Showing papers on "Interferometry published in 2017"

First Light for GRAVITY: Phase Referencing Optical Interferometry for the Very Large Telescope Interferometer

Abstract: GRAVITY is a new instrument to coherently combine the light of the European Southern Observatory Very Large Telescope Interferometer to form a telescope with an equivalent 130 m diameter angular resolution and a collecting area of 200 m$^2$. The instrument comprises fiber fed integrated optics beam combination, high resolution spectroscopy, built-in beam analysis and control, near-infrared wavefront sensing, phase-tracking, dual beam operation and laser metrology [...]. This article gives an overview of GRAVITY and reports on the performance and the first astronomical observations during commissioning in 2015/16. We demonstrate phase tracking on stars as faint as m$_K$ ~ 10 mag, phase-referenced interferometry of objects fainter than m$_K$ ~ 15 mag with a limiting magnitude of m$_K$ ~ 17 mag, minute long coherent integrations, a visibility accuracy of better than 0.25 %, and spectro-differential phase and closure phase accuracy better than 0.5°, corresponding to a differential astrometric precision of better than 10 microarcseconds ({\mu}as). The dual-beam astrometry, measuring the phase difference of two objects with laser metrology, is still under commissioning. First observations show residuals as low as 50 {\mu}as when following objects over several months. We illustrate the instrument performance with the observations of archetypical objects for the different instrument modes. Examples include the Galactic Center supermassive black hole and its fast orbiting star S2 for phase referenced dual beam observations and infrared wavefront sensing, the High Mass X-Ray Binary BP Cru and the Active Galactic Nucleus of PDS 456 for few {\mu}as spectro-differential astrometry, the T Tauri star S CrA for a spectro-differential visibility analysis, {\xi} Tel and 24 Cap for high accuracy visibility observations, and {\eta} Car for interferometric imaging with GRAVITY.

First light for GRAVITY: Phase referencing optical interferometry for the Very Large Telescope Interferometer

Abstract: GRAVITY is a new instrument to coherently combine the light of the European Southern Observatory Very Large Telescope Interferometer to form a telescope with an equivalent 130 m diameter angular resolution and a collecting area of 200 m2. The instrument comprises fiber fed integrated optics beam combination, high resolution spectroscopy, built-in beam analysis and control, near-infrared wavefront sensing, phase-tracking, dual-beam operation, and laser metrology. GRAVITY opens up to optical/infrared interferometry the techniques of phase referenced imaging and narrow angle astrometry, in many aspects following the concepts of radio interferometry. This article gives an overview of GRAVITY and reports on the performance and the first astronomical observations during commissioning in 2015/16. We demonstrate phase-tracking on stars as faint as mK ≈ 10 mag, phase-referenced interferometry of objects fainter than mK ≈ 15 mag with a limiting magnitude of mK ≈ 17 mag, minute long coherent integrations, a visibility accuracy of better than 0.25%, and spectro-differential phase and closure phase accuracy better than 0.5°, corresponding to a differential astrometric precision of better than ten microarcseconds (μas). The dual-beam astrometry, measuring the phase difference of two objects with laser metrology, is still under commissioning. First observations show residuals as low as 50 μas when following objects over several months. We illustrate the instrument performance with the observations of archetypical objects for the different instrument modes. Examples include the Galactic center supermassive black hole and its fast orbiting star S2 for phase referenced dual-beam observations and infrared wavefront sensing, the high mass X-ray binary BP Cru and the active galactic nucleus of PDS 456 for a few μas spectro-differential astrometry, the T Tauri star S CrA for a spectro-differential visibility analysis, ξ Tel and 24 Cap for high accuracy visibility observations, and η Car for interferometric imaging with GRAVITY.

The Fabry-Perot Interferometer : History, Theory, Practice and Applications

Abstract: Historical Background Basic Elements of Optical Spectroscopy The Plane Fabry-Perot Interferometer Practical Operation of Plane Fabry-Perot Interferometers The Spherical Fabry-Perot Interferometer Multiple and Multi-Pass Interferometers Applications to Atomic Spectroscopy Application to Astronomy and Astrophysics Application to Light Scattering Studies of Materials Applications to Metrology, Optical Bistability, Velocimetry, Infrared, Sensors, Plasma Physics, and Miscellaneous Devices Appendices References and Further Reading Index

Electromagnetic evidence that SSS17a is the result of a binary neutron star merger

Abstract: Eleven hours after the detection of gravitational wave source GW170817 by the Laser Interferometer Gravitational-Wave Observatory and Virgo Interferometers, an associated optical transient, SSS17a, was identified in the galaxy NGC 4993. Although the gravitational wave data indicate that GW170817 is consistent with the merger of two compact objects, the electromagnetic observations provide independent constraints on the nature of that system. We synthesize the optical to near-infrared photometry and spectroscopy of SSS17a collected by the One-Meter Two-Hemisphere collaboration, finding that SSS17a is unlike other known transients. The source is best described by theoretical models of a kilonova consisting of radioactive elements produced by rapid neutron capture (the r-process). We conclude that SSS17a was the result of a binary neutron star merger, reinforcing the gravitational wave result.

Phase Shift in an Atom Interferometer due to Spacetime Curvature across its Wave Function.

Abstract: Spacetime curvature induces tidal forces on the wave function of a single quantum system. Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces. The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold. Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.

Electromagnetic Evidence that SSS17a is the Result of a Binary Neutron Star Merger

Abstract: 11 hours after the detection of gravitational wave source GW170817 by the Laser Interferometer Gravitational-Wave Observatory and Virgo Interferometers, an associated optical transient SSS17a was discovered in the galaxy NGC 4993. While the gravitational wave data indicate GW170817 is consistent with the merger of two compact objects, the electromagnetic observations provide independent constraints of the nature of that system. Here we synthesize all optical and near-infrared photometry and spectroscopy of SSS17a collected by the One-Meter Two-Hemisphere collaboration. We find that SSS17a is unlike other known transients. The source is best described by theoretical models of a kilonova consisting of radioactive elements produced by rapid neutron capture (the r-process). We find that SSS17a was the result of a binary neutron star merger, reinforcing the gravitational wave result.

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling

Abstract: We propose a new imaging technique for radio and optical/infrared interferometry. The proposed technique reconstructs the image from the visibility amplitude and closure phase, which are standard data products of short-millimeter very long baseline interferometers such as the Event Horizon Telescope (EHT) and optical/infrared interferometers, by utilizing two regularization functions: the $\ell_1$-norm and total variation (TV) of the brightness distribution. In the proposed method, optimal regularization parameters, which represent the sparseness and effective spatial resolution of the image, are derived from data themselves using cross validation (CV). As an application of this technique, we present simulated observations of M87 with the EHT based on four physically motivated models. We confirm that $\ell_1$+TV regularization can achieve an optimal resolution of $\sim 20-30$% of the diffraction limit $\lambda/D_{\rm max}$, which is the nominal spatial resolution of a radio interferometer. With the proposed technique, the EHT can robustly and reasonably achieve super-resolution sufficient to clearly resolve the black hole shadow. These results make it promising for the EHT to provide an unprecedented view of the event-horizon-scale structure in the vicinity of the super-massive black hole in M87 and also the Galactic center Sgr A*.

Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer.

Abstract: In an unseeded SU(1,1) interferometer composed of two cascaded degenerate parametric amplifiers, with direct detection at the output, we demonstrate a phase sensitivity overcoming the shot noise limit by 2.3 dB. The interferometer is strongly unbalanced, with the parametric gain of the second amplifier exceeding the gain of the first one by a factor of 2, which makes the scheme extremely tolerant to detection losses. We show that by increasing the gain of the second amplifier, the phase supersensitivity of the interferometer can be preserved even with detection losses as high as 80%. This finding can considerably improve the state-of-the-art interferometry, enable sub-shot-noise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.

Parametric feedback cooling of levitated optomechanics in a parabolic mirror trap

Abstract: Levitated optomechanics, a new experimental physics platform, holds promise for fundamental science and quantum technological sensing applications. We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force. We demonstrate parametric feedback cooling of all three motional degrees of freedom from room temperature to a few millikelvin. A single laser at 1550 nm and a single photodiode are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26 to 160 nm are trapped without feedback to 10−5 mbar, and with feedback-engaged, the pressure is reduced to 10−6 mbar. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor in excess of 4×107 is evaluated. This particle manipulation is key to building a nanoparticle matter-wave interferometer in order to test the quantum superposition principle in the macroscopic domain.

Recent advancements in optical fiber hydrogen sensors

Abstract: A review for optical fiber hydrogen sensors based on palladium (Pd) and tungsten oxide (WO3) thin films is presented, with specific focus on the measurement methods, probe structures, and sensing properties of different sensors. Firstly, the theoretical models behind the optical fiber hydrogen sensors, as well as their practical limitations, are addressed. Secondly, four mainstream measurement methods, including intensity, fiber Bragg grating (FBG), interferometer, surface plasmon resonance (SPR), which have been proposed to sense the physicochemical properties variations of sensitive thin films when exposed to hydrogen, are reviewed. Then, the advantages and disadvantages of all the above measurement methods are also discussed and compared. Finally, the existing problems and future prospects of optical fiber hydrogen sensors are pointed out.

Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer

Abstract: An SU(1,1) interferometer, which replaces the beam splitters in a Mach–Zehnder interferometer with nonlinear interactions, offers the potential of achieving improved phase sensitivity in applications with low optical powers. We present a novel variation on the SU(1,1) interferometer in which the second nonlinear interaction is replaced with balanced homodyne detection. We show theoretically that this “truncated SU(1,1) interferometer” can achieve the same potential phase sensitivity as the conventional SU(1,1) interferometer. We build an experimental realization of this device using seeded four-wave mixing in Rb85 vapor as the nonlinear interaction, thus employing a bright two-mode squeezed state as the phase-sensing quantum state inside the interferometer. Measurements as a function of operating point show that even with ≈35% loss, this device can surpass the standard quantum limit by 4 dB. This device is simpler to build and operate than the conventional SU(1,1) interferometer, and also eliminates some sources of loss, thus making it useful for applications in precision metrology.

Continuously tunable ultra-thin silicon waveguide optical delay line

Abstract: As light cannot be stopped or directly stored in any media, optical delay lines are usually used to temporally trap the optical signals. We report a wide-range continuously tunable optical delay line chip consisting of a ring resonator array and a Mach–Zehnder interferometer (MZI) switch array on the 60-nm-thick silicon waveguide platform. The ring delay line provides continuous delay tuning of more than 10 ps with a push–pull differential tuning method. The MZI switchable delay line provides digitally programmable delay tuning with a resolution of 10 ps upon reconfiguration of the MZI switches to establish different optical routing paths. Dual-stage MZI switches are used to ensure low crosstalk with an improved signal-to-noise ratio. The delay line chip can generate a maximum delay of >1 ns with an on-chip insertion loss of 12.4 dB. Optical pulse time-division multiplexing and quasi-arbitrary waveform generation are realized based on the delay line chip. These results represent a significant step towards the realization of highly reconfigurable optical signal processors enabled by optical delay manipulation with broad applications for optical communications and microwave photonics.

Pumped-Up SU(1,1) Interferometry

Abstract: Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it suffers from one major drawback: Only those particles outcoupled from the pump mode contribute to the phase measurement. Since the number of particles outcoupled to these "side modes" is typically small, this limits the interferometer's absolute sensitivity. We propose an alternative "pumped-up" approach where all the input particles participate in the phase measurement and show how this can be implemented in spinor Bose-Einstein condensates and hybrid atom-light systems-both of which have experimentally realized SU(1,1) interferometry. We demonstrate that pumped-up schemes are capable of surpassing the shot-noise limit with respect to the total number of input particles and are never worse than conventional SU(1,1) interferometry. Finally, we show that pumped-up schemes continue to excel-both absolutely and in comparison to conventional SU(1,1) interferometry-in the presence of particle losses, poor particle-resolution detection, and noise on the relative phase difference between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes the advantages of conventional SU(1,1) interferometry into the regime of high absolute sensitivity, which is a necessary condition for useful quantum-enhanced devices.

Sensitivity-enhanced temperature sensor by hybrid cascaded configuration of a Sagnac loop and a F-P cavity

Abstract: A hybrid cascaded configuration consisting of a fiber Sagnac interferometer (FSI) and a Fabry-Perot interferometer (FPI) was proposed and experimentally demonstrated to enhance the temperature intensity by the Vernier-effect. The FSI, which consists of a certain length of Panda fiber, is for temperature sensing, while the FPI acts as a filter due to its temperature insensitivity. The two interferometers have almost the same free spectral range, with the spectral envelope of the cascaded sensor shifting much more than the single FSI. Experimental results show that the temperature sensitivity is enhanced from −1.4 nm/°C (single FSI) to −29.0 (cascaded configuration). The enhancement factor is 20.7, which is basically consistent with theoretical analysis (19.9).

Highly sensitive temperature sensor using a Sagnac loop interferometer based on a side-hole photonic crystal fiber filled with metal.

Abstract: A highly sensitive temperature sensor based on an all-fiber Sagnac loop interferometer combined with metal-filled side-hole photonic crystal fiber (PCF) is proposed and demonstrated. PCFs containing two side holes filled with metal offer a structure that can be modified to create a change in the birefringence of the fiber by the expansion of the filler metal. Bismuth and indium were used to examine the effect of filler metal on the temperature sensitivity of the fiber-optic temperature sensor. It was found from measurements that a very high temperature sensitivity of −9.0 nm/°C could be achieved with the indium-filled side-hole PCF. The experimental results are compared to numerical simulations with good agreement. It is shown that the high temperature sensitivity of the sensor is attributed to the fiber microstructure, which has a significant influence on the modulation of the birefringence caused by the expansion of the metal-filled holes.

Sensitivity amplification of fiber-optic in-line Mach–Zehnder Interferometer sensors with modified Vernier-effect

Abstract: In this paper, a novel sensitivity amplification method for fiber-optic in-line Mach-Zehnder interferometer (MZI) sensors has been proposed and demonstrated. The sensitivity magnification is achieved through a modified Vernier-effect. Two cascaded in-line MZIs based on offset splicing of single mode fiber (SMF) have been used to verify the effect of sensitivity amplification. Vernier-effect is generated due to the small free spectral range (FSR) difference between the cascaded in-line MZIs. Frequency component corresponding to the envelope of the superimposed spectrum is extracted to take Inverse Fast Fourier Transform (IFFT). Thus we can obtain the envelope precisely from the messy superimposed spectrum. Experimental results show that a maximum sensitivity amplification factor of nearly 9 is realized. The proposed sensitivity amplification method is universal for the vast majority of in-line MZIs.

Single-spot two-dimensional displacement measurement based on self-mixing interferometry

Abstract: The simultaneous and independent measurements of in-plane and out-of-plane displacements are significant issues to be solved in research. Here a novel system to realize single-spot two-dimensional (2D) displacement measurement of a noncooperative target is reported. The performance of the system is tested in the displacement measurement of an aluminum target with a rough surface. 2D random movement and 2D movement with different parameters of Lissajous figures are measured by the system. The ranges of the 2D displacement measurement reach 500 μm and the accuracies reach the submicron scale. The resolutions of the two dimensions are all better than 5 nm. The measurement system is based on laser heterodyne self-mixing interferometry with frequency multiplexing, which has advantages such as noncontact, nondestruction, nanometer-scale resolution and high sensitivity. The method is promising to be applied in 2D deformation tests of materials, 2D rotor vibration measurement, 2D positioning of particles, thermal expansion coefficient measurement, and other applications.

Interferometry and Synthesis in Radio Astronomy

Abstract: Preface -- Introduction and Historical Review -- Introductory Theory of Interferometry and Synthesis Imaging -- Analysis of the Interferometer Response -- Geometric Relationships and Polarimetry -- Antennas and Arrays -- Response of the Receiving System -- Design of the Analog Receiving System -- Digital Signal Processing -- Very-Long-Baseline Interferometry -- Calibration and Fourier Transformation of Visibility Data -- Deconvolution, Adaptive Calibration and Applications -- Interferometer Techniques for Astrometry and Geodesy -- Propagation Effects -- Van Cittert-Zernike Theorem, Spatial Coherence and Scattering -- Radio Interference -- Related Techniques -- Principal Symbols -- Index.

Mirrors used in the LIGO interferometers for first detection of gravitational waves.

Abstract: For the first time, direct detection of gravitational waves occurred in the Laser Interferometer Gravitational-wave Observatory (LIGO) interferometers. These advanced detectors require large fused silica mirrors with optical and mechanical properties and have never been reached until now. This paper details the main achievements of these ion beam sputtering coatings.

Atom-Based Sensing of Weak Radio Frequency Electric Fields Using Homodyne Readout.

Abstract: We utilize a homodyne detection technique to achieve a new sensitivity limit for atom-based, absolute radio-frequency electric field sensing of 5 μV cm−1 Hz−1/2. A Mach-Zehnder interferometer is used for the homodyne detection. With the increased sensitivity, we investigate the dominant dephasing mechanisms that affect the performance of the sensor. In particular, we present data on power broadening, collisional broadening and transit time broadening. Our results are compared to density matrix calculations. We show that photon shot noise in the signal readout is currently a limiting factor. We suggest that new approaches with superior readout with respect to photon shot noise are needed to increase the sensitivity further.

Endowing a plain fluidic chip with micro-optics: a holographic microscope slide.

Abstract: Lab-on-a-Chip (LoC) devices are extremely promising in that they enable diagnostic functions at the point-of-care Within this scope, an important goal is to design imaging schemes that can be used out of the laboratory In this paper, we introduce and test a pocket holographic slide that allows digital holography microscopy to be performed without an interferometer setup Instead, a commercial off-the-shelf plastic chip is engineered and functionalized with this aim The microfluidic chip is endowed with micro-optics, that is, a diffraction grating and polymeric lenses, to build an interferometer directly on the chip, avoiding the need for a reference arm and external bulky optical components Thanks to the single-beam scheme, the system is completely integrated and robust against vibrations, sharing the useful features of any common path interferometer Hence, it becomes possible to bring holographic functionalities out of the lab, moving complexity from the external optical apparatus to the chip itself Label-free imaging and quantitative phase contrast mapping of live samples are demonstrated, along with flexible refocusing capabilities Thus, a liquid volume can be analyzed in one single shot with no need for mechanical scanning systems

Attosecond-Resolution Hong-Ou-Mandel Interferometry

Abstract: When two indistinguishable photons are each incident on separate input ports of a beamsplitter they `bunch' deterministically, exiting via the same port as a direct consequence of their bosonic nature. This two-photon interference effect has long-held the potential for application in precision measurement of time delays, such as those induced by transparent specimens with unknown thickness profiles. However, the technique has never achieved resolutions significantly better than the few femtosecond (micron)-scale other than in a common-path geometry that severely limits applications. Here we develop the precision of HOM interferometry towards the ultimate limits dictated by statistical estimation theory, achieving few-attosecond (or nanometre path length) scale resolutions in a dual-arm geometry, thus providing access to length scales pertinent to cell biology and mono-atomic layer 2D materials.

Single-shot phase-shifting incoherent digital holography

Abstract: We propose single-shot incoherent digital holography in which a single-path in-line configuration and phase-shifting interferometry are adopted Space-division multiplexing and polarization states of the waves are utilized to implement parallel phase-shifting holography A single-path setup in parallel phase-shifting is constructed to capture an incoherent hologram easily with a compact system An instantaneous and three-dimensional (3D) object image is obtained without undesired diffraction waves using parallel phase-shifting The validity of the proposed technique is experimentally demonstrated for both transparent and reflective objects

Multiaxis atom interferometry with a single-diode laser and a pyramidal magneto-optical trap

Abstract: Atom interferometry has become one of the most powerful technologies for precision measurements. To develop simple, precise, and versatile atom interferometers for inertial sensing, we demonstrate an atom interferometer measuring acceleration, rotation, and inclination by pointing Raman beams toward individual faces of a pyramidal mirror. Only a single-diode laser is used for all functions, including atom trapping, interferometry, and detection. Efficient Doppler-sensitive Raman transitions are achieved without velocity selecting the atom sample, and with zero differential AC Stark shift between the cesium hyperfine ground states, increasing signal-to-noise and suppressing systematic effects. We measure gravity along two axes (vertical and 45° to the vertical), rotation, and inclination with sensitivities of 6 μm/s2/Hz, 300 μrad/s/Hz, and 4 μrad/Hz, respectively. This work paves the way toward deployable multiaxis atom interferometers for geodesy, geology, or inertial navigation.

Self-referenced frequency combs using high-efficiency silicon-nitride waveguides.

Abstract: We utilize silicon-nitride waveguides to self-reference a telecom-wavelength fiber frequency comb through supercontinuum generation, using 11.3 mW of optical power incident on the chip. This is approximately 10 times lower than conventional approaches using nonlinear fibers and is enabled by low-loss (<2 dB) input coupling and the high nonlinearity of silicon nitride, which can provide two octaves of spectral broadening with incident energies of only 110 pJ. Following supercontinuum generation, self-referencing is accomplished by mixing 780-nm dispersive-wave light with the frequency-doubled output of the fiber laser. In addition, at higher optical powers, we demonstrate f-to-3f self-referencing directly from the waveguide output by the interference of simultaneous supercontinuum and third harmonic generation, without the use of an external doubling crystal or interferometer. These hybrid comb systems combine the performance of fiber-laser frequency combs with the high nonlinearity and compactness of photonic waveguides, and should lead to low-cost, fully stabilized frequency combs for portable and space-borne applications.

The impact of modelling errors on interferometer calibration for 21 cm power spectra

Abstract: We study the impact of sky-based calibration errors from source mismodeling on 21\,cm power spectrum measurements with an interferometer and propose a method for suppressing their effects. While emission from faint sources that are not accounted for in calibration catalogs is believed to be spectrally smooth, deviations of true visibilities from model visibilities are not, due to the inherent chromaticity of the interferometer's sky-response (the "wedge"). Thus, unmodeled foregrounds, below the confusion limit of many instruments, introduce frequency structure into gain solutions on the same line-of-sight scales on which we hope to observe the cosmological signal. We derive analytic expressions describing these errors using linearized approximations of the calibration equations and estimate the impact of this bias on measurements of the 21\,cm power spectrum during the Epoch of Reionization (EoR). Given our current precision in primary beam and foreground modeling, this noise will significantly impact the sensitivity of existing experiments that rely on sky-based calibration. Our formalism describes the scaling of calibration with array and sky-model parameters and can be used to guide future instrument design and calibration strategy. We find that sky-based calibration that down-weights long baselines can eliminate contamination in most of the region outside of the wedge with only a modest increase in instrumental noise.

Compact and field-portable 3D printed shearing digital holographic microscope for automated cell identification.

Abstract: We propose a low-cost, compact, and field-portable 3D printed holographic microscope for automated cell identification based on a common path shearing interferometer setup. Once a hologram is captured from the portable setup, a 3D reconstructed height profile of the cell is created. We extract several morphological cell features from the reconstructed 3D height profiles, including mean physical cell thickness, coefficient of variation, optical volume (OV) of the cell, projected area of the cell (PA), ratio of PA to OV, cell thickness kurtosis, cell thickness skewness, and the dry mass of the cell for identification using the random forest (RF) classifier. The 3D printed prototype can serve as a low-cost alternative for the developing world, where access to laboratory facilities for disease diagnosis are limited. Additionally, a cell phone sensor is used to capture the digital holograms. This enables the user to send the acquired holograms over the internet to a computational device located remotely for cellular identification and classification (analysis). The 3D printed system presented in this paper can be used as a low-cost, stable, and field-portable digital holographic microscope as well as an automated cell identification system. To the best of our knowledge, this is the first research paper presenting automatic cell identification using a low-cost 3D printed digital holographic microscopy setup based on common path shearing interferometry.

Generalized interferometry – I: theory for interstation correlations

Abstract: S U M M A R Y We develop a general theory for interferometry by correlation that (i) properly accounts for heterogeneously distributed sources of continuous or transient nature, (ii) fully incorporates any type of linear and nonlinear processing, such as one-bit normalization, spectral whitening and phase-weighted stacking, (iii) operates for any type of medium, including 3-D elastic, heterogeneous and attenuating media, (iv) enables the exploitation of complete correlation waveforms, including seemingly unphysical arrivals, and (v) unifies the earthquake-based two-station method and ambient noise correlations. Our central theme is not to equate interferometry with Green function retrieval, and to extract information directly from processed interstation correlations, regardless of their relation to the Green function. We demonstrate that processing transforms the actual wavefield sources and actual wave propagation physics into effective sources and effective wave propagation. This transformation is uniquely determined by the processing applied to the observed data, and can be easily computed. The effective forward model, that links effective sources and propagation to synthetic interstation correlations, may not be perfect. A forward modelling error, induced by processing, describes the extent to which processed correlations can actually be interpreted as proper correlations, that is, as resulting from some effective source and some effective wave propagation. The magnitude of the forward modelling error is controlled by the processing scheme and the temporal variability of the sources. Applying adjoint techniques to the effective forward model, we derive finite-frequency Fréchet kernels for the sources of the wavefield and Earth structure, that should be inverted jointly. The structure kernels depend on the sources of the wavefield and the processing scheme applied to the raw data. Therefore, both must be taken into account correctly in order to make accurate inferences on Earth structure. Not making any restrictive assumptions on the nature of the wavefield sources, our theory can be applied to earthquake and ambient noise data, either separately or combined. This allows us (i) to locate earthquakes using interstation correlations and without knowledge of the origin time, (ii) to unify the earthquake-based two-station method and noise correlations without the need to exclude either of the two data types, and (iii) to eliminate the requirement to remove earthquake signals from noise recordings prior to the computation of correlation functions. In addition to the basic theory for acoustic wavefields, we present numerical examples for 2-D media, an extension to the most general viscoelastic case, and a method for the design of optimal processing schemes that eliminate the forward modelling error completely. This work is intended to provide a comprehensive theoretical foundation of full-waveform interferometry by correlation, and to suggest improvements to current passive monitoring methods.

A phase-stable dual-comb interferometer

Abstract: Improvements to dual-comb interferometers will benefit precision spectroscopy and sensing, distance metrology, tomography, telecommunications etc. A specific requirement of such interferometers is to enforce mutual coherence between the two combs over the measurement time. With feed-forward relative stabilization of the carrier-enveloppe offset frequencies, we experimentally realize such mutual coherence over times that exceed 300 seconds, two orders of magnitude longer than state-of-the-art systems. Illustration is given with near-infrared Fourier transform molecular spectroscopy, where two combs of slightly different repetition frequencies replace a scanning two-beam interferometer. Our technique can be implemented with any frequency comb generators including microresonators or quantum cascade lasers.