Numerical Calculation for the Line-of-Sight Attitudes of Multi-Address Transceivers without 2:1 Transmissions for Space Laser Communication Networking

Abstract

In order to optimize space laser communication networking, the 2:1 transmissions for all reflectors on a multi-address transceiver can be removed. However, without the 2:1 transmissions, the reflectors exhibit doubled optical coupling effect in rotation, which reduces the numerical calculation precision of the attitudes of the reflectors’ lines-of-sight (LOS). In the present study, using Snell’s law of reflection and Euler’s theorem, a mathematical model for the attitudes of the LOS of multiple reflectors without 2:1 transmissions was established, and a method was proposed for an indirect numerical calculation of the attitudes of the LOS by creating a Snell transformation matrix. This method eliminates the influence of the doubled optical coupling effect on the numerical solution of the line-of-sight attitudes of multi-reflectors. Compared to the direct numerical calculation method using the angular velocity, the calculation precisions achieved using the proposed method exhibited improvements of 3, 5, and 3 orders of magnitude in the three conical motions, respectively. The indirect calculation method and the numerical calculation model proposed in the present study, therefore, provide a theoretical basis for applying reflectors without 2:1 transmissions to multi-address transceivers.