1,343 research outputs found
Learning Dictionaries with Bounded Self-Coherence
Sparse coding in learned dictionaries has been established as a successful
approach for signal denoising, source separation and solving inverse problems
in general. A dictionary learning method adapts an initial dictionary to a
particular signal class by iteratively computing an approximate factorization
of a training data matrix into a dictionary and a sparse coding matrix. The
learned dictionary is characterized by two properties: the coherence of the
dictionary to observations of the signal class, and the self-coherence of the
dictionary atoms. A high coherence to the signal class enables the sparse
coding of signal observations with a small approximation error, while a low
self-coherence of the atoms guarantees atom recovery and a more rapid residual
error decay rate for the sparse coding algorithm. The two goals of high signal
coherence and low self-coherence are typically in conflict, therefore one seeks
a trade-off between them, depending on the application. We present a dictionary
learning method with an effective control over the self-coherence of the
trained dictionary, enabling a trade-off between maximizing the sparsity of
codings and approximating an equiangular tight frame.Comment: 4 pages, 2 figures; IEEE Signal Processing Letters, vol. 19, no. 12,
201
Readout and Control of a Power-recycled Interferometric Gravitational-wave Antenna
Interferometric gravitational wave antennas are based on Michelson
interferometers whose sensitivity to small differential length changes has been
enhanced by adding multiple coupled optical resonators. The use of optical
cavities is essential for reaching the required sensitivity, but sets
challenges for the control system which must maintain the cavities near
resonance. The goal for the strain sensitivity of the Laser Interferometer
Gravitational-wave Observatory (LIGO) is 10^-21 rms, integrated over a 100 Hz
bandwidth centered at 150 Hz. We present the major design features of the LIGO
length and frequency sensing and control system which will hold the
differential length to within 5 10^-14 m of the operating point. We also
highlight the restrictions imposed by couplings of noise into the gravitational
wave readout signal and the required immunity against them.Comment: Presentation at ICALEPCS 2001, San Jose, November 2001, (WECT003), 3
page
Hadronic Atoms and Effective Interactions
We examine the problem of hadronic atom energy shifts using the technique of
effective interactions and demonstrate equivalence with the conventional
quantum mechanical approach.Comment: 22 page latex file with 2 figure
An all-optical trap for a gram-scale mirror
We report on a stable optical trap suitable for a macroscopic mirror, wherein
the dynamics of the mirror are fully dominated by radiation pressure. The
technique employs two frequency-offset laser fields to simultaneously create a
stiff optical restoring force and a viscous optical damping force. We show how
these forces may be used to optically trap a free mass without introducing
thermal noise; and we demonstrate the technique experimentally with a 1 gram
mirror. The observed optical spring has an inferred Young's modulus of 1.2 TPa,
20% stiffer than diamond. The trap is intrinsically cold and reaches an
effective temperature of 0.8 K, limited by technical noise in our apparatus.Comment: Major revision. Replacement is version that appears in Phy. Rev.
Lett. 98, 150802 (2007
Determination and optimization of mode matching into optical cavities by heterodyne detection
We report on a novel high-sensitivity method to characterize and improve mode matching into optical cavities. This method is based on heterodyne detection of cylindrical transverse cavity modes. A specially designed annular-segmented photodiode is used to measure the amplitude of nonresonant modes reflected by the cavity. Our measurements allow us to optimize cavity mode matching to nearly 99.98% and will play an important diagnostic role in gravitational-wave detectors
A dispersion theoretical approach to the threshold amplitudes of pion photoproduction
We give predictions for the partial wave amplitudes of pion photoproduction
near threshold by means of dispersion relations at fixed t. The free parameters
of this approach are determined by a fit to experimental data in the energy
range 160 MeV 420 MeV. The observables near threshold are
found to be rather sensitive to the amplitudes in the resonance region, in
particular to the (1232) and (1440). We obtain a good agreement
with the existing threshold data for both charged and neutral pion production.
Our predictions also agree well with the results of chiral perturbation theory,
except for neutral pion production off the neutron.Comment: 16 pages LATEX including 4 postscript figure
Squeezed light for advanced gravitational wave detectors and beyond
Recent experiments have demonstrated that squeezed vacuum states can be injected into gravitational wave detectors to improve their sensitivity at detection frequencies where they are quantum noise limited. Squeezed states could be employed in the next generation of more sensitive advanced detectors currently under construction, such as Advanced LIGO, to further push the limits of the observable gravitational wave Universe. To maximize the benefit from squeezing, environmentally induced disturbances such as back scattering and angular jitter need to be mitigated. We discuss the limitations of current squeezed vacuum sources in relation to the requirements imposed by future gravitational wave detectors, and show a design for squeezed light injection which overcomes these limitations
Precise calibration of LIGO test mass actuators using photon radiation pressure
Precise calibration of kilometer-scale interferometric gravitational wave
detectors is crucial for source localization and waveform reconstruction. A
technique that uses the radiation pressure of a power-modulated auxiliary laser
to induce calibrated displacements of one of the ~10 kg arm cavity mirrors, a
so-called photon calibrator, has been demonstrated previously and has recently
been implemented on the LIGO detectors. In this article, we discuss the
inherent precision and accuracy of the LIGO photon calibrators and several
improvements that have been developed to reduce the estimated voice coil
actuator calibration uncertainties to less than 2 percent (1-sigma). These
improvements include accounting for rotation-induced apparent length variations
caused by interferometer and photon calibrator beam centering offsets, absolute
laser power measurement using temperature-controlled InGaAs photodetectors
mounted on integrating spheres and calibrated by NIST, minimizing errors
induced by localized elastic deformation of the mirror surface by using a
two-beam configuration with the photon calibrator beams symmetrically displaced
about the center of the optic, and simultaneously actuating the test mass with
voice coil actuators and the photon calibrator to minimize fluctuations caused
by the changing interferometer response. The photon calibrator is able to
operate in the most sensitive interferometer configuration, and is expected to
become a primary calibration method for future gravitational wave searches.Comment: 13 pages, 6 figures, accepted by Classical and Quantum Gravit
Precise calibration of LIGO test mass actuators using photon radiation pressure
Precise calibration of kilometer-scale interferometric gravitational wave
detectors is crucial for source localization and waveform reconstruction. A
technique that uses the radiation pressure of a power-modulated auxiliary laser
to induce calibrated displacements of one of the ~10 kg arm cavity mirrors, a
so-called photon calibrator, has been demonstrated previously and has recently
been implemented on the LIGO detectors. In this article, we discuss the
inherent precision and accuracy of the LIGO photon calibrators and several
improvements that have been developed to reduce the estimated voice coil
actuator calibration uncertainties to less than 2 percent (1-sigma). These
improvements include accounting for rotation-induced apparent length variations
caused by interferometer and photon calibrator beam centering offsets, absolute
laser power measurement using temperature-controlled InGaAs photodetectors
mounted on integrating spheres and calibrated by NIST, minimizing errors
induced by localized elastic deformation of the mirror surface by using a
two-beam configuration with the photon calibrator beams symmetrically displaced
about the center of the optic, and simultaneously actuating the test mass with
voice coil actuators and the photon calibrator to minimize fluctuations caused
by the changing interferometer response. The photon calibrator is able to
operate in the most sensitive interferometer configuration, and is expected to
become a primary calibration method for future gravitational wave searches.Comment: 13 pages, 6 figures, accepted by Classical and Quantum Gravit
Adaptive thermal compensation of test masses in advanced LIGO
As the first generation of laser interferometric gravitational wave detectors
near operation, research and development has begun on increasing the
instrument's sensitivity while utilizing the existing infrastructure. In the
Laser Interferometer Gravitational Wave Observatory (LIGO), significant
improvements are being planned for installation in ~2007, increasing strain
sensitivity through improved suspensions and test mass substrates, active
seismic isolation, and higher input laser power. Even with the highest quality
optics available today, however, finite absorption of laser power within
transmissive optics, coupled with the tremendous amount of optical power
circulating in various parts of the interferometer, result in critical
wavefront deformations which would cripple the performance of the instrument.
Discussed is a method of active wavefront correction via direct thermal
actuation on optical elements of the interferometer. A simple nichrome heating
element suspended off the face of an affected optic will, through radiative
heating, remove the gross axisymmetric part of the original thermal distortion.
A scanning heating laser will then be used to remove any remaining
non-axisymmetric wavefront distortion, generated by inhomogeneities in the
substrate's absorption, thermal conductivity, etc. A proof-of-principle
experiment has been constructed at MIT, selected data of which are presented.Comment: 11 pages, 7 figures, submitted to Classical and Quantum Gravit
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