near the ground in warm climates generally vary between 10−14and 10−12m−2/3, the latter of which is considered strong turbulence [17].
Contribution of Beam Wander to Pointing Angles and RMS Noise
The variance σB2 of beam wander induced by the turbulence can be evaluated as [17]:
σB2 = 1.44Cn2L3ω−o1/3 (5.3)
Evaluating this with the inferredCn2 under turbulent conditions yields a standard deviation in beam wander of σB = 0.8mm, which over a 40m round trip corresponds to a ∼20µm
angular displacement. This is in good agreement with the standard deviation in the pointing feedback when locked (∼17µrad). To analyse the effect this has on the power we evaluated the overlap integral between the transmitted Gaussian beam with initial waist of 7mm, propagation distance z = 40m, and the fibres mode (Gaussian with waist 9µm) with a 0.8mm offset just after propagating through the collimator (f= 37.1mm). Refer to equations 2.1 and 3.5 for the mathematical expressions used in this analysis. From this we form an estimate that beam wander contributed around 2dB in the rms noise of the received power. This estimation is reasonably close to the measured 3.5dB noise suppression as expected. In light of this, the results fairly convincingly demonstrated that the system stably tracked turbulent induced beam wander in the presence of large (∼20dB), turbulent effects such as scintillation.
5.5
Summary of Results
A transceiver (self-beacon) based dither locked tracking and pointing system was developed and tested in the laboratory over a 40m (roundtrip) link with both direct and heterodyne detection schemes. For each system, locked pointing precisions on the order of µrad were demonstrated. For the direct detection scheme, various noise sources were also introduced along the channel. By inducing large vibrations in the corner cube the system was ac- tively capable of tracking the vibrations thus suppressing the associated jitter noise in the received power. In particular for lower frequencies (<20Hz) suppression of up to 40dB in pointing jitter was achieved. Strong turbulence was also introduced along the channel incurring effects such as scintillation, fluctuations in the angle of arrival, and beam wan- der. In the presence of such noise sources the dither locking system was capable of stably tracking the turbulent induced beam wander, while being insensitive to the other noise sources such as scintillation.
Chapter 6
Mount Stromlo Field Trial -
Demonstrating Stabilised Optical
Frequency Transfer with Dither
Locked Beam Pointing
Figure 6.1: Mount Stromlo field trial of a free space stabalised optical frequency transfer using dither locked beam pointing
This chapter provides an overview of a collaborative project between ANU and Dr Sascha Schediwy and Mr David Gozzard from the University of Western Australia (UWA). The projects aim was to demonstrate a stabilised optical frequency transfer through free space using dither locked beam pointing. This was demonstrated over a two week period at the Mount Stromlo Observatory using Electro Optic Systems (EOS) facilities. Schediwy and Gozzard are both experienced in the field of Metrology and have specialisation in frequency dissemination techniques [49]. Accordingly the design and development of the phase stabilisation system was entirely undertaken by them, and the author takes no credit for it. This chapter will begin however with a brief overview of the phase stabilisation system developed at UWA, and how the dither locked ATP scheme was integrated with it. We will then describe our preparation for the field trial including power budgets and optical designs, and then finally we present a critical review of the field trial and the results.
6.1
Phase Stabilisation Module Overview
The aim of UWAs phase stabilisation module was to test the applicability of a demon- strated method of stabilised frequency dissemination through fibre optic networks in free space. The operating principle of this method is that thermal fluctuations will cause changes in the optical path length of a beam, inducing fluctuations in the phase and therefore frequency of a received signal. The relationship between a phase fluctuation Φ(t) and a frequency fluctuation ∆ω is:
∆ω= 1 2π
d
dtΦ(t) (6.1)
And a change in optical path length ∆L induces a ∆Φ = k∆L shift in phase, where
k is the wave number. Assuming that the changes in path length along the channel are primarily thermal in nature, it is reasonable to assume that these changes will be relatively static over a round trip of the laser beam. Accordingly denote the stabilised (zero noise) path length L such that over a round trip the beams observed optical path length of an unstable link will beL+ ∆L. Under the above assumption that this is static then ∆ω = dtdΦ(t) = 0 and hence by measuring the round trip signal coherently we can detect the phase shift imparted by ∆L and feedback to suppress it.
This encompasses the design of the phase stabilisation module. A stable laser is passed through an AOM which imparts a frequency shiftωA1 = 70M Hz before propagat-
ing along a channel to the receiver site. Here part of the received signal is passed through a second AOM which imparts another frequency shift ωA2 = 50M Hz and then reflected
back via a faraday mirror to the transmitter site such that it double passes the channel and the AOMs. At the receiver site this reflected signal is then detected coherently with the original laser source and the received beatnote can be expressed:
S= sin (2(ωA1+ωA2)t+ 2∆Φ) (6.2)
Mixing with 2(ωA1+ωA2) and low pass filtering we get:
§6.1 Phase Stabilisation Module Overview 47
Linearising (assuming ∆Φ is small) gets us a signal of the phase noise ∆Φ. This is fed back to modulate the phase of the transmitter AOM to effectively cancel the links phase noise. It is worth noting that the remote AOM at the receiver site is used so that the detected heterodyne beatnote corresponds only to signals which have been received and reflected from the receiver site. This makes the applied feedback somewhat immune to parasitic reflections. UWAs module was designed as a transceiver so that both the transmitter and receiver were contained within the module, and it was built to be ruggedised so it was fit for travel. In-order to measure the stability of the transfer the receiver site used heterodyne detection. The stability of the beatnote was then measured using a frequency counter. The module consisted of a 17 rack mount internally holding the laser, all the spliced optics and electronics with output and input ports. Figure 6.2 shows the module layout.
Figure 6.2: UWA phase stabilisation module
Earlier in July Mr Gozzard visited the ANU for two weeks to integrate the module with the dither locked beam pointing system. This was done by taking the beatnote at the transmitter site (used to generate an error signal for the frequency stabilisation) and adding an additionalπ/2 phase shift such that it was in a separate quadrature to the signal used to stabilise the frequency. This was then mixed with the local oscillator and filtered such that when the frequency was stabilised this signal would be locked to a constant. Hence this separate signal was fed into the FPGA to implement the dither lock control under a direct detection scheme. It is worth noting that the dither locking system was not implemented on the signals at the receiver site for a few reasons. First of all during the initial visit of Mr Gozzard the dither locking system had not been developed for coherent detection, and second of all there would have been difficulty in accessing the required signal due to the power requirements of the frequency counter for optimal operation, as well as the inaccessibility of the spliced optics in the module. Figure 6.3 shows schematics of the system. In-terms of the free space optics, fibre capables from UWAs module were ran to the optical breadboard described in chapter 5 which was mounted on the tripod.
UWA phase stabilisation module Dither locked beam pointing integrated with UWA phase stabilisation module
Figure 6.3: [left] Simplified schematic of UWAs frequency stabilisation module [Right] Dither locked beam pointing integrated into frequency stabilisation module.