Optimizing Convolution Direction and Template Selection for Difference Image Analysis

Abstract: Difference image analysis (DIA) is a powerful tool for studying time-variable phenomena, and has been used by many time-domain surveys. Most DIA algorithms involve matching the spatially-varying PSF shape between science and template images, and then convolving that shape in one image to match the other. The wrong choice of which image to convolve can introduce one of the largest sources of artifacts in the final difference image. We introduce a quantitative metric to determine the optimal convolution direction that depends not only on the sharpness of the images measured by their FWHM, but also on their exposure depths. With this metric, the optimal convolution direction can be determined a priori, depending only on the FWHM and depth of the images. This not only simplifies the process, but also makes it more robust and less prone to creating sub-optimal difference images due to the wrong choice of the convolution direction. As an additional benefit, for a large set of images, we define a Figure-of-Merit based on this metric, which allows us to rank a list of images and determine the ones best suited to be used as templates, thus streamlining and automating the data reduction process.