Rayleigh width

X X z location of line center in cm -1 pressure of sample gas multiplied by optical path length distance from center of line image expressed in Rayleigh widths... 

Fig. 2 Diffraction image of an entrance-slit element. Abscissa z is distance in Rayleigh widths ordinate E is proportional to electric-field amplitude.

We have defined z0 = wD/2f A as the half-width of the geometrical image of the entrance slit, as measured in Rayleigh widths. Referring to the Si function defined in Section IV.A.l of Chapter 1 we now may write... 

Fig, 26. Experimental dispersion curve of the Kr monolayer and measured line width broadening As of the Kr creation phonon peaks. The solid line in the dispersion plot is the clean Pt(lll) Rayleigh phonon dispersion curve and the dashed line the longitudinal phonon bulk band edge of the Pt(l 11) substrate, both in the r Mn azimuth which is coincident with the r Kk, azimuth. 

Av Avc Rayleigh resolution in wave-number units half-width yc/4rc observed when collision broadening dominates (given in hertz)... 

What meaning do these two-point resolution criteria have in describing the deconvolution process, that is, resolution before and after deconvolution Although width criteria may be applied to derive suitable before-after ratios, the Rayleigh criterion raises an interesting question. Because the diffraction pattern is an inherent property of the observing instrument, would it not be best to reserve this criterion to describe optical performance The effective spread function after deconvolution is not sine squared anyway. 

We recommend that the Rayleigh criterion and Fourier frequency cutoff Q be used as fundamental specifications of optical performance, but that other criteria such as full width at half maximum be used in describing widths before and after deconvolution and in specifying spread functions having other than sine-squared shape. 

This equation has an extremely important interpretation. In its differential form it means that, in two dimensions (with the x-axis lying in the plane of the interface between the solid and the fluid and the z-axis lying normal to the plane), if a pressure pjnc(x ) with implicit frequency dependence exp(iwt) acts along a strip in the y-direction at x of width dx, then the Rayleigh wave that is excited will propagate and the response in the fluid immediately above the surface at x will be... 

The spectrum consists of three components. The first term represents an unshifted line called the Rayleigh line, which is a Lorentzian with a halfwidth at half-maximum given by Acoc(q) = Dpq2. The next two terms represent a doublet called the Brillouin doublet. These are two Lorentzian lines shifted symmetrically from the origin by co = csq, each having half-width at half-maximum, AcoB(q) = Tq2. 

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

The solution discussed above has, as parameters, Raw, the Darcy-modified Rayleigh number based on the enclosure width, and A. the enclosure aspect ratio HfW. Some typical results computed with the above program are shown in Figs. 10.29 and 10.30. 

Using these values the Darcy-modified Rayleigh number based on the width of the enclosure is ... 

---