Difference image analysis: extension to a spatially varying photometric scale factor and other considerations

D. M. Bramich*, Keith Horne, M. D. Albrow, Y. Tsapras, C. Snodgrass, R. A. Street, M. Hundertmark, Noe Kains, A. Arellano Ferro, R. Figuera Jaimes, Sunetra Giridhar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


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 optimizations that may be capitalized 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.

Original languageEnglish
Pages (from-to)2275-2289
Number of pages15
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Publication statusPublished - Jan 2013


  • methods: statistical
  • techniques: image processing
  • techniques: photometric
  • methods: data analysis


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