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Applied Optics

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

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

Published Sep 1, 1984• 11 citations
Publisher

Abstract

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.

DOI
10.1364/ao.23.003024

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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
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.
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.
A level-crossing detection method is presented and developed based on measurement of the normalized second factorial moment n((2))(T) of the photon-counting distribution of the resultant fluorescence. Expression n((2))(T) is obtained, and the errors expected in the determination of signal width and crossing field are theoretically studied. The validity of the approximations performed to establish the theoretical model is proved by an experiment with a square-wave periodically modulated light beam.
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