High-precision Phase Measurement Research Articles

Closure phase studies toward direct detection of light from hot Jupiters

AbstractPrecision closure phase measurements obtained with ground-based long baseline optical interferometers is a promising way to directly detect light from nearby hot Jupiters. Here we present our closure phase simulations for the CHARA array for several bright hot Jupiters, υ And b, 51 Peg b, and τ Boo b. The maximum possible closure phase signals from these hot Jupiters are very small, for example, only ∼0.17 degrees for υ And b, requiring very high precision and stable closure phase measurements. We present preliminary results of a closure phase study on test object β Tau and hot Jupiter system υ And, both obtained with the MIRC instrument at the CHARA array. We demonstrate that directly detecting the light from hot Jupiters is feasible using high precision closure phase measurements obtained by CHARA-MIRC along with its sub-milli-arcsecond resolution, although challenges remain.

Detuned Twin-Signal-Recycling for ultrahigh-precision interferometers

We propose a new interferometer technique for high-precision phase measurements such as those in gravitational wave detection. The technique utilizes a pair of optically coupled resonators that provide identical resonance conditions for the upper as well the lower phase modulation signal sidebands. This symmetry significantly reduces the noise spectral density in a wide frequency band compared with single-sideband recycling topologies of current and planned gravitational wave detectors. Furthermore, the application of squeezed states of light becomes less demanding.

Atmospheric Studies with the Tri-Band Beacon Instrument on the COSMIC Constellaion

Radio frequency transmissions from each satellite in the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) can be used to study the plasma in the upper atmosphere by (1) providing profiles and two dimensional images of the ionosphere and (2) monitoring phase and amplitude scintillations induced in radio waves propagating through the ionosphere. In addition, the received radio data can be applied to the neutral atmosphere by (a) detecting horizontal fluctuations in tropospheric water vapor and (b) yielding accurate position data for satellite drag and neutral density determination. A three-frequency radio beacon called the Tri-Band Beacon (TBB) is being developed for the COSMIC pro-gram to provide transmissions at VHF, UHF and L-band. Tomographic imaging of the ionosphere is a recently developed technique that uses integrated measurements and computer reconstructions to determine electron densities. The integral of electron density along vertical or oblique paths is obtained by employing radio transmissions from low-earth-orbiting (LEO) COSMIC satellite transmitters to a chain of receivers on the earth’s surface. Analyzing the total electron content (TEC) data using computerized ionospheric tomography (CIT) produces two-dimensional maps of the ionospheric plasma. Difficulties associated with CIT arise from the non-unique ness of the reconstructions owing to limited angle measurements or non optimal receiver. Improvements in both reconstruction algorithms and CIT measurement systems are being implemented for the COSMIC mission by combining the GPS occultation data with the TBB measurements of TEC. once the ionospheric effects on the radio wave propagation have been de termined, the Doppler shifts of the UHF and VHF transmissions can be analyzed to give positioning of the COSMIC satellites to within a few meters. By measuring the effects of the atmospheric drag on the COSMIC satellites, global data for neutral densities in the upper atmosphere can he obtained. There is an additional phase delay of the VHF/UHFIL-bands from the neutral constituents of the troposphere. This phase delay can be used to provide measurements of integrated water vapor. The spatial distribution of water vapor density may be determined with high precision phase measurements from a linear array of ground receivers observing the L-band transmissions of the COSMIC TBB.

Error-Compensating Phase Measuring Algorithms in a Fizeau Inter ferometer

In phase-shifting Fizeau interferometers, nonlinear motion of the phase shifter and multiple-beam interference are the most common sources of systematic errors affecting high-precision phase measurement. A new class of algorithms with extended compensating capability for these errors is proposed. Measurement errors for the new algorithms and two groups of conventional algorithms: discrete Fourier algorithms and the Schwider-Larkin-Hibino algorithms are estimated as a function of the number of sampled images when these systematic error sources are equally dominant. It is shown that the conventional phase-measuring algorithms produce significant errors when the reflectivity of the testing surface exceeds ten percent. Also, these algorithms have an optimum number of samples at around seven with which the residual errors become minimum. The new class of algorithms shows a substantial reduction of the residual errors when the number of samples exceeds ten. There is no optimum number of samples for the new algorithms. For fewer than six samples, discrete Fourier algorithms which have no error-compensating capability for the nonlinearity of phase modulation give a minimum error.

Measurement of displacement vector fields of extended objects

The main effort in laser metrology during the last 15 years has been focussed on the development of high precision phase measurement techniques, since the phase is the primary quantity for interferometrical testing. However, the phase distribution gives only a first impression of the deformation of the surface. In practice, the three-dimensional displacement components are required if the mechanical behaviour of the object under load is to be investigated. To calculate displacement components some further quantities are necessary, e.g. the three coordinates of the object points. Although the contour measurement can also be reduced to a phase measurement problem, the measurement of three-dimensional displacements is more complex than a high precision phase evaluation. From the practical point of view, four main tasks have to be performed: planning of the experiment, design of the interferometer, acquisition of data and evaluation of data. This paper deals with a discussion of the theoretical background of the last three procedures concerning the state of the art and describes some general rules as well as some problems remaining to be solved for the investigation of extended specimens.

The Aharonov-Bohm effect and its applications to observations of the microscopic world

Just as the field of coherent optics was opened up by the advent of the laser beam, coherent electron optics has been propelled forward by the development of a field-emission beam which is both bright and monochromatic. This development has made it feasible to observe high-contrast electron interference patterns even in real time, thereby making it possible to carry out fundamental experiments in physics once regarded as «thought experiments» such as the confirmation of the Aharonov-Bohm effect. It has also facilitated high-precision phase measurements by electron holography. The latter technique has enabled the observation of magnetization distribution in a ferromagnetic material and magnetic fluxons in a superconductor.

Use of the fast Fourier transform method for analyzing linear and equispaced Fizeau fringes

The Fourier transform method is applied to analyze the initial phase of linear and equispaced Fizeau fringes. We develop an algorithm for high-precision phase measurement by using the Fourier coefficient that corresponds to the spatial frequency of the Fizeau fringes, and we describe methods for determining the fringe carrier frequency. Errors caused by carrier frequency fluctuation and data truncation are studied theoretically and by computer simulation. To demonstrate the method we apply it to the real-time calibration of a piezoelectric transducer mirror in a Twyman-Green interferometer.

High precision phase measurement using reduced sine and cosine tables

A high-precision phase measurement technique, which can accurately determine the phase even when the signals are distorted by harmonics, was presented previously by the author (ibid., vol.38, p.954-60, Oct. 1989). He proposes a microprocessor-based hardware implementation of the technique. The hardware implementation requires two reduced tables: a sine table and a cosine table. If each table has i(i+5)/2 entries, then the phase can be accurately determined even if the signals are distorted by any number of harmonics in the range of second through ith harmonics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High precision phase measurement using adaptive sampling

The conventional phase measurement techniques introduce error in the phase when the input signals are distorted by harmonics. A novel technique, known as adaptive sampling, for high-precision phase measurement is introduced. A digital signal-processing approach is used in this technique. The maximum sampling rate required for this technique is h+2 samples/cycle of the input signals, i.e. (h+2)f sampless, where h, is the highest harmonic present in the signals and f is the fundamental frequency of the signals. This sampling rate is way below the Nyquist sampling rate (more than 2hf samples/s) when h is a large number. In the adaptive sampling technique the sampling rate is started from three samples/cycle and then is gradually increased until the phase is correctly measured. This phase measurement technique has been verified using synthesized signals. >

Acoustic-surface-wave amplitude and phase measurements using laser probes

The investigation of acoustic-field distributions on free surfaces is important in several different classes of application. Measurements of the phase of acoustic surface waves using optical probes allow direct measurement of their velocity. A number of different optical-probe types are compared on the basis of sensitivity and stability. The operation and design of an optical heterodyne probe, capable of high-precision phase and group-velocity measurement, is described.