Multi-link laser interferometer architecture for a next generation GRACE
Date
2017
Authors
Francis, Samuel Peter
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Abstract
When GRACE Follow-On (GRACE-FO) launches, it will be the first
time a laser interferometer has been used to measure displacement
between spacecraft. In the future, interspacecraft laser
interferometry will be used in LISA, a space-based gravitational
wave detector, that requires the change in separation between
three spacecraft to be measured with a resolution of 1 pm/rtHz.
The sensitivity of an interspacecraft interferometer is
potentially limited by spacecraft degrees-of-freedom, such as
rotation, coupling into the
interspacecraft displacement measurement. GRACE-FO and LISA
therefore have strict requirements placed on the positioning and
alignment of the interferometers during spacecraft integration.
Decades of work has gone into adapting traditionally lab-based
techniques for these space applications. As an example, GRACE-FO
stops rotation of the two spacecraft from coupling into
displacement using the triple mirror assembly. The triple mirror
assembly is a precision optic, comprised of three mirrors, that
function as a retroreflector. Provided the triple mirror assembly
vertex coincides with the spacecraft centre of mass, any
spacecraft rotation will asymmetrically lengthen and shorten the
optical pathlengths of the incoming and outgoing beams, ensuring
that the round trip pathlength between the spacecraft is
unaffected. To achieve the required displacement sensitivity, the
triple mirror assembly vertex must be positioned within 0.5 mm of
the spacecraft centre of mass, making spacecraft integration
challenging.
In this thesis a new, all-fibre interferometer architecture is
presented that aims to simplify the positioning and alignment of
space-based interferometers. Using multiple interspacecraft link
measurements and high-speed signal processing the interspacecraft
displacement is synthesised in post-processing. The multi-link
interferometry concept is similar to the triple mirror assembly's
symmetric suppression of rotation, however, since the
rotation-to-pathlength cancellation is performed in
post-processing, the weighting of each interspacecraft link
measurement can be optimised to completely cancel any rotation
coupled error. Consequently, any uncertainty in the positioning
of the multi-link interferometer during spacecraft integration
can be corrected for in post-processing. The strict hardware
integration requirements of current interferometers can therefore
be relaxed, enabling a new class of simpler, cheaper missions.
The multi-link concept is evaluated as a potential interferometer
architecture for a next generation GRACE mission. The multi-link
GRACE concept uses several fibre coupled optical heads on each
spacecraft to form multiple interspacecraft links between
spacecraft. To cancel rotation coupled error from rotation of
both spacecraft, 9 interspacecraft links are formed between 3
optical heads positioned on each spacecraft. Displacement is
measured in both directions along each link using digitally
implemented phasemeters. The 18
interspacecraft displacement measurements are then combined using
artificial delays and different weights to cancel laser frequency
equivalent displacement noise, fibre pathlength fluctuations and
rotation coupled displacement error.
The interferometer uses digitally enhanced heterodyne
interferometry to multiplex the
multiple link beatnotes; Time delay interferometry is used to
suppress the laser frequency
displacement noise and fibre fluctuations; and, to simplify the
acquisition of the multiple interspacecraft links, the beam
divergence out of each optical head is made sufficiently large so
that links can be acquired without requiring a dedicated link
acquisition strategy. Although this design simplifies the
spacecraft integration and alignment it comes with some
challenges: without an active link acquisition, the received
power on the distant spacecraft could be considerably lower than
in GRACE-FO; time delay interferometry has not been tested on a
GRACE-like interferometer; and the cancellation of
rotation-to-pathlength coupled error using a weighted average of
multiple link measurements has not been demonstrated. Three
experiments are presented in this thesis, addressing these
challenges.
In both GRACE-FO and LISA, phasemeters are used to track the
phase of the lasers transmitted along each interspacecraft link.
Tracking the phase of optical signals with low signal-to-noise
ratios (SNR) is difficult because the higher, relative noise can
lead to nonlinear behaviour in the phasemeter. In the first
experiment presented in this thesis, the dominant noise sources
-- laser frequency noise and shot noise -- that limit the
phasemeter's ability to track low SNR signals are analysed. By
optimising the phasemeter bandwidth to
minimise the error from these two noise sources, the probability
of nonlinear phasemeter behaviour is also minimised. A benchtop
demonstration was performed to verify the analysis, with the
bandwidth optimisation used to track a 30 fW free-running signal
- the lowest power signal that has been tracked to date. The
analysis indicates that subfemtowatt signals could be tracked if
the laser frequency is pre-stabilised.
The second experiment describes the development of a time delay
interferometry combination for a GRACE-like interferometer that
recovers the displacement sensitivity of the phase locked
GRACE-FO interferometer. The combination could be used to test
time delay interferometry on GRACE-FO as part of the LISA
Experience On Grace OpticalPayload (LEGOP) project. It also
demonstrates time delay interferometry could be used on a
GRACE-like interferometer for laser frequency displacement noise
suppression. The proposed test uses a tone assisted time delay
interferometric ranging (TDIR) algorithm to determine the delays
required to suppress the displacement noise due to one laser in
the displacement measurement between the GRACE spacecraft. Under
simulated GRACEFO
conditions, the tone assisted TDIR algorithm was used to suppress
the laser frequency equivalent displacement noise by 8 orders of
magnitude. This was below the residual laser frequency
displacement noise requirement on GRACE-FO of 20 nm/rtHz. An
experimental test of the algorithm demonstrated the capabilities
of the proposed algorithm in the presence of large path length
fluctuations, a macroscopic optical delay and different
electronic delays.
The third experiment tested the multi-link GRACE architecture. In
the benchtop experiment a local spacecraft with 3 optical heads
was modeled. Pitch and yaw of the local spacecraft were emulated
using the tip and tilt actuators on a piezo-electric steering
mirror. The displacement was measured along 3 links formed
between the local optical heads and a single distant spacecraft
optical head. Using a weighted average of the 3 link
measurements, rotation-to-pathlength coupled error from the
simulated pitch and yaw of the local spacecraft were suppressed
by up to 18 dB. In addition to spacecraft rotation, tones were
injected to model laser frequency noise, fibre uctuations and an
`interspacecraft'displacement signal. The laser noise, fibre
noise and rotation-to-pathlength noise were all suppressed down
to the 1 nm/rtHz measurement noise floor without affecting the
measurement of the `interspacecraft' displacement signal.
The results of the three experiments, along with a prediction of
the displacement sensitivity in a multi-link GRACE, verify the
feasibility of the multi-link architecture. More testing and
development is needed however before a multi-link GRACE can be
realised, with a number of these tests outlined in the
discussion.
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Keywords
Laser, Interferometry, Metrology, Gravity, Digital Signal Processing, Space
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