Optical Layout

So far different concepts have been discussed on abstract block diagram level. The actual optical implementation of the interferometer can be accomplished in various ways. In general one can distinguish two different types: on-axis or off-axis layouts.

5.3.3.1 On-axis Layout

An on-axis interferometer has a common optical path for the receive and transmit beam along the line-of-sight. Since the main measurement is the distance variation between the CoM of the satellites, it seems a natural choice to use this axis for the interferometric measurement. In principle an on-axis interferometer can be realized with only a few components, however, it turns out that these simple concepts do not allow to obtain sensible power ratios between local oscillator beam, transmit beam and received beam. This drawback can be avoided by exploiting different polarization states of the light. With polarizing beam splitters (PBS) and waveplates a sensible ratio between local oscillator power and transmit beam power can be selected and the received light can be separated from the local light on the optical bench (if required).

However, this increases the complexity of the interferometer and the amount of optical components.

The introduction of additional components in interferometers should be minimized, because additional optical components might yield negative side effects, which need to be analyzed (see Table 5-2). It is beneficial to keep space interferometers as simple as possible.

An on-axis layout is in particular useful if a common telescope for the received and transmit beam is envisaged. It increases the received light power and magnifies the transmit beam, which yields a smaller beam divergence in the far field. This allows using less laser power or allows to increase the satellite separation as in the LISA mission concept.

An examplary on-axis layout with telescope is depicted in Figure 5-13. One major challenge is the determination of the laser interferometer point of minimal coupling (POMC), which minimizes the rotation-to-pathlength coupling. The POMC is usually dependent on the optical layout, beam parameters, component misalignments etc. For ideal interferometers the POMC might have zero rotation-to-pathlength coupling for rotations around all axes (yaw, pitch and roll). However, in general there are three different axes (lines) of zero coupling for each rotation axis (yaw, pitch and roll). In an ideal interferometer the axes (lines) intersect in one point, which is the zero coupling point for all rotations at the same time. In general in non-perfect interferometers the three axes (lines) do not intersect and therefore the POMC is determined as the point with least distance to all three axes (lines) or else as the point with minimum total coupling from all 3 axes. It is often useful to apply even some weighting between the axis, therefore the POMC might depend on definitions and weighting parameters.

For on-axis layouts the POMC is in general located close to the optical axis, whereby the longitudinal position is dependent on the parameters like wavefront curvatures (waist location) and imaging systems. It may be laterally shifted, if the optical bench show some linear tilt-to-length couplings, which should be avoided by sensible optical design. It is therefore required to measure the optical axis precisely w.r.t. the interferometer housing for the determination of the POMC, which is non-trivial since it is not directly physical accessible (by probing). Often the POMC is also just called Reference Point (RP).

Figure 5-13: e.motion on-axis interferometer concept [9]. The POMC of this interferometer coincides with the accelerometer center.

Table 5-2: Potential negative side effects of (additional) optical components. Some effects may cancel in an interferometric measurement, if both interference beams are affected in the same way.

Effect Description Counteraction / Mitigation

Temperature coupling 5-14. It is evident that such a concept can be realized with significant less complexity, since the use of polarizing components is not required. Often (in ideal) interferometers the POMC for the full round-trip pathlength measurement can be determined as arithmetic mean of a POMC in the transmit path (TX-POMC) and of a POMC in the receive path (RX-POMC). The TX-POMC is given by the waist position of the transmit beams (or more precisely by the center of wavefront curvature at the distant spacecraft), while the RX-POMC is close to the receive beam axis. The axis is defined by the center of the portions of the received wavefront, which interfere later with the local oscillator (in Figure 5-14) it is the flat top beam directly at the receive aperture). The longitudinal position of the POMC along the axis is determined by quadratic couplings measured with the photodetectors on one satellite, while lateral offsets may be induced by linear tilt-to-pathlength couplings. In general each photodetector has its own POMC, however, the points can usually be co-located by adjusting some distances (as done in

Figure 5-14). Ideally the interferometer would be placed within the spacecraft, such that POMC and satellite CoM coincide. This minimizes the rotation-to-pathlength coupling. However, for NGGM-like gravimetric missions usually an accelerometer (accelerometer reference point) needs to be located at the satellite CoM, therefore the optical layout has to ensure that the POMC is outside the interferometer housing and that it can coincide physically with satellite CoM and accelerometer RP.

One should emphasize, that the precise measurement of beam axes and of TX- and RX-POMC is challenging.

Another drawback of the layout shown in Figure 5-14 is the lack of an easy way of implementing a beam steering mechanism, which allows compensating spacecraft rotations by minimizing the local DWS signal (=maximizing interferometer signal level) and ensuring thereby pointing of the TX beam to the distant satellite. The mirror M1 can be used for the purpose in case of yaw-rotations, however, pitch rotations are “compensated” in the opposite direction and therefore misalignments would be doubled.

Figure 5-14: Simple off-axis concept. TX-Point of Minimal Coupling (POMC) is the center of wavefront curvature (measured in the far-field at the distant satellite), RX-POMC is given as intersection point of local-oscillator beam (axis) with the recombination beamsplitter (RBS). The total interferometer POMC is given by the arithmetic mean (center of gravity) of both points.

5.3.3.3 Off-axis Racetrack Layout

The racetrack layout is a special type of an off-axis layout, which utilizes an additional retro-reflector.

It has initially been suggested by William Folkner (JPL – NASA) and further elaborated by the AEI for the GRACE Follow-On Laser Ranging Interferometer. It was born out of necessity, since the GRACE Follow-On mission uses an on-axis Microwave Ranging Instrument and propellant tanks, which occupy the line-of-sight. It turned out that it has several attractive properties, which make the design also suitable for future spacecraft-to-spacecraft interferometers. Namely,

 A beam steering mechanism can be implemented easily, which allows to simultaneously maximize the interferometer contrast and signal-to-noise ratio (minimize DWS signal) and to compensate local spacecraft jitter, such that the transmit beam is sent out always in the direction of the distant satellite.

 No polarization optics are required: only 2 transmissive optics on the optical bench and 3 reflective components of the hollow corner-cube are within the sensitive measurement path for each satellite (see Figure 5-15)

 Off-racetrack pathlength fluctuations are suppressed by a high factor (dashed lines in Figure 5-15). The sensitive measurement path is the racetrack with solid red/blue lines in Figure 5-15.

 A two-lens telescope on the optical bench images the receive aperture and the steering

 The interferometer POMC coincides with the TMA (corner-cube) vertex (see Figure 5-16) in the ideal case. Misalignments or motion of the optical bench do not change the colocation of both points due to the special properties of corner-cubes. In addition offsets in 𝑥-direction between POMC and CoM influence the measurement only in second order.

 The POMC can be placed outside physically present interferometer hardware, e.g. into the accelerometer

A small fraction of the received light on each satellite is transmitted through the beamsplitter and does not propagate to the photodetector, which slightly decreases the signal-to-noise ratio. For Signal-to-Noise or Carrier-to-Signal-to-Noise-density limited interferometers like LISA, which are dominated by noise due to the low received power, this might be an argument against a racetrack configuration.

However, as pointed out later, the sensitivity of satellite-to-satellite interferometry in LEO is not dominated by the carrier-to-noise density with current mission proposals and therefore a small loss in the received power is uncritical.

Figure 5-15: GRACE Follow-On Laser Ranging Interferometer with offset phase-locked transponder and corner-cube retro-reflector (Triple Mirror Assembly, TMA) on each satellite.

Figure 5-16: POMC in GRACE Follow-On LRI is collocated with the TMA vertex. Due to the special properties of corner-cubes, the geometrical pathlength between RX-POMC and point Q is 𝟐 ∙ 𝒔, as well as between 𝒘𝟎 and Q. Effects in beamsplitter and compensation plate are omitted.