Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Spectroscopy Letters

Analysis of Two Spectral Lines with Gaussian Profile by Using Photon Statistics. Comparison with Other Profile Shapes

Manuel P. Cagigal, Felipe González

Published Jul 1, 1986• 0 citations
Publisher

Abstract

In this paper we study the behavior of the errors involved in the determination of the parameters characterizing two spectral lines with Gaussian profile by means of the measurement of the intensity correlation function g(2)(τ) and by a multichannel system. The results obtained with both methods are compared. We also compare this results with those obtained when two lines with Lorentzian profile are analyzed.

DOI
10.1080/00387018608069266

Related papers

Analysis Of Two Spectral Lines By Photon Statistics.

Manuel P. Cagigal, Felipe González, M. Á. Rebolledo

Analysis of two spectral lines by photon statistics.M.P.Cagigal, F.Gonzalez and M.A.RebolledoDepartamento de Optica y E.M., Universidad de Santander.Facultad de Ciencias, Avda. de los Castros, 39005 Santander, SpainAbstractThe possibility of analyzing two spectral lines by measuring the second -order factorialmoment,n(2)(T), is studied. The results are compared with the ones obtained with a multicha-nnel analyzer system.IntroductionPhoton statistics is a powerful tool with which fluctuating light beams can be analyzed.So photon statistics has been used to analyze light beams from Rayleigh scattering experi-ments with macromolecules in solution1 -4 excited by laser light. In these experiments the intensity of the resulting light beam fluctuates at random.Photon statistics can be also used to analyze fluctuating light beams where the intensityfluctuates in a quasi- deterministic way as a function of time. This occurs in an experimentwhere the velocity of a fluid is measured by a laser Doppler technique2,5,6. In such an ex-periment a sinusoidal intensity modulated by a Gaussian profile is obtained when a particlepasses through the scattering volume. Since the distance between two consecutive particlesis a random variable, the intensity of the resulting light beam is not completely determinis

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 27, 1985•0 citations

Analysis of a spectrum of two Lorentzian or Gaussian lines by measuring n^(2)(T)

Felipe González, M. Á. Rebolledo, Manuel P. Cagigal

In this paper we study the possibility of analyzing a low intensity light beam whose spectrum has two lines with Lorentzian or Gaussian profiles by measuring n(2)(T) (the normalized second-order factorial moment). To do this the spectrum is scanned periodically by a spectrometer, and the normalized second-order factorial moment of the beam intensity at the exit aperture of the spectrometer is measured. The errors involved in the determination of the width, relative height, and separation between the two lines are calculated and discussed.

Applied Optics•Sep 1, 1984•11 citations

Determination of the Parameters Characterizing a Two Lines Spectrum by Measuring n(2)(T): Rectangular Profiles Approximation

M. Á. Rebolledo, Felipe González

In the present paper we study the possibility of analyzing a light beam with a spectrum of two lines, by measuring the normalized second order factorial moment of the photon-counting distribution of the light beam. Two lines with rectangular profile are considered in order to simplify calculations and experiments. The error in the determination of width, separation and relative height of lines is studied by means of an experimentally checked theoretical model.

Spectroscopy Letters•May 1, 1983•5 citations

Spectral modulation by controlled source correlations

Avshalom Gamliel, E. Wolf

It has recently been shown that correlations between source fluctuations throughout the source region can lead to frequency shifts of spectral lines.1,2 We consider the more general problem of modifying the spectrum of the emitted radiation by making a suitable choice of the degree of spatial coherence of the source. To illustrate the potential of this method we consider a simple configuration of two small sources emitting light with identical spectra. We demonstrate that some source correlations can generate multiple spectral lines from a single spectral line of either a Gaussian or Lorentzian profile. Spectral line-shape parameters such as width, amplitude, center frequency, and functional form can also be controlled.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Intensity-Correlation Spectroscopy

Vittorio Degiorgio, J. B. Lastovka

In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.

Physical Review A•Nov 1, 1971•103 citations

Factorial Moment of Two Poissonian Lights Superposed on Gaussian-Lorentzian Light

Hideaki Satō, Norihito Suzuki

A photon counting method is adapted to spectroscopy in very low intensity, as it is useful for data acquisition. There are two Poissonian lights which cannot be discriminated by this method. One is coherent light, and the other is Gaussian-Lorentzian light with infinite spectral linewidth. In this experiment, Gaussian-Lorentzian light with finite spectral linewidth was superposed on each Poissonian light, and the difference of the two radiation mechanisms was determined by profiles of the second-order factorial moment of the photon counting distribution.

Japanese Journal of Applied Physics•Jun 1, 1981•0 citations
In this paper we study the behavior of the errors involved in the determination of the parameters characterizing two spectral lines with Gaussian profile by means of the measurement of the intensity correlation function g(2)(τ) and by a multichannel system. The results obtained with both methods are compared. We also compare this results with those obtained when two lines with Lorentzian profile are analyzed.
Analysis of two spectral lines by photon statistics.M.P.Cagigal, F.Gonzalez and M.A.RebolledoDepartamento de Optica y E.M., Universidad de Santander.Facultad de Ciencias, Avda. de los Castros, 39005 Santander, SpainAbstractThe possibility of analyzing two spectral lines by measuring the second -order factorialmoment,n(2)(T), is studied. The results are compared with the ones obtained with a multicha-nnel analyzer system.IntroductionPhoton statistics is a powerful tool with which fluctuating light beams can be analyzed.So photon statistics has been used to analyze light beams from Rayleigh scattering experi-ments with macromolecules in solution1 -4 excited by laser light. In these experiments the intensity of the resulting light beam fluctuates at random.Photon statistics can be also used to analyze fluctuating light beams where the intensityfluctuates in a quasi- deterministic way as a function of time. This occurs in an experimentwhere the velocity of a fluid is measured by a laser Doppler technique2,5,6. In such an ex-periment a sinusoidal intensity modulated by a Gaussian profile is obtained when a particlepasses through the scattering volume. Since the distance between two consecutive particlesis a random variable, the intensity of the resulting light beam is not completely determinis
In this paper we study the possibility of analyzing a low intensity light beam whose spectrum has two lines with Lorentzian or Gaussian profiles by measuring n(2)(T) (the normalized second-order factorial moment). To do this the spectrum is scanned periodically by a spectrometer, and the normalized second-order factorial moment of the beam intensity at the exit aperture of the spectrometer is measured. The errors involved in the determination of the width, relative height, and separation between the two lines are calculated and discussed.
It has recently been shown that correlations between source fluctuations throughout the source region can lead to frequency shifts of spectral lines.1,2 We consider the more general problem of modifying the spectrum of the emitted radiation by making a suitable choice of the degree of spatial coherence of the source. To illustrate the potential of this method we consider a simple configuration of two small sources emitting light with identical spectra. We demonstrate that some source correlations can generate multiple spectral lines from a single spectral line of either a Gaussian or Lorentzian profile. Spectral line-shape parameters such as width, amplitude, center frequency, and functional form can also be controlled.
In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.
A photon counting method is adapted to spectroscopy in very low intensity, as it is useful for data acquisition. There are two Poissonian lights which cannot be discriminated by this method. One is coherent light, and the other is Gaussian-Lorentzian light with infinite spectral linewidth. In this experiment, Gaussian-Lorentzian light with finite spectral linewidth was superposed on each Poissonian light, and the difference of the two radiation mechanisms was determined by profiles of the second-order factorial moment of the photon counting distribution.