Difference Image Analysis: Extension to a Spatially Varying Photometric Scale Factor and Other Considerations

TL;DR

This paper extends difference image analysis (DIA) by introducing a spatially varying photometric scale factor, improving accuracy for wide-field imaging affected by transparency and airmass variations, and offers optimized algorithms validated on real and simulated data.

Contribution

The paper introduces a novel framework for DIA that includes a spatially varying photometric scale factor and mixed-resolution delta basis functions, enhancing flexibility and computational efficiency.

Findings

Validated on simulated data showing improved accuracy.

Demonstrated on real data with successful difference imaging.

Provided optimized algorithms for practical implementation.

Abstract

We present a general framework for matching the point-spread function (PSF), photometric scaling, and sky background between two images, a subject which is commonly referred to as difference image analysis (DIA). We introduce the new concept of a spatially varying photometric scale factor which will be important for DIA applied to wide-field imaging data in order to adapt to transparency and airmass variations across the field-of-view. Furthermore, we demonstrate how to separately control the degree of spatial variation of each kernel basis function, the photometric scale factor, and the differential sky background. We discuss the common choices for kernel basis functions within our framework, and we introduce the mixed-resolution delta basis functions to address the problem of the size of the least-squares problem to be solved when using delta basis functions. We validate and demonstrate our algorithm on simulated and real data. We also describe a number of useful optimisations that may be capitalised on during the construction of the least-squares matrix and which have not been reported previously. We pay special attention to presenting a clear notation for the DIA equations which are set out in a way that will hopefully encourage developers to tackle the implementation of DIA software.