Pair-based Analytical model for Segmented Telescopes Imaging from Space for sensitivity analysis

Abstract

The imaging and spectroscopy of habitable worlds will require large-aperture space-based telescopes, to increase the collecting area and the angular resolution. These large telescopes will necessarily use segmented primaries to fit in a rocket. However, these massively segmented mirrors make high-contrast performance very difficult to achieve and stabilize, compared to more common monolithic primaries. Despite space telescopes operating in a friendlier environment than ground-based telescopes, remaining vibrations and resonant modes on the segments can still deteriorate the performance.In this context, we present the Pair-based Analytical model for Segmented Telescopes Imaging from Space (PASTIS) that enables the establishment of a comprehensive error budget, both in term of segment alignment and stability. Using this model, one may evaluate the influence of the segment cophasing and surface quality evolution on the final images and contrasts, and set up requirements for any given mission. One can also identify the dominant modes of a given geometry for a given coronagraphic instrument and design the feedback control systems accordingly.In this paper, we first develop and validate this analytical model by comparing its outputs to the images and contrasts predicted by an end-to-end simulation. We show that the contrasts predicted using PASTIS are accurate enough compared to the end-to-end propagation results, at the exo-Earth detection level. Second, we develop a method for a fast and efficient error budget in term of segment manufacturing and alignment that takes into account the disparities of the segment effects on the final performance. This technique is then applied on a specific aperture to provide static and quasi-static requirements on each segment for local piston and 45 • -astigmatism aberrations. Finally we discuss potential application of this new technique to future missions.

Wavefront error tolerancing for direct imaging of exo-Earths with a large segmented telescope in space

“…and then to their arbitrary combinations. The feasibility of this has already been shown in the analytical approach 8 and should hence be regarded as a mere functional addition. Further contribution to the understanding of segment-level cophasing errors and stability will be provided through the analysis of scaling laws that will address the sensitivity to system parameters like segment number, size and shape, their relative size with respect to the total telescope pupil, geometrical arrangement, or different coronagraph types.…”

“…Following the derivation in the original paper, it appears that Eq. 3 can be expressed as a sum of interference patterns between all segment pairs, weighed by an envelope given by the Fourier transform of the Zernike polynomial being studied (segment piston here) [8,:…”

Analytical decomposition of Zernike and hexagonal modes over a hexagonal segmented optical aperture

“…The analytical method presented in this paper has many potential applications in particular in astronomical instrumentation with highly segmented telescopes (ELTs). For instance, our method could be used both as a complement and an extension of the work presented in [26]. In this study, an analytical error budget is proposed to infer the impact of the cophasing misalignment on the coronagraphic performances.…”

“…In this study, an analytical error budget is proposed to infer the impact of the cophasing misalignment on the coronagraphic performances. The analytical model proposed in [26] offers the advantage of being low time consuming by avoiding long Monte-Carlo simulation. Complementing this analytical study by our analytical method for the Zernike decomposition is thus a must.…”

“…It can be used to perform a modal control of an adaptive optic system or to allow high-performance open-loop correction of optical aberrations in a segmented pupil environment. A recent study presented in [26] proposes to analyze the performance of a coronagraphic system under the presence of local piston and tip-tilt on each of the segments. Including in this formalism an analytical formulation of global orthonormal modes over a segmented pupil would allow a more precise description of the effects at stake in this process.…”