The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. The three-spacecraft constellation forms a nearly-equilateral triangle, which experiences flexing along its orbit around the Sun. These time-varying and unequal armlengths require to process measurements with time-delay interferometry (TDI) to synthesize virtual equal-arm interferometers, and reduce the otherwise overwhelming laser frequency noise. Algorithms compatible with such TDI combinations have recently been proposed in order to suppress the phase fluctuations of the onboard ultra-stable oscillators (USO) used as reference clocks.
In this paper, we propose a new method to cancel USO noise in TDI combinations. This method has comparable performance to existing algorithms, but is more general as it can be applied to most TDI combinations found in the literature. We compute analytical expressions for the residual clock noise before and after correction, accounting for the effect of time-varying beatnote frequencies, previously neglected. We present results of numerical simulations that are in agreement with our models, and show that clock noise can be suppressed below required levels. The suppression algorithm introduces a new modulation noise, for which we propose a partial mitigation. This modulation noise remains the limiting effect for clock-noise suppression, setting strict timing requirements on the sideband generation.
Space-based gravitational-wave observatories such as the Laser Interferometer Space Antenna (LISA) use time-shifted and time-scaled linear combinations of differential laser-phase beat signals to cancel the otherwise overwhelming laser frequency noise. Nanosecond timing precision is needed to accurately form these Time-Delay Interferometry (TDI) combinations which defines a ~1 meter requirement on the inter-spacecraft ranging capability. The University of Florida Hardware-in-the-loop LISA Interferometry Simulator (UFLIS) has been used to test Time-Delay Interferometry in a configuration which …
The Laser Interferometer Space Antenna is a foreseen space-based gravitational wave detector, which aims to detect 10^20 strains in the frequency range from 0.1 mHz to 1 Hz. It is a triangular constellation of three spacecraft, with equal sides of 2,5 x 10^9 m, where every spacecraft hosts a pair of telescopes that simultaneously transmit and receive laser beams measuring the constellation arms by heterodyning the received wavefronts with local references. Due to the spacecraft and constellation jitters, the interfering (received and local) wavefronts become misaligned. We investigate analytic…
In a space based gravitational wave antenna like LISA, involving long light paths linking distant emitter/receiver spacecrafts, signal detection amounts to measuring the light-distance variationsthrough a phase change at the receiver. This is why spurious phase fluctuations due to various mechanical/thermal effects must be carefully studied. We consider here a possible pointing jitter in the light beam sent from the emitter. We show how the resulting phase noise depends on the quality of the wavefront due to the incident beam impinging on the telescope and due to the imperfections of the teles…
The aim of the Laser Interferometer Space Antenna (LISA) is to detect gravitational waves through a phase modulation in long (2.5 Mkm) laser light links between spacecraft. Among other noise sources to be addressed are the phase fluctuations caused by a possible angular jitter of the emitted beam. The present paper follows our preceding one (Vinet et al 2019 Class. Quant. Grav. 36, 205 003) based on an analytical study of the far field phase. We address here a numerical treatment of the phase, to first order in the emitted wavefront aberrations, but without any assumptions on the static bias t…
The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. Laser frequency noise enters the interferometric measurements and dominates the expected gravitational signals by many orders of magnitude. Time-delay interferometry (TDI) is a technique that reduces this laser noise by synthesizing virtual equal-arm interferometric measurements. Laboratory experiments and numerical simulations have confirmed that this reduction is sufficient to meet the scientific goals of the mission in proof-of-concept setups. In…
The LISA mission will likely be a signal dominated detector, such that one challenge is the separation of the different astrophysical sources, and to distinguish between them and the instrumental noise. One of the goals of LISA is to probe the early Universe by detecting stochastic GW backgrounds. As correlation with other detectors is not possible for LISA, discrimination of such a GW background from the instrumental noise requires a good estimate of the latter. To this purpose we have revisited Time Delay Interferometry (TDI) to look for new TDI signal combinations that fulfill the laser fre…
The success of LISA Pathfinder in demonstrating the LISA drag-free requirement paved the road of using space missions for detecting low-frequency and middle-frequency GWs. The new LISA GW mission proposes to use arm length of 2.5 Gm (1 Gm = 106 km). The TAIJI GW mission proposes to use arm length of 3 Gm. In order to attain the requisite sensitivity, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for original LISA,…
With the purpose of understanding how time delay interferometry (TDI) combinations can best be used for the characterisation of LISA instrumental noise, we revisit their laser frequency noise cancellation properties. We have developed an algorithm to search for all possible combinations that suppress noise at the same level as the X, Y and Z classical combination. The algorithm calculates delays using symbolic formulas that explicitly include velocities and accelerations of satellites up to the relevant order. In addition, once a combination has been identified, delays are verified by solving …
We present a comprehensive simulation of the spatial acquisition of optical links for the LISA mission in the in-field pointing architecture, where a fast pointing mirror is used to move the field-of-view of the optical transceiver, which was studied as an alternative scheme to the baselined telescope pointing architecture. The simulation includes a representative model of the far-field intensity distribution and the beam detection process using a realistic detector model, and a model of the expected platform jitter for two alternative control modes with different associated jitter spectra. Fo…
Laser frequency stabilization is a critical part of the interferometry measurement system of space-based gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA). Arm locking as a proposed frequency stabilization technique, transfers the stability of the long arm lengths to the laser frequency. The arm locking sensor synthesizes an adequately filtered linear combination of the inter-spacecraft phase measurements to estimate the laser frequency noise, which can be used to control the laser frequency. At the University of Florida we developed the hardware-based Univ…
Compact Galactic binary systems with orbital periods of a few hours are expected to be detected in gravitational waves (GW) by LISA or a similar mission. At present, these so-called verification binaries provide predictions for GW frequency and amplitude. A full polarisation prediction would provide a new method to calibrate LISA and other GW observatories, but requires resolving the orientation of the binary on the sky, which is not currently possible. We suggest a method to determine the elusive binary orientation and hence predict the GW polarisation, using km-scale optical intensity interf…
Tilt-to-length (TTL) noise from angular jitter in LISA is projected to be the dominant noise source in the milli-Hertz band unless corrected in post-processing. The correction is only possible after removing the overwhelming laser phase noise using time-delay interferometry (TDI). We present here a frequency domain model that describes the effect of angular motion of all three spacecraft on the interferometric signals after propagating through TDI. We then apply a Fisher information matrix analysis to this model to calculate the minimum uncertainty with which TTL coupling coefficients may be e…
The space-based gravitational-wave observatory LISA relies on a form of synthetic interferometry (time-delay interferometry, or TDI) where the otherwise overwhelming laser phase noise is canceled by linear combinations of appropriately delayed phase measurements. These observables grow in length and complexity as the realistic features of the LISA orbits are taken into account. In this paper we outline an implicit formulation of TDI where we write the LISA likelihood directly in terms of the basic phase measurements, and we marginalize over the laser phase noises in the limit of infinite laser…
We report on the first demonstration of time-delay interferometry (TDI) for LISA, the Laser Interferometer Space Antenna. TDI was implemented in a laboratory experiment designed to mimic the noise couplings that will occur in LISA. TDI suppressed laser frequency noise by approximately 10^9 and clock phase noise by 6x10^4, recovering the intrinsic displacement noise floor of our laboratory test bed. This removal of laser frequency noise and clock phase noise in post-processing marks the first experimental validation of the LISA measurement scheme.
eLISA/NGO is a new gravitational wave detection proposal with arm length of 10^6 km and one interferometer down-scaled from LISA. Just like LISA and ASTROD-GW, in order to attain the requisite sensitivity for eLISA/NGO, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for LISA and ASTROD-GW with one arm dysfunctional by using the CGC 2.7 ephemeris. The results are well below their respective limits which the laser fr…
One of the atom interferometer gravitational wave missions proposed by Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested gravitational wave sensitivity set by the atom state detection shot noise level that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20 mHz, and had better sensitivity from 20 to 500 mHz. The separation between the spacecraft was 1,000 km, with atom interferometers 200 m long and shades from sunlight used at each end. A careful analysis of many error sources was included, but requirements on the time-stability of both the laser wavefr…
We present a study of the use and limits of the Time-Delay Interferometry null channels for in flight estimation of the Laser Interferometer Space Antenna instrumental noise. The paper considers how the two main limiting noise sources, test-mass acceleration noise and interferometric phase measurement noise, propagate through different Time-Delay Interferometry channels: the Michelson combination X that is the most sensitive to gravitational waves, then the less-sensitive combinations $α$, and finally the null channel $ζ$. We note that the null channel $ζ$, which is known to be equivalent to a…
Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA), a gravitational-wave observatory sensitive in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking includ…
In this paper, we describe a hybrid-extended Kalman filter algorithm to synchronize the clocks and to precisely determine the inter-spacecraft distances for space-based gravitational wave detectors, such as (e)LISA. According to the simulation, the algorithm has significantly improved the ranging accuracy and synchronized the clocks, making the phase-meter raw measurements qualified for time- delay interferometry algorithms.
Time-delay interferometry (TDI) is a processing step essential for the scientific exploitation of LISA, as it reduces the otherwise overwhelming laser noise in the interferometric measurements. The fundamental idea is to define new laser-noise-free observables by combining appropriately time-shifted measurements. First- and second-generation TDI combinations cancel laser noise under the assumption that the LISA armlengths are constant or evolve linearly with time, respectively. We recently extended TDI by solving for the laser-noise-free combinations implicitly, writing the likelihood of the d…
LISA Non-Linear Dynamics and Tilt-To-Length Coupling
Universität Heidelberg（海德堡大学）；KU Leuven（荷语鲁汶大学）；Leuven Gravity Institute, KU Leuven（荷语鲁汶大学引力研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
We present recent sensitivity measurements of the LISA Technology Package interferometer with articulated mirrors as test masses, actuated by piezo-electric transducers. The required longitudinal displacement resolution of 9 pm/sqrt[Hz] above 3 mHz has been demonstrated with an angular noise that corresponds to the expected in on-orbit operation. The excess noise contribution of this test mass jitter onto the sensitive displacement readout was completely subtracted by fitting the angular interferometric data streams to the longitudinal displacement measurement. Thus, this cross-coupling consti…
We present a mission concept, the Geostationary Antenna for Disturbance-Free Laser Interferometry (GADFLI), for a space-based gravitational-wave interferometer consisting of three satellites in geostationary orbit around the Earth. Compared to the nominal design of the Laser Interferometer Space Antenna (LISA), this concept has the advantages of significantly decreased requirements on the telescope size and laser power, decreased launch mass, substantially improved shot noise resulting from the shorter 73000 km armlengths, simplified and less expensive communications, and an overall lower cost…
The future space-based gravitational wave observatory LISA will consist of a constellation of three spacecraft in a triangular constellation, connected by laser interferometers with 2.5 million-kilometer arms. Among other challenges, the success of the mission strongly depends on the quality of the cancellation of laser frequency noise, whose power lies eight orders of magnitude above the gravitational signal. The standard technique to perform noise removal is time-delay interferometry (TDI). TDI constructs linear combinations of delayed phasemeter measurements tailored to cancel laser noise t…
Alternative approach to time-delay interferometry with optical frequency comb
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；Center for Research and Exploration in Space Science and Technology, NASA/GSFC（NASA/戈达德太空飞行中心空间科学与技术研究探索中心）；Massachusetts Institute of Technology（麻省理工学院）；University of Arizona（亚利桑那大学）
Time-delay interferometry (TDI) is a data processing technique for LISA designed to suppress the otherwise overwhelming laser noise by several orders of magnitude. It is widely believed that TDI can only be applied once all phase or frequency measurements from each spacecraft have been synchronized to a common time frame. We demonstrate analytically, using as an example the commonly-used Michelson combination X, that TDI can be computed using the raw, unsynchronized data, thereby avoiding the need for an initial synchronization processing step and significantly simplifying the initial noise re…
The Laser Interferometer Space Antenna (LISA) is a future space-based gravitational wave (GW) detector designed to be sensitive to sources radiating in the low frequency regime (0.1 mHz to 1 Hz). LISA's interferometer signals will be dominated by laser frequency noise which has to be suppressed by about 7 orders of magnitude using an algorithm called Time-Delay Interferometry (TDI). Arm locking has been proposed to reduce the laser frequency noise by a few orders of magnitude to reduce the potential risks associated with TDI. In this paper, we present an updated performance model for arm locki…
The ultimate astronomical observatory would be a formation flying interferometer in space, immune to atmospheric turbulence and absorption, free from atmospheric and telescope thermal emission, and reconfigurable to adjust baselines according to the required angular resolution. Imagine the near/mid-infrared sensitivity of the JWST and the far-IR sensitivity of Herschel but with ALMA-level angular resolution, or imagine having the precision control to null host star light across 250m baselines and to detect molecules from the atmospheres of nearby exo-Earths. With no practical engineering limit…
The arm length and the isolation in space enable LISA to probe for signals unattainable on ground, opening a window to the sub-Hz gravitational-wave universe. The coupling of unavoidable angular spacecraft jitter into the longitudinal displacement measurement, an effect known as tilt-to-length (TTL) coupling, is critical for realizing the required sensitivity of picometer$/\sqrt{\rm{Hz}}$. An ultra-stable interferometer testbed has been developed in order to investigate this issue and validate mitigation strategies in a setup representative of LISA, and in this paper it is operated in the long…
Impact of the noise knowledge uncertainty for the science exploitation of cosmological and astrophysical stochastic gravitational wave background with LISA
The analysis of gravitational wave (GW) datasets is based on the comparison of measured time series with theoretical templates of the detector's response to a variety of source parameters. For LISA, the main scientific observables will be the so-called time-delay interferometry (TDI) combinations, which suppress the otherwise overwhelming laser noise. Computing the TDI response to GW involves projecting the GW polarizations onto the LISA constellation arms, and then combining projections delayed by a multiple of the light propagation time along the arms. Both computations are difficult to perf…
Searching systematically for coupling of laser and phase-modulation noise in heterodyne interferometry
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Center for Research and Exploration in Space Science and Technology, NASA/GSFC（NASA/GSFC空间科学与技术研究探索中心）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
Overlap reduction functions for a polarized stochastic gravitational-wave background in the Einstein Telescope-Cosmic Explorer and the LISA-Taiji networks
本文将基于球谐展开的重叠减少函数计算方法推广到第三代地基 Einstein Telescope-Cosmic Explorer 网络及 LISA-Taiji 空间联合任务，以分析极化随机引力波背景。
The Laser Interferometer Space Antenna is a foreseen gravitational wave detector, which aims to detect $10^{-20}$ strains in the frequency range from 0.1 mHz to 1 Hz. It is a triangular constellation, with equal sides of $2,5 \times 10^9$ m, of three spacecraft, where heterodyne interferometry measures the spacecraft distances. The stray light from the powerful transmitted beam can overlap with the received one and interfere with the heterodyne signal. We investigated the contribution of random phase variations of the stray photons to the noise of the heterodyne signal. A balanced detection sc…
Tilt-to-length coupling is a technical term for the cross-coupling of angular or lateral jitter into an interferometric phase signal. It is an important noise source in precision interferometers and originates either from changes in the optical path lengths or from wavefront and clipping effects. Within this paper, we focus on geometric TTL coupling and categorize it into a number of different mechanisms for which we give analytic expressions. We then show that this geometric description is not always sufficient to predict the TTL coupling noise within an interferometer. We, therefore, discuss…
LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena's follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localizati…
Time delay interferometry with minimal null frequencies and shortened time span
Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术研究院）；Department of Physics, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院物理系）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）
Inter satellite laser interferometry is a central component of future space-borne gravity instruments like LISA, eLISA, NGO and future geodesy missions. The inherently small laser wavelength allows to measure distance variations with extremely high precision by interfering a reference beam with a measurement beam. The readout of such interferometers is often based on tracking phasemeters, able to measure the phase of an incoming beatnote with high precision over a wide range of frequencies. The implementation of such phasemeters is based on all digital phase-locked loops, hosted in FPGAs. Here…
