3.4.1 Movable optical sub-assemblies
We show in fig.3.5an overview of the LISA payload. Each satellite carries two MOSAs, which are mounted with a roughly 60◦ angle, each pointing towards one of the other two spacecraft (bottom of fig.3.5). This angle is adjustable by about 2◦ to allow compensations for deviations from a perfect triangular constellation due to orbital mechanics [10].
Each MOSA is a rigid structure connecting the optical bench (OB) with a telescope and a gravitational reference sensor (GRS) (top-left of fig.3.5). The telescope (left) is used for light transmission and reception towards the distant spacecraft, while the GRS (right) houses the test-mass. The OB is mounted in-between telescope and GRS, and carries the optical components needed for interferometry.
3.4.2 Gravitational reference sensors
We described in section2.2that a GW creates a periodic modulation of the light travel time between two test masses. This result is only valid under the condition that the test-masses are actually free-falling, i.e., that no non-gravitational forces are acting on them.
Although the spacecraft themselves are on nominally free-falling orbits around the sun, they are in reality un-shielded from the influence of, e.g., solar winds and micro-meteorites. As has been confirmed by LISA-Pathfinder, these effects create jitters of the spacecraft position at a level which would spoil our GW measurements [12].
3.4 payload overview 31
Figure 3.6:Sketch of the LISA optical layout, from [55].
Each optical bench carries three inter-ferometers, allow-ing a readout of the inter-spacecraft and spacecraft-testmass seperation, as well as a reference measure-ment between the two lasers on the space-craft.
A solution, which was also demonstrated by LISA pathfinder, is that each spacecraft will house two small cubic test-masses which act as gravitational reference points for the measurements. Their position relative to the spacecraft will be read out using dedicated interferometers.
The test-masses themselves are housed in a gravitational reference sensor (GRS). It is responsible for most functionality regarding the test mass. In particular, each GRS has to be able to securely hold the test-mass during launch, before releasing it into free-fall for science operations. The test-mass then stays enclosed inside the GRS, where it is shielded from external influences and controlled along the non-sensitive degrees of freedom to avoid collisions with the spacecraft [10]. Along the sensitive direction, the test-masses are ’drag-free’, meaning that the spacecraft follows the test-mass motion instead, as described in section3.4.4.
3.4.3 Optical layout and split interferometry
The overall optical layout for each LISA satellite is outlined in fig.3.6.
Each OB has an associated local laser. In addition, the two OBs on each spacecraft are inter-connected by an optical fibre, such that a total of 3 different laser beams are available on each OB:
• The local beam, which is being emitted towards the far spacecraft and the adjacent optical bench,
• the distant beam, incoming from the distant spacecraft through the telescope, which carries the GW signal, and
• the adjacent beam, incoming from the adjacent OB on the same space-craft, which is used as a local reference.
These are used to construct three different interferometers:
32 the laser interferometer space antenna
• The ISC interferometer3, which beats the distant beam against the local one,
• the reference interferometer, which beats the adjacent beam against the local one,
• and the test-mass interferometer, which also beats the adjacent beam against the local one, but includes an additional reflection off the local test mass.
Most noise sources, such as LFN, are common in the reference and test-mass interferometer. Thus, we can combine the measurements from these two interferometers to cancel this common noise and get a high-precision readout of the seperation between test-mass and the local optical bench.
This information can be used in conjunction with the ISC interferometer, which measures the seperation between the local and distant optical bench, to synthesize a high-precision readout of the seperation between the two test-masses at the ends of one LISA link.
In addition, the reference interferometer readout can also be used to remove LFN of one of the two lasers on each spacecraft.
This concept is called split-interferometry, and the actual signal combinations are computed on-ground out of the individual interferometric readouts. We discuss this in detail in chapter12.
3.4.4 DFACS
In addition to allowing a post-processing correction for jitters of the spacecraft, the interferometric readout of the test-mass position
In addition, the DFACS also uses capacitative readouts of the test-mass orientation provided by the GRS [10].
will also be used in the drag-free attitude control system (DFACS) to adjust the spacecraft trajectories such that they follow the test-masses on their free-fall trajectory. Since there are two test-masses, the spacecraft can’t follow both of them in all degrees of freedom. Instead, each of the test-masses is only free-falling along some degrees of freedom, including the sensitive axes connecting to the distant spacecraft, while their position in the other ones is controlled by electro-static actuators. The DFACS then only ensures drag-free control of the spacecraft positions along three translational degrees of freedom [10].
As experimentally demonstrated in LISA-Pathfinder [12], the DFACS is not perfect4, such that although the spacecraft tries to follow the test-mass mo-tion in the sensitive direcmo-tion, there is still a significant amount of residual spacecraft displacement noise in the inter-spacecraft interferometer carrying the gravitational wave signal. This will be compensated in a post-processing step, as described in section3.4.3.
3 This interferometer is sometimes also called the ’long-arm interferometer’ or ’science interfer-ometer’.
4 The main noise sources limiting the DFACS performance are thruster noise and the finite gain of the DFACS control loops (G. Heinzel, personal communication,2021).