# Title-to-Length Coupling Analysis of an Off-Axis Optical Bench Design for NGGM
## 2 Off-Axis Optical Bench Design  
To make the present work self contained, we shall first give a brief description of the new proposed off-axis optical bench layout [7]. We shall also add a few refined details to the optical design. Compared with the optical design of the Grace Follow-on mission, our proposed off-axis optical bench layout is more compact in that there is no separation of the triple-mirror assembly with the optical bench. Instead, a combination of lens systems and rooftop mirrors is employed to generate a laser retro-reflector. Lens systems are also used to image the rotation of the beams to the centre of the photodiodes and the transmitter reference point. Further, an open loop control is added to minimise on orbit the offset between the phase centre and the centre of mass of a satellite. As we shall see in a moment, the TTL coupling of the proposed off-axis optical bench may be efficiently suppressed. The design of the off-axis optical bench is shown in Figure 1. Clipped by the receiving aperture, the receiving (RX) beam emitted by the remote satellite transmits through lens L1 and is then split by beamsplitter BS1. Approximately 90% of the initial RX beam is equally split by beamsplitter BS2, then passes through lenses L4 and L5, respectively, and is then captured by the quadrant photodiodes. The local (LO) Gaussian beam enters the optical bench through a fibre coupler, and the waist of the beam is placed at the surface of the fast-steering mirror (FSM). After passing through lens L2 and being split by BS1, 10% of the initial LO beam is reflected to BS2 and then interferes with the RX beam, while the majority of the split beam transmits to lens L3 and is then reflected by the rooftop mirrors M1 and M2; it then propagates to the remote satellite. The angle between the rooftop mirrors is set to be 135\({}^{\mathrm{o}}\), and both mirrors are perpendicular to the baseplate. In addition, both beamsplitters employed in the optical bench have a wedge of 0.5\({}^{\mathrm{o}}\), which serve to reduce the impact of the back scattered stray light. The reference point of the optical setup is denoted by RP. The interfering beams are received by the quadrant photodiodes QPD1 and QPD2. The phase signals derived from the beatnotes are then used to calculate the longitudinal pathlength signal (LPS) variations and the differential wavefront sensing signals. An automatic beam alignment system based on the DWS signals is employed in the optical bench in order to compensate the misalignment caused by the attitude jitter of the satellites [8]. The angular motion of the satellites results in an additional tilt of the RX beam when it impinges on the QPDs. The horizontal and vertical DWS signals are then used to measure the relative angle between the interfering beams, which will be fed back to the FSM mirror. In this way, the LO beam is steered by the FSM, yielding a zero value in the DWS\({}_{\mathrm{h}}\) and DWS\({}_{\mathrm{v}}\) and forcing the interfering beams to be parallel again [8; 9]. We shall call this process DWS feedback control. Five keplerian telescope lens systems are employed in this optical layout: L1-L4 and L1-L5 as the RX lens systems; L2-L4 and L2-L5 as the LO lens systems; and L2-L3 as the TX lens systems. The points of rotation of the beams are imagined to the centre of the photodiodes by the lens systems, and the optical path lengths between the front and back focal points of the lens systems are supposed to be unchanged; thus, the beam walk is  
Figure 1: Schematic drawing of the off-axis optical bench design. The RX beam and TX beam enter and exit the optical bench through different light paths. minimized. In addition, the beams are expanded and compressed through the lens systems, so that the sizes of the beams are adjusted to match the active area of the QPDs [9]. The front focus of L1 is placed at the centre of the receiving aperture, while the back focal points of L4 and L5 locate at the centre of the active area of the QPDs.