Evaluation method for the design results of space gravitational-wave telescopes

Abstract

Unlike traditional imaging telescopes, space gravitational-wave telescope has higher requirements for wavefront error and must meet the stability requirement of tilt-to-length (TTL). The tolerance analysis results of current telescopes can judge whether the wavefront error meets the requirements, but they cannot be used as the judgment result of the TTL noise coupling coefficient of the telescope. To analyze the influence of manufacturing errors of the telescope on the coupling coefficient of TTL noise, based on the error amount and the Zernike polynomial first-order sensitivity matrix, we established the sensitivity matrix of the mapping relationship between telescope manufacturing errors and coupling coefficients. For example, consider the design results of an off-axis four-mirror space gravitational-wave telescope. If the wavefront error was used as the judgment result to determine the tolerance distribution, the cumulative probability of the coupling coefficient meeting the requirements would be 66.7%. Furthermore, using the coupling coefficient as the control requirement and determining the tolerance allocation results according to the coupling coefficient sensitivity matrix, the cumulative probability increased to 93.8%. The necessity of using the coupling coefficient as an evaluation method for the design results of gravitational-wave telescopes was verified. This evaluation method can provide meaningful guidance for the design results of gravitational-wave telescopes.