Multi-link laser interferometer architecture for a next generation GRACE

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.