Atmospheric turbulence can cause a significant performance degradation in free-space optical communication systems. It is well known that the effect of turbulence can be reduced by performing aperture averaging and/or employing spatial diversity at the receiver. In this paper, we provide a synthesis on the effectiveness of these techniques under different atmospheric turbulence conditions from a telecommunication point of view. In particular, we quantify the performance improvement in terms of average bit error rate (BER) and outage capacity, which are among important parameters in practice. The efficiency of channel coding and the feasibility of exploiting time diversity in aperture averaging receivers are discussed as well. We also compare single- and multiple-aperture systems from the point of view of fading reduction by considering uncorrelated fading on adjacent apertures for the latter case. We show that when the receiver is background noise limited, the use of multiple apertures is largely preferred to a single large aperture under strong turbulence conditions. A single aperture is likely to be preferred under moderate turbulence conditions, however. When the receiver is thermal noise limited, even under strong turbulence conditions, the use of multiple apertures is interesting only when working at a very low BER. We also provide discussions on several practical issues related to system implementation.

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Fading Reduction by Aperture Averaging and Spatial Diversity in Optical Wireless Systems

In the area of long-baseline nulling interferometry, high rejection ratios are needed to cancel out the light of a bright central source and look for nearby faint structures or companions. These rejection requirements directly translate into drastic optical constraints. We discuss the possibility of using single-mode waveguides for such applications. Conversely to simple pinholes, single-mode waveguides efficiently correct wave-front defects of both high- and low-order spatial frequencies, ensure a perfect matching of the amplitude profiles coming from the various beams, and can be used with almost optimum coupling efficiency over a broad optical bandpass (typically an octave). They then appear to greatly enhance the feasibility of high-dynamic interferometric coronagraphs.

Use of single-mode waveguides to correct the optical defects of a nulling interferometer.

We describe an adaptive optical fiber coupling system for free- space optical communication comprising a micro-electromechanical deformable mirror and a VLSI gradient descent controller for model-free performance optimization. A comparison of Strehl ratio maximization with direct model-free coupling efficiency optimization revealed an advantage of the latter method.

Fiber coupling with adaptive optics for free-space optical communication

Bidirectional ground-satellite laser links suffer from turbulence-induced scintillation and phase distortion. We study the impact of turbulence on coherent detection and the related phase noise that restricts time and frequency transfer precision. We evaluate the capacity to obtain a two-way cancellation of atmospheric effects despite the asymmetry between up- and downlink that limits the link reciprocity. For ground-satellite links, the asymmetry is induced by point-ahead angle and possibly the use, for the ground terminal, of different transceiver diameters, in reception and emission. The quantitative analysis is obtained thanks to refined end-to-end simulations under realistic turbulence and wind conditions as well as satellite kinematics. These temporally resolved simulations allow characterizing the coherent detection in terms of time series of heterodyne efficiency and phase noise for different system parameters. We show that tip-tilt correction on ground is mandatory at reception for the downlink and as a pre-compensation of the uplink. Besides, thanks to the large tilt angular correlation, the correction is shown to be efficient on uplink despite the point-ahead angle. Very good two-way compensation of turbulent effects is obtained even with the asymmetries. The two-way differential phase noise is reduced to $1{\mathrm{rad}}^{2}$, with the best fractional frequency stability below $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ after 1-s averaging time.

Impact of turbulence on high-precision ground-satellite frequency transfer with two-way coherent optical links

Context. Earth-sized planets around nearby stars are being detected for the first time by ground-based radial velocity and space-based transit surveys. This milestone is opening the path toward the definition of instruments able to directly detect the light from these planets, with the identification of bio-signatures as one of the main objectives. In that respect, both the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA) have identified nulling interferometry as one of the most promising techniques. The ability to study distant planets will however depend on the amount of exozodiacal dust in the habitable zone of the target stars. Aims. We assess the impact of exozodiacal clouds on the performance of an infrared nulling interferometer in the Emma X-array configuration. The first part of the study is dedicated to the effect of the disc brightness on the number of targets that can be surveyed and studied by spectroscopy during the mission lifetime. In the second part, we address the impact of asymmetric structures in the discs such as clumps and offset which can potentially mimic the planetary signal. Methods. We use the DarwinSIM software which was designed and validated to study the performance of space-based nulling interferometers. The software has been adapted to handle images of exozodiacal discs and to compute the corresponding demodulated signal. Results. For the nominal mission architecture with 2-m aperture telescopes, centrally symmetric exozodiacal dust discs about 100 times denser than the solar zodiacal cloud can be tolerated in order to survey at least 150 targets during the mission lifetime. Considering modeled resonant structures created by an Earth-like planet orbiting at 1 AU around a Sun-like star, we show that this tolerable dust density goes down to about 15 times the solar zodiacal density for face-on systems and decreases with the disc inclination. Conclusions. Whereas the disc brightness only affects the integration time, the presence of clumps or offset is more problematic and can hamper the planet detection. Based on the worst-case scenario for debris disc structures, the upper limit on the tolerable exozodiacal dust density is approximately 15 times the density of the solar zodiacal cloud. This gives the typical sensitivity that we will need to reach on exozodiacal discs in order to prepare the scientific programme of future Earth-like planet characterisation missions.

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Nulling interferometry: impact of exozodiacal clouds on the performance of future life-finding space missions

The coupling between a turbulence-distorted optical beam and a single-mode waveguide is addressed. The coupling efficiency and the coupled phase are derived, both without aberrations and with small aberrations. These analytical expressions are validated by numerical simulations. Correction with adaptive optics is investigated. In the general case, the Strehl ratio is a pessimistic estimator, and the coupled phase is different and has a smaller variance than the classical phase averaged over the pupil. Application fields are heterodyne detection and stellar interferometry, for which spatial and modal filtering are distinguished.

Cyril Ruilier

Papers

Coupling of large telescopes and single-mode waveguides: application to stellar interferometry