LISA telescope: phase noise due to pointing jitter

Abstract

In a space based gravitational wave antenna like LISA, involving long light paths linking distant emitter/receiver spacecrafts, signal detection amounts to measuring the light-distance variations through a phase change at the receiver. This is why spurious phase fluctuations due to various mechanical/thermal effects must be carefully studied. We consider here a possible pointing jitter in the light beam sent from the emitter. We show how the resulting phase noise depends on the quality of the wavefront due to the incident beam impinging on the telescope and due to the imperfections of the telescope itself. Namely, we numerically assess the crossed influence of various defects (aberrations and astigmatisms), inherent to a real telescope with pointing fluctuations.

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

“…Unfortunately, the mirrors building the telescope are not perfect and distortions of the phase surface, called aberrations, exist. It has been shown [4] that those defects, coupled with mispointing and fluctuations (jitter) can cause a phase noise at reception. It is essential to assess this noise and compare it to the sensitivity level required by LISA.…”

“…Δ is the disk of radius a in the plane z=0. We now consider, as we did in our preceding paper [4], that the beam is emitted with a mispointing error that contains both a static value defined by the angles (θ 0 , ψ 0 ), and a dynamic jitter defined by angles (θ 1 (t), ψ 1 (t)). This gives an additional phase factor in equation (2): with dy y y º -0 1 .…”

“…The parameter w (the telescope's aperture a being fixed) has an optimum value resulting from a compromise between diffraction losses (too small w) and clipping losses (too large w). The optimum value (see [4]) is a/w=1.12. However clipping losses result in scattered light issues which are attenuated by taking a slightly suboptimal value a/w=1.5.…”

“…Among all possible spurious effects able to perturb the measurement, there is thus a possible misalignment of the emitted beam due to any permanent (mechanical) or transient (intrinsic laser jitter) mispointing. We have addressed the question in a recent paper [4], where we used an analytical approach. We have shown that spurious effects are due to the conjunction of three elements:…”

“…A conclusion is given in section 4. Section 5 is an Annex that provides a comparison with the results presented in our previous publication [4].…”