Showing papers on "Interferometry published in 2006"
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TL;DR: An experiment where a micromechanical resonator is used as a mirror in a very high-finesse optical cavity, and its displacements are monitored with unprecedented sensitivity, and a radiation-pressure-induced instability of the resonators is observed.
Abstract: Cooling of mechanical resonators is the focus of much research effort because of possible applications in ultra-high precision measurements such as gravitational wave detection. It is also of fundamental interest as using this technique it may be possible to observe a transition between classical and quantum behaviour of a mechanical system. Three groups report advances in this area. Gigan et al. and Arcizet et al. used radiation pressure to freeze out thermal vibrations of tiny mechanical microresonators, or micromirrors. In the right conditions, the mirrors cool from room temperature to about 10 K without outside influence. Once the technique is refined it should be possible to achieve further cooling and to observe the quantum ground state of a micromirror experimentally. In the third paper, Dustin Kleckner and Dirk Bouwmeester use optical feedback to cool a micromirror to sub-kelvin temperatures. A micromechanical resonator is used as a mirror in a very high-finesse optical cavity, and its displacements are monitored with unprecedented sensitivity. By detuning the laser frequency with respect to the cavity resonance, a drastic cooling of the microresonator by intracavity radiation pressure is observed, down to an effective temperature of 10 kelvin. Recent table-top optical interferometry experiments1,2 and advances in gravitational-wave detectors3 have demonstrated the capability of optical interferometry to detect displacements with high sensitivity. Operation at higher powers will be crucial for further sensitivity enhancement, but dynamical effects caused by radiation pressure on the interferometer mirrors must be taken into account, and the appearance of optomechanical instabilities may jeopardize the stable operation of the next generation of interferometers4,5,6. These instabilities7,8 are the result of a nonlinear coupling between the motion of the mirrors and the optical field, which modifies the effective dynamics of the mirror. Such ‘optical spring’ effects have already been demonstrated for the mechanical damping of an electromagnetic waveguide with a moving wall9, the resonance frequency of a specially designed flexure oscillator10, and the optomechanical instability of a silica microtoroidal resonator11. Here we present an experiment where a micromechanical resonator is used as a mirror in a very high-finesse optical cavity, and its displacements are monitored with unprecedented sensitivity. By detuning the laser frequency with respect to the cavity resonance, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 kelvin. For opposite detuning, efficient heating is observed, as well as a radiation-pressure-induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a micromechanical resonator12,13,14, either by passive15 or active cooling techniques16,17,18.
890 citations
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21 May 2006TL;DR: LIGO as discussed by the authors is a trio of extremely sensitive Michelson interferometers built to detect gravitational waves from space, and the results of their recent observations are described in detail.
Abstract: LIGO is a trio of extremely sensitive Michelson interferometers built to detect gravitational waves from space. We describe predicted sources of gravitational waves, our detectors, and the results of our recent observations.
839 citations
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TL;DR: In this article, passive image interferometry is used to continuously monitor small temporal changes of seismic velocities in the subsurface of Mt. Merapi volcano, which is independent of sources in the classical sense and requires just one or two permanent seismic stations.
Abstract: [1] We propose passive image interferometry as a technique for seismology that allows to continuously monitor small temporal changes of seismic velocities in the subsurface. The technique is independent of sources in the classical sense and requires just one or two permanent seismic stations. We retrieve the Green’s functions that we use for interferometry from ambient seismic noise. Applying passive image interferometry to data from Merapi volcano we show that velocity variations can be measured with an accuracy of 0.1% with a temporal resolution of a single day. At Mt. Merapi the velocity variations show a strong seasonal influence and we present a depth dependent hydrological model that describes our observations solely based on precipitation. Citation: Sens
610 citations
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TL;DR: In this paper, a detection technique for scattering-type near-field optical microscopy capable of background interference elimination in the entire near-UV to far-IR spectral range is presented.
Abstract: The authors present a detection technique for scattering-type near-field optical microscopy capable of background interference elimination in the entire near-UV to far-IR spectral range. It simultaneously measures near-field optical signal amplitude and phase by interferometric detection of scattered light utilizing a phase-modulated reference wave. They compare its background suppression efficiency to other known methods and experimentally show that it provides a reliable near-field optical material contrast even in the case where both noninterferometric and homodyne interferometric detection methods fail.
468 citations
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TL;DR: The polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnacs loop, implying a broken time-reversal symmetry state in the superconducting state of Sr2 RuO4, similar to 3He-A.
Abstract: The polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop We observed nonzero Kerr rotations as big as 65 nanorad appearing below Tc in large domains Our results imply a broken time-reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3He-A
434 citations
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04 Aug 2006
TL;DR: The Permanent Scatterer Technique and Integer Least Squares Estimator were used in this article to compute the STUN algorithm for real-time real-world data processing problems, respectively.
Abstract: The Permanent Scatterer Technique.- The Integer Least-Squares Estimator.- The STUN Algorithm.- Synthetic Data Experiments.- Real Data Processing.- Conclusions and Recommendations.
362 citations
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National Institutes of Natural Sciences, Japan1, University of Tokyo2, Kyoto University3, Goddard Space Flight Center4, Osaka City University5, Waseda University6, Hirosaki University7, Columbia University8, Nihon University9, Tokyo Keizai University10, Osaka University11, Tohoku University12, Rikkyo University13, University of Texas at Brownsville14, Shibaura Institute of Technology15, Japan Aerospace Exploration Agency16, National Institute of Advanced Industrial Science and Technology17, Tokai University18, National Institute of Information and Communications Technology19, Kindai University20, University of Wisconsin–Milwaukee21, Ochanomizu University22, Liverpool John Moores University23, Lancaster University24, Hiroshima University25, California Institute of Technology26, University of Electro-Communications27, Rochester Institute of Technology28, National Defense Academy of Japan29, Niigata University30, University of Southampton31, Osaka Institute of Technology32, Albert Einstein Institution33, Aristotle University of Thessaloniki34, Nagoya University35, Nagaoka University of Technology36, University of Illinois at Urbana–Champaign37, Tokyo Institute of Technology38
TL;DR: DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) as discussed by the authors is the future Japanese space gravitational wave antenna, which aims at detecting various kinds of gravitational waves between 1 mHz and 100 Hz frequently enough to open a new window of observation for gravitational wave astronomy.
Abstract: DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. It aims at detecting various kinds of gravitational waves between 1 mHz and 100 Hz frequently enough to open a new window of observation for gravitational wave astronomy. The pre-conceptual design of DECIGO consists of three drag-free satellites, 1000 km apart from each other, whose relative displacements are measured by a Fabry–Perot Michelson interferometer. We plan to launch DECIGO in 2024 after a long and intense development phase, including two pathfinder missions for verification of required technologies.
342 citations
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TL;DR: A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed and is applied to an information security system based on double random-phase encoding in the Fresnel domain.
Abstract: Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.
337 citations
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TL;DR: The X-ray phase tomography of biological samples is reported in this paper, which is based on Xray Talbot interferometry, and imaging results obtained for a cancerous rabbit liver and a mouse tail with synchrotron radiation are presented.
Abstract: The X-ray phase tomography of biological samples is reported, which is based on X-ray Talbot interferometry. Its imaging principle is described in detail, and imaging results obtained for a cancerous rabbit liver and a mouse tail with synchrotron radiation are presented. Because an amplitude grating is needed to construct an X-ray Talbot interferometer, a high-aspect-ratio grating pattern was fabricated by X-ray lithography and gold electroplating. X-ray Talbot interferometry has an advantage that it functions with polychromatic cone-beam X-rays. Finally, the compatibility with a compact X-ray source is discussed.
327 citations
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TL;DR: A new atom gyroscope using a butterfly geometry is introduced, providing a full inertial base for the atom interferometer, and the present sensitivity and the possible improvements are discussed.
Abstract: We have developed an atom interferometer providing a full inertial base. This device uses two counterpropagating cold-atom clouds that are launched in strongly curved parabolic trajectories. Three single Raman beam pairs, pulsed in time, are successively applied in three orthogonal directions leading to the measurement of the three axis of rotation and acceleration. In this purpose, we introduce a new atom gyroscope using a butterfly geometry. We discuss the present sensitivity and the possible improvements.
327 citations
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TL;DR: The Big Bang Observer is a proposed space-based gravitational-wave detector intended as a follow-on mission to the Laser Interferometer Space Antenna (LISA), designed to detect the stochastic background of gravitational waves from the early universe as discussed by the authors.
Abstract: The Big Bang Observer is a proposed space-based gravitational-wave detector intended as a follow on mission to the Laser Interferometer Space Antenna (LISA). It is designed to detect the stochastic background of gravitational waves from the early universe. We discuss how the interferometry can be arranged between three spacecraft for this mission and what research and development on key technologies are necessary to realize this scheme.
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TL;DR: In this article, the authors present a general theory of coda wave interferometry, and show how the time-shifted correlation coefficient can be used to estimate the mean and variance of the distribution of travel-time perturbations.
Abstract: Coda waves are sensitive to changes in the subsurface because the strong scattering that generates these waves causes them to repeatedly sample a limited region of space. Coda wave interferometry is a technique that exploits this sensitivity to estimate slight changes in the medium from a comparison of the coda waves before and after the perturbation. For spatially localized changes in the velocity, or for changes in the source location, the travel-time perturbation may be different for different scattering paths. The coda waves that arrive within a certain time window are therefore subject to a distribution of travel-time perturbations. Here I present the general theory of coda wave interferometry, and show how the time-shifted correlation coefficient can be used to estimate the mean and variance of the distribution of travel-time perturbations. I show how this general theory can be used to estimate changes in the wave velocity, in the location of scatterer positions, and in the source location.
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TL;DR: In this paper, an innovative data reduction method for single-mode interferometry is presented based on a direct modelling of the fringes in the detector plane, which is specifically developed for the AMBER instrument, the three-beam combiner of the Very Large Telescope Interferometer.
Abstract: We present in this paper an innovative data reduction method for single-mode interferometry. It has been specifically developed for the AMBER instrument, the three-beam combiner of the Very Large Telescope Interferometer, but can be derived for any single-mode interferometer. The algorithm is based on a direct modelling of the fringes in the detector plane. As such, it requires a preliminary calibration of the instrument in order to obtain the calibration matrix which builds the linear relationship between the interferogram and the interferometric observable, that is the complex visibility. Once the calibration procedure has been performed, the signal processing appears to be a classical least square determination of a linear inverse problem. From the estimated complex visibility, we derive the squared visibility, the closure phase and the spectral differential phase. The data reduction procedures are gathered into the so-called amdlib software, now available for the community, and presented in this paper. Furthermore, each step of this original algorithm is illustrated and discussed from various on-sky observations conducted with the VLTI, with a focus on the control of the data quality and the effective execution of the data reduction procedures. We point out the present limited performances of the instrument due to VLTI instrumental vibrations, difficult to calibrate.
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TL;DR: In this paper, the authors presented a derivation of the stationary phase principle of seismic interferometry for a homogeneous medium with one horizontal reflector and without a free surface, and showed that the correlation of the waves recorded at two receivers correctly gives both the direct wave and the singly reflected waves.
Abstract: Seismic interferometry is a technique for estimating the Green’s function that accounts for wave propagation between receivers by correlating the waves recorded at these receivers. We present a derivation of this principle based on the method of stationary phase. Although this derivation is intended to be educational, applicable to simple media only, it provides insight into the physical principle of seismic interferometry. In a homogeneous medium with one horizontal reflector and without a free surface, the correlation of the waves recorded at two receivers correctly gives both the direct wave and the singly reflected waves. When more reflectors are present, a product of the singly reflected waves occurs in the crosscorrelation that leads to spurious multiples when the waves are excited at the surface only. We give a heuristic argument that these spurious multiples disappear when sources below the reflectors are included. We also extend the derivation to a smoothly varying heterogeneous background medium.
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TL;DR: In this article, a single-band-pass tunable microwave filter was proposed based on a broadband optical source and a fiber Mach-Zehnder interferometer and showed a high Q factor over a tuning range of 5-17 GHz.
Abstract: The authors present the theoretical analysis and experimental demonstration of a novel single-bandpass tunable microwave filter. The filter is based on a broadband optical source and a fiber Mach-Zehnder interferometer and shows a high Q factor over a tuning range of 5-17 GHz. A generalized analysis considering that the optical signal propagates along optical delay lines with a dispersion slope different from zero is presented.
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TL;DR: In this article, the Permanent Scatterers (PS) analysis was applied at a regional scale as support for landslide inventory mapping and at local scale for the monitoring of single well-known slope movements.
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TL;DR: An optical setup to achieve superresolution in microscopy using holographic recording is presented and optically implemented the approach for a low-numerical-aperture commercial microscope objective.
Abstract: An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.
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TL;DR: An interferometric method that enables to measure the optical path delay between two consecutive femtosecond laser pulses by way of dispersive interferometry to unprecedented precision over extensive ranges is described.
Abstract: We describe an interferometric method that enables to measure the optical path delay between two consecutive femtosecond laser pulses by way of dispersive interferometry. This method allows a femtosecond laser to be utilized as a source of performing absolute distance measurements to unprecedented precision over extensive ranges. Our test result demonstrates a non-ambiguity range of ~1.46 mm with a resolution of 7 nm over a maximum distance reaching ~0.89 m.
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TL;DR: In this article, the second order harmonic amplitude of a Rayleigh surface wave propagating in metallic specimens is measured using a laser-based ultrasonic technique, and the results show that there is a significant increase in the second-order harmonic amplitude at monotonic tensile loads above the material's yield stress.
Abstract: A reliable laser-based ultrasonic technique is developed to measure the second order harmonic amplitude of a Rayleigh surface wave propagating in metallic specimens. Rayleigh waves are experimentally generated with a wedge transducer and detected with a heterodyne laser interferometer. The capability of this system to measure the nonlinear contribution present in Rayleigh surface waves is demonstrated, and these results are interpreted in terms of a parameter developed for Rayleigh surface waves which corresponds to the nonlinear parameter of a longitudinal wave, β. The proposed measurement technique is used to assess damage in nickel-base high temperature alloy specimens, and the evolution of material nonlinearity under various loading conditions is quantitatively measured in terms of the increasing amplitude of the second order harmonic. These results show that there is a significant increase in the second order harmonic amplitude at monotonic tensile loads above the material’s yield stress, and that du...
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TL;DR: The review provides a concise explanation of principles of operation of different optical coherence tomography methods and a comparative analysis of their advantages and disadvantages is presented in relation to specific applications.
Abstract: An optical coherence tomography (OCT) apparatus includes an optical source, an interferometer generating an object beam and a reference beam, a transverse scanner 11 for scanning an object with said object beam, and a processor for generating an OCT image from an OCT signal returned by said interferometer. At least the optical source, the interferometer, and the scanner are mounted on a common translation stage 30 displaceable towards and away from said object. The optical components mounted on the stage are configured to maintain a coherence gate C in approximate coincidence with the focus F during the displacement of the transition stage.
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TL;DR: An interferometric detection scheme is used to directly detect single gold nanoparticles with a diameter as small as 5 nm in an aqueous environment and it is shown thatgold nanoparticles can be readily distinguished from background scatterers by exploiting the wavelength dependence of their plasmon resonances.
Abstract: We use an interferometric detection scheme to directly detect single gold nanoparticles with a diameter as small as 5 nm in an aqueous environment. We demonstrate both confocal and wide-field detection of nanoparticles and study signal strength as a function of particle size. Furthermore, we demonstrate a detection speed up to 2 micros. We also show that gold nanoparticles can be readily distinguished from background scatterers by exploiting the wavelength dependence of their plasmon resonances. Our studies pave the way for the application of this detection scheme for particle tracking in biological systems.
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TL;DR: A system based on digital holographic interferometry for the measurement of vibrations is presented and by combination of the deformations recorded at different times it is possible to reconstruct the vibration of the object.
Abstract: A system based on digital holographic interferometry for the measurement of vibrations is presented. A high-power continuous laser (10 W) and a high-speed CCD camera are used. Hundreds of holograms of an object that has been subjected to dynamic deformation are recorded. The acquisition speed and the time of exposure of the detector are determined by the vibration frequency. Two methods are presented for triggering the camera in order to acquire at a given phase of the vibration. The phase of the wavefront is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. The deformation of the object is obtained from the phase. By combination of the deformations recorded at different times it is possible to reconstruct the vibration of the object.
01 Jan 2006
Abstract: While conventional interferometric synthetic aperture radar (InSAR) is a very effective technique for measuring crustal deformation, almost any interferogram includes large areas where the signals decorrelate and no measurement is possible. Consequently, most InSAR studies to date have focused on areas that are dry and sparsely vegetated. A relatively new analysis technique, permanent scatterer InSAR, overcomes the decorrelation problem by identifying resolution elements whose echo is dominated by a single scatterer in a series of interferograms. This technique has been useful for analysis of urban areas, where angular structures produce efficient reflectors that dominate background scattering. However, man-made structures are absent from most of the Earth’s surface. Furthermore, this technique requires, a priori, an approximate temporal model for the deformation, whereas characterizing the temporal pattern of deformation is commonly one of the aims of any study. We have developed a new method of analysis, StaMPS, using spatial correlation of interferogram phase to find a network of stable pixels in all terrains, with or without buildings. Prior knowledge of temporal variations in the deformation rate is not required. We refer to these pixels as persistent scatterers (PS). A key component of our method is the development of two algorithms to unwrap a three-dimensional series of interferograms. We observe temporally-variable deformation, using an initial version of StaMPS, in data acquired over Long Valley caldera in California, for a period when deformation rates varied significantly. The inferred displacements of the PS compare well with ground truth. Using an enhanced version of StaMPS, we detect a period of steady deflation within the Volcán Alcedo caldera in the Galápagos Islands between 1997 and 2001, which we model with a contracting ellipsoidal magma
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TL;DR: The potential of broadband L-band SAR systems for ionospheric TEC mapping is studied and it is shown that phase advance and group delay can be measured by interferometric and correlation techniques, respectively.
Abstract: Ionospheric propagation effects have a significant impact on the signal properties of low-frequency synthetic aperture radar (SAR) systems. Range delay, interferometric phase bias, range defocusing, and Faraday rotation are the most prominent ones. All the effects are a function of the so-called total electron content (TEC). Methods based on two-frequency global positioning system observations allow measuring TEC in the ionosphere with coarse spatial resolution only. In this letter, the potential of broadband L-band SAR systems for ionospheric TEC mapping is studied. As a basis, the dispersive nature of the ionosphere and its effects on broadband microwave radiation are theoretically derived and analyzed. It is shown that phase advance and group delay can be measured by interferometric and correlation techniques, respectively. The achievable accuracy suffices in mapping small-scale ionospheric TEC disturbances. A differential TEC estimator that separates ionospheric from tropospheric contributions is proposed
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TL;DR: The observation of an unpredictable behavior of a simple, two-path, electron interferometer of high contrast Aharonov-Bohm (AB) oscillations defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.
Abstract: We report the observation of an unpredictable behavior of a simple, two-path, electron interferometer. Utilizing an electronic analog of the well-known optical Mach-Zehnder interferometer, with current carrying edge channels in the quantum Hall effect regime, we measured high contrast Aharonov-Bohm (AB) oscillations. Surprisingly, the amplitude of the oscillations varied with energy in a lobe fashion, namely, with distinct maxima and zeros (namely, no AB oscillations) in between. Moreover, the phase of the AB oscillations was constant throughout each lobe period but slipped abruptly by $\ensuremath{\pi}$ at each zero. The periodicity of the lobes defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.
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30 May 2006TL;DR: An interferometer for X-rays, in particular hard X-ray, for obtaining quantitative phase contrast images, includes a standard polychromatic X ray source, a diffractive optical beam splitter other than a Bragg crystal in transmission geometry, and a position-sensitive detector with spatially modulated detection sensitivity as mentioned in this paper.
Abstract: An interferometer for X-rays, in particular hard X-rays, for obtaining quantitative phase contrast images, includes a standard polychromatic X-ray source, a diffractive optical beam splitter other than a Bragg crystal in transmission geometry, and a position-sensitive detector with spatially modulated detection sensitivity.
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TL;DR: In this paper, the authors present highly sensitive optical biosensors based on integrated Mach-Zehnder interferometers, which have been designed to have high surface sensitivity and monomode behaviour.
Abstract: We present highly sensitive optical biosensors able to be fully integrated in lab-on-a-chip microsystems using standard CMOS compatible processes. These optical biosensors are based on integrated Mach–Zehnder interferometers, which have been designed to have high surface sensitivity and monomode behaviour. As a biosensing application of the devices we show the real-time detection of the covalent immobilization and hybridization of DNA strands without labelling. In order to achieve a lab-on-a-chip portable microsystem, we present the integration of the sensor with a CMOS compatible microfluidic system using SU-8 photolithography patterned layers.
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23 Oct 2006TL;DR: In this article, the authors used swept-wavelength interferometry for distributed fiber-optic strain and temperature sensing in single mode and gradient index multimode fiber, which was used to measure strain in a four-strand multimode cable under twist.
Abstract: We describe use of swept-wavelength interferometry for distributed fiber-optic strain and temperature sensing in single mode and gradient index multimode fiber. The method is used to measure strain in a four-strand multimode cable under twist.
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TL;DR: This work presents a high-spectral-resolution and experimentally simple version of spectral interferometry using optical fibers and crossed beams, called SEA TADPOLE, which achieves spectral super-resolution, yielding the pulse spectrum with even better resolution.
Abstract: We present a high-spectral-resolution and experimentally simple version of spectral interferometry using optical fibers and crossed beams, which we call SEA TADPOLE. Rather than using collinear unknown and reference pulses separated in time to yield spectral fringes-and reduced spectral resolution-as in current versions, we use time-coincident pulses crossed at a small angle to generate spatial fringes. This allows the extraction of the spectral phase with the full spectrometer resolution, which allows the measurement of much longer and more complex pulses. In fact, SEA TADPOLE achieves spectral super-resolution, yielding the pulse spectrum with even better resolution. Avoiding collinear beams and using fiber coupling also vastly simplify alignment. We demonstrate SEA TADPOLE by measuring a chirped pulse, a double pulse separated by 14 ps, and a complex pulse comprising two trains of pulses with a time-bandwidth product of ~400.
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TL;DR: In this paper, an interferometric method for determining the phase variation of electronic wave packets in momentum space is presented, and demonstrated its applicability to the fundamental process of single-photon ionization.
Abstract: Acomplete quantum-mechanical description of matter and its interaction with the environment requires detailed knowledge of a number of complex parameters. In particular, information about the phase of wavefunctions is important for predicting the behaviour of atoms, molecules or larger systems. In optics, information about the evolution of the phase of light in time1 and space2 is obtained by interferometry. To obtain similar information for atoms and molecules, it is vital to develop analogous techniques. Here we present an interferometric method for determining the phase variation of electronic wave packets in momentum space, and demonstrate its applicability to the fundamental process of single-photon ionization. We use a sequence of extreme-ultraviolet attosecond pulses3,4 to ionize argon atoms and an infrared laser field, which induces a momentum shear5 between consecutive electron wave packets. The interferograms that result from the interaction of these wave packets provide useful information about their phase. This technique opens a promising new avenue for reconstructing the wavefunctions6,7 of atoms and molecules and for following the ultrafast dynamics of electronic wave packets.