Оценка экваториальных координат объектов на цифровом кадре для длиннофокусных и короткофокусных телескопов

Abstract

В статье разработаны вычислительные методы определения экваториальных координат небесных объектов по оценке их положения на цифровом кадре. Разработанные методы учитывают особенности астрономической редукции в длиннофокусных и короткофокусных оптических системах. Для каждой из них проведен сравнительный анализ точности положения объектов в случае применения рассмотренных методов. Результаты анализа показали обоснованность применения методов прямой координатной редукции для кадров, полученных с использованием длиннофокусных оптических систем, и обратной для кадров из короткофокусных оптических систем.

Computational methods for determining equatorial coordinates of celestial objects based on an assessment of their positions on the digital frame are described. These methods are based on the possibility of representing errors in celestial objects positions mappings in the form of reduction equation which depends only on the object’s location in the frame. To assess the coefficients of the reduction model the modified Levenberg-Marquardt algorithm was used that allowed to eliminate the problem with accumulation of computational errors for ill-conditioned matrix of reduction model partial derivatives. The developed methods take into account the peculiarities of astronomical reduction in long-focus and short-focus optical systems. These systems have different types of optical aberrations that negatively affect accuracy of objects positions determination that leads to the problem of choosing optimal model for each one. With using of digital images obtained from both types of optical systems the comparative analysis of the accuracy of the position of objects in case of application of considered methods have been carried out. As the investigated objects in the analysis the set of reference stars as well as stars identified with UCAC4 have been used. The results showed reasonableness of applying direct coordinate reduction methods for frames obtained by using long-focus optical systems. According to the analysis results for short-focus optical systems it is advisable to use the reverse coordinate reduction methods.