arXiv subjects

Gerhard Heinzel

Publications and source records attributed to Gerhard Heinzel.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2023

Non-geometric tilt-to-length coupling in precision interferometry: mechanisms and analytical descriptions

This paper is the second in a set of two investigating tilt-to-length (TTL) coupling. TTL describes the cross-coupling of angular or translational jitter into an interferometric phase signal and is an important noise source in precision interferometers, including space gravitational wave detectors like LISA. We discussed in 10.1088/2040-8986/ac675e the TTL coupling effects originating from optical path length changes, i.e. geometric TTL coupling. Within this work, we focus on the wavefront and detector geometry dependent TTL coupling, called non-geometric TTL coupling, in the case of two interfering fundamental Gaussian beams. We characterise the coupling originating from the properties of the interfering beams, i.e. their absolute and relative angle at the detector, their relative offset and the individual beam parameters. Furthermore, we discuss the dependency of the TTL coupling on the geometry of the detecting photodiode. Wherever possible, we provide analytical expressions for the expected TTL coupling effects. We investigate the non-geometric coupling effects originating from beam walk due to the angular or translational jitter of a mirror or a receiving system. These effects are directly compared with the corresponding detected optical path length changes in 10.1088/2040-8986/ac675e. Both together provide the total interferometric readout. We discuss in which cases the geometric and non-geometric TTL effects cancel one-another. Additionally, we list linear TTL contributions that can be used to counteract other TTL effects. Altogether, our results provide key knowledge to minimise the total TTL coupling noise in experiments by design or realignment.

physics.optics↗

arXiv2023

The influence of laser relative intensity noise in the Laser Interferometer Space Antenna

LISA is an upcoming ESA mission that will detect gravitational waves in space by interferometrically measuring the separation between free-falling test masses at picometer precision. To reach the desired performance, LISA will employ the noise reduction technique time-delay interferometry (TDI), in which multiple raw interferometric readouts are time shifted and combined into the final scientific observables. Evaluating the performance in terms of these TDI variables requires careful tracking of how different noise sources propagate through TDI, as noise correlations might affect the performance in unexpected ways. One example of such potentially correlated noise is the relative intensity noise (RIN) of the six lasers aboard the three LISA satellites, which will couple into the interferometric phase measurements. In this article, we calculate the expected RIN levels based on the current mission architecture and the envisaged mitigation strategies. We find that strict requirements on the technical design reduce the effect from approximately 8.7 pm/rtHz per inter-spacecraft interferometer to that of a much lower sub-1 pm/rtHz noise, with typical characteristics of an uncorrelated readout noise after TDI. Our investigations underline the importance of sufficient balanced detection of the interferometric measurements.

gr-qc↗

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↗

arXiv2022

Experimental verification of intersatellite clock synchronization at LISA performance levels

The Laser Interferometer Space Antenna (LISA) aims to observe gravitational waves in the mHz regime over its 10-year mission time. LISA will operate laser interferometers between three spacecrafts. Each spacecraft will utilize independent clocks which determine the sampling times of onboard phasemeters to extract the interferometric phases and, ultimately, gravitational wave signals. To suppress limiting laser frequency noise, signals sampled by each phasemeter need to be combined in postprocessing to synthesize virtual equal-arm interferometers. The synthesis in turn requires a synchronization of the independent clocks. This article reports on the experimental verification of a clock synchronization scheme down to LISA performance levels using a hexagonal optical bench. The development of the scheme includes data processing that is expected to be applicable to the real LISA data with minor modifications. Additionally, some noise coupling mechanisms are discussed.

astro-ph.IM↗

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↗

arXiv2020

Tracking length and differential wavefront sensing signals from quadrant photodiodes in heterodyne interferometers with digital phase-locked loop readout

We propose a method to track signals from quadrant photodiodes (QPD) in heterodyne laser interferometers that employ digital phase-locked loops for phase readout. Instead of separately tracking the four segments from the QPD and then combining the results into length and Differential Wavefront Sensing (DWS) signals, this method employs a set of coupled tracking loops that operate directly on the combined length and angular signals. Benefits are increased signal-to-noise ratio in the loops and the possibility to adapt the loop bandwidths to the different dynamical behavior of the signals being tracked, which now correspond to physically meaningful observables. We demonstrate an improvement of up to 6 dB over single-segment tracking, which makes this scheme an attractive solution for applications in precision inter-satellite laser interferometry in ultra-low-light conditions.

physics.ins-det↗

arXiv2020

Single-element dual-interferometer for precision inertial sensing

Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout.

physics.ins-det↗

arXiv2019

Compact multi-fringe interferometry with sub-picometer precision

Deep frequency modulation interferometry combines optical minimalism with multi-fringe readout. Precision however is key for applications such as optical gradiometers for satellite geodesy or as dimensional sensor for ground-based gravity experiments. We present a single-component interferometer smaller than a cubic inch. Two of these are compared to each other to demonstrate tilt and displacement measurements with a precision of less than $20\,\mathrm{nrad}/\sqrt{\mathrm{Hz}}$ and $1\,\mathrm{pm}/\sqrt{\mathrm{Hz}}$ at frequencies below $1\,\mathrm{Hz}$.

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↗

arXiv2019

Picometer-stable hexagonal optical bench to verify LISA phase extraction linearity and precision

The Laser Interferometer Space Antenna (LISA) and its metrology chain have to fulfill stringent performance requirements to enable the space-based detection of gravitational waves. This implies the necessity of performance verification methods. In particular, the extraction of the interferometric phase, implemented by a phasemeter, needs to be probed for linearity and phase noise contributions. This Letter reports on a hexagonal quasimonolithic optical bench implementing a three-signal test for this purpose. Its characterization as sufficiently stable down to picometer levels is presented as well as its usage for a benchmark phasemeter performance measurement under LISA conditions. These results make it a candidate for the core of a LISA metrology verification facility.

astro-ph.IM↗

arXiv2019

LISA Pathfinder

Since the 2017 Nobel Prize in Physics was awarded for the observation of gravitational waves, it is fair to say that the epoch of gravitational wave astronomy (GWs) has begun. However, a number of interesting sources of GWs can only be observed from space. To demonstrate the feasibility of the Laser Interferometer Space Antenna (LISA), a future gravitational wave observatory in space, the LISA Pathfinder satellite was launched on December, 3rd 2015. Measurements of the spurious forces accelerating an otherwise free-falling test mass, and detailed investigations of the individual subsystems needed to achieve the free-fall, have been conducted throughout the mission. This overview article starts with the purpose and aim of the mission, explains satellite hardware and mission operations and ends with a summary of selected important results and an outlook towards LISA. From the LISA Pathfinder experience, we can conclude that the proposed LISA mission is feasible.

astro-ph.IM↗

arXiv2018

LISA Pathfinder Platform Stability and Drag-free Performance

The science operations of the LISA Pathfinder mission has demonstrated the feasibility of sub-femto-g free-fall of macroscopic test masses necessary to build a LISA-like gravitational wave observatory in space. While the main focus of interest, i.e. the optical axis or the $x$-axis, has been extensively studied, it is also of interest to evaluate the stability of the spacecraft with respect to all the other degrees of freedom. The current paper is dedicated to such a study, with a focus set on an exhaustive and quantitative evaluation of the imperfections and dynamical effects that impact the stability with respect to its local geodesic. A model of the complete closed-loop system provides a comprehensive understanding of each part of the in-loop coordinates spectra. As will be presented, this model gives very good agreements with LISA Pathfinder flight data. It allows one to identify the physical noise source at the origin and the physical phenomena underlying the couplings. From this, the performances of the stability of the spacecraft, with respect to its geodesic, are extracted as a function of frequency. Close to $1 mHz$, the stability of the spacecraft on the $X_{SC}$, $Y_{SC}$ and $Z_{SC}$ degrees of freedom is shown to be of the order of $5.0\ 10^{-15} m\ s^{-2}/\sqrt{Hz}$ for X and $4.0 \ 10^{-14} m\ s^{-2}/\sqrt{Hz}$ for Y and Z. For the angular degrees of freedom, the values are of the order $3\ 10^{-12} rad\ s^{-2}/\sqrt{Hz}$ for $Θ_{SC}$ and $3\ 10^{-13} rad\ s^{-2}/\sqrt{Hz}$ for $H_{SC}$ and $Φ_{SC}$.

astro-ph.IM↗

arXiv2018

Towards the LISA Backlink: Experiment design for comparing optical phase reference distribution systems

LISA is a proposed space-based laser interferometer detecting gravitational waves by measuring distances between free-floating test masses housed in three satellites in a triangular constellation with laser links in-between. Each satellite contains two optical benches that are articulated by moving optical subassemblies for compensating the breathing angle in the constellation. The phase reference distribution system, also known as backlink, forms an optical bi-directional path between the intra-satellite benches. In this work we discuss phase reference implementations with a target non-reciprocity of at most $2π\,\mathrm{μrad/\sqrt{Hz}}$, equivalent to $1\,\mathrm{pm/\sqrt{Hz}}$ for a wavelength of $1064\,\mathrm{nm}$ in the frequency band from $0.1\,\mathrm{mHz}$ to $1\,\mathrm{Hz}$. One phase reference uses a steered free beam connection, the other one a fiber together with additional laser frequencies. The noise characteristics of these implementations will be compared in a single interferometric set-up with a previously successfully tested direct fiber connection. We show the design of this interferometer created by optical simulations including ghost beam analysis, component alignment and noise estimation. First experimental results of a free beam laser link between two optical set-ups that are co-rotating by $\pm 1^\circ$ are presented. This experiment demonstrates sufficient thermal stability during rotation of less than $10^{-4}\,\mathrm{K/\sqrt{Hz}}$ at $1\,\mathrm{mHz}$ and operation of the free beam steering mirror control over more than 1 week.

physics.ins-det↗

arXiv2017

Sub-pm/$\mathrm{\mathbf{\sqrt{\rm Hz}}}$ non-reciprocal noise in the LISA backlink fiber

The future space-based gravitational wave detector Laser Interferometer Space Antenna (LISA) requires bidirectional exchange of light between its two optical benches on board of each of its three satellites. The current baseline foresees a polarization-maintaining single-mode fiber for this backlink connection. Phase changes which are common in both directions do not enter the science measurement, but differential ("non-reciprocal") phase fluctuations directly do and must thus be guaranteed to be small enough. We have built a setup consisting of a Zerodur$^{\rm TM}$ baseplate with fused silica components attached to it using hydroxide-catalysis bonding and demonstrated the reciprocity of a polarization-maintaining single-mode fiber at the 1 pm/$\sqrt{\textrm{Hz}}$ level as is required for LISA. We used balanced detection to reduce the influence of parasitic optical beams on the reciprocity measurement and a fiber length stabilization to avoid nonlinear effects in our phase measurement system (phase meter). For LISA, a different phase meter is planned to be used that does not show this nonlinearity. We corrected the influence of beam angle changes and temperature changes on the reciprocity measurement in post-processing.

physics.ins-det↗

arXiv2017

Laser-Frequency Stabilization via a Quasimonolithic Mach-Zehnder Interferometer with Arms of Unequal Length and Balanced dc Readout

Low frequency high precision laser interferometry is subject to excess laser-frequency-noise coupling via arm-length differences which is commonly mitigated by locking the frequency to a stable reference system. This approach is crucial to achieve picometer level sensitivities in the 0.1 mHz to 1 Hz regime, where laser frequency noise is usually high and couples into the measurement phase via arm-length mismatches in the interferometers. Here we describe the results achieved by frequency stabilising an external cavity diode laser to a quasi-monolithic unequal arm-length Mach-Zehnder interferometer read out at mid-fringe via balanced detection. We find this stabilization scheme to be an elegant solution combining a minimal number of optical components, no additional laser modulations and relatively low frequency noise levels. The Mach-Zehnder interferometer has been designed and constructed to minimize the influence of thermal couplings and to reduce undesired stray light using the optical simulation tool ifocad. We achieve frequency-noise levels below 100 Hz/$\sqrt{\textrm{Hz}}$ at 1 Hz and are able to demonstrate the LISA frequency prestabilization requirement of 300 Hz/$\sqrt{\textrm{Hz}}$ down to frequencies of 100 mHz by beating the stabilized laser with an iodine-locked reference.

physics.ins-det↗