# Title-to-Length Coupling Analysis of an Off-Axis Optical Bench Design for NGGM
## 4 Global TTL Coupling
### Reference Point Offset and Attitude Jitter  
To estimate the TTL coupling noise generated by the coupling of the offset with attitude jitter, the centre of rotation of the optical bench is slightly shifted to a new point away from RP, and the optical bench is rotated around the new centre of rotation for \(\pm\)2 mrad in yaw and pitch degrees of freedom, respectively. In the case of the GRACE Follow-on mission, The offset between the vertex point of the TMA and the CoM is of the order of 100 \(\upmu\)m [18; 19]. We shall set this as the maximum offset in our simulation. At the same time, the proposed optical design contains an open loop that can be used to control the position of RP on orbit (see Figure 3). Preliminary estimates indicate that the offset may be minimised to the level of \(\upmu\)m. We shall study the TTL noise within the range of 1 \(\upmu\)m and 100 \(\upmu\)m. Results are shown in Figure 11.  
Further simulation results reveal that the global TTL coupling of the pitch degree of freedom is mainly affected by the deviations on the \(z\)-axis, while the change of the global TTL coupling in the yaw degree of freedom is mainly affected by the offsets on the \(y\)-axis, depicted in Figure 11. For an offset of 100 \(\upmu\)m in \(y\) and \(z\), respectively, a global TTL variation of 200 \(\upmu\)m/rad is generated, which must be suppressed. For the GRACE Follow-on mission, the reference point offset is approximately 100 mm. However, even though this quantity is known after calibration, it can only be subtracted in the 1B data processing. In our design, it is hoped that this offset may be corrected on orbit. The reasons for doing this are as follows. Firstly, with a view that future NGGM and beyond will have better LRI measurement sensitivity to the level of a few tenths of nm, it is not clear whether the standard orbit manoeuvre is able to go under the micrometer level. Secondly, from the perspective of technological development and lessons to be learnt for gravitational wave detection, it would be instructive if we have a way to suppress the reference point offset on board. For a comparison with the GRACE Follow-on mission, given that the attitude jitter is around mrad, a TTL coupling factor of 200 mm per radian will generate 100 nm in LRI ranging error. This is smaller than that of the GRACE Follow-on mission, but still a subtraction in the 1B processing is needed. Offset between the RP and the CoM in the proposed new off-axis design is expected to be reduced to the level of 1 \(\upmu\)m by an open loop RP correction mechanism in orbit, and results are shown in Figure 12. According to the parameters used in our IfoCAD simulation, the resolution and the tilt angle of the FSM used in the open loop can be easily achieved by commercial components. Even for commercial products, the resolution can reach approximately 20 nrad. For the piston noise, our experience in gravitational wave detection suggests that we may reduce it to a very low level and will not disturb the nanometer level measurement. The result of micrometer  
Figure 10: Illustration of the global TTL coupling noise. The local optical bench is rotated along the RP point in different rotational degrees of freedom. A photodiode, with a sufficient active area, represents the remote satellite located at 100 km away from the TX-RP of the local optical bench [7].  
is not a very demanding requirement for an FSM. Currently, we are also looking at an alternative optical method to adjust the reference point offset.