By D. W. Goodwin
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Extra resources for Advances in Quantum Electronics. Volume 2
The linewidth error can therefore be expressed as or» 1 or» where R is the count rate per coherence area per coherence time. This expres sion provides the continuous curve on the left of Fig. 16. In the opposite limit where n and A/Ac are both much greater than one the error dependence for full correlation is ^^«[w'är'f (96) for n -> oo, A/Ac -> oo. For large A/Ac f(A/Ac) oc Ì/A and so the error becomes proportional to Ac, as found by Degiorgio and Lastovka for the three parameter fit. Assuming that the effect of clipping can be factored out, the value of A/Ac = 10 will be 8Γ/Γ = 11-1% which may be compared with 3-5% for A/Ac = 1-0.
It brings a new precision to the worl over that possible with analogue light beating methods. Several groups whe have pioneered studies using the older light beating methods are at presen PHOTON STATISTICS AND PHOTON-CORRELATION SPECTROSCOPY 57 equipping themselves with digital photon-correlation intruments to use in future work. There is, happily, substantial agreement at the present time on the broad validity of a "background-corrected" (Sengers and Keyes, 1971) mode-mode coupling approach to the theory, both for pure fluids and binary mixtures, but accurate experiments will continue to be necessary for many years to investigate detailed predictions in many different critical systems.
150) to express them in terms of the normalized first-order or field autocorrelation function g w -_ <**(ry-(0)) <7> For a Lorentzian spectrum of half width at half height Tand centre frequency ω0 this takes the form S(1)(T) = e x p ( - r | T | + /cü0T) There is no difficulty in performing the integration in (61) and the sums in (54) (Jakeman et al, 1971c). The first term in equation (54) may be obtained using a somewhat different approach. By definition, Var (Λ(Τ)Λ(0)) = <«2(τ)«2(0)> - <«(φ(0)>2 (62) This can be written in terms of the moments of the integrated intensity dis tribution following the procedure used to obtain equation (60): Var(«(rM0)) =