Mario L. Vicuña, Jorge F. Silva, Rene A. Mendez, Marcos E. Orchard, Sebastian Espinosa, Jeremy Tregloan-Reed
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We demonstrate that these estimators provide quasi-unbiased joint estimations of the flux and background, with a variance that approaches the CRLB very tightly and are, hence, optimal, unlike the case of sequential estimation used commonly in astronomical photometry which is sub-optimal. We compare our predictions with numerical simulations of realistic observations, as well as with observations of a bona fide non-variable stellar source observed with TESS, and compare it to the results from the sequential estimation of background and flux, confirming our theoretical expectations. Our practical estimators can be used as benchmarks for general photometric pipelines, or for applications that require maximum precision and accuracy in absolute photometry.","PeriodicalId":20820,"journal":{"name":"Publications of the Astronomical Society of the Pacific","volume":null,"pages":null},"PeriodicalIF":3.3000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Photometry of Point Sources: Joint Source Flux and Background Determination on Array Detectors—from Theory to Practical Implementation\",\"authors\":\"Mario L. Vicuña, Jorge F. Silva, Rene A. Mendez, Marcos E. Orchard, Sebastian Espinosa, Jeremy Tregloan-Reed\",\"doi\":\"10.1088/1538-3873/ad0ca3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study the joint determination of source and background flux for point sources as observed by digital array detectors. We explicitly compute the two-dimensional Cramér–Rao absolute lower bound (CRLB) as well as the performance bounds for high-dimensional implicit estimators from a generalized Taylor expansion. This later approach allows us to obtain computable prescriptions for the bias and variance of the joint estimators. We compare these prescriptions with empirical results from numerical simulations in the case of the weighted least squares estimator (introducing an improved version, denoted stochastic weighted least-squares) as well as with the maximum likelihood estimator, finding excellent agreement. We demonstrate that these estimators provide quasi-unbiased joint estimations of the flux and background, with a variance that approaches the CRLB very tightly and are, hence, optimal, unlike the case of sequential estimation used commonly in astronomical photometry which is sub-optimal. We compare our predictions with numerical simulations of realistic observations, as well as with observations of a bona fide non-variable stellar source observed with TESS, and compare it to the results from the sequential estimation of background and flux, confirming our theoretical expectations. 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Optimal Photometry of Point Sources: Joint Source Flux and Background Determination on Array Detectors—from Theory to Practical Implementation
In this paper we study the joint determination of source and background flux for point sources as observed by digital array detectors. We explicitly compute the two-dimensional Cramér–Rao absolute lower bound (CRLB) as well as the performance bounds for high-dimensional implicit estimators from a generalized Taylor expansion. This later approach allows us to obtain computable prescriptions for the bias and variance of the joint estimators. We compare these prescriptions with empirical results from numerical simulations in the case of the weighted least squares estimator (introducing an improved version, denoted stochastic weighted least-squares) as well as with the maximum likelihood estimator, finding excellent agreement. We demonstrate that these estimators provide quasi-unbiased joint estimations of the flux and background, with a variance that approaches the CRLB very tightly and are, hence, optimal, unlike the case of sequential estimation used commonly in astronomical photometry which is sub-optimal. We compare our predictions with numerical simulations of realistic observations, as well as with observations of a bona fide non-variable stellar source observed with TESS, and compare it to the results from the sequential estimation of background and flux, confirming our theoretical expectations. Our practical estimators can be used as benchmarks for general photometric pipelines, or for applications that require maximum precision and accuracy in absolute photometry.
期刊介绍:
The Publications of the Astronomical Society of the Pacific (PASP), the technical journal of the Astronomical Society of the Pacific (ASP), has been published regularly since 1889, and is an integral part of the ASP''s mission to advance the science of astronomy and disseminate astronomical information. The journal provides an outlet for astronomical results of a scientific nature and serves to keep readers in touch with current astronomical research. It contains refereed research and instrumentation articles, invited and contributed reviews, tutorials, and dissertation summaries.