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The active tracking system described above was designed to compensate slow beam wander and beam drifts that would have led to a loss of the optical link. Of course, the transmitted quantum signal could be used much more efficiently with a narrower beam, using fast beam-steering and higher-order wave front precompensation techniques in an adaptive transmitter configuration. Possible realisations, and the potential of such methods shall be briefly investigated in this section.

The conventional adaptive optics approach for atmospheric compensation is based on wave front sensing and reconstruction. When applied to free-space laser communica- tions, a part of the received beam (or, alternatively, a beacon beam) is directed to a wave front sensor, for instance a Shack-Hartmann sensor, or a Shearing interferometer. The wave front is reconstructed from the measured data and used to calculate the con- trol signals for the actuators of the wave front corrector, usually a deformable mirror of some kind. This scheme has been successfully implemented in a number of mostly astronomical systems [148, 149] before its potential for horizontal path optical commu- nications was investigated. In [150], Levine et al. calculated the power spectral density for various Zernike polynomial modes2 _{[151] to determine the degree of the expected}

corrections that can be accomplished by means of modal correction. There is, however,

2_{Virtually any realistic wave front Φ(r, θ) can be decomposed into a 2-dimensional Fourier series of}

Zernike polynomials. Low order Zernike modes correspond to piston, tilt, focus, astigmatism, coma errors, and so on.

Figure 4.9: Example of the OGS tracking software output. Top left: Image acquired by the Coud´e camera during twilight. Next to the bright spot of the beacon laser the silhouette of the NOT dome is visible; the dark ring around the centre is the iris in the plane of the Coud´e focus. Bottum left: deviation of the beacon from its target position. Right top and bottum: calculated corrections of telescope coordinates.

a fundamental difference to astronomical systems, where the turbulence-induced wave front perturbations occur near the receiver telescope, and where intensity fluctuations are relatively weak: In laser communication applications, the beam-affecting turbulence is distributed along the entire propagation path [150, 152]. In this case, both phase and amplitude of the propagating wave get corrupted, requiring, strictly speaking, a com- pensation of phase as well as amplitude. Although phase-only correction of the wave front is theoretically sufficient only for a propagation distance in the near field, it has nevertheless been demonstrated to provide significant improvement in the transmitted beam quality for large distance optical communications [150]. Applied to the central figure of merit in laser communications, it was found that the bit-error rate can be im- proved by more than an order of magnitude even with lower-order compensation up to 40 Zernike modes [153, 154].

More recently, adaptive optical systems with more than one phase correction device have been proposed, that can compensate for both amplitude and phase abberations that result from propagation through a turbulent medium [155–157]. This class of multicon- jugate adaptive optical (MCAO) systems is distinct from an earlier approach to MCAO

4.4 Adaptive optics

systems, which aimed at increasing the compensated field of view beyond the isoplanatic angle, using multiple wave-front sensing beacons and a tomographic approach based on the geometrical optics approximation.

Yet, with scintillation conditions becoming stronger, experiments showed a significant degradation in the correction achievable by conventional phase-conjugate adaptive optics systems [152]. The primary identified reason for this is that strong intensity fluctuations make wave front reconstruction in practice very difficult in zones with almost no intensity. In mathematical terms, strong scintillation leads to the occurrence of a large number of branch points in the phase of the optical field, that cause the phase reconstruction algorithm to produce results that do not adequately match the actual phase [158].

In strong scintillation conditions, it is desireable to avoid wave front measurements completely. As an alternative approach, it can be attempted to control the wave front corrector by ”blind“ (model-free) optimisation of a system performance figure of merit, called metric, or cost function. The general idea is to minimise or maximise the cost function by making small adjustments to the phase correction devices, measuring the effect on the cost function to calculate a derivative, and then following the gradient that will minimise or maximise the cost function. A common choice for the metric is the

Strehl ratio, which denotes the ratio of the peak intensity in the far field spot to the peak intensity of the spot formed by an equivalent, diffraction limited, aberration free system. One difficulty with the model-free optimisation technique is its iterative nature to find the optimum control signal, which imposes speed requirements both on the com- putational speed of the control algorithm and on the control bandwidth of the phase actuator. On the other hand, a useful performance metric, like the received power level, or the coupling efficiency into an optical fibre, may readily be available in typical laser communications systems. With a microelectromechanical deformable mirror (MEMS), and a highly integrated microcontroller system implementing a stochastic parallel gra- dient descent algorithm, speeds up to 11.000 iterations/s have been achieved [159, 160], which seems sufficient for real-time compensation of atmospheric turbulence.

The subject of maximising the useful transmitted power in a two-telescope system was more generally addressed in a paper by Barchers and Fried [161]. They found that if one uses an adaptive optical system in each telescope, and simply uses the received beam as the wave front sensing beacon, a natural convergent iteration occurs, leading to maximum transmission of power through a turbulent medium. Any combination of means of controlling adaptive optical systems in each telescope will solve the optimal power transmission problem. Simulations indicate that for a uniform distribution of the strength of turbulence, 95% transmission of laser power is attained when both telescopes can achieve full-wave compensation, provided that the aperture diameter D of the two telescopes is greater than twice the Fresnel length √λL.

In conclusion of this short overview, the use of higher-order adaptive optics could help achieve higher link efficiency in the future, even with smaller optics. This is, of course, highly attractive for any free space quantum key distribution system, and in particular for satellite-based QKD.

The experimental setup of a QKD experiment is naturally divided into three building blocks, namely the transmitter (Alice), the quantum channel, and the receiver (Bob). While the linking quantum channel has been characterised in the preceding chapter, this chapter describes the individual parts of the experimental setup in detail. Alice’s signal states were generated as laser diode pulses, which were strongly attenuated to an average photon number below one photon per pulse. The transmitter setup utilised a separate diode for each linear polarisation, taking advantage of the high intrinsic polarisation of the diodes. The beams were overlapped and routed to the transmitter telescope via a single-mode fibre. At the receiver end, a large diameter receiving telescope was employed to collect as many photons of the turbulence-spread beam as possible. The collected light was directed to the receiver module, where the signal pulses were detected and their polarisation was analysed. This measurement was performed with the help of polarisation optics and a set of four Silicon avalanche photodiodes for single photon detection. The exact arrival time of each pulse is recorded to allow for properly assigning the detected events to the sent signals.

5.1 The transmitter

The transmitter setup consists of the transmitter module, which generates the signal pulses, and thetransmitter telescope to collimate and direct the light over the free-space optical channel to the receiver. Two different versions of the transmitter module were used during the experiments: The initial version had 4 laser diodes, and decoy pulses were created by switching on two laser diodes simultaneously. The second generation of the transmitter module was extended to 8 laser diodes to provide separate sets of laser diodes for signal pulses and brighter decoy pulses. The two versions of the transmitter module are presented and characterised separately in §5.1.2; the transmitter telescope is described in§5.1.4.