Rayleigh criterion

Figure 3.4 (a) Diffraction pattern produced by a narrow slit, (b) The Rayleigh criterion for... 

Using the Rayleigh criterion, the resolution of the mth diffraction order is then given by... 

In more modem terms, the "Rayleigh criterion" states that positive energy is transferred to the acoushc wave if the pressure fluctuation and heat release fluctuation are in phase. This criterion is usually written in an integral form ... 

The resolution or "resolving power" of a light microscope is usually specified as the minimum distance between two lines or points in the imaged object, at which they will be perceived as separated by the observer. The Rayleigh criterion [42] is extensively used in optical microscopy for determining the resolution of light microscopes. It imposes a resolution limit. The criterion is satisfied, when the centre of the Airy disc for the first object occurs at the first minimum of the Airy disc of the second. This minimum distance r can then be calculated by Equation (3). 

Table 1 Approximate values for r (Rayleigh criterion) estimated for three characteristic wavenumbers typical instrument parameters for transmission and ATR experiments assumed...

Rayleigh criterion The rule-of-thumb for the spectral resolution of two transitions. 

Rayleigh criterion chem The criterion for spontaneous pressure oscillations to accompany combustion, namely, that combustion progresses more rapidly or efficiently during the compression phase of the pressure oscillation than during the rarefaction phase. ra-le krT,tir-e-3n ... 

It might seem that Lord Rayleigh s proposal is somewhat arbitrary even if two lines are separated by a somewhat smaller distance, it will be apparent that two lines are present rather than one. Sparrow s criterion (Strong, 1958) does, in fact, say that two lines may be termed just resolved when spaced so that the dip first appears. The Rayleigh criterion, however, gives rise to particularly simple expressions for resolving power. 

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. 

An additional question arises concerning the way the Rayleigh criterion terminology has traditionally been used. There is a vague perception that the Rayleigh limit is a barrier to be penetrated only by supernatural means— that it is a limit of the most fundamental kind. And so it is, but only in a sense... 

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. 

For natural convection, a correlation was established between the Nusselt criterion, which compares convective and conductive resistances to heat transfer and the Rayleigh criterion, which compares buoyancy forces with viscous friction ... 

The Rayleigh criterion can also be written as a function of the Grashof criterion, which compares convective with conductive heat transfer and the Prandtl criterion, which compares the momentum diffusivity (kinematic viscosity) with the thermal diffusivity ... 

Step 3 assumes natural convection. This may be difficult, because at 10 °C above the melting point, the viscosity may be too high for an efficient natural convection. This can be checked by calculating the Rayleigh criterion. The height of the tank is 1.8 m, but since it is not always full, a height of 0.9 m can be taken. With a dynamic viscosity of... 

This Rayleigh number corresponds to a turbulent film along the wall, but its value is close to the lower end of turbulent flow. If, for example, the viscosity increases to 1000 mPa s, the Rayleigh criterion is only 108. Moreover, it is not... 

A third attempt could be to improve the natural convection. This could be achieved by a higher storage temperature that would also lead to a lower viscosity increasing the Rayleigh criterion. But this would also lead to an exponential increase of the heat release rate. Hence the situation cannot be improved in this way. 

The radius, r, of the Airy Disc is given by the Rayleigh criterion equation which is shown in Eq. 1. ... 

All detection phenomena that use interference or diffraction have a natural limit, known as the Rayleigh criterion The maximum resolution obtainable with light of wavelength X is at best ... 

As we shall see, scanned probe microscopies are exempt from the Rayleigh criterion, because the images are not obtained by interference or diffraction, but are scanned piezoelectrically, that is, mechanically. 

Figure 9.20. RHS terms in the acoustic energy equation for Case 2 Rayleigh criterion (solid) acoustic flux (dotted).

Figure 3.1-5 Two monochromatic rays are regarded as resolved, when the first minimum of the diffraction pattern of one ray is coincident with the maximum of the other ray Rayleigh criterion.

A is at the position of the first minimum of the pattern of A2. In this case, the Rayleigh criterion is satisfied (Fig. 3.1-5). The different angles are a consequence of the angular dispersion d

dispersive elements the gratings or prisms. 

Dictated by the diffraction limit of light, the lateral resolution of a far-held optical microscope is dehned as the smallest distance between two features that can still be resolved in the image and is given by Rayleigh criterion as [5]... 

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