# On-Axis Optical Bench for Laser Ranging Instruments in Future Gravity Missions
## 2 On-Axis LRI Optical Bench Design
Mirrors M3 and M1 fold the light path, reducing the footprint of the OB, and providing sufficient space for the installation of the accelerometer, also depicted in Figure 2. M1 can also deflect the light out of the XY plane, in case that the S/C c.m. were out-of-plane from the OB. The position and orientation of M1 can be adjusted during the integration of the instrument to achieve collocation of the S/C c.m. and the RP, which greatly simplifies the placement of the OB itself. The acquisition system is composed of an imaging system and a focal plane detector to image the RX light. Such a scheme is commonly used in space laser communication terminals [20]. A critical requirement is the alignment stability of the optical axis of the interferometer with respect to the acquisition system, which is--in our opinion--a well-known and solvable challenge for space missions with optical instruments. Angular motion of the local spacecraft perturbs the RX-LO wavefront overlap, yielding average and huge differential and parasitic common-mode phase changes at the different segments of the quadrant photodiodes. In contrast, angular motion of the distant spacecraft yields changes of the received light power, but leaves the wavefront overlap largely unaffected. The differential phase between QPD segments, i.e., the differential wavefront sensing signals \(\mathrm{DWS_{h}}\) and \(\mathrm{DWS_{v}}\)[21], measure the relative tilt and tip between the interfering fields. In consequence, the DWS signals can be used in a feedback loop for transmit beam pointing or for spacecraft attitude control. In our OB design, two independent control loops are used to actuate the tip and tilt degrees of the FSM, yielding \(\mathrm{DWS_{h}}\sim 0\) and \(\mathrm{DWS_{v}}\sim 0\), as sensed by one of the quadrant photoreceivers, thus ensuring that the interfering fields' phase fronts are aligned at the detectors regardless of the S/C attitude. The cross coupling of the angular jitter of the spacecraft into the interferometric range measurement, or TTL coupling, is of critical importance, and can be suppressed to a large extent by means of employing suitable imaging systems (IS). These consist of a set of lenses that are placed in the beam path, and together image the point of rotation of the beam onto the center of the photodiodes such that the detector is in a pupil plane where beam walk is minimized while the angular tilt of the wavefront is maximized. They also serve the purpose of compressing or enlarging the beams according to what is desired, e.g., to adapt the size of the interfering beams to the active area of the photodiodes, or to enlarge the size of the transmit beam in order to decrease its divergence. In the proposed OB architecture, a total of five two-lens Keplerian telescope imaging systems are implemented: two of the so-called RX IS, which share lens L3 (L3-L1 and L3-L2); two of the so-called LO IS, which share lens L4 (L4-L1 and L4-L2); and the so-called TX IS (L4-L3). All of these imaging systems contain mirrors, beamsplitters and waveplates between the first and second lens. The RX IS's keep the received light beam at a fixed position on the photoreceivers independent of the incidence angle at the receive aperture, and the LO IS's do the same for the local oscillator beam independent of the steering mirror state. On the other hand, the TX IS ensures that, when the FSM actuation with closed DWS loops is engaged, the  
Figure 2: Optical bench layout. The green arrows depict the path and direction of the local oscillator and transmit beams, which originate from a single beam injected into the bench via a fiber injector. The red arrows depict the path and direction of the receive beam, which couples into the bench via mirror M1. The polarization state of each beam is indicated (RHC—right hand circular; LHC—left hand circular). The receive and transmit reference points (RX/TX RP) coincide in the left focal plane of lens L3, along the optical axis between mirrors M3 and M1.