Coupling of wavefront errors and jitter in the LISA interferometer: far-field propagation

Abstract

The Laser Interferometer Space Antenna (LISA) is a gravitational wave detector, which aims to detect 10−20 strains in the frequency range from 0.1 mHz to 0.1 Hz. It is a constellation of three spacecrafts, an equilateral triangle with side length of m, where interferometry monitors the spacecraft distances. Aberrations and jitter of the wavefront sent by a spacecraft to the next combine to cause a measurement noise. The paper investigates analytically this coupling, including beam clipping and far-field propagation, and develops criteria for the assessment of the wavefront quality. It also gives the results of Monte Carlo simulations of the measurement noise for arbitrary wavefront aberrations and jitters.

Coupling of wavefront errors and pointing jitter in the LISA interferometer: misalignment of the interfering wavefronts

“…However, owing to the large dispersion, a wavefront quality at least equal to λ/20 might be necessary. These results extend and complement our investigation of how the measured spacecraft distance is coupled to the transmitter jitter [6] and open the way to a full start-to-end analysis of the phase noise.…”

“…Aberrations and jitter of the wavefront sent by a spacecraft to the next cause a measurement noise. In a previous paper, we investigated the propagation of the wavefront aberrations and the noise of the measured distance originated by the coupling of the aberrations with the transmitter jitter [6]. We found that the sensitivity to the jitter increases from 0.02 pm/nrad to 0.28 pm/nrad when the optical quality of the transmitted wavefront decreases from λ/40 to λ/10.…”

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

“…We can also compare our order of magnitude calculations with the estimates given by Sasso et al [7]. Their estimate, given by their table 3, is δL=0.07 pm/nrad for an amplitude of Zernike of λ/20.…”

“…Consequently, wavefront error, as discussed in this article, contributes only to a part of the total tilt-to-length coupling for LISA. The subject of wavefront errors and beam jitter in the LISA optical system has, of course, been the subject of other studies [7,9]. For many years this has been recognized as an important problem for LISA [10].…”

“…If we look at our equation (22), and ignoring the spectral densities, with σ/λ ∼ 1/20, one has δL ∼ 65 pm for θ 1 =10 nrad, or 6.5 pm/nrad, which is two orders of magnitude higher. Also, we have used 700 nrad for the static mispointing where a value of 10 nrad is used in [7]. However we must keep in mind that we have cumulated all aberrations in a worst case scenario, whereas their approach is based on Monte-Carlo methods, in which some defects can randomly cancel others.…”