Mathematical model of the mirror system of the Millimetron observatory and a description of the method of pre-measurement of the telescope within this model

A mirror geometry control system for the Millimetron Observatory is being created to work as part of the on-board complex of scientific equipment. The system is designed to monitor the quality of the space telescope’s mirror system and use the data received as feedback signals for pre-setting and tuning the telescope’s optical system in outer space. The goal of the system is estimation of the multidimensional vector of unknown parameters of the telescope’s mirror system by indirect measurements obtained as a result of the measurement of the telescope by 3D scanning. A mathematical model has been created, numerically describing the process of pre-measurement of the mirror system of the Millimetron Observatory using optical control marks on the surface of the mirror system. The linear mathematical model allows to link the actual indirect measurements of the mirror system with the unknown biases of its parameters, determining the shape of the telescope. A formula has been developed for the optimal reverse problem solver in the process of pre-measurement of the mirror system. The method of measuring the components of the telescope as part of its pre-setting is described. The measurement of control marks is based on a onboard 3D scanner embedded in the design of the mirror system control system. The error analysis was carried out using the optimal solver, and a covariance matrix was obtained for the error vector of estimated parameter.