An Improved Technique for the Photometry and Astrometry of Faint Companions DANIEL BURKE School of Physics, National University of Ireland, Galway, Ireland; daniel.burke@nuigalway.ie SZYMON GLADYSZ European Organisation for Astronomical Research in the Southern Hemisphere; sgladysz@eso.org LEWIS ROBERTS Jet Propulsion Laboratory, California Institute of Technology; lewis.c.roberts@jpl.nasa.gov NICHOLAS DEVANEY School of Physics, National University of Ireland, Galway, Ireland; nicholas.devaney@nuigalway.ie AND CHRIS DAINTY School of Physics, National University of Ireland, Galway, Ireland; c.dainty@nuigalway.ie Received 2009 May 19; accepted 2009 June 5; published 2009 June 29 ABSTRACT. We propose a new approach to differential astrometry and photometry of faint companions in adap- tive optics images. It is based on a prewhitening matched filter, also referred to in the literature as the Hotelling observer. We focus on cases where the signal of the companion is located within the bright halo of the parent star. Using real adaptive optics data from the 3 m Shane telescope at the Lick Observatory, we compare the performance of the Hotelling algorithm with other estimation algorithms currently used for the same problem. The real single-star data are used to generate artificial binary objects with a range of magnitude ratios. In most cases, the Hotelling observer gives significantly lower astrometric and photometric errors. In the case of high Strehl ratio (SR) data (SR ≈ 0:5), the differential photometry of a binary star with a Δm ¼ 4:5 and a separation of 0.6″ is better than 0.1 mag; a factor of 2 lower than the other algorithms considered. 1. INTRODUCTION Differential astrometry and photometry of faint companions in adaptive optics (AO) observations is an important new prob- lem in astronomy (Roberts et al. 2005, 2007). Methods are currently being developed for application to Extremely Large Telescope (ELT) images of exoplanets (Kasper et al. 2008). For exoplanets, differential photometry can be used to derive the planetary mass assuming one of the theoretical models for either reflected or internal light (Baraffe et al. 2003). Hence, an estimate of the planet’ s mass could in principle be derived from a single image. The importance of accurate binary star pho- tometry lies in determining one of the most basic properties of a star: its mass. When the mass of a survey of stars is esti- mated accurately, this information can serve as a test of stellar formation and evolution models (Turner et al. 2008). We propose a new likelihood-maximization method based on using the Hotelling observer (Barrett et al. 1995) to extract as- trometry and photometry of faint companions in AO-corrected images. The Hotelling observer is an algorithm derived from statistical decision theory. When used to detect features, the algorithm/observer applies one or more linear operations to the data and the results of these operations are used to make a de- cision regarding the nature of the recorded feature, e.g., whether it represents a signal or noise. Furthermore, a modified version of the algorithm can be used to estimate features of objects al- ready classified as real. In this article, we discuss the estimation accuracy of the Hotelling observer and not its reliability as a detection scheme; for the latter, see Caucci et al. (2007). The accuracy of the Hotelling approach is compared to other commonly used algorithms using test data. The chosen algo- rithms are StarFinder (Diolaiti et al. 2000) and Fitstars (ten Brummelaar et al. 2000). In § 2 we review these and other algo- rithms which have been applied to the tasks of extracting astrometry and photometry from AO images of binary stars. The Hotelling observer for computing astrometry and photometry is derived in § 3. In § 4 a description of the observations and data reduction is presented, followed in § 5 with a comparison of the astrometric and photometric accuracy of the three algorithms. 767 PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE P ACIFIC, 121:767–777, 2009 July © 2009. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.