Phase stability of photoreceivers in intersatellite laser interferometers.

A photoreceiver (PR) is required for the opto-electrical conversion of signals in intersatellite laser interferometers. Noise sources that originate or couple in the PR reduce the system carrier-to-noise-density, which is often represented by its phase noise density. In this work, we analyze the common noise sources in a PR used for space-based interferometry. Additionally, we present the results from the characterization of the PRs in GRACE-FO, a mission which will pioneer intersatellite laser interferometry. The estimated phase noise is shot-noise limited at 10-4 rad/Hz1/2 down to 10-2 Hz, almost 4 orders of magnitude below the instrument top level requirement (0.5 rad/Hz1/2). Below 10-2 Hz, the PR finite phase response noise dominates but the levels still comply with the instrument requirement. The sub-mHz noise levels and the PR electronic noise have been identified as key design factors for the LISA PR.

Laser beam steering for GRACE Follow-On intersatellite interferometry.

The GRACE Follow-On satellites will use, for the first time, a Laser Ranging Interferometer to measure intersatellite distance changes from which fluctuations in Earth's geoid can be inferred. We have investigated the beam steering method that is required to maintain the laser link between the satellites. Although developed for the specific needs of the GRACE Follow-On mission, the beam steering method could also be applied to other intersatellite laser ranging applications where major difficulties are common: large spacecraft separation and large spacecraft attitude jitter. The beam steering method simultaneously coaligns local oscillator beam and transmitted beam with the laser beam received from the distant spacecraft using Differential Wavefront Sensing. We demonstrate the operation of the beam steering method on breadboard level using GRACE satellite attitude jitter data to command a hexapod, a six-degree-of-freedom rotation and translation stage. We verify coalignment of local oscillator beam/ transmitted beam and received beam of better than 10 µrad with a stability of 10 µrad/ √Hz in the GRACE Follow-On measurement band of 0.002...0.1 Hz. Additionally, important characteristics of the beam steering setup such as Differential Wavefront Sensing signals, heterodyne efficiency, and suppression of rotation-to-pathlength coupling are investigated and compared with analysis results.

Laser link acquisition demonstration for the GRACE Follow-On mission.

We experimentally demonstrate an inter-satellite laser link acquisition scheme for GRACE Follow-On. In this strategy, dedicated acquisition sensors are not required-instead we use the photodetectors and signal processing hardware already required for science operation. To establish the laser link, a search over five degrees of freedom must be conducted (± 3 mrad in pitch/yaw for each laser beam, and ± 1 GHz for the frequency difference between the two lasers). This search is combined with a FFT-based peak detection algorithm run on each satellite to find the heterodyne beat note resulting when the two beams are interfered. We experimentally demonstrate the two stages of our acquisition strategy: a ± 3 mrad commissioning scan and a ± 300 µrad reacquisition scan. The commissioning scan enables each beam to be pointed at the other satellite to within 142 µrad of its best alignment point with a frequency difference between lasers of less than 20 MHz. Scanning over the 4 alignment degrees of freedom in our commissioning scan takes 214 seconds, and when combined with sweeping the laser frequency difference at a rate of 88 kHz/s, the entire commissioning sequence completes within 6.3 hours. The reacquisition sequence takes 7 seconds to complete, and optimizes the alignment between beams to allow a smooth transition to differential wavefront sensing-based auto-alignment.

Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling.

The GRACE Follow-On mission will monitor fluctuations in Earth's geoid using, for the first time, a Laser Ranging Interferometer to measure intersatellite distance changes. We have investigated the coupling between spacecraft rotation and the intersatellite range measurement that is incurred due to manufacturing and assembly tolerances of the Triple Mirror Assembly (TMA), a precision retroreflector to ensure alignment between in- and outgoing laser beams. The three TMA mirror planes intersect in a virtual vertex to which satellite displacements are referenced. TMA manufacturing tolerances degrade this ideal vertex, however, a Point of Minimal Coupling (PMC) between spacecraft rotation and displacement exists. This paper presents the experimental location of the PMC under pitch and yaw rotations for a prototype TMA. Rotations are performed using a hexapod, while displacements are monitored with heterodyne laser interferometry to verify the PMC position. Additionally, the vertex of the three TMA mirror planes is measured using a Coordinate Measuring Machine and compared to the PMC position. In the pitch and yaw axes, the biggest deviation between TMA vertex and PMC was 50 ± 64 µm. Thus, within the measurement uncertainties, no difference between TMA vertex and PMC could be observed. This is a key piece of information for integration of the TMA into the spacecraft: It is sufficient to use the readily-available TMA vertex location to ensure minimal rotation-to-displacement coupling during the mission.

Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset.

A method based on phase-shifting Fizeau interferometry is presented with which retroreflectors with large incoming-outgoing beam separations can be tested. The method relies on a flat Reference Bar that is used to align two auxiliary mirrors parallel to each other to extend the aperture of the interferometer. The method is applied to measure the beam coalignment of a prototype Triple Mirror Assembly of the GRACE Follow-On Laser Ranging Interferometer, a future satellite-to-satellite tracking device for Earth gravimetry. The Triple Mirror Assembly features a lateral beam offset of incoming and outgoing beam of 600 mm, whereas the acceptance angle for the incoming beam is only about ±2 mrad. With the developed method, the beam coalignment of the prototype Triple Mirror Assembly was measured to be 9 µrad with a repeatability of below 1 µrad.

High-bandwidth laser frequency stabilization to a fiber-optic delay line.

Stabilization of laser frequency to interferometers with a large time delay in one arm is of significant interest to space-based gravitational wave detectors such as the Laser Interferometer Space Antenna. A recently proposed technique allows a control bandwidth larger than the inverse delay time to be achieved. We present experimental results demonstrating laser frequency stabilization to an optical fiber delay line. A control bandwidth approximately 50 times the inverse delay time is demonstrated.

Photothermal effects in passive fiber Bragg grating resonators.

Photothermal effects in passive Fabry-Perot resonators are caused by the conversion of circulating optical energy into heat as a result of absorption. This results in thermal change in the resonator's optical path length, the round-trip phase, and hence the resonance condition. We describe a simplified dynamic numerical model for photothermal effects in passive fiber Bragg grating resonators and present results of their experimental observation.

Electro-optic modulator capable of generating simultaneous amplitude and phase modulations.

We report on the analysis and prototype characterization of a dual-electrode electro-optic modulator that can generate both amplitude and phase modulations with a selectable relative phase, termed a quadrature variable modulator (QVM). All modulation states can be reached by tuning only the electrical inputs, facilitating real-time tuning, and the device has shown good suppression and stability properties. A mathematical analysis is presented, including the development of a geometric-phase representation for modulation. The experimental characterization of the device shows that relative suppressions of 38, 39, and 30 dB for phase, single sideband, and carrier-suppressed modulations, respectively, can be obtained as well as that the device is well behaved when scanning continuously through the parameter space of modulations. The QVM is compared with existing optical configurations that can produce amplitude and phase-modulation combinations in the context of applications such as the tuning of lock points in optical-locking schemes, single-sideband applications, modulation fast-switching applications, and applications requiring combined modulations.