## Author(s)

Wang, Zhizhao, Yang, Shuju, Wu, Kaihang, Wang, Xiaojie, Duan, Huizong, Liang, Yurong, Zhang, Xuefeng, Yeh, Hsien-Chi## Abstract

Tilt-to-length (TTL) coupling is expected to be one of the major noise sources in the interferometric phase readouts in TianQin mission. Arising from the angular motion of spacecraft (SC) and the onboard movable optical subassemblies (MOSAs), TTL noise needs to be removed in postprocessing after suppressing the laser phase noise with time-delay interferometry (TDI) technique. In this article, we show that we can estimate the TTL coupling coefficients using the null TDI channel ζ and remove the TTL noise in the commonly used Michelson variables with the estimated coefficients. We introduce the theoretical model of TTL noise in TDI and consider linear drifts in the linear TTL coefficients for noise estimation and subtraction. The TTL coefficients with drifts are estimated successfully with an accuracy of 10 μm/rad in our numerical simulation. We discuss the impact of point-ahead angle compensation error and wavefront error, and find it necessary to estimate linear drift coefficients and quadratic TTL coefficients to keep TTL noise residuals below the 0.3 pm noise reference curve. However, the estimation accuracy suffers greatly from the correlation between yaw jitter measurements that contain the same SC jitter. Assuming all angular jitters induced by MOSAs are independent, choosing a frequency range with relatively higher MOSA yaw jitter noise levels is beneficial to the TTL coefficient estimation.

## Figures

Labeling conventions used for spacecraft, MOSAs and laser links. The test mass, optical bench and telescope in each MOSA are drawn in yellow, cyan and orange respectively. The red lines represent the laser links while the blue curves between optical benches represent the backlink fibers for TMIs and RFIs.

Reference frames on SC1 as an example. The SC frame is shown in blue and the two MOSA frames are shown in purple. The opening angle between the two MOSAs, also known as the breathing angle, varies around $60^\circ$ due to the orbital mechanics of the triangular constellation.

Residual noise levels after laser noise suppression (red) and clock noise reduction (black) with $\zeta$ in the absence of TTL noise. The green trace is higher than the 1 pm noise reference curve (orange) at frequencies below 1 mHz mainly due to the sideband readout noise (dashed blue).

TTL noise subtraction from $\zeta_\text{corr}^q$ (red). The residual noise and the TTL noise estimation error are shown in black and blue respectively. The green trace represents the estimation error in the case that drift coefficients are not included in TTL noise estimation and subtraction.

Residual noise level in $X$, $Y$ and $Z$ after subtracting the TTL noise and clock noise. Below 7 mHz it is dominated by TM acceleration noise (dashed green) and armlength mismatch of the virtual interferometer for TDI (dashed black). The blue and solid green traces represent TTL noise residuals in $X$ with and without drift estimation.

Unprimed in-plane (upper plot) and out-of-plane PAAs (lower plot) of 90 days in TianQin. The mean value of each in-plane PAA (approximately $-23.07\ \upmu\text{rad}$) has been subtracted.

TTL noise in $X$ with PAAs on day 1, and TTL noise residuals under different conditions after subtraction.

TTL noise in $X$ with PAAs on day 32, and TTL noise residuals under different conditions after subtraction.

Residual noise levels in $X$ after removing the TTL noise and clock noise under different MOSA yaw jitter levels.

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