arXiv subjects

Vitali Müller

Publications and source records attributed to Vitali Müller.

12 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

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↗

arXiv2025

Evaluation of Deployable Solar Panels on GRACE-like Satellites by Closed-Loop Simulations

Future satellite gravimetry missions seek to surpass the performance of CHAMP, GOCE, GRACE, and GRACE-FO to meet increasing scientific and operational demands. These missions will integrate advanced technologies, including optical and quantum accelerometers, high-precision inter-satellite laser ranging, and micro-Newton electric thrusters. However, increased power demands for sensors and propulsion systems require larger solar panels, constrained by payload mass and launcher limitations. This study assesses the impact of modified satellite shapes on gravity field recovery (GFR) using closed-loop simulation. Five satellite configurations were analyzed: a standard shape and variations with single and double solar panels mounted on the top and bottom of the satellite body, each modeled with distinct finite element models and moments of inertia. Orbit simulations accounted for non-spherical static gravity and time-variable non-gravitational forces. Performance of a simplified gravitational reference sensor (SGRS) with optical interferometer test mass displacement readout was evaluated. The air drag coefficient, a complex parameter influenced by multiple factors, was varied from 2.25 (standard) to 4.5 (double-panel). Time-variable gravity background models were excluded to isolate instrument performance effects. Gravity models were evaluated in the spectral domain using Degree RMS of spherical harmonic coefficient differences. Discrepancies between configurations stemmed primarily from variations in SGRS actuation noise due to satellite cross-sectional area. Convergence of residuals in the spectral domain for the double-panel configuration under different drag coefficients confirmed the dominant role of SGRS performance in GFR accuracy.

physics.geo-ph↗

arXiv2024

Benefit of enhanced electrostatic and optical accelerometry for future gravimetry missions

Twenty years of gravity observations from various satellite missions have provided unique data about mass redistribution processes in the Earth system. This paper studies the benefit of enhanced electrostatic and novel optical accelerometers and gradiometers for the future gravimetry missions. One of the limiting factors in the current space gravimetry missions is the drift of the Electrostatic Accelerometers (EA). This study focuses on the modeling of enhanced EAs with laser-interferometric readout, so called 'optical accelerometers', and on evaluating their performance for gravity field recovery in future satellite missions. In this paper, we simulate gravimetry missions in multiple scopes, applying the various software modules for satellite dynamics integration, accelerometer (ACC) and gradiometer simulation and gravity field recovery. The total noise budget of the modeled enhanced Electrostatic and optical ACCs show a similar sensitivity as the ACC concepts from other research groups. Parametrization w.r.t. ACCs test mass (TM) weight and the gap between the test mass and surrounding electrode housing confirmed previously known results that an ACC with a heavier TM and larger gap will have better performance. Our results suggest that the anticipated gain of novel ACCs might at some point be potentially limited by noise from the inter-satellite laser ranging interferometry. In order to present the advantage of the novel sensors, time-variable background models and associated aliasing errors were not considered in our simulations. Utilization of enhanced EA and optical ACC show a significant improvement of accuracy w.r.t. current GRACE-like EA. Also, their benefit in double satellite pairs in a so called 'Bender' constellations as well as in the combination of low-low satellite-to-satellite tracking with cross-track gradiometry has been investigated.

physics.geo-ph↗

arXiv2023

Disturbances from Single Event Upsets in the GRACE Follow-On Laser Ranging Interferometer

The Gravity Recovery And Climate Experiment - Follow On (GRACE-FO) satellite mission (2018-now) hosts the novel Laser Ranging Interferometer (LRI), a technology demonstrator for proving the feasibility of laser interferometry for inter-satellite ranging measurements. The GRACE-FO mission extends the valuable climate data record of changing mass distribution in the system Earth, which was started by the original GRACE mission (2002-2017). The mass distribution can be deduced from observing changes in the distance of two low-earth orbiters employing interferometry of electromagnetic waves in the K-Band for the conventional K-Band Ranging (KBR) and in near-infrared for the novel LRI. This paper identifies possible radiation-induced Single Event Upset (SEU) events in the LRI phase measurement. We simulate the phase data processing within the Laser Ranging Processor (LRP) and use a template-based fitting approach to determine the parameters of the SEU and subtract the events from the ranging data. Over four years of LRI data, 29 of such events were identified and characterized.

physics.space-ph↗

arXiv2022

Scale Factor Determination for the GRACE-Follow On Laser Ranging Interferometer including Thermal Coupling

The GRACE Follow-On satellites carry the very first inter-spacecraft Laser Ranging Interferometer (LRI). After more than four years in orbit, the LRI outperforms the sensitivity of the conventional Microwave Instrument (MWI). However, in the current data processing scheme, the LRI product still needs the MWI data to determine the unknown absolute laser frequency, representing the ruler for converting the raw phase measurements into a physical displacement in meters. In this paper, we derive formulas for precisely performing that conversion from the phase measurement into a range, accounting for a varying carrier frequency. Furthermore, the dominant errors due to knowledge uncertainty of the carrier frequency as well as uncorrected time biases are derived. In the second part, we address the dependency of the LRI on the MWI in the currently employed cross-calibration scheme and present three different models for the LRI laser frequency, two of which are largely independent of the MWI. Furthermore, we analyze the contribution of thermal variations on the scale factor estimates and the LRI-MWI residuals. A linear model called Thermal Coupling (TC) is derived that significantly reduces the differences between LRI and MWI to a level where the MWI observations limit the comparison.

astro-ph.IM↗

arXiv2022

Comparing GRACE-FO KBR and LRI ranging data with focus on carrier frequency variations

The GRACE Follow-On satellite mission measures distance variations between the two satellites in order to derive monthly gravity field maps, indicating mass variability on Earth on a few 100 km scale due to hydrology, seismology, climatology and others. This mission hosts two ranging instruments, a conventional microwave system based on K(a)-band ranging (KBR) and a novel laser ranging instrument (LRI), both relying on interferometric phase readout. In this paper we show how the phase measurements can be converted into range data using a time-dependent carrier frequency (or wavelength) that takes potential intraday variability in the microwave or laser frequency into account. Moreover, we analyze the KBR-LRI residuals and discuss which error and noise contributors limit the residuals at high and low Fourier frequencies. It turns out that the agreement between KBR and LRI biased range observations can be slightly improved by considering intraday carrier frequency variations in the processing. Although the effect is probably small enough to have little relevance for gravity field determination at the current precision level, the analysis is of relevance for detailed instrument characterization and potentially for future more precise missions.

physics.ins-det↗

arXiv2022

On-axis Optical Bench for Laser Ranging Instruments in future gravity missions

The Laser Ranging Interferometer onboard the Gravity Recovery and Climate Experiment Follow-On mission proved the feasibility of an interferometric sensor for inter-satellite length tracking with sub-nanometer precision, establishing an important milestone for space laser interferometry and the general expectation that future gravity missions will employ heterodyne laser interferometry for satellite-to-satellite ranging. In this paper we present the design of an on-axis optical bench for next-generation laser ranging which enhances the received optical power and the transmit beam divergence, enabling longer interferometer arms and relaxing the optical power requirement of the laser assembly. All design functionalities and requirements are verified by means of computer simulations. A thermal analysis is carried out to investigate the robustness of the proposed optical bench to the temperature fluctuations found in orbit.

physics.ins-det↗

arXiv2021

Revisiting the Light Time Correction in Gravimetric Missions Like GRACE and GRACE Follow-On

The gravity field maps of the satellite gravimetry missions GRACE (Gravity Recovery and Climate Experiment) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites' center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the non-zero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth's potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.

astro-ph.IM↗

arXiv2019

On orbit performance of the GRACE Follow-On Laser Ranging Interferometer

The Laser Ranging Interferometer (LRI) instrument on the Gravity Recovery and Climate Experiment (GRACE) Follow-On mission has provided the first laser interferometric range measurements between remote spacecraft, separated by approximately 220 km. Autonomous controls that lock the laser frequency to a cavity reference and establish the 5 degree of freedom two-way laser link between remote spacecraft succeeded on the first attempt. Active beam pointing based on differential wavefront sensing compensates spacecraft attitude fluctuations. The LRI has operated continuously without breaks in phase tracking for more than 50 days, and has shown biased range measurements similar to the primary ranging instrument based on microwaves, but with much less noise at a level of $1\,{\rm nm}/\sqrt{\rm Hz}$ at Fourier frequencies above 100 mHz.

astro-ph.IM↗

arXiv2013

Octahedron configuration for a displacement noise-cancelling gravitational wave detector in space

We study for the first time a three-dimensional octahedron constellation for a space-based gravitational wave detector, which we call the Octahedral Gravitational Observatory (OGO). With six spacecraft the constellation is able to remove laser frequency noise and acceleration disturbances from the gravitational wave signal without needing LISA-like drag-free control, thereby simplifying the payloads and placing less stringent demands on the thrusters. We generalize LISA's time-delay interferometry to displacement-noise free interferometry (DFI) by deriving a set of generators for those combinations of the data streams that cancel laser and acceleration noise. However, the three-dimensional configuration makes orbit selection complicated. So far, only a halo orbit near the Lagrangian point L1 has been found to be stable enough, and this allows only short arms up to 1400 km. We derive the sensitivity curve of OGO with this arm length, resulting in a peak sensitivity of about $2\times10^{-23}\,\mathrm{Hz}^{-1/2}$ near 100 Hz. We compare this version of OGO to the present generation of ground-based detectors and to some future detectors. We also investigate the scientific potentials of such a detector, which include observing gravitational waves from compact binary coalescences, the stochastic background and pulsars as well as the possibility to test alternative theories of gravity. We find a mediocre performance level for this short-arm-length detector, between those of initial and advanced ground-based detectors. Thus, actually building a space-based detector of this specific configuration does not seem very efficient. However, when alternative orbits that allow for longer detector arms can be found, a detector with much improved science output could be constructed using the octahedron configuration and DFI solutions demonstrated in this paper. (abridged)

gr-qc↗