Ghost Beam Suppression in Deep Frequency Modulation Interferometry for Compact On-Axis Optical Heads.

We present a compact optical head design for wide-range and low noise displacement sensing using deep frequency modulation interferometry (DFMI). The on-axis beam topology is realised in a quasi-monolithic component and relies on cube beamsplitters and beam transmission through perpendicular surfaces to keep angular alignment constant when operating in air or in a vacuum, which leads to the generation of ghost beams that can limit the phase readout linearity. We investigated the coupling of these beams into the non-linear phase readout scheme of DFMI and implemented adjustments of the phase estimation algorithm to reduce this effect. This was done through a combination of balanced detection and the inherent orthogonality of beat signals with different relative time-delays in deep frequency modulation interferometry, which is a unique feature not available for heterodyne, quadrature or homodyne interferometry.

Fiber backscatter under increasing exposure to ionizing radiation.

The Laser Interferometer Space Antenna (LISA) will measure gravitational waves by utilizing inter-satellite laser links between three triangularly-arranged spacecraft in heliocentric orbits. Each spacecraft will house two separate optical benches and needs to establish a phase reference between the two optical benches which requires a bidirectional optical connection, e.g. a fiber connection. The sensitivity of the reference interferometers, and thus of the gravitational wave measurement, could be hampered by backscattering of laser light within optical fibers. It is not yet clear if the backscatter within the fibers will remain constant during the mission duration, or if it will increase due to ionizing radiation in the space environment. Here we report the results of tests on two different fiber types under increasing intensities of ionizing radiation: SM98-PS-U40D by Fujikura, a polarization maintaining fiber, and HB1060Z by Fibercore, a polarizing fiber. We found that both types react differently to the ionizing radiation: The polarization maintaining fibers show a backscatter of about 7 ppm·m-1 which remains constant over increasing exposure. The polarizing fibers show about three times as much backscatter, which also remains constant over increasing exposure. However, the polarizing fibers show a significant degradation in transmission, which is reduced to about one third.

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.

Phase stability of photoreceivers in intersatellite laser interferometers.

A photoreceiver (PR) is required for the opto-electrical conversion of signals in intersatellite laser interferometers. Noise sources that originate or couple in the PR reduce the system carrier-to-noise-density, which is often represented by its phase noise density. In this work, we analyze the common noise sources in a PR used for space-based interferometry. Additionally, we present the results from the characterization of the PRs in GRACE-FO, a mission which will pioneer intersatellite laser interferometry. The estimated phase noise is shot-noise limited at 10-4 rad/Hz1/2 down to 10-2 Hz, almost 4 orders of magnitude below the instrument top level requirement (0.5 rad/Hz1/2). Below 10-2 Hz, the PR finite phase response noise dominates but the levels still comply with the instrument requirement. The sub-mHz noise levels and the PR electronic noise have been identified as key design factors for the LISA PR.

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 deep frequency modulation interferometry.

Experiments for space and ground-based gravitational wave detectors often require a large dynamic range interferometric position readout of test masses with 1 pm/√Hz precision over long time scales. Heterodyne interferometer schemes that achieve such precisions are available, but they require complex optical set-ups, limiting their scalability for multiple channels. This article presents the first experimental results on deep frequency modulation interferometry, a new technique that combines sinusoidal laser frequency modulation in unequal arm length interferometers with a non-linear fit algorithm. We have tested the technique in a Michelson and a Mach-Zehnder Interferometer topology, respectively, demonstrated continuous phase tracking of a moving mirror and achieved a performance equivalent to a displacement sensitivity of 250 pm/Hz at 1 mHz between the phase measurements of two photodetectors monitoring the same optical signal. By performing time series fitting of the extracted interference signals, we measured that the linearity of the laser frequency modulation is on the order of 2% for the laser source used.

Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision.

Precision phase readout of optical beat note signals is one of the core techniques required for intersatellite laser interferometry. Future space based gravitational wave detectors like eLISA require such a readout over a wide range of MHz frequencies, due to orbit induced Doppler shifts, with a precision in the order of µrad/√Hz at frequencies between 0.1 mHz and 1 Hz. In this paper, we present phase readout systems, so-called phasemeters, that are able to achieve such precisions and we discuss various means that have been employed to reduce noise in the analogue circuit domain and during digitisation. We also discuss the influence of some non-linear noise sources in the analogue domain of such phasemeters. And finally, we present the performance that was achieved during testing of the elegant breadboard model of the LISA phasemeter, which was developed in the scope of a European Space Agency technology development activity.

Deep frequency modulation interferometry.

Laser interferometry with pm/Hz precision and multi-fringe dynamic range at low frequencies is a core technology to measure the motion of various objects (test masses) in space and ground based experiments for gravitational wave detection and geodesy. Even though available interferometer schemes are well understood, their construction remains complex, often involving, for example, the need to build quasi-monolithic optical benches with dozens of components. In recent years techniques have been investigated that aim to reduce this complexity by combining phase modulation techniques with sophisticated digital readout algorithms. This article presents a new scheme that uses strong laser frequency modulations in combination with the deep phase modulation readout algorithm to construct simpler and easily scalable interferometers.

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.

Highspeed multiplexed heterodyne interferometry.

Digitally enhanced heterodyne interferometry is a metrology technique that uses pseudo-random noise codes for modulating the phase of the laser light. Multiple interferometric signals from the same beam path can thereby be isolated based on their propagation delay, allowing one to use advantageous optical layouts in comparison to classic laser interferometers. We present here a high speed version of this technique for measuring multiple targets spatially separated by only a few centimetres. This allows measurements of multiplexed signals using free beams, making the technique attractive for several applications requiring compact optical set-ups like for example space-based interferometers. In an experiment using a modulation and sampling rate of 1.25 GHz we are able to demonstrate multiplexing between targets only separated by 36 cm and we achieve a displacement measurement noise floor of <3 pm/√Hz at 10 Hz between them. We identify a limiting excess noise at low frequencies which is unique to this technique and is probably caused by the finite bandwidth in our measurement set-up. Utilising an active clock jitter correction scheme we are also able to reduce this noise in a null measurement configuration by one order of magnitude.

Advanced phasemeter for deep phase modulation interferometry.

We present the development of an advanced phasemeter for the deep phase modulation interferometry technique. This technique aims for precise length measurements with a high dynamic range using little optical hardware. The advanced phasemeter uses fast ADCs and an FPGA to implement a design of multiple single-bin Fourier transforms running at high sampling rates. Non-linear noise sources in the design were analyzed and suppressed. A null measurement with an optical beatnote signal using λ = 1064nm was conducted. It showed a sensitivity of 0.8µrad/√Hz below 10Hz and 13.3µrad/√Hz above, with a large dynamic range. The shown performance could enable the measuring of optical path lengths with sensitivities down to 0.14pm/√Hz and 2.3pm/√Hz, respectively, over several fringes in an interferometric setup.

Digitally enhanced homodyne interferometry.

We present two variations of a novel interferometry technique capable of simultaneously measuring multiple targets with high sensitivity. The technique performs a homodyne phase measurement by application of a four point phase shifting algorithm, with pseudo-random switching between points to allow multiplexed measurement based upon propagation delay alone. By multiplexing measurements and shifting complexity into signal processing, both variants realise significant complexity reductions over comparable methods. The first variant performs a typical coherent detection with a dedicated reference field and achieves a displacement noise floor 0.8 pm/√Hz above 50 Hz. The second allows for removal of the dedicated reference, resulting in further simplifications and improved low frequency performance with a 1 pm/√Hz noise floor measured down to 20 Hz. These results represent the most sensitive measurement performed using this style of interferometry whilst simultaneously reducing the electro-optic footprint.