The analysis of the far-field phase and the tilt-to-length error contribution in space-based laser interferometry

Abstract

The arm length of the space-based interferometer for gravitational wave detection is 108~109 m, 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 /25 wavefront RMS (=1064 nm). 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.

The impact of telescope aberrations on the magnitude of tilt to length coupling noise in space based gravitational wave detectors

“…The optical system design was carried out with the goal of achieving a wavefront error RMS < λ/250 at the telescope exit pupil [19][20][21]. The final design resulted in a wavefront error RMS value of 0.0035λ at the telescope exit pupil, as shown in figure 9 (left), meeting the target requirement.…”

“…Moreover, the Tianqin gravitational wave detector is an aperture conjugate system, effectively suppressing the diffraction effect. Therefore, the flat-top beam received by the receiving end telescope and transmitted through the telescope system to the detector can be represented as a flat-top beam [17][18][19] with wavefront aberration W(ρ,θ), where: (ρ,θ) .…”

“…Li established a sensitivity matrix mapping the telescope manufacturing errors and coupling coefficients based on the error amount and Zernike polynomials first-order sensitivity matrix, and analyzed the impact of telescope manufacturing errors on TTL noise coupling coefficients [18]. Xiao proposed that TTL error can be added as a piston term during pointing, which helps to bring the static point closer to the z-axis and reduce the phase noise detected at the static point [19]. However, published research mainly focuses on simulation analysis of TTL coupling noise on optical platforms and during space transmission.…”

On point-ahead angle control strategies for TianQin

“…Previous studies have revealed that the wavefront of an emitted beam is not ideally spherical but distorted in reality, which leads to additional phase noise at the receiving satellite when combined with pointing jitters of the emitting beam (see, e.g. [17,[21][22][23][24]). Various factors including aberration in the optical system contribute to this phase deviation which is denoted by w e (x, y, z).…”

Effect of the focusing system on measurements in gravitational wave detection telescope

“…The z 0 is the piston term, which is omitted because it does not cause any changes in the TTL-coupling noise. The z 1 = 2ρ cos θ represents the tilt term in the x-direction, and z 2 = 2ρ sin θ represents the tilt term in the y-direction [14]. By combining the tilt terms in equation ( 6), the wavefront aberration at the exit pupil of the telescope for any pointing deviation angle α can be expressed as:…”