Fringe Visibility Measurements Research Articles

The fringe visibility measurements on the complex s-plane: A novel method for the fringe visibility measurement

In this work, a novel theoretical technique to measure the fringe visibility ν of a low-coherence interference pattern is proposed. The new technique is called Fringe Visibility Measurement on the S-Plane (FVM-SP) because it is developed on the s-plane. The FVM-SP technique only requires to know the pole and zero location of the modulated function, which is filtered from the interference pattern. Since the optical parameter ν can take the necessary values into the interval 0 to 1, some limits are determined for the FVM-SP. The limits are specified on the complex plane and obtained analyzing the pole-zero map of a modulated function. In the numerical experiments, our proposal FVM-SP and the traditional technique are compared performing two series of experiments. In the one, a low-frequency interference pattern is considered, ωo=12rads and the fringe visibility ν is between 0 and 1 with a step of 0.1. While, in the second series, a high-frequency interference pattern is used, ωo=62831.853rads and the fringe visibility ν had the same values. Based on our numerical results, both methods produce close results. When the interference pattern has a low frequency, the mean errors were 7 × 10−4 and 17.5 × 10−4. However, if the pattern has a high frequency, the average errors were 3×10-4 and 7×10-4, respectively. The traditional technique is based on the intensity of the interference pattern while the FVM-SP is based on its frequency.The Fringe Visibility Measurement on the S-Plane technique is applied for the case 1D and it has potential application on signal demodulation and low-coherence system analysis.

Simultaneous Measurement of Fringe Visibility and Path Predictability of Wave-Particle Duality**Supported by the National Science Foundation (INSPIRE CREATIV) under Grant No PHY-1241032, the Robert A. Welch Foundation under Grant No A-1261, and the National Natural Science Foundation of China under Grant No 11664018.

An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young’s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters.

Coherence Length and Vibrations of the Coherence Beamline I13 at the Diamond Light Source

I13 is a 250 m long hard x-ray beamline for imaging and coherent diffraction at the Diamond Light Source. The beamline (6 keV to 35 keV) comprises two independent experimental endstations: one for imaging in direct space using x-ray microscopy and one for imaging in reciprocal space using coherent diffraction based imaging techniques [1]. In particular the coherence experiments pose very high demands on the performance on the beamline instrumentation, requiring extensive testing and optimisation of each component, even during the assembly phase. Various aspects like the quality of optical components, the mechanical design concept, vibrations, drifts, thermal influences and the performance of motion systems are of particular importance. In this paper we study the impact of the front-end slit size (FE slit size), which determines the horizontal source size, onto the coherence length and the detrimental impact of monochromator vibrations using in-situ x-ray metrology in conjunction with fringe visibility measurements and vibration measurements, based on centroid tracking of an x-ray pencil beam with a photon-counting detector.

The Keck Interferometer

The Keck Interferometer (KI) combined the two 10 m W. M. Keck Observatory telescopes on Mauna Kea, Hawaii, as a long-baseline near- and mid-infrared interferometer. Funded by NASA, it operated from 2001 until 2012. KI used adaptive optics on the two Keck telescopes to correct the individual wavefronts, as well as active fringe tracking in all modes for path-length control, including the implementation of cophasing to provide long coherent integration times. KI implemented high sensitivity fringe-visibility measurements at H (1.6 μm), K (2.2 μm), and L (3.8 μm) bands, and nulling measurements at N band (10 μm), which were used to address a broad range of science topics. Supporting these capabilities was an extensive interferometer infrastructure and unique instrumentation, including some additional functionality added as part of the NSF-funded ASTRA program. This paper provides an overview of the instrument architecture and some of the key design and implementation decisions, as well as a description of all of the key elements and their configuration at the end of the project. The objective is to provide a view of KI as an integrated system, and to provide adequate technical detail to assess the implementation. Included is a discussion of the operational aspects of the system, as well as of the achieved system performance. Finally, details on V2 calibration in the presence of detector nonlinearities as applied in the data pipeline are provided.

Hot circumstellar material resolved aroundβ Pic with VLTI/PIONIER

We aim at resolving the circumstellar environment around beta Pic in the near-infrared in order to study the inner planetary system (< 200 mas, i.e., ~4 AU). Precise interferometric fringe visibility measurements were obtained over seven spectral channels dispersed across the H band with the four-telescope VLTI/PIONIER interferometer. Thorough analysis of interferometric data was performed to measure the stellar angular diameter and to search for circumstellar material. We detected near-infrared circumstellar emission around beta Pic that accounts for 1.37% +/- 0.16% of the near-infrared stellar flux and that is located within the field-of-view of PIONIER (i.e., ~200 mas in radius). The flux ratio between this excess and the photosphere emission is shown to be stable over a period of 1 year and to vary only weakly across the H band, suggesting that the source is either very hot (> 1500 K) or dominated by the scattering of the stellar flux. In addition, we derived the limb-darkened angular diameter of beta Pic with an unprecedented accuracy (theta_LD= 0.736 +/- 0.019 mas). The presence of a small H-band excess originating in the vicinity of beta Pic is revealed for the first time thanks to the high-precision visibilities enabled by VLTI/PIONIER. This excess emission is likely due to the scattering of stellar light by circumstellar dust and/or the thermal emission from a yet unknown population of hot dust, although hot gas emitting in the continuum cannot be firmly excluded.

Spectral interferometric microscope with tandem liquid-crystal Fabry-Perot interferometers for extension of the dynamic range in three-dimensional step-height measurement.

The maximum measurable range of a spectral interference microscope depends on the coherence length of the light transmitted by its tunable spectral filter. To achieve a large range in step-height measurement we have developed a new tunable spectral filter that uses tandem liquid-crystal Fabry-Perot interferometers (LC-FPIs), which can simultaneously attain both a high spectral resolution and a large tuning range. Fringe visibility measurements were carried out, and it was found that the coherence length of the light transmitted through tandem LC-FPIs is two times larger than that transmitted through a single LC-FPI. Using this novel tunable spectral filter, we developed a new spectral interference microscope for the measurement of three-dimensional shapes of discontinuous objects. Experimental results of step-height measurements both with a single LC-FPI and with tandem LC-FPIs are presented for a combination of standard steel gauge block sets with 1-, 99-, and 100-microm steps. A large range (1-100 microm) of measurement with submicrometer resolution was achieved with tandem LC-FPIs that was not possible with our previous system in which a single LC-FPI was used.

Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers

We use a numerical simulation to investigate the effectiveness of pinhole spatial filters for optical/IR interferometers and to compare them with single-mode optical fibre spatial filters and interferometers without spatial filters. We show that fringe visibility measurements in interferometers containing spatial filters are much less affected by changing seeing conditions than equivalent measurements without spatial filters. This reduces visibility calibration uncertainties, and hence can reduce the need for frequent observations of separate astronomical sources for calibration of visibility measurements. We also show that spatial filters can increase the signal-to-noise ratios (SNRs) of visibility measurements and that pinhole filters give SNRs within 17 per cent of the values obtained with single-mode fibres for aperture diameters up to 3r0. Given the simplicity of the use of pinhole filters we suggest that it represents a competitive, if not optimal, technique for spatial filtering in many current and next generation interferometers.

Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers

We use a numerical simulation to investigate the effectiveness of pinhole spatial filters at optical/IR interferometers and to compare them with single-mode optical fibre spatial filters and interferometers without spatial filters. We show that fringe visibility measurements in interferometers containing spatial filters are much less affected by changing seeing conditions than equivalent measurements without spatial filters. This reduces visibility calibration uncertainties, and hence can reduce the need for frequent observations of separate astronomical sources for calibration of visibility measurements. We also show that spatial filters can increase the signal-to-noise ratios of visibility measurements and that pinhole filters give signal-to-noise ratios within 17% of values obtained with single-mode fibres for aperture diameters up to 3r_0. Given the simplicity of the use of pinhole filters we suggest that it represents a competitive, if not optimal, technique for spatial filtering in many current and next generation interferometers.

Progress in FWSD non-linear effects with XRLs

Progress of a four-wave sum difference frequency generation scheme to convert coherent soft X-ray radiation to shorter wavelengths, using a plasma medium is discussed. Results are presented from a preliminary experiment, involving the Ne-like Ni XRL (λ XRL = 0.023 μm) mixed in phase-matched mode with a Nd:glass laser (λ OPT = 1.054 μm) in a Na-like Argon plasma. A 25 mm single slab target of Ni pumped with ∼ 200 J of energy from 5 optical beams has routinely produced ∼ 3 mJ of XRL energy at 23.1 nm. The XRL was split and recombined and information from fringe visibility measurements has been used to estimate the degree of spatial coherence in the XRL. Characterisation of the gas jet mixing medium has been carried out through emission spectroscopy and optical interferometry.

Power dependence of the injection lock band of angled-grating distributed feedback lasers

Experimental measurements of the injection lock band of an angled-grating distributed feedback laser have been performed systematically as a function of the unlocked slave laser power. Fringe visibility measurements were used to ascertain the quality of the lock between the master and slave laser as a function of master coupling level and frequency detuning. Experimental data show increasing spectral instabilities under optical injection as the slave laser power is increased, resulting in the stable portion of the lock band decreasing in width.

Simulation of the effects of atmospheric turbulence on mid-infrared visibility measurements with the mid-infrared interferometric instrument for the Very Large Telescope Interferometer

The mid-infrared interferometric instrument is one of three instruments that will equip the focus of the Very Large Telescope Interferometer. During the design phase of the instrument we made use of a program of simulations to define the constraints imposed by atmospheric turbulence. We present our results for the estimated fringe motion, during a typical sampling time of 100 ms, and for the estimated fringe visibility with and without tip-tilt correction. Our simulations were run assuming an outer scale of turbulence of 25 m against an infinite value as strictly implied by Kolmogorov statistics. The results show that this has positive consequences for our applications, above all as far as fringe motion is concerned. We also take into consideration the effect of background noise on the accuracy of the fringe visibility measurements and the effect of self-fringe tracking, which has been simulated by a linear fringe-tracker algorithm.

Pupil-size effects in fiber optic stellar interferometry.

The effects of finite telescope pupil sizes on the measurement of fringe visibility in fiber optic stellar interferometry are described. It is shown theoretically that the measured fringe visibility is equal to the cross correlation of the magnitude of the source's mutual coherence function with the cross correlation of the telescopes' effective pupil functions. If the telescopes' effective pupil diameters are not small compared with the width of the source's mutual coherence function, then the measured fringe visibility will be correspondingly distorted. The theoretical results are verified experimentally in a fiber optic Mach-Zehnder interferometer.

Injection locking of broad-area angled grating DFB lasers

The injection locking properties of an angled-grating distributed feedback laser have been measured experimentally. Fringe visibility measurements were used to ascertain the quality of the phase lock between the master and slave laser as a function of master coupling level and frequency detuning. Experimental results show an asymmetric lockband with the stable lock region increasing in width as the coupling is increased.

Dispersion in stellar interferometry: simultaneous optimization for delay tracking and visibility measurements

In long-baseline optical stellar interferometry, it is necessary to maintain optical path equality between the two arms of an interferometer in order to measure the fringe visibility. There will be errors in matching the optical paths because of a number of factors, and it is desirable to use an automatic system to monitor and correct such path errors. One type of system is a delay tracker, based on imaging of the channeled spectrum. The tracking algorithm is designed to maintain a fixed number of fringes, ideally linearly spaced, across the observed spectral band. This results in a constant optical path difference, which may be incompatible with the requirement of path equality for the measurement of fringe visibility. In a practical interferometer that uses an optical path-length compensator operating in air, there is a complication since air paths introduce differential dispersion. This dispersion can be compensated for by including dispersion correction. By modifying the operation of an appropriately designed dispersion corrector, we show that it is possible to make the optical path difference zero at the measurement wavelength and, at the same time, to produce linearly spaced channel fringes across the tracking band.

Scintillation in Optical Stellar Interferometry

ABSTRACTThe signal measured by a stellar interferometer consists of a coherent part that contains information about the fringe visibility and an incoherent part that is usually removed at an early stage of the data processing. If this separation is not done, the scintillation noise associated with the incoherent term can systematically bias the measurement of fringe visibility, and it is important to take this into consideration when designing detection systems for stellar interferometry. On the other hand, the scintillation noise can provide additional information about atmospheric turbulence. This may prove to be useful in the reduction of data obtained interferometrically.

Simultaneous displacement and temperature sensing using a white light interrogated low finesse cavity in line with a fiber Bragg grating

A fiber optic sensing system for simultaneous measurement of displacement and temperature is presented. It is based on the use of a low finesse extrinsic Fabry-Pérot cavity and a fiber Bragg grating for temperature compensation. A white light tandem interferometric technique is used to recover the signal from the low finesse cavity, providing both fringe visibility and phase measurements. These, together with the fiber grating signal, give two equations that can be used to simultaneously determine temperature and displacement. Theoretical analysis of the sensing scheme is performed. Experimental results are presented which validate theoretical predictions and also demonstrate the feasibility of this sensing system in practical applications.

Single-mode optical fibre linkages of large telescopes at visible wavelengths: experimental results

In this paper we present results of an experiment in which the link between two 1.2 m telescopes was obtained using single-mode optical fibres with polarization-preserving cores. An additional novelty of this experiment is the use of a tipping - tilting stabilization system on each telescope. We present results for the measured coupling efficiency with and without tip/tilt stabilization. Furthermore, we present white-light fringe-visibility measurements obtained on light from the star Alpha Bootis.

Absolute distance interferometry with two-wavelength fringe visibility measurement

A new version of interferometer construction for absolute distance measurement is presented. It is based on measuring the contrast of a two-wavelength interference pattern with using a CO2 laser generating a pair of optical wavelengths simultaneously.

Fast, common-path, switchable, achromatic phase-shifter for polarization interferometry

Abstract A fast switchable phase-shifter using a pair of liquid-crystal devices with a switching angle of 60° is described. This phase-shifter can be placed in the common path traversed by the two orthogonally polarized beams emerging from a polarization interference microscope and used for digital phase measurements over a wide range of wavelengths. It can also be used in a stellar interferometer with orthogonally polarized beams for measurements of fringe visibility with white light.

Fast, common-path, switchable, achromatic phase-shifter for polarization interferometry

A fast switchable phase-shifter using a pair of liquid-crystal devices with a switching angle of 60° is described. This phase-shifter can be placed in the common path traversed by the two orthogonally polarized beams emerging from a polarization interference microscope and used for digital phase measurements over a wide range of wavelengths. It can also be used in a stellar interferometer with orthogonally polarized beams for measurements of fringe visibility with white light.