Eigenvalue translation method for mode calculations (original) (raw)
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Frequency-domain interferometer simulation with higher-order spatial modes
Classical and Quantum Gravity, 2004
Finesse is a software simulation allowing one to compute the optical properties of laser interferometers used by interferometric gravitational-wave detectors today. This fast and versatile tool has already proven to be useful in the design and commissioning of gravitational-wave detectors. The basic algorithm of Finesse numerically computes the light amplitudes inside an interferometer using Hermite-Gauss modes in the frequency domain. In addition, Finesse provides a number of commands for easily generating and plotting the most common signals including power enhancement, error and control signals, transfer functions and shot-noise-limited sensitivities. Among the various simulation tools available to the gravitational wave community today, Finesse provides an advanced and versatile optical simulation based on a general analysis of user-defined optical setups and is quick to install and easy to use.
Single-mode versus multimode interferometry: A performance study
Astronomy and Astrophysics, 2004
We compare performances of ground-based single-mode and multimode (speckle) interferometers in the presence of partial Adaptive Optics correction of atmospheric turbulence. It is first shown that for compact sources (i.e. sources smaller than the Airy disk of a single telescope) not entirely resolved by the interferometer, the remarkable property of spatial filtering of single-mode waveguides coupled with AO correction significantly reduces the speckle noise which arises from residual wavefront corrugations. Focusing on those sources, and in the light of the AMBER experiment (the near infrared instrument of the VLTI), we show that single-mode interferometry produces a better Signal-to-Noise Ratio on the visibility than speckle interferometry. This is true for bright sources (K < 5), and in any case as soon as Strehl ratio of 0.2 is achieved. Finally, the fiber estimator is much more robust -by two orders of magnitude -than the speckle estimator with respect to Strehl ratio variations during the calibration procedure. The present analysis theoretically explains why interferometry with fibers can produce visibility measurements with a very high precision, 1% or less.
Three mode interactions as a precision monitoring tool for advanced laser interferometers
Classical and Quantum Gravity, 2014
Three-mode opto-acoustic interactions in advanced laser interferometer gravitational wave detectors have high sensitivity to thermally excited ultrasonic modes in their test masses. Three mode interaction signal gain can change by 100% for thermally induced radius of curvature variations ~ 10 -5 , allowing the monitoring of thermal distortions corresponding to wavefront changes ~2 × 10 -13 m. We show that the three-mode gain for single cavity interactions can be monitored by observing beat signals in the transmitted or reflected light due to the thermal excitation of the many hundreds of detectable acoustic modes. We show that three mode interaction signals can be used at low optical power to predict parametric instabilities that could occur at higher power. In addition, at any power, the observed mode amplitudes can be used to control the interferometer operating point against slow environmental perturbations. We summarize data on an 80m cavity that demonstrates these effects and propose testing on full scale interferometer cavities to evaluate whether the technique has practical benefits that can be extended from single cavities to dual recycling interferometers.
The phase calculation is a powerful measurement technique that allows the reconstruction of 3D profiles from interferogram intensity. In this article a new phase extraction algorithm is presented. This algorithm uses the BEMD technique (Bidimensional Empirical Mode Decomposition) for the evaluation of the phase distribution from a single uncarrier interferogram. The proposed method requires the numerical addition of a high spatial frequency carrier and application of the wavelet transform of the Fourier transform. An evaluation was made through a numerical simulation on simulated and real fringes to validate and confirm the performance of the proposed algorithm. The main advantage of this technique is its ability to provide a metrological solution for the fast dynamic analysis.
Interferometry XIV: Applications
Proceedings of Spie the International Society For Optical Engineering, 2008
The papers included in this volume were part of the technical conference cited on the cover and title page. Papers were selected and subject to review by the editors and conference program committee. Some conference presentations may not be available for publication. The papers published in these proceedings reflect the work and thoughts of the authors and are published herein as submitted. The publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.
Vortex mode transformation interferometry
Journal of Optics, 2019
Whilst many techniques exist for generation of an optical vortex, there remains a need for new devices and methods that can also provide vortex generation with higher powers, greater flexibility of wavelength, and generation beyond the lowest-order Laguerre–Gaussian L G 01 mode to address a broader range of practical applications. This work reveals how an all-mirror based interferometric mode transformation system can provide these properties including revealing, for the first time, the generation of a much richer set of vortex mode patterns than might have been thought possible previously. A new developed theoretical formulation, confirmed with excellent agreement by experimental demonstrations in an imbalanced Sagnac interferometer, shows interferometric transformation is possible for all orders of Laguerre–Gaussian L G 0 l modes into a rich set of high quality higher-order vortex and vortex superposition. The interferometric approach is shown to be configurable to increase or dec...
Accurate and precise characterization of linear optical interferometers
We combine single-and two-photon interference procedures for characterizing any multi-port linear optical interferometer accurately and precisely. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced precision is attained by curve fitting to measured quantities based on a Poissonian shot noise assumption, and we employ bootstrapping statistics to quantify the resultant degree of precision. A scattershot approach is devised to effect a reduction in the experimental time required to characterize the interferometer.
Numerical simulations of vibration in phase-shifting interferometry
Applied Optics, 1996
Computer simulations predict the expected rms measurement error in a phase-shifting interferometer in the presence of mechanical vibrations. The simulations involve a numerical resolution of a nonlinear mathematical model and are performed over a range of vibrational frequencies and amplitudes for three different phase-shift algorithms. Experimental research with an interference microscope and comparison with analytical solutions verify the numerical model. r 1996 Optical Society of America