The analysis of the far-field phase and the tilt-to-length error contribution in space-based laser interferometry
Q. F. Xiao, Hui‐Zong Duan, Min Ming, Jingyi Zhang, Fan Zhu, Yuwei Jiang, Hsien‐Chi Yeh
Abstract
Abstract The arm length of the space-based interferometer for gravitational wave detection is 10 8 –10 9 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> </mml:math> , and picometer precision is required. The wavefront error in the far-field coupled with the pointing jitter is a major noise source, which raises higher requirements of the wavefront quality of the telescope. By extending the analytical solutions of the far-field phase to 21 Zernike aberrations, this paper demonstrates that the far-field phase could be regarded as the sum of the effects of the individual aberrations and a phase plane with its slope related to the wavefront RMS. For individual aberrations, only low-order aberrations have a significant effect on the far-field phase, but high-order aberrations will contribute to the coupling terms which is shown as a phase slope. So there is a definite corresponding relationship between the aberrations and the far-field phase, and it can be easily illustrated graphically. Based on the analytical solutions of the far-field phase, we proposed to consider the tilt-to-length (TTL) error together with the far-field phase. The TTL error is also one of the main noise sources in space-based laser interferometry, which presents big difficulties in the optical system. We found that TTL error could be added to the far-field phase as a piston term during pointing, which then help to bring the stationary point closer to the z -axis and reduce the phase noise detected at the stationary point. By considering the TTL together with the far-field phase, the requirement of the telescope could be λ /25 wavefront RMS ( λ = 1064 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>nm</mml:mtext> </mml:mrow> </mml:math> ). And there will be a large tolerance range for the TTL error, so it is only necessary to evaluate the TTL error and limit it to a suitable range, not to eliminate it.