arXiv subjects

Christoph Bode

Publications and source records attributed to Christoph Bode.

5 recordsLinked to original sources

arXiv2026

Beam angle-locked loop in laser interferometry

Maintaining precise beam coalignment is essential in laser interferometry, particularly for interspacecraft missions where angular misalignments introduce tilt-to-length coupling noise and risk complete link failure. This work presents a comprehensive theoretical and experimental framework for the beam angle-locked loop, which maintains coalignment between two interfering beams. Minute angular misalignments are detected via differential wavefront-sensing signals, which are used as the error signal for feedback control. A detailed linear control model incorporating an angle detector, a digital filter, a proportional-integral-double-integral servo, a digital-to-analog converter, and a beam-steering mechanism is developed. Using loop transfer functions, we establish a noise-propagation model that quantifies the contributions of individual components to both out-of-loop and in-loop angle errors. The analytical results are experimentally validated using a transponder-based interferometric link spanning two optical benches, with a hexapod simulating spacecraft attitude jitter. The measured transfer functions and coalignment performance agree well with theoretical predictions, yielding a pointing stability better than 10 urad$/\sqrt{\text{Hz}}$ between 0.2 mHz and 1 Hz. Furthermore, a loop-optimization strategy is demonstrated to minimize angle misalignment within a target frequency band by tuning the servo gain, without requiring hardware modifications. This validated framework provides a reliable architecture for designing and optimizing active beam alignment in laser interferometry.

physics.optics↗

arXiv2026

Nested active pointing control for interspacecraft laser interferometry

Precise pointing control is a critical requirement for interspacecraft laser interferometry, as angular misalignment introduces measurement noise and even leads to laser link loss. We present a nested control architecture that uses differential wavefront sensing signals to drive a fast steering mirror (FSM) to track the incoming beam, while feeding the FSM's angular changes back to the attitude and orbit control system (AOCS) to suppress angle-dependent optical path variations. This scheme is experimentally validated in our hexapod-based setup. Relative to standalone FSM actuation, the nested configuration enhanced pointing stability by 6.9 dB and 4.9 dB in the horizontal and vertical directions across the frequency band from 3 mHz to the AOCS actuation's unity-gain frequency. Additionally, tilt-to-length coupling was suppressed by an order of magnitude below 6 mHz and by two orders of magnitude below 0.45 mHz. These results demonstrate the feasibility of nested active pointing control for future interspacecraft laser interferometry missions.

physics.optics↗

arXiv2026

Mathematical derivation and verification of the amplitude of LISA's interferometric signals on an ultra-stable interferometer testbed

The Laser Interferometer Space Antenna (LISA) mission aims to detect gravitational waves by interferometrically measuring the change of separation between free-falling test masses (TMs). LISA's interferometers must deliver pm/rtHz sensitivity while accommodating beam tilts up to 1 mrad at the photodiodes, which degrade the interferometric amplitude and increase the induced readout noise coupling. This paper uses an analytical framework developed by the authors in a previous work, based on minimal and justified approximations, that relates beam tilt to the resulting heterodyne signal amplitude in a generic two-beam interferometer with circular-area photodiodes (PDs). A set of interferometric topologies is analyzed, all of high relevance for LISA. We derive the exact amplitude response for an infinite detector and a closed-form approximation for finite detectors, and we validate both against numerical simulations and experimental measurements on an ultra-stable LISA-representative testbed. We then use this model to quantify the phase-noise amplification arising from reduced signal-to-noise ratio (SNR) under tilt, showing that curvature mismatches between the interfering beams substantially enhance this effect. Finally, we introduce a compact function that captures the angular dependence of correlated and uncorrelated phase noises in quadrant photodiode (QPD)-based readouts. Here, a new noise feature, caused by wavefront curvature mismatch, is predicted and measured for the first time. These results indicate that controlling wavefront curvature mismatch in the test mass interferometer (TMI) is essential to limit excess phase noise. The models and results derived in this paper, although originating in the context of LISA, are general and can be applied to any interferometric topology undergoing tilts with pivot on the detector plane.

astro-ph.IM↗

arXiv2025

Experimental Demonstration of an On-Axis Laser Ranging Interferometer for Future Gravity Missions

We experimentally demonstrate a novel interferometric architecture for next-generation gravity missions, featuring a laser ranging interferometer (LRI) that enables monoaxial transmission and reception of laser beams between two optical benches with a heterodyne frequency of 7.3 MHz. Active beam steering loops, utilizing differential wavefront sensing (DWS) signals, ensure co-alignment between the receiving (RX) beam and the transmitting (TX) beam. With spacecraft attitude jitter simulated by hexapod-driven rotations, the interferometric link achieves a pointing stability below 10 urad/$\mathrm{\sqrt{Hz}}$ in the frequency range between 0.2 mHz and 0.5 Hz, and the fluctuation of the TX beam's polarization state results in a reduction of 0.14\% in the carrier-to-noise-density ratio over a 15-hour continuous measurement. Additionally, tilt-to-length (TTL) coupling is experimentally investigated using the periodic scanning of the hexapod. Experimental results show that the on-axis LRI enables the inter-spacecraft ranging measurements with nanometer accuracy, making it a potential candidate for future GRACE-like missions.

physics.optics↗

arXiv2024

Experimental end-to-end demonstration of intersatellite absolute ranging for LISA

The Laser Interferometer Space Antenna (LISA) is a gravitational wave detector in space. It relies on a post-processing technique named time-delay interferometry (TDI) to suppress the overwhelming laser frequency noise by several orders of magnitude. This algorithm requires intersatellite-ranging monitors to provide information on spacecraft separations. To fulfill this requirement, we will use on-ground observatories, optical sideband-sideband beatnotes, pseudo-random noise ranging (PRNR), and time-delay interferometric ranging (TDIR). This article reports on the experimental end-to-end demonstration of a hexagonal optical testbed used to extract absolute ranges via the optical sidebands, PRNR, and TDIR. These were applied for clock synchronization of optical beatnote signals sampled at independent phasemeters. We set up two possible PRNR processing schemes: Scheme 1 extracts pseudoranges from PRNR via a calibration relying on TDIR; Scheme 2 synchronizes all beatnote signals without TDIR calibration. The schemes rely on newly implemented monitors of local PRNR biases. After the necessary PRNR treatments (unwrapping, ambiguity resolution, bias correction, in-band jitter reduction, and/or calibration), Scheme 1 and 2 achieved ranging accuracies of 2.0 cm to 8.1 cm and 5.8 cm to 41.1 cm, respectively, below the classical 1 m mark with margins.

astro-ph.IM↗