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