Automatic alignment of optical interferometers

Two-Axial Measurement of the Angular Microdeflection of a Laser Beam Using One Single-Axis Sensor

The majority of current methods for measuring the angular deflection of a laser beam enable measurement only in one selected plane. However, there are tasks in which measurements of laser beam deflections in 3D are required. In this paper, we present a way of enabling two-axial measurements of the deflection of a beam based on a single-axis sensor. The key idea is to direct a laser beam, alternately, into one of two arms of a measurement system. In the first arm, the beam is transmitted directly to the angular sensor, while in the second, the beam is directed to the sensor via a special optical element that rotates the plane of the beam deflection; in other words, this element changes the deflection in the horizontal plane into a deflection in the vertical plane, and vice versa. To alternate the path of the beam, a variable phase retarder and a polarising beamsplitter are used. The proposed technique was experimentally verified, and the results confirm its effectiveness.

Coherent angular signal amplification using an optical cavity

Precision angular sensing is an essential technology in physical experiments. Unlike length sensing with a laser beam, it has been thought that sensitivity to the angular motion cannot be enhanced with the help of an optical cavity. A method of angular signal amplification using an optical cavity, called the cavity-amplified angular sensor (CAAS), is proposed. By adjusting or compensating for the Gouy phase of the cavity, the electric field of the laser generated in proportion to the target rotation is coherently stacked in the proposed method. The advantage of this method over other angular sensors is its high sensitivity with the small sensing spot size. Three possible optical configurations are considered, of which two experimentally available ones are investigated. The angular signal amplification is demonstrated for both of them. Based on the theoretical calculation for a realistic model, the fundamental angular sensing noise level is expected to be as low as 10^-15rad/Hz^1/2, with a 1 mm laser beam size and 10 mW laser power.

Review of the Advanced LIGO Gravitational Wave Observatories Leading to Observing Run Four

Gravitational waves from binary black hole and neutron star mergers are being regularly detected. As of 2021, 90 confident gravitational wave detections have been made by the LIGO and Virgo detectors. Work is ongoing to further increase the sensitivity of the detectors for the fourth observing run, including installing some of the A+ upgrades designed to lower the fundamental noise that limits the sensitivity to gravitational waves. In this review, we will provide an overview of the LIGO detectors optical configuration and lock acquisition procedure, discuss the detectors’ fundamental and technical noise limits, show the current measured sensitivity, and explore the A+ upgrades currently being installed in the detectors.

Pure modulation and accurate measurement of optical beam's tilt and displacement

We developed a tilt modulation technique of a laser beam with a wedged crystal. Combined with a phase-compensating crystal, a pure tilt modulation with a wide bandwidth (actually determined by the bandwidth of electro-optic crystals) is realized. By Fourier transformation with a lens, the tilt signal is transformed into displacement. With homodyne detection using a local oscillator of the first-order Hermite-Gauss mode (HG₁₀) and a 4F phase-monitoring system, we measure the displacement and tilt of a laser probe beam. This technique can be used in metrology, such as Newtonian gravitational constant determination and gravitational wave detection, or the calibration of a spatial sensor, such as tilt/displacement sensors.

Power coupling losses for misaligned and mode-mismatched higher-order Hermite-Gauss modes

This paper analytically and numerically investigates misalignment and mode-mismatch-induced power coupling coefficients and losses as a function of Hermite-Gauss (HG) mode order. We show that higher-order HG modes are more susceptible to beam perturbations when, for example, coupling into optical cavities: the misalignment and mode-mismatch-induced power coupling losses scale linearly and quadratically with respect to the mode indices, respectively. As a result, the mode-mismatch tolerance for the ${{\rm HG}_{3,3}}$ mode is reduced to a factor of 0.28 relative to the currently used ${{\rm HG}_{0,0}}$ mode. This is a potential hurdle to using higher-order modes to reduce thermal noise in future gravitational-wave detectors.

Differential wavefront sensing and control using radio-frequency optical demodulation

Differential wavefront sensing is an essential technique for optimising the performance of many precision interferometric experiments. Perhaps the most extensive application of this is for alignment sensing using radio-frequency beats measured with quadrant photodiodes. Here we present a new technique that uses optical demodulation to measure such optical beats at high resolutions using commercial laboratory equipment. We experimentally demonstrate that the images captured can be digitally processed to generate wavefront error signals and use these in a closed loop control system for correct wavefront errors for alignment and mode-matching a beam into an optical cavity to 99.9%. This experiment paves the way for the correction of even higher order errors when paired with higher order wavefront actuators. Such a sensing scheme could find use in optimizing complex interferometers consisting of coupled cavities, such as those found in gravitational wave detectors, or simply just for sensing higher order wavefront errors in heterodyne interferometric table-top experiments.

Laser acquisition experimental demonstration for space gravitational wave detection missions

The laser acquisition-pointing technique is one of the most important techniques for space gravitational wave detection missions, like the Taiji program and the LISA (Laser Interferometer Space Antenna) program. The laser acquisition system suppresses the laser deviation angle to 1 µrad at the receiving aperture. Corresponding to 80 times of telescope magnification, the acquisition accuracy should reach 80 µrad at the acquisition camera. In order to verify the feasibility of the laser acquisition scheme, a laser acquisition ground simulation experimental system is designed and constructed. The experimental system simulates the actual acquisition process of the Taiji from three aspects: optical path, acquisition accuracy and acquisition scanning process. In the experiment, the coupling between the laser acquisition system and the laser pointing system is considered by introducing the DWS (Differential Wave-front Sensing) technique to calibrate the reference position of the acquisition camera and read out the acquisition precision. Due to limited beam propagation distance in the ground experiment, the in-flat top properties of the transmitting beam will greatly affect the acquisition precision. Based on the analysis of the influence, an improved acquisition ground simulation scheme is introduced. The experimental results indicate that the experimental system can achieve the acquisition accuracy of sub-10 µrad magnitude at the acquisition camera. The experimental system realizes methodological demonstration of the acquisition scheme. The results offer the experimental foundation and theoretical basis for the acquisition system of the Taiji/LISA program.

Interferometer Sensing and Control for the Advanced Virgo Experiment in the O3 Scientific Run

Advanced Virgo is a 2nd-generation laser interferometer based in Cascina (Italy) aimed at the detection of gravitational waves (GW) from astrophysical sources. Together with the two USA-based LIGO interferometers they constitute a network which operates in coincidence. The three detectors observed the sky simultaneously during the last part of the second Observing Run (O2) in August 2017, and this led to two paramount discoveries: the first three-detector observation of gravitational waves emitted from the coalescence of a binary black hole system (GW170814), and the first detection ever of gravitational waves emitted from the coalescence of a binary neutron star system (GW170817). Coincident data taking was re-started for the third Observing Run (O3), which started on 1st April 2019 and lasted almost one year. This paper will describe the new techniques implemented for the longitudinal controls with respect to the ones already in use during O2. Then, it will present an extensive description of the full scheme of the angular controls of the interferometer, focusing on the different control strategies that are in place in the different stages of the lock acquisition procedure, which is the complex sequence of operations by which an uncontrolled, “free” laser interferometer is brought to the final working point, which allows the detector to reach the best sensitivity.

Advanced LIGO Laser Systems for O3 and Future Observation Runs

The advanced LIGO gravitational wave detectors need high power laser sources with excellent beam quality and low-noise behavior. We present a pre-stabilized laser system with 70 W of output power that was used in the third observing run of the advanced LIGO detectors. Furthermore, the prototype of a 140 W pre-stabilized laser system for future use in the LIGO observatories is described and characterized.

Tilt-to-length noise coupled by wavefront errors in the interfering beams for the space measurement of gravitational waves

The space-based gravitational wave detection programs, like the Laser Interferometer Space Antenna (LISA) or the Taiji program, aim to detect gravitational waves in space with a triangular constellation of three spacecraft. The unavoidable jitters of the spacecraft and the pointing will couple with the misalignment of the interfering beams into the longitudinal path length readout. This effect is called tilt-to-length (TTL) coupling, which is one of the keys to achieving the required measuring accuracy of 1pm/Hz. In terms of two phase definitions (the LISA Pathfinder (LPF) signal and the Average Phase (AP) signal), we implement the comprehensive theoretical analysis concerning the effect of aberrations on TTL coupling noise. In addition, we analytically derive that the proper lateral shift of the interfering beams relative to the detector can partly cancel out the TTL noise coupled with aberrations, especially coma and trefoil aberrations for the AP signal. Based on the above results, the meaningful guidance can be provided for the design and construction of the optical system in LISA or Taiji.

Architecture and performance analysis of an optical metrology terminal for satellite-to-satellite laser ranging

Interferometric laser ranging is an enabling technology for high-precision satellite-to-satellite tracking within the context of Earth observation, gravitational wave detection, or formation flying. In orbit, the measurement system is affected by environmental influences, particularly satellite attitude jitter and temperature fluctuations, imposing an instrument design with a high level of thermal stability and insensitivity to rotations around the spacecraft center of mass. The new design concept presented here combines different approaches for dynamic heterodyne laser ranging and features the inherent beam-tracking capabilities of a retroreflector in a mono-axial configuration. It allows for a continuously adjustable distance between the optical bench and the location of its fiducial point, facilitating future inter-satellite tracking with nanometer accuracy, e.g., the next-generation gravity mission.

Fake tilts in differential wavefront sensing

Two-beam interferometry is a tool of high-precision length-metrology, where displacements are measured to within sub-nanometer resolution and accuracy. Differential wavefront sensing - via phase detection by segmented photodiodes - adds the capability of simultaneously measuring the target translation and rotation. This paper gives an analytical model explaining the observation of fake tilts by a combined x-ray and optical interferometer.

Multi-axis heterodyne interferometry at MHz frequencies: a short-arm measurement demonstration for LISA with off-the-shelf hardware

We report the design, construction, and operation of a multi-axis heterodyne interferometry (MAHI) system operating at MHz heterodyne frequencies, which provides a testbed for technologies to be used in the Laser Interferometer Space Antenna (LISA) space-based gravitational wave mission. The system was calibrated for measurement of the piston, pitch, and yaw of a three-axis piezo-actuated mirror, giving measured calibration values that closely match those predicted by a simulation based on Gaussian beam tracing. The piston sensitivity of the MAHI system in the LISA band was measured to be below 10  pm Hz^-1/2 for frequencies above 4 mHz and below 1  pm Hz^-1/2 for frequencies above 35 mHz. The sensitivity is limited above 2 Hz by the mechanical vibrations of the apparatus and below 1 mHz by dimensional changes caused by temperature fluctuations. Evidence points towards scattered light as the limiting noise source at intermediate frequencies. The angular sensitivity of the MAHI system was measured to be close to or below 10  nrad Hz^-1/2 for frequencies above 4 mHz and below 1  nrad Hz^-1/2 for frequencies above 100 mHz. Noise budgets for both length and angle were determined, indicating the areas in which improvements must be made in order to reach increased sensitivity. The current operating sensitivity already provides a useful testbed for LISA technologies and a potential blueprint for future ground segment equipment.

In-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 degrees of freedom two-way laser link between remote spacecraft succeeded on the first attempt. Active beam pointing based on differential wave front 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  nm/sqrt[Hz] at Fourier frequencies above 100 mHz.

High-performance phase camera as a frequency selective laser wavefront sensor for gravitational wave detectors

We have designed, built and tested a high-performance phase camera, which can observe laser wavefronts in a large range of sideband frequencies. Our phase camera scans the laser beam over a pinhole diode and uses a heterodyne technique to independently assess the information in the upper and lower sidebands of up to five different modulation frequencies. Amplitude and phase images, consisting of 2¹⁴ points each, are obtained every second for each of the 11 demodulated frequencies in parallel. The achieved sensitivity is about 4×10^-3 rad (λ/1600 at λ = 1064 nm) at the center of the beam, corresponding to a wavefront deformation of 0.7 nm, and drops to about 3 nm over the beam size. This sensitivity is extremely useful for diagnostic purposes in gravitational wave detectors and fits the requirements for control loops in Advanced Virgo. We report on the design, realization and performance of our phase camera.

A phase modulating homodyne interferometer with tilting error compensation by use of an integrated four-photodetector

The tilting error of the measuring reflector moving with the measured object influences the accuracy of displacement measurement in laser interferometers. To solve this problem, a phase modulating homodyne interferometer with tilting error compensation is proposed for precision displacement measurement. In this interferometer, the displacement and tilting angle of the measured object are obtained simultaneously by differentially processing the phase changes of four interference signals detected with an integrated four-photodetector, and the obtained tilting angle is used to compensate its influence on the displacement result. The optical configuration of this interferometer is designed, and the displacement measurement with tilting error compensation is presented. An experimental setup is constructed, and the feasibility and effectiveness of the proposed interferometer are demonstrated.

Three-degrees-of-freedom laser interferometer based on differential wavefront sensing with wide angular measurement range

We present a three-degrees-of-freedom laser interferometer based on differential wavefront sensing with a wide angular measurement range. To obtain measurement signals with a high AC/DC ratio and improve the linearity of differential wavefront sensing in a wide range angular displacement measurement, a fiber bundle instead of a quadrant photodiode is applied to receive the interference light. Meanwhile, a decoupled algorithm with quadratic correction derived by the ray tracing method and kinematic analysis is detailed in the case of the wide range angular displacement. The simulation and experimental results prove that the laser interferometer with the proposed structure could realize hundreds of microradian range of angular displacement measurement, which are expanded in the differential wavefront sensing.

Mitigating Mode-Matching Loss in Nonclassical Laser Interferometry

Strongly squeezed states of light are a key technology in boosting the sensitivity of interferometric setups, such as in gravitational-wave detectors. However, the practical use of squeezed states is limited by optical loss, which reduces the observable squeeze factor. Here, we experimentally demonstrate that introducing squeezed states in additional, higher-order spatial modes can significantly improve the observed nonclassical sensitivity improvement when the loss is due to mode-matching deficiencies. Our results could be directly applied to gravitational-wave detectors, where this type of loss is a major contribution.

Interference sensor for ultra-precision measurement of laser beam angular deflection

A new interference sensor for ultra-precise measurement of laser beam angular deflection is proposed. The angular tilt of the measuring device, in relation to the beam axis, can also be measured. The theoretical basis of the angle evaluation presented is based upon analyzing the fringe period, as well as the suggested optical setup and design of the device. Calculating algorithms for the evaluation of the beam angle change, the influence of the fringe phase on angle measurement, and the metrological feasibilities are also detailed herein. The main source of measurement errors is explored, and the influence of the sensor's positioning procedure in relation to the laser beam on the repeatability of the processing function is statistically analyzed. The results show that the sensor resolution reaches 25 nrad with an accuracy better than 1% in the measuring range 350 µrad. Finally, the potential applications of the interference sensor are described.

Inter-satellite laser link acquisition with dual-way scanning for Space Advanced Gravity Measurements mission

Laser link acquisition is a key technology for inter-satellite laser ranging and laser communication. In this paper, we present an acquisition scheme based on the differential power sensing method with dual-way scanning, which will be used in the next-generation gravity measurement mission proposed in China, called Space Advanced Gravity Measurements (SAGM). In this scheme, the laser beams emitted from two satellites are power-modulated at different frequencies to enable the signals of the two beams to be measured distinguishably, and their corresponding pointing angles are determined by using the differential power sensing method. As the master laser beam and the slave laser beam are decoupled, the dual-way scanning method, in which the laser beams of both the master and the slave satellites scan uncertainty cones simultaneously and independently, can be used, instead of the commonly used single-way scanning method, in which the laser beam of one satellite scans and that of the other one stares. Therefore, the acquisition time is reduced significantly. Numerical simulation and experiments of the acquisition process are performed using the design parameters of the SAGM mission. The results show that the average acquisition time is less than 10 s for a scanning range of 1-mrad radius with a success rate of more than 99%.

Predictor-corrector framework for the sequential assembly of optical systems based on wavefront sensing

Alignment of optical components is crucial for the assembly of optical systems to ensure their full functionality. In this paper we present a novel predictor-corrector framework for the sequential assembly of serial optical systems. Therein, we use a hybrid optical simulation model that comprises virtual and identified component positions. The hybrid model is constantly adapted throughout the assembly process with the help of nonlinear identification techniques and wavefront measurements. This enables prediction of the future wavefront at the detector plane and therefore allows for taking corrective measures accordingly during the assembly process if a user-defined tolerance on the wavefront error is violated. We present a novel notation for the so-called hybrid model and outline the work flow of the presented predictor-corrector framework. A beam expander is assembled as demonstrator for experimental verification of the framework. The optical setup consists of a laser, two bi-convex spherical lenses each mounted to a five degree-of-freedom stage to misalign and correct components, and a Shack-Hartmann sensor for wavefront measurements.

Alignment sensing for optical cavities using radio-frequency jitter modulation

Alignment sensing is often required in precision interferometry applications such as Advanced LIGO in order to achieve the optimum performance. Currently favored sensing schemes rely on the use of two separate radio-frequency (RF) quadrant photodetectors and Gouy phase telescopes to determine the alignment of a beam relative to an optical cavity axis. In this paper, we demonstrate an alternative sensing scheme that has potential advantages over the current standard schemes. We show that by using electro-optic beam deflectors to impose RF jitter sidebands on a beam, it is possible to extract full alignment signals for two in-line optical cavities from just one single-element photodetector in reflection of each cavity.

Interferometric wavefront sensing with a single diode using spatial light modulation

We present a new technique for the fine alignment sensing of optical interferometers. Unlike conventional wavefront sensing systems, which use multielement photodiodes, this approach works with a single-element photodiode, in combination with a spatial light modulator (SLM) and digitally enhanced heterodyne interferometry. As all signals pass through a single photodetection and analog path, the technique exhibits high common-mode rejection to low frequency errors present in conventional systems. By changing the modulation pattern on the SLM, the technique can also be extended to sensing higher-order wavefront errors. In this paper, we demonstrate the technique experimentally and compare performance with a conventional heterodyne wavefront sensing system. This may improve and simplify alignment systems in space-based interferometers such as the planned LISA gravitational wave detector and provide a way to optimize the power in laser cavities not possible with the traditional segmented diode approach.

Interferometer techniques for gravitational-wave detection

Several km-scale gravitational-wave detectors have been constructed worldwide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review, we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.

Coherently combined master oscillator fiber power amplifiers for Advanced Virgo

Stable low-noise high-power lasers are indispensable in advancing the strain sensitivity of interferometric gravitational wave detectors. Advanced LIGO and Advanced Virgo are currently under commissioning and require about 200 W of single-frequency laser power, while the future detector design may require up to the order of 500 W. In this Letter, we present the design and, to the best of our knowledge, the first experimental demonstration of the laser system for Advanced Virgo that is based on coherently combined fiber laser amplifiers. We show the long-term performance of two 40 W fiber laser amplifiers, as well as their characterization in terms of beam quality, power noise, phase noise, and beam pointing. Moreover, a simple and compact setup utilizing fibered modulators and actuators for the coherent beam combination of these two fiber laser amplifiers is reported. A combination efficiency of about 96% was achieved, and no spurious noise was observed.

Characterization of optical systems for the ALPS II experiment

ALPS II is a light shining through a wall style experiment that will use the principle of resonant enhancement to boost the conversion and reconversion probabilities of photons to relativistic WISPs. This will require the use of long baseline low-loss optical cavities. Very high power build up factors in the cavities must be achieved in order to reach the design sensitivity of ALPS II. This necessitates a number of different sophisticated optical and control systems to maintain the resonance and ensure maximal coupling between the laser and the cavity. In this paper we report on the results of the characterization of these optical systems with a 20 m cavity and discuss the results in the context of ALPS II.

Spatially resolved photodiode response for simulating precise interferometers

Quadrant photodiodes (QPDs) are used in laser interferometry systems to simultaneously detect longitudinal displacement of test masses and angular misalignment between the two interfering beams. The latter is achieved by means of the differential wavefront sensing (DWS) technique, which provides ultra-high precision for measuring angular displacements. We have developed a setup to obtain the spatially resolved response of QPDs that, together with an extension of the simulation software IfoCAD, allows us to use the measured response in simulations and accurately predict the desired longitudinal and DWS phase observables. Three different commercial off-the-shelf QPD candidates for space-based interferometry were characterized. The measured response of one QPD was used in optical simulations. Nonuniformities in the response of the device and crosstalk between segments do not introduce significant variations in the longitudinal and DWS measurands with respect to the standard case when a uniform QPD without crosstalk is used.

Experimental demonstration of reduced tilt-to-length coupling by a two-lens imaging system

The coupling between beam tilt and longitudinal path length readout in a setup representing a LISA test mass interferometer was reduced to below 2 µm/rad using a two lens imaging system. This was achieved by the use of a homodyne equal arm-length Mach-Zehnder interferometer and suppression of the dominating effects of higher order Gaussian modes and longitudinal actuator movement. The latter was subtracted using the phase signal of a large single element photo diode.

GW150914: The Advanced LIGO Detectors in the Era of First Discoveries

Following a major upgrade, the two advanced detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) held their first observation run between September 2015 and January 2016. With a strain sensitivity of 10^{-23}/sqrt[Hz] at 100 Hz, the product of observable volume and measurement time exceeded that of all previous runs within the first 16 days of coincident observation. On September 14, 2015, the Advanced LIGO detectors observed a transient gravitational-wave signal determined to be the coalescence of two black holes [B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016)], launching the era of gravitational-wave astronomy. The event, GW150914, was observed with a combined signal-to-noise ratio of 24 in coincidence by the two detectors. Here, we present the main features of the detectors that enabled this observation. At full sensitivity, the Advanced LIGO detectors are designed to deliver another factor of 3 improvement in the signal-to-noise ratio for binary black hole systems similar in mass to GW150914.

Alignment sensing and control for squeezed vacuum states of light

Beam alignment is an important practical aspect of the application of squeezed states of light. Misalignments in the detection of squeezed light result in a reduction of the observable squeezing level. In the case of squeezed vacuum fields that contain only very few photons, special measures must be taken in order to sense and control the alignment of the essentially dark beam. The GEO 600 gravitational wave detector employs a squeezed vacuum source to improve its detection sensitivity beyond the limits set by classical quantum shot noise. Here, we present our design and implementation of an alignment sensing and control scheme that ensures continuous optimal alignment of the squeezed vacuum field at GEO 600 on long time scales in the presence of free-swinging optics. This first demonstration of a squeezed light automatic alignment system will be of particular interest for future long-term applications of squeezed vacuum states of light.

The advanced LIGO input optics

The advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics subsystem is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article, we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.

Advanced technologies for future ground-based, laser-interferometric gravitational wave detectors

We present a review of modern optical techniques being used and developed for the field of gravitational wave detection. We describe the current state-of-the-art of gravitational waves detector technologies with regard to optical layouts, suspensions and test masses. We discuss the dominant sources and noise in each of these subsystems and the developments that will help mitigate them for future generations of detectors. We very briefly summarise some of the novel astrophysics that will be possible with these upgraded detectors.

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.

Methodological demonstration of laser beam pointing control for space gravitational wave detection missions

In space laser interferometer gravitational wave (G.W.) detection missions, the stability of the laser beam pointing direction has to be kept at 10 nrad/√Hz. Otherwise, the beam pointing jitter noise will dominate the noise budget and make the detection of G.W. impossible. Disturbed by the residue non-conservative forces, the fluctuation of the laser beam pointing direction could be a few μrad/√Hz at frequencies from 0.1 mHz to 10 Hz. Therefore, the laser beam pointing control system is an essential requirement for those space G.W. detection missions. An on-ground test of such beam pointing control system is performed, where the Differential Wave-front Sensing technique is used to sense the beams pointing jitter. An active controlled steering mirror is employed to adjust the beam pointing direction to compensate the jitter. The experimental result shows that the pointing control system can be used for very large dynamic range up to 5 μrad. At the interested frequencies of space G.W. detection missions, between 1 mHz and 1 Hz, beam pointing stability of 6 nrad/√Hz is achieved.

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.

Length control of an optical resonator using second-order transverse modes

We present the analysis of an unorthodox technique for locking a laser to a resonant optical cavity. Error signals are derived from the interference between the fundamental cavity mode and higher-order spatial modes of order two excited by mode mismatch. This scheme is simple, inexpensive, and, in contrast to similar techniques, first-order insensitive to beam jitter. After mitigating sources of technical noise, performance is fundamentally limited by quantum shot noise.

Interference method for ultra-precision measurement and compensation of laser beam angular deflection

A new interferometric method for ultra-precise measurement of laser-beam angular deflection is proposed. The angular tilt of a measuring device in relation to the beam axis also can be measured. The method is based on interference fringe period analysis in the selected plane of measurement. The theoretical basis and experimental verification of the method are presented. It is shown that by using the proposed technique, it is possible to measure the laser beam angular deflection or instability with ultrahigh resolution reaching single nanoradians. The proposed method allows the measurement and further compensation of laser beam deflections in a very compact design.

Angular control of optical cavities in a radiation-pressure-dominated regime: the Enhanced LIGO case

We describe the angular sensing and control (ASC) of 4 km detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO). Enhanced LIGO, the culmination of the first generation LIGO detectors, operated between 2009 and 2010 with about 40 kW of laser power in the arm cavities. In this regime, radiation-pressure effects are significant and induce instabilities in the angular opto-mechanical transfer functions. Here we present and motivate the ASC design in this extreme case and present the results of its implementation in Enhanced LIGO. Highlights of the ASC performance are successful control of opto-mechanical torsional modes, relative mirror motions of ≤ 1×10(-7) rad rms, and limited impact on in-band strain sensitivity.

Feedback control of optical beam spatial profiles using thermal lensing

A method for active control of the spatial profile of a laser beam using adaptive thermal lensing is described. A segmented electrical heater was used to generate thermal gradients across a transmissive optical element, resulting in a controllable thermal lens. The segmented heater also allows the generation of cylindrical lenses, and provides the capability to steer the beam in both horizontal and vertical planes. Using this device as an actuator, a feedback control loop was developed to stabilize the beam size and position.

Bicell-photodetector in the Fourier plane as a fiber optic homodyne phase demodulator: theoretical model and experimental results

A concept of the Young interference experiment has been applied in the design of a fiber optic homodyne phase demodulator. The system is based on a bicell-photodetector in the Fourier plane. The above system has been designed, described, and verified together with an estimation of the minimization of phase measurement error in connection with the distance between photodetectors, wavelength, and focal length of the Fourier lens. The fundamental investigation concerning the choice of a distance between photodetectors and its influence on the demodulator's linearity has been presented and discussed as well.

Interferometric characterization and modeling of pathlength errors resulting from beamwalk across mirror surfaces in LISA

An alternative payload concept with in-field pointing for the laser interferometer space antenna utilizes an actuated mirror in the telescope for beam tracking to the distant satellite. This actuation generates optical pathlength variations due to the resulting beamwalk over the surface of subsequent optical components, which could possibly have a detrimental influence on the accuracy of the measurement instrument. We have experimentally characterized such pathlength errors caused by a λ/10 mirror surface and used the results to validate a theoretical model. This model is then applied to predict the impact of this effect for the current optical design of the LISA off-axis wide-field telescope.

Aligning a reflection cavity by Anderson's method

The sounding rocket principle of equivalence measurement uses a set of four laser gauges operating in Fabry-Perot cavities to determine the relative acceleration of two test masses that are chemically different. One end of each cavity is a flat mirror on a test mass. Because the test masses are unconstrained and thus expected to rotate slightly during measurement, and because the distance measurements are made at the sub-picometer level, it is essential to have real-time alignment of the beam entering the cavity. However, the cavity must be used in reflection and space is limited. We show that Anderson's alignment method can be used in reflection, but that it requires that the Fabry-Perot cavity have mirrors with significantly unequal reflectivities.

Invited review article: Interferometric gravity wave detectors

A direct detection of gravitational waves is still lacking today. A network of several earthbound interferometric detectors is currently operating with a continuously improving sensitivity. The window of interest for observation has a lower cut off in the frequency domain below some tens of hertz, determined by the effect of seismic motion. For larger frequencies, the sensitivity is limited by thermal effects below few hundreds of hertz and by the quantum nature of light above that value. Each of these sources of noise pose a big technological challenge to experimentalists, and there are big expectations for the next generation of detectors. A reduction of thermal effects by at least one order of magnitude will be obtained with new and carefully designed materials. At that point the quantum nature of light will become an issue, and the use of quantum non-demolition techniques will become mandatory. In this review, we discuss interferometric detection of gravitational waves from an instrumental point of view. We try to address conceptually important issues with an audience of non-experts in mind. A particular emphasis is given to the description of the current limitations and to the perspectives of beating them.

Experimental demonstration of weak-light laser ranging and data communication for LISA

Interferometric gravitational wave detectors with an unequal and time-varying arm length configuration like the Laser Interferometer Space Antenna rely on time-delay interferometry (TDI) for laser frequency noise subtraction. However, the TDI algorithm requires a laser ranging scheme with meter accuracy over a five million kilometer arm length. At the end of each arm only about 100 pW of light power will be detected for gravitational wave measurements and only 1% of this power can be used for laser ranging in order to avoid degradation in the phase stability of the science measurements. Here, we present the first experimental demonstration of such a ranging scheme at 1 pW power levels using a Direct Sequence Spread Spectrum (DS/SS) modulation. This type of modulation also enables optical communication by encoding data with ranging signals and provides significant noise reduction against spurious interfering signals for bidirectional ranging. Experimental results show ranging measurements of 42 cm at 3 Hz and the viability of highly reliable data transfer at several kilobits per second.

Deep phase modulation interferometry

We have developed a method to equip homodyne interferometers with the capability to operate with constant high sensitivity over many fringes for continuous real-time tracking. The method can be considered as an extension of the "J1 . . .J4" methods, and its enhancement to deliver very sensitive angular measurements through Differential Wavefront Sensing is straightforward. Beam generation requires a sinusoidal phase modulation of several radians in one interferometer arm. On a stable optical bench, we have demonstrated a long-term sensitivity over thousands of seconds of 0.1 mrad/√Hz that correspond to 20 pm/ √Hz in length, and 10 nrad/ √Hz in angle at millihertz frequencies.

Angular instability due to radiation pressure in the LIGO gravitational-wave detector

We observed the effect of radiation pressure on the angular sensing and control system of the Laser Interferometer Gravitational-Wave Observatory (LIGO) interferometer's core optics at LIGO Hanford Observatory. This is the first measurement of this effect in a complete gravitational-wave interferometer. Only one of the two angular modes survives with feedback control, because the other mode is suppressed when the control gain is sufficiently large. We developed a mathematical model to understand the physics of the system. This model matches well with the dynamics that we observe.

Interferometer Techniques for Gravitational-Wave Detection

Several km-scale gravitational-wave detectors have been constructed world wide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques, however, the complex optical layouts provide a new challenge. In this review we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.