A method of optimal image subtraction: development of the mathematics and software for general use in astronomical research

Miller, J. Patrick (2008) A method of optimal image subtraction: development of the mathematics and software for general use in astronomical research. PhD thesis, James Cook University.

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This thesis presents a new and scalable implementation of an optimal image subtraction (termed “OIS”) method proposed by Alard & Lupton (1998). A novel feature of this work is that it is written in the most commonly used image processing language, Interactive Data Language (IDL), and can be easily used by other astronomy research groups. In fact, one research group at the Departamento Sistema Solar Instituto de Astrofísica de Andalucía at the direction of Dr. J.L. Ortiz uses the IDL code in its work with trans-Neptunian objects (TNO) light curves.

The code is tested extensively on professional image sets. Subtractions from the IDL code show the detection of brightness-varying objects including supernovae (SNe), active galactic nuclei (AGN), and variable stars, and position-changing objects including Main Belt asteroids, Kuiper Belt objects, comets, and SNe light echoes. Sought, but not yet detected, was an exoplanet transit.

Original astronomical discoveries are presented including SN 2006al, and SN 2006bi. Presented also is a subtraction that effectively separates SN 1999av from its host galaxy using an image set from two different telescopes. New AGN candidates are presented, some of which do not appear in the literature. Also presented are the discoveries of 76 Main Belt asteroids made by student participants in the International Asteroid Search Campaign.

A complete derivation is presented of the linear system of equations for the space-varying kernel used in the OIS method. The set of vectors that define the Gaussian components basis (GCB) are presented, and a new delta function basis (DFB) is introduced and shown to produce better subtractions than the GCB.

A complete derivation of the linear system of equations, to correct the differential background, is presented. Also presented is the re-definition of the basis vectors used to conserve the photometric flux. This presentation proves the conversation of the flux, and includes a number of proofs of theorems involving two-dimensional convolutions.

The OIS method uses sub-images, called “stamps”, that are small sections of images, each containing one star, used to define the kernel. An automated stamp selection procedure was designed utilizing utilities from the Goddard Space Flight Center (GSFC) IDL User’s Astronomy Library. This procedure is presented including the masking of bad pixels within the image sets prior to selecting the stamps.

The Magnier method is presented that aligns image sets with no or small differential rotation. The sub-pixel adjustment issue is addressed using two methods, piecewise cubic splines and polynomial interpolation convolution kernels. The complete derivation of these convolution kernels is presented.

An attempt to define the quality of an OIS using a quality index is presented. This attempt is only partially successful. It identifies improvements in subtractions using the delta function basis, but not the Gaussian components basis. The quality index shows that the DFB produces better subtractions than the GCB.

Finally, a complete listing of the IDL source of the computer codes is found in the appendix. These listings include the differential background correction, alignment and sub-pixel adjustment, masking of moving object and SNe subtractions, and the space varying kernel OIS method. The original IDL source code is available upon request.

Item ID: 2067
Item Type: Thesis (PhD)
Keywords: optimal image subtraction, astronomical research, interactive data language, convolution kernels, space-varying kernels, vectors, stamp selection, differential background correction, photometric flux, image alignment, masking, space imaging, OIS, IDL codes
Date Deposited: 19 Jan 2009 04:53
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