Numerical solutions for phase noise due to pointing jitter with the LISA telescope

Accurate simulation of the propagation of light between the spacecraft of the laser interferometer space antenna (LISA) gravitational wave observatory will be a vital tool in determining the optical design of the telescopes used in the constellation. In this work, we examine the methods available for numerical simulation of this propagation, and consider the effect of an aberrated transmitting telescope (Tx) on the light collected by the receiving telescope (Rx). Propagation software has been developed using direct numerical integration methods, and has been validated by comparison to analytical solutions for particular cases. Zernike modal aberrations up to and including primary spherical have been considered in the Tx, and, in particular, the effects of defocus, astigmatism and coma were examined. It was found that minimization of the even radial order aberrations in Tx resulted in a reduced wavefront error at Rx, while odd aberrations such as coma can displace the maximum irradiance away from the optical axis. Thus careful consideration of the impact of telescope aberrations will be required to minimise detrimental effects on the detection of gravitational waves.

Section: Validation Of the Propagation Codementioning

confidence: 99%

“…A limitation of these methods is that, for higher order aberrations, the equations become unmanageable [8]. The method presented in this work therefore takes a numerical approach, validated extensively by comparison to known analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Beam propagation simulations for LISA in the presence of telescope aberrations

Kenny

Devaney

2020

“…In 2019, Vinet's research showed that the coupling of wavefront errors and pointing jitter noise can only be reduced through special processing of the telescope's optical system, indicating that achieving RMS wavefront distortion less than λ/500, which is currently beyond the capabilities of state-of-the-art technologies [2]. In recent years, researchers from various countries have conducted theoretical simulations on wavefront errors and pointing jitter noise in different gravitational wave detection backgrounds [6][7][8], and the research results generally impose stringent requirements on the wavefront imaging quality of telescopes.…”

Section: Introductionmentioning

confidence: 99%

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

Fan,

Fang,

Hai

et al. 2023

Telescopes primarily transmit and receive laser beams over long distances as part of a gravitational wave interferometric measurement system. Due to factors such as optical design, fabrication, and alignment, the wavefront at the exit pupil of the telescope inevitably experiences distortion, resulting in wavefront aberrations that couple with pointing jitter to generate tilt-to-length (TTL) coupling noise. During the process of gravitational wave detection, the large distance between the primary and secondary mirrors and temperature fluctuations in space can cause significant axial misalignment between them. This results in a substantial displacement of the primary-secondary mirror system’s primary focus along the axial direction, further degrading the wavefront at the exit pupil of the telescope. The TTL coupling noise caused in this scenario will affect the detection of gravitational waves, thus requiring the adjustment of the position of the three-four mirror system through the focusing system to minimize TTL coupling noise. In this paper, the model for TTL coupling noise was established using the first 36 orders of Zernike polynomials. The misalignment model of the primary-secondary mirror system was derived using geometric optics theory. The study investigates the influence of the telescope focusing system before and after focusing on the wavefront aberrations and TTL coupling noise at the exit pupil of the telescope. The analysis indicates that with a misalignment of 7.56 μm in the axial distance between the primary and secondary mirrors, the addition of a focusing system reduces the wavefront error at the exit pupil of the telescope from 0.0328 λ to 0.0046 λ. Furthermore, the maximum coupling noise between wavefront distortion and pointing jitter is reduced from 4 pm Hz−1/2 to 0.4 pm Hz−1/2. This provides valuable insights for the design of gravitational wave detection telescopes and the study of focusing systems.

“…Recently, Sasso et al extended this analysis by considering Gaussian profile, transmitting beam clipping and more terms of Zernike polynomials [10]. Vinet et al carried out theoretical and numerical analysis of a far field optical model and proposed a requirement on the wavefront distortion of the telescope optics for LISA [11,12]. Kenny analyzed the wavefront distortion composed of the first 11 terms of Zernike polynomials, and obtained that only those terms with even noll index are relevant to the measured phase error coupling to the beam alignment [13].…”

Section: Introductionmentioning

confidence: 99%

Analysis on the coupling effect of wavefront distortion and pointing misalignment in space laser interferometry

Min¹,

Jiang²,

Zhang³

et al. 2021

Space-based gravitational wave detection aims to measure gravitational waves with strains of down to 10−20 in 10−4 Hz ∼ 1 Hz frequency band. In order to achieve this measurement sensitivity, inter-satellite laser interferometry with picometer precision for an armlength of 108 ∼ 109 m is required. However, the coupling of the transmitting-beam misalignment and the wavefront distortion results in a non-negligible measurement error of intersatellite laser interferometry. Considering a wavefront distortion model composed of the first 55 terms of Zernike polynomials, we analyze the coupling effect of beam misalignment and wavefront distortion in both analytical and numerical methods. Calculation results show that the position of the stationary point is mainly determined by defocus, astigmatism and coma of the wavefront distortion of the transmitting beam. Moreover, a large defocus and small coma are preferred to achieve a better alignment of the stationary pointing direction with the inter-satellite line-of-sight, such that the coupling noise and received laser power can be optimized.