27.—The Zeros of Optical Coherence Functions and their Utility in the Study of Spectra

1972 ◽  
Vol 70 ◽  
pp. 281-293
Author(s):  
G. M. Thomas
Keyword(s):  
Spectral Line ◽  
Finite Number ◽  
Optical Spectrum ◽  
Infinite Product ◽  
Coherence Function ◽  
Michelson Interferometer ◽  
Number Of Zeros ◽  
Interference Fringes ◽  
Auxiliary Experiment ◽  
Band Limited

SynopsisThis paper shows that the coherence function associated with a band-limited optical spectrum is expressible as an infinite product involving its zeros. Only a finite number of zeros are physically significant and these can be determined from measurements of the visibility of interference fringes; but an ambiguity remains in the sign of the imaginary part of each zero. If the spectrum is to be recovered using the visibility measurements, an auxiliary experiment is needed to supply the necessary signs, but it need not be especially accurate. If the signs are not known there is only a limited number of different spectra that are compatible with the visibility measurements. Finally it is suggested that wavelength measurements made on an asymmetric spectral line with a Michelson interferometer may yield differing results when used with long and short delays.

scholarly journals Dilation of Time Dilation

2017 ◽  
Vol 9 (6) ◽  
pp. 67
Author(s):  
Tadeusz Wajda
Keyword(s):  
Light Pulse ◽  
Michelson Interferometer ◽  
Time Dilation ◽  
Constant Time ◽  
Theory Of Relativity ◽  
Speed Of Light ◽  
Time Intervals ◽  
Interference Fringes ◽  
Fundamental Error ◽  
Transportation Speed

The study addresses the issue of the so-called time dilation in the sense of the origin of its creation and the physical existence.Based on the work of Lorentz, who the lack of displacement of interference fringes in the Michelson interferometer explained wrongly with, shortening one arm of the interferometer, I propose the construction of the light pulse clock, in which to measure the rate of the passage of time is used constancy speed of light in vacuum.Light clock, the construction of which is described in the paper, stationary in relation to the ether, will measure constant time intervals. The same clock transported, will slow down the pace of his walk as a function of transportation speed v and that is a novelty, will slow depending on its orientation relative to the direction of motion. Light clock transported transversely with respect to the stationary clock will slow gamma times, transported lengthwise will slow gamma to the second power.Basing on the obtained dependences I maintain that time dilation defined in the theory of relativity (SR) as the slowing of the lapse of time, does not physically exist and identification the varying pace of walk clock with the pace of lapse of time I consider a fundamental error resulting from the postulates of this theory.

scholarly journals Fundamental Aspects of Aperture Synthesis with Limited or No Phase Information

1979 ◽  
Vol 49 ◽  
pp. 67-82
Author(s):  
J.E. Baldwin ◽  
P.J. Warner
Keyword(s):  
Coherence Function ◽  
Aperture Synthesis ◽  
Phase Information ◽  
Mutual Coherence ◽  
Interference Fringes ◽  
Mutual Coherence Function

Much ingenuity has been devoted to the determination of mutual coherence functions at radio wavelengths. Measurements of the amplitude and phase of the interference fringes with uncertainties of only 1 percent are now attainable. Unfortunately the atmosphere intervenes between the measured quantities and the mutual coherence function itself and the phase uncertainties introduced by the ionospheric and tropospheric irregularities are often the factor limiting the quality of radioastronomical maps.

scholarly journals DUAL EQUATION AND INVERSE PROBLEM FOR AN INDEFINITE STURM–LIOUVILLE PROBLEM WITH M TURNING POINTS OF EVEN ORDER

2012 ◽  
Vol 17 (5) ◽  
pp. 618-629
Author(s):  
Hamidreza Marasi ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Infinite Product ◽  
Turning Points ◽  
Liouville Problem ◽  
Product Representation ◽  
Dual Equation ◽  
Number Of Zeros ◽  
Even Order ◽  
Sturm Liouville ◽  
Infinite Product Representation

In this paper the differential equation y″ + (ρ 2 φ 2 (x) –q(x))y = 0 is considered on a finite interval I, say I = [0, 1], where q is a positive sufficiently smooth function and ρ 2 is a real parameter. Also, [0, 1] contains a finite number of zeros of φ 2 , the so called turning points, 0 < x 1 < x 2 < … < x m < 1. First we obtain the infinite product representation of the solution. The product representation, satisfies in the original equation. As a result the associated dual equation is derived and then we proceed with the solution of the inverse problem.

scholarly journals Study of XUV beam splitter flatness for use on a Michelson interferometer

2004 ◽  
Vol 22 (3) ◽  
pp. 279-284 ◽  
Author(s):  
ANNE-SOPHIE MORLENS ◽  
PHILIPPE ZEITOUN ◽  
LAURENT VANBOSTAL ◽  
PASCAL MERCERE ◽  
GRÉGORY FAIVRE ◽  
...  
Keyword(s):  
Beam Splitter ◽  
Ion Beam ◽  
Michelson Interferometer ◽  
Fourier Transform Spectrometer ◽  
Ion Beam Sputtering ◽  
X Ray ◽  
Interference Fringes ◽  
Beam Sputtering ◽  
20 Nm ◽  
Better Than

A XUV Michelson interferometer has been developed by LIXAM/CEA/LCFIO and has been tested as a Fourier-transform spectrometer for measurement of X-ray laser line shape. The observed strong deformation of the interference fringes limited the interest of such an interferometer for plasma probing. Because the fringe deformation was coming from a distortion of the beam splitter (5 × 5 mm2open aperture, about 150 nm thick), several parameters of the multilayer deposition used for the beam splitter fabrication have been recently optimized. The flatness has been improved from 80 nm rms obtained by using the ion beam sputtering technique, to 20 nm rms by using the magnetron sputtering technique. Over 3 × 3 mm2, the beam splitter has a flatness better than 4 nm rms.

scholarly journals Interference fringes in a nonlinear Michelson interferometer based on spontaneous parametric down-conversion

2021 ◽  
Vol 29 (20) ◽  
pp. 32006
Author(s):  
Chen Yang ◽  
Zhi-Yuan Zhou ◽  
Liu-Long Wang ◽  
Yan Li ◽  
Shi-Kai Liu ◽  
...  
Keyword(s):  
Michelson Interferometer ◽  
Interference Fringes ◽  
Parametric Down Conversion ◽  
Down Conversion

scholarly journals On the Ritt order and type of a certain class of functions defined byBE-Dirichletian elements

1999 ◽  
Vol 22 (3) ◽  
pp. 445-458
Author(s):  
Marcel Berland
Keyword(s):  
Finite Number ◽  
Entire Functions ◽  
Number Of Zeros ◽  
Order And Type ◽  
Class Of Functions

We introduce the notions of Ritt order and type to functions defined by the series∑n=1∞fn(σ+iτ0)exp(−sλn),      s=σ+iτ,(σ,τ)∈R×R                                            (*)indexed byτ0onR, where(λn)1∞is aD-sequence and(fn)1∞is a sequence of entire functions of bounded index with at most a finite number of zeros. By definition, the series areBE-Dirichletian elements. The notions of order and type of functions, defined byB-Dirichletian elements, are considered in [3, 4]. In this paper, using a technique similar to that used by M. Blambert and M. Berland [6], we prove the same properties of Ritt order and type for these functions.

scholarly journals A compact static birefringent interferometer for the measurement of upper atmospheric winds: concept, design and lab performance

2021 ◽  
Author(s):  
Tingyu Yan ◽  
Jeffery A. Langille ◽  
William E. Ward ◽  
William A. Gault ◽  
Alan Scott ◽  
...  
Keyword(s):  
Imaging System ◽  
Michelson Interferometer ◽  
Concept Design ◽  
Low Velocity ◽  
Design And Optimization ◽  
Interference Fringes ◽  
Imaging Interferometer ◽  
Airglow Emissions ◽  
Wind Measurements

Abstract. A new compact static birefringent Doppler wind imaging interferometer has been developed for the purpose of observing upper atmospheric winds using suitably isolated airglow emissions. The instrument, called the Birefringent Doppler Wind imaging Interferometer (BIDWIN), combines a field widened birefringent delay plate placed between two crossed Wollaston prisms with an imaging system, waveplates and polarizers to produce four fixed 90-degree phase stepped images of the interference fringes conjugate to the scene of interest. A four-point algorithm is used to extract line of sight Doppler wind measurements across the image of the scene. The arrangement provides a similar throughput to that of a field widened Michelson interferometer, albeit constructed without moving parts. Consequently, the instrument provides a compact, lightweight and robust alternative. In this paper, the instrument concept is presented and the design and optimization of a prototype version of the instrument is discussed. Characterization of the lab prototype is presented and the performance of the instrument is examined by applying the instrument to measure a low velocity two-dimensional Doppler wind field with a high precision (5 m/s) in the lab.

scholarly journals DIGITAL IDENTIFICATION OF THE EMISSION SPECTRUM LINES OF MAGNETRON DISCHARGE

2019 ◽  
pp. 35-38
Author(s):  
I.A. Afanasіeva ◽  
S.N. Afanasiev ◽  
V.V. Bobkov ◽  
V.V. Gritsyna ◽  
D.R. Drozdov ◽  
...  
Keyword(s):  
Spectral Line ◽  
Optical Spectrum ◽  
Discharge Plasma ◽  
Magnetron Discharge ◽  
Qualitative And Quantitative ◽  
Python Programming Language ◽  
Digital Identification ◽  
Quantitative Characteristics ◽  
Python Programming ◽  
Qualitative And Quantitative Characteristics

To obtain the qualitative and quantitative characteristics of the discharge plasma spectrum in the Python programming language, a multifunctional interactive GUI-application OSA (Optical Spectrum Analyzed) was created. The application allows you to download a digital image of the optical spectrum, automatically determine the wavelength of the selected spectral line and do elements interpretation.

On a criterion for oscillatory solutions of a linear differential equation of the second order

1940 ◽  
Vol 36 (3) ◽  
pp. 283-287 ◽  
Author(s):  
J. C. P. Miller
Keyword(s):  
Differential Equation ◽  
Finite Number ◽  
Linear Differential Equation ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Number Of Zeros ◽  
Independent Variable ◽  
Linear Differential

This paper gives a criterion for determining whether real, non-zero solutions of a linear differential equation of the second order have an infinite or a finite number of zeros, or, in short, are oscillatory or non-oscillatory, as the independent variable tends to infinity.

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