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We describe a Simplified Gravitational Reference Sensor (S-GRS), an ultra-precise inertial sensor for future Earth geodesy missions. These sensors are used to measure or compensate for all non-gravitational accelerations of the host spacecraft so that they can be removed in the data analysis to recover spacecraft motion due to Earth's gravity field, which is the main science observable. Low-low satellite-to-satellite tracking missions like GRACE-FO that utilize laser ranging interferometers are technologically limited by the acceleration noise performance of their electrostatic accelerometers, in addition to temporal aliasing associated with Earth's dynamic gravity field. The S-GRS is estimated to be at least 40 times more sensitive than the GRACE accelerometers and more than 500 times more sensitive if operated on a drag-compensated platform. The improved performance is enabled by increasing the mass of the sensor's test mass, increasing the gap between the test mass and its electrode housing, removing the small grounding wire used in the GRACE accelerometers and replacing them with a UV LED-based charge management system. This level of improvement allows future missions to fully take advantage of the sensitivity of the GRACE-FO laser Ranging Interferometer in the gravity recovery analysis. The S-GRS concept is a simplified version of the flight-proven LISA Pathfinder GRS. Our performance estimates are based on models vetted during the LISA Pathfinder flight and the expected Earth orbiting spacecraft environment based on flight data from GRACE-FO. The relatively low volume, mass, and a power consumption enables use of the S-GRS on ESPA-class microsatellites, reducing launch costs or enabling larger numbers of satellite pairs to be utilized to improve the temporal resolution of Earth gravity field maps., Comment: Corrected typos, clarified some sentences, and added references

The first terrestrial gravitational wave interferometers have dramatically underscored the scientific value of observing the Universe through an entirely different window, and of folding this new channel of information with traditional astronomical data for a multimessenger view. The Laser Interferometer Space Antenna (LISA) will broaden the reach of gravitational wave astronomy by conducting the first survey of the millihertz gravitational wave sky, detecting tens of thousands of individual astrophysical sources ranging from white-dwarf binaries in our own galaxy to mergers of massive black holes at redshifts extending beyond the epoch of reionization. These observations will inform - and transform - our understanding of the end state of stellar evolution, massive black hole birth, and the co-evolution of galaxies and black holes through cosmic time. LISA also has the potential to detect gravitational wave emission from elusive astrophysical sources such as intermediate-mass black holes as well as exotic cosmological sources such as inflationary fields and cosmic string cusps., Comment: White Paper submitted to Astro2020 (2020 Decadal Survey on Astronomy and Astrophysics). v2: fixed a reference

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.

Recent advances at JPL in experimentation and design for LISA interferometry include the demonstration of Time Delay Interferometry using electronically separated end stations, a new arm-locking design with improved gain and stability, and progress in flight readiness of digital and analog electronics for phase measurements., Comment: 11 pages, 9 figures, LISA 8 Symposium, Stanford University, 2010

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., Comment: 4 pages, 4 figures, to appear in Physical Review Letters end of May 2010

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A document discusses a solution-assisted contacting technique for optical contacting. An optic of surface flatness Lambda/20 was successfully contacted with one of moderate surface quality, or Lambda/4. Optics used were both ultra-low expansion (ULE) glass (Lambda/4 and Lambda/20) and fused silica (Lambda/20). A stainless steel template of the intended interferometer layout was designed and constructed with three contact points per optic. The contact points were all on a common side of the template. The entire contacting jig was tilted at about 30 . Thus, when the isopropanol was applied, each optic slid due to gravity, resting on the contact points. All of the contacting was performed in a relatively dusty laboratory. A number of successful contacts were achieved where up to two or three visible pieces of dust could be seen. These were clearly visible due to refraction patterns between the optic and bench. On a number of optics, the final step of dropping isopropyl between the surfaces was repeated until a successful contact was achieved. The new procedures realized in this work represent a simplification for optical contacting in the laboratory. They will both save time and money spent during the contacting process, and research and development phases. The techniques outlined are suitable for laboratory experiments, research, and initial development stages.

Digitally enhanced heterodyne interferometry (DI) is a laser metrology technique employing pseudo-random noise (PRN) codes phase-modulated onto an optical carrier. Combined with heterodyne interferometry, the PRN code is used to select individual signals, returning the inherent interferometric sensitivity determined by the optical wavelength. The signal isolation arises from the autocorrelation properties of the PRN code, enabling both rejection of spurious signals (e.g., from scattered light) and multiplexing capability using a single metrology system. The minimum separation of optical components is determined by the wavelength of the PRN code.

Spurious interference limits the performance of many interferometric measurements. Digitally enhanced interferometry (DEI) improves measurement sensitivity by augmenting conventional heterodyne interferometry with pseudo-random noise (PRN) code phase modulation. DEI effectively changes the measurement problem from one of hardware (optics, electronics), which may deteriorate over time, to one of software (modulation, digital signal processing), which does not. DEI isolates interferometric signals based on their delay. Interferometric signals are effectively time-tagged by phase-modulating the laser source with a PRN code. DEI improves measurement sensitivity by exploiting the autocorrelation properties of the PRN to isolate only the signal of interest and reject spurious interference. The properties of the PRN code determine the degree of isolation.

A phasemeter for estimating the phase of a signal. For multi-tone signals, multiple phase estimates may be provided. An embodiment includes components operating in the digital domain, where a sampled input signal is multiplied by cosine and sine terms to provide estimates of the inphase and quadrature components. The quadrature component provides an error signal that is provided to a feedback loop, the feedback loop providing a model phase that tends to track the phase of a tone in the input signal. The cosine and sine terms are generated from the model phase. The inphase and quadrature components are used to form a residual phase, which is added to the model phase to provide an estimate of the phase of the input signal. Other embodiments are described and claimed.

This work represents a radical simplification in the design of the optical head needed for high-precision laser ranging applications. The optical head is now a single fiber-optic collimator with dimensions of order of 1 1 2 cm, which can be easily integrated into the system being measured with minimal footprint.

Point-to-point laser metrology systems can be used to stabilize large structures at the nanometer levels required for precision optical systems. Existing sensors are large and intrusive, however, with optical heads that consist of several optical elements and require multiple optical fiber connections. The use of point-to-point laser metrology has therefore been limited to applications where only a few gauges are needed and there is sufficient space to accommodate them. Range-Gated Metrology is a signal processing technique that preserves nanometer-level or better performance while enabling: (1) a greatly simplified optical head - a single fiber optic collimator - that can be made very compact, and (2) a single optical fiber connection that is readily multiplexed. This combination of features means that it will be straightforward and cost-effective to embed tens or hundreds of compact metrology gauges to stabilize a large structure. In this paper we describe the concept behind Range-Gated Metrology, demonstrate the performance in a laboratory environment, and give examples of how such a sensor system might be deployed.

Figure 1 shows a simplified block diagram of an improved optoelectronic system for locking the phase of one laser to that of another laser with an adjustable offset frequency specified by the user. In comparison with prior systems, this system exhibits higher performance (including higher stability) and is much easier to use. The system is based on a field-programmable gate array (FPGA) and operates almost entirely digitally; hence, it is easily adaptable to many different systems. The system achieves phase stability of less than a microcycle. It was developed to satisfy the phase-stability requirement for a planned spaceborne gravitational-wave-detecting heterodyne laser interferometer (LISA). The system has potential terrestrial utility in communications, lidar, and other applications. The present system includes a fast phasemeter that is a companion to the microcycle-accurate one described in High-Accuracy, High-Dynamic-Range Phase-Measurement System (NPO-41927), NASA Tech Briefs, Vol. 31, No. 6 (June 2007), page 22. In the present system (as in the previously reported one), beams from the two lasers (here denoted the master and slave lasers) interfere on a photodiode. The heterodyne photodiode output is digitized and fed to the fast phasemeter, which produces suitably conditioned, low-latency analog control signals which lock the phase of the slave laser to that of the master laser. These control signals are used to drive a thermal and a piezoelectric transducer that adjust the frequency and phase of the slave-laser output. The output of the photodiode is a heterodyne signal at the difference between the frequencies of the two lasers. (The difference is currently required to be less than 20 MHz due to the Nyquist limit of the current sampling rate. We foresee few problems in doubling this limit using current equipment.) Within the phasemeter, the photodiode-output signal is digitized to 15 bits at a sampling frequency of 40 MHz by use of the same analog-to-digital converter (ADC) as that of the previously reported phasemeter. The ADC output is passed to the FPGA, wherein the signal is demodulated using a digitally generated oscillator signal at the offset locking frequency specified by the user. The demodulated signal is low-pass filtered, decimated to a sample rate of 1 MHz, then filtered again. The decimated and filtered signal is converted to an analog output by a 1 MHz, 16-bit digital-to-analog converters. After a simple low-pass filter, these analog signals drive the thermal and piezoelectric transducers of the laser.

A digital phase meter has been designed to satisfy stringent requirements for measuring differences between phases of radio-frequency (RF) subcarrier signals modulated onto laser beams involved in the operation of a planned space-borne gravitational-wave-detecting heterodyne laser interferometer. The capabilities of this system could also be used in diverse terrestrial applications that involve measurement of signal phases, including metrology, navigation, and communications.

This paper evaluates isx of the most promising solutions: the Linear Dual Chopped Bracewell (DCB), X-Array, Diamond DCB, Z-Array, Linear-3 and Triangle architectures.

This presentation discusses the requirements, performance, and future plans for the Laser Interferometer Space Antenna (LISA).

The Terrestrial Planet Finder interferometer design concepts are large and complex systems that must operate in environments that are impractical to reproduce in preflight testing. The structurally-connected design is 36 meters long - longer than all but one thermal vacuum chamber in existence. The formation flying design will be comprised of up to five separate spacecraft, each with a sunshield over 15 meters on a side, and is designed to operate with formation sizes spanning over 100 meters to very close formations. System-level verification of the performance of the designs will need to rely on analytical modeling. The effort to model the many physical aspects of the designs under study is under way*. This paper describes the program of modeling for the TPF-I concepts. The program includes a number of types of models, such as the standard stand-alone optics, thermal, and structural models, as well as an end-to-end performance model of the project system called the Observatory Simulation. Aspects of each model are discussed including the purpose, methods of implementation (software applications), and approaches to validation. Program-level considerations (such as model-to-model integration and configuration management) are also discussed. Given that there are at least seven different organizations contributing to model developments and more than twenty separate models, these are special challenges.