Correlation Function Profile Analysis in Laser Light Scattering. III. An Iterative Procedure

Correlation Function Profile Analysis in Laser Light Scattering. III. An Iterative Procedure


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Chapter in Photon Correlation Techniques in Fluid Mechanics: Proceedings of the 5th International Conference at Kiel-Damp, Fed. Rep. of Germany, May 23–26, 1982: edited by Erich O. Schulz-DuBois

Chapter Abstract:

In photoelectron correlation function profile analysis, the inversion of the Laplace transform ∣∣g(l)(τ)∣∣=∫0∞G(Γ)e−ΓτdΓ (1) to obtain the normalized linewidth distribution function G(Γ) from the net electric field correlation function g(l)(τ) is essentially an unresolved ill-conditioned problem, where Γ and τ are, respectively, the characteristic linewidth and the delay time. In practice, g(l)(τ) contains noise and the integral has upper (b) and lower (a) bounds. Consequently, in order to remove the ill-conditioning, we need to have estimates of both the signal-to-noise ratio and the width, in terms of the support ratio γ(≡ b/a), of the linewidth distribution function. However, asg(l)(τ) depends upon the delay time range of our experiment, we now encounter a problem whereby our experimental conditions and the results we hope to obtain are interactive. Then, the success of a laser light scattering experiment depends upon (1) a proper choice of experimental conditions, as well as (2) appropriate inversion of the measured g(l)(τ) to obtain G(Γ). Thirdly, further analysis of G (Γ) is often required to obtain the desired information, such as molecular weight distribution, internal motions, etc. These three requirements are highly interdependent and the experimenter must be aware of the uncertainties introduced at each step. In this article, we propose an iterative procedure that tries to meet the above requirements.

About the book:

Photon correlation is a kind of spectroscopy designed to identify optical frequency shifts and line-broadening effects in the range of many MHz down to a few Hz. The optical intensity is measured in terms of single photon­ detection events which result in current pulses at the output of photomulti­ plier tubes. This signal is processed in real time in a special-purpose paral­ lel processor known as a correlator. The resulting photon correlation func­ tion, a function in the time domain, contains the desired spectral informa­ tion, which may be extracted by a suitable algorithm. Due to the non-intrusive nature and the sound theoretical basis of photon correlation, the phenomena under study are not disturbed, and the parameters in question can be precisely evaluated. For these reasons photon correlation has become a valuable and in many instances indispensable technique in two distinct fields. One of these is velocimetry in fluid flow. This includes hydro- and aerodynamic processes in liquids, gases, or flames where the velo­ city field may be stationary, time periodic, or turbulent, and may range from micrometers per second for motion inside biological cells to one kilometer per second for supersonic flow. The other major field is stochastic particle propagation due to Brownian motion.



Publication Date





Berlin, Heidelberg


Dispersion, Photomultiplier, Profil, Schliere, Schlieren photography, convection, dynamics, flow, fluid mechanics, laser, light scattering, scattering, spectroscopy, stability, turbulence




Part of the Springer Series in Optical Sciences book series (SSOS, volume 38)

Correlation Function Profile Analysis in Laser Light Scattering. III. An Iterative Procedure