Tilt-to-length noise coupled by wavefront errors in the interfering beams for the space measurement of gravitational waves

Abstract

The space-based gravitational wave detection programs, like the Laser Interferometer Space Antenna (LISA) or the Taiji program, aim to detect gravitational waves in space with a triangular constellation of three spacecraft. The unavoidable jitters of the spacecraft and the pointing will couple with the misalignment of the interfering beams into the longitudinal path length readout. This effect is called tilt-to-length (TTL) coupling, which is one of the keys to achieving the required measuring accuracy of 1 p m / H z . In terms of two phase definitions (the LISA Pathfinder (LPF) signal and the Average Phase (AP) signal), we implement the comprehensive theoretical analysis concerning the effect of aberrations on TTL coupling noise. In addition, we analytically derive that the proper lateral shift of the interfering beams relative to the detector can partly cancel out the TTL noise coupled with aberrations, especially coma and trefoil aberrations for the AP signal. Based on the above results, the meaningful guidance can be provided for the design and construction of the optical system in LISA or Taiji.

Optical system design of large-aperture space gravitational wave telescope

“…1 More importantly, to analyze the complete GW signal, the coupling coefficient between wavefront error and TTL noise should be suppressed within AE25 pm∕μrad. [8][9][10][11][12][13] 2.2 Initial Structural Design Spherical aberration, coma aberration, astigmatism, field curvature, and distortion are common aberrations in reflective optical systems. The wave aberration of the optical system can be expressed using Seidel coefficients as follows:…”

“…According to existing literature, the LISA path finder (LPF) and average phase (AP) signals are two analytical methods used for calculating the coupling of wavefront error and TTL noise. 8 Compared to the LPF signal, the AP signal can reduce the coupling of TTL noise and wavefront error to a greater extent, thereby reducing the requirement for the wavefront error. In practical situations, several factors such as the imaging system, diaphragm position, and wave aberration at the exit pupil of the telescope affect TTL coupling noise.…”

“…Although, it is difficult to quantitatively analyze the contribution of a single factor to TTL coupling noise, the noise source can be suppressed. Thus far, [8][9][10][11][12][13] Zhao presented a comprehensive theoretical analysis of the influence of telescope aberration on TTL coupling noise, proposed that the coupling coefficient should be suppressed at AE25 pm∕μrad, analyzed the contribution of TTL coupling noise of the prototype of the Taiji project telescope principle, and determined whether the final optical path stability has exceeded 3 pm∕ p Hz. 14 Based on the current disclosed research related to GW telescopes, 11,[15][16][17][18] Livas and Fan designed an off-axis four-mirror telescope with a magnification of 40× and an entrance pupil diameter of 200 and 220 mm, respectively.…”

“…The wavefront error at the exit pupil of the system is coupled with tilt-to-length (TTL) noise, which is the main source of noise in the detection system after shot noise. According to existing literature, the LISA path finder (LPF) and average phase (AP) signals are two analytical methods used for calculating the coupling of wavefront error and TTL noise 8 . Compared to the LPF signal, the AP signal can reduce the coupling of TTL noise and wavefront error to a greater extent, thereby reducing the requirement for the wavefront error.…”

“…Although, it is difficult to quantitatively analyze the contribution of a single factor to TTL coupling noise, the noise source can be suppressed. Thus far, 8 – 13 Zhao presented a comprehensive theoretical analysis of the influence of telescope aberration on TTL coupling noise, proposed that the coupling coefficient should be suppressed at ±25 pm/μrad, analyzed the contribution of TTL coupling noise of the prototype of the Taiji project telescope principle, and determined whether the final optical path stability has exceeded 3 pm/√Hz 14 …”