Optimal Image Subtraction implementation

Version : 2.1

Author(s) : C. Alard (alard@iap.fr), R. H. Lupton

License : Free

Website : http://www.iap.fr/users/alard/package.html

Installs from Open Source Astronomy for Linux cd 3

Disk space required for installation is 68.01 Kb

A new method designed for optimal subtraction of two images with different seeing. Using image subtraction appears to be essential for the full analysis of the microlensing survey images, however a perfect subtraction of two images is not easy as it requires the derivation of an extremely accurate convolution kernel. Some empirical attempts to find the kernel have used the Fourier transform of bright stars, but solving the statistical problem of finding the best kernel solution has never really been tackled. We demonstrate that it is possible to derive an optimal kernel solution from a simple least square analysis using all the pixels of both images, and also show that it is possible to fit the differential background variation at the same time. We also show that PSF variations can also be easily handled by the method. To demonstrate the practical efficiency of the method, we analyzed some images from a Galactic Bulge field monitored by the OGLE II project. We find that the residuals in the subtracted images are very close to the photon noise expectations. We also present some light curves of variable stars, and show that, despite high crowding levels, we get an error distribution close to that expected from photon noise alone. We thus demonstrate that nearly optimal differential photometry can be achieved even in very crowded fields. We suggest that this algorithm might be particularly important for microlensing surveys, where the photometric accuracy and completeness levels could be very significantly improved by using this method

There are 3 essential steps to follow to make light curves of variables objects

Image registration

The goal of image registration is to re-map each image on the same grid. The reference system, or common grid is usually one of the image. The output of this procedure will be a FITS image interpolated on the reference grid.

This procedure involve 2 steps:

- Getting the astrometric transform, X=f(x_ref,y_ref )

- Making image interpolation (Bicubic Splines)

Image Subtraction

This is the main program, and the core of the new method presented in the 2 papers. Before you run the code, you need to make a good reference image by stacking some of your best images. Then you can use the image subtraction code to adjust the reference image to the seeing of each individual image (which have been previously registered and interpolated).

The image subtraction code can process the whole frame by small pieces, it is especially useful in case of large images which can be processed with limited memory ressources.

The code has 2 level of rejection for variable objects:

- Checking that each individual star does not show flux variations

- Checking the chi-square for each individual star

The final output of the code will a subtracted image of the flux variation beween the individualimage and the reference frame.

Photometry

This package will make photometry of variable objects by using the subtracted images. The flux of the variable will be calculated using profile fitting photometry at fixed position. As for the image subtraction code, the frame can be also treated by small pieces. The profile of each frame is calculated by making median stacking of a few reference stars.