i
1
∑∣N i∣
: some set of Heuristics
: their power laws
: normalisation by summed root
Reference image selection
Potential heuristics:
● Signal-to-noise,
● Centroid accuracy,
● Width accuracy,
● Width precision,
S
αc
αw
βw
PSF Simulation
Simple 2D Gaussian
Given flux
Given seeing
Sub-pixel offset
Given background
Photon noise
PSF Simulation
Assumption:
A good reference image is one in which the PSF can be accurately characterised
FOM=(S1×αw−12×αc
−13×βw
−13)613
PSF Simulation
FOM ∝(∏i H iN i)
1
∑i∣N i∣
“Testing”
OGLE-III – 20 random epochs(Kindly provided by Łukasz Wyrzykowski)
● Low background● High saturation● Well sampled
VVV Science Verification● Infrared regime (discussed previously)● Working with sky-added images
OGLE
OGLE
OGLE
VVV
VVV
Future work
● Difference image testing
● Numerical kernel simulation
● Optimise FOM
“Conclusion”
ReferenceImage
Selection
DIAPipeline
(VVV-ISIS)
Lightcurves
VVV
Bulge
data