In a multi-link GRACE, beam divergence over the 200 km spacecraft separation will cause the light arriving from the distant spacecraft to have a beam width on the order of 100 m. The optical heads can therefore be positioned on the vertices of the spacecraft, with separations around 1 m, and still receive light. Increasing the separation increases the sensitivity to rotation, providing a stronger calibration signal when determining the spacecraft weights that minimise rotational coupling.
In contrast, modelling spacecraft separations in a benchtop experiment larger than a few metres is difficult. Consequently the optical head separation in the benchtop experiment needs to be sufficiently small such that the optical heads collectively cover an area smaller than the beam width of the distant source.
To replicate the function of the optical head in the proof of principle experiment, two options were considered:
• Use collimators that are compact and can be positioned close together
• Approximate the optical head using conventional optics
At first, Graded Index (GRIN) lenses were used to construct compact collimators that could then be bundled close together. Figure 6.2 (a) shows a schematic explaining the
Chapter 6 Cancelling rotation coupled noise with multi-link interferometry
alignment sleeve fibre ferrule GRIN lens
Ø1.8 mm
(a) GRIN lens construction
(b) Single GRIN lens optical head
(c) GRIN lens optical head array
Figure 6.2: Early GRIN lens based optical head prototype
construction of a single GRIN optical head. In (b) a single GRIN optical head is shown and in (c) a GRIN lens optical head array that was used in initial investigations of the rotation-to-pathlength coupling is shown. The 1-inch aluminum plate houses 4 GRIN lens optical heads. The GRIN optical heads were constructed using a Thorlabs 0.23 pitch GRIN lens (GRIN2310A), a pigtailed ferrule (SMPF0110-APC) and a GRIN lens/ferrule alignment sleeve. An 8◦angled interface between the ferrule and lens was used to minimise back reflections with the reference reflection coming from the output face of the GRIN lens. The optical heads were assembled with a UV curing glue with a refractive index matched to the ferrule.
The GRIN lens optical heads had a diameter of 1.8 mm but were housed in brass sleeves with diameters of 5 mm to protect the lens assemblies and provide strain relief to the fibres. The optical heads at the vertices of the triangular array were then separated by 12 mm with the 4th optical head at the centre of the array used as a truth measurement. The goal of the experiment was to demonstrate that the truth measurement could be reconstructed by a weighted average of the three outer head measurements.
The 12 mm separation between optical heads in the GRIN lens optical head assembly proved to be too large for the beam sizes that could be achieved in the lab, so alternatives had to be considered. For simplicity it was decided that an optical head did not need to be built1 instead opting to use a number of conventional optics - fibre collimators, beam splitters and a reference flat - to simulate the function of the optical head. The optical head concept is compared with the approximate optical head in Figure 6.3.
As Figure 6.3 demonstrates, given the optical heads are essentially fibre collimators with a common reference plane, their function can be easily emulated using free-space optics. In Figure 6.3(a) an ideal optical head assembly with three optical heads is shown. The output of the optical head is partially reflective allowing some of the light along each link to be reflected at the output providing the local fibre reference measurement.
6.1 Designing a multi-link proof of principle experiment link B link A link C refe re n ce optical heads B C A
(a) Ideal optical head
50:50 reference flat (30:70) link B link C 50:50 link A re fe re n ce output collimators collimator B C A reference flat 50:50
(b)Experimental optical head approximation
Figure 6.3: The 3 element optical head in (a) remaps three fibre inputs into a triangle configura- tion. The output of the optical head is made partially reflective to produce reflections at the output of each fibre for the local oscillator. The optical head used in the proof of principle experiment, shown in (b), was modeled in free-space using a combination of fibre collimators, beam splitters and a reference flat. The shaded region shows the optics that replace the single optical head device in (a).
Figure 6.3(b) shows that the optical head in (a) can be replicated using 3 collimators and 4 beamsplitters. Two of the beamsplitters are used to steer the collimated beams so that they are parallel at the output reference and confined within a small area. A third beamsplitter is used to balance the power in the links. The fourth is an in-line beamsplitter with a reflectivity of 30% that is used as the reference. The light along each link reflects off the reference, providing a local oscillator for the heterodyne detection. The noise in the air along each link is equivalent to the fibre noise that would occur along each fibre link. This is partially canceled in the heterodyne detection and fully canceled in the round-trip combination. The pathlengths along each link between the collimator and reference flat are macroscopically matched so that the links will have equal delays in the DEHI multiplexing.
The optics used to approximate the optical head are shown in Figure 6.4. The ‘optical head’ collimators A, B and C were aligned to the reference flat, maximising the coupling of the reflected light along link into the 3 fibres. The actuators on the collimator and beam splitter mounts were used to steer the beams so that they approximated a triangular optical head at the reference flat.
The disadvantage of approximating the optical head with conventional optics is the extra loss due to the beamsplitters. On a single pass, only 25% of the light from each collimator reaches the output. The light reflected from the reference flat that couples back into the fibre is only 1.875% of the emitted light (not including coupling losses back into the fibre). Although only 2 beamsplitters are needed to align the 3 optical head beams, a third beamsplitter is shown in Figure 6.4. This was needed to balance the local oscillator power in each link.
Chapter 6 Cancelling rotation coupled noise with multi-link interferometry
Figure 6.4: Optical head approximation. The three collimators A, B, and C are combined using
two beam splitters to approximate a triangular optical head array at the reference flat. The
reflected light from the reference flat is used as the local oscillator in each link allowing the free- space optical paths between the collimators and reference flat to be removed from the displacement measurement in post-processing in the same manner as the fibre pathlength fluctuations.