Introduction Observations PSF fitting Photometry Results

Defocused PSF-fitting PhotometryRoPACS Network Workshop - May 2010

Hannu Parviainen

Instituto de Astrof́ısica de Canarias

11.05.2010

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results

1 IntroductionThe light curveDefocused PSF

2 ObservationsObservations

3 PSF fitting PhotometryPSF model 1PSF model 2Fitting

4 Results

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results The light curve Defocused PSF

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results The light curve Defocused PSF

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results The light curve Defocused PSF

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results The light curve Defocused PSF

PSF

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results The light curve Defocused PSF

PSF

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results Observations

Observations

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results Observations

Observations

GJ436(b)

Bright (6.3 in H)

Distance 10.2 pc

Observations - 13.03.2010

H filter

1.5 s. integration

Defocused to ≈ 8 pix ring

200 images / cube

W-setup (4.6’ fow)

40 cubes → 8000 images

Challenges (problems)

No comparison star

Misbehaving dome →vignetting

Defocusing

Reduces the noise due topixel-to-pixel variation

Smooths out the noise due tosky variation

Allows for longer integration ofbright targets

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results PSF model 1 PSF model 2 Fitting

PSF Fitting Photometry

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results PSF model 1 PSF model 2 Fitting

Why?

What

Model the shape of the psf

Fit the model to the data

Calculate flux from the model

Why

PSF spread over a large numberof pixels

Vignetted part can be excluded

But only if the effects due tothe vignetting are confinedLess pixels to fit → increasesscatter

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results PSF model 1 PSF model 2 Fitting

PSF model

PSF model

Center (x ,y)n concentric rings

AmplitudeWidthRadius

Rings

Gaussians

Evaluation of exp is slow!Infinite support

Quartic polynomials

Only multiplicationsLess elegant but fastClipping → finite support

Quartic polynomial

fi(r) = a+4a(r4/4w − r2/2w

)

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results PSF model 1 PSF model 2 Fitting

PSF model

PSF model

Center (x ,y)n concentric rings

AmplitudeWidthRadius

Rings

Gaussians

Evaluation of exp is slow!Infinite support

Quartic polynomials

Only multiplicationsLess elegant but fastClipping → finite support

Amplitude

Center

Width

Quartic polynomial

fi(r) = a+4a(r4/4w − r2/2w

)

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results PSF model 1 PSF model 2 Fitting

PSF model

PSF model

PSF(r) =n

∑i

fi(r)

Flux

F(r) = 2π

∫rPSF(r)dr

F(r) = 2π

∫r

n

∑i

fi(r)dr

F(r) = 2π

n

∑i

∫r fi(r)dr

0 2 4 6 8 10 12 14 16

Flux integration

Flux is a sum of polynomials

Fast, minimizes numerical errors

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results PSF model 1 PSF model 2 Fitting

Fitting

Differential evolution (DE)

Global optimization algorithm

Fast, robust, easy to implement

Price, Storn, and Lampinen(2005)

Implementation

Fortran, Python, NumPy, andPyFITS

Trivial parallelization with MPI

Implementation

Iterative optimization ofparameter space bounds

Increases stability

Performance

0.2 - 0.8 sec/image for the 3ring model (11 free parameters)

Other

Calculates centers of defocusedpsf’s → aperture photometry

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results

Results

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results

PSF fitting example

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results

Final light curve

Hannu Parviainen Defocused PSF-fitting Photometry

Introduction Observations PSF fitting Photometry Results

Thank you!

Hannu Parviainen Defocused PSF-fitting Photometry