Airy distribution

This is called the Airy distribution, and is illustrated in Fig.6.28. The maximum intensity... 

Fig.6.28. Airy distribution from a Fabry-Perot interferometer...

The traditional analysis has then used a Gaussian to approximate both the Airy disk and sinc distribution as in Fig. 6 (Primot et al., 1990 Welsh and Gardner, 1989). The value of a in Eq. 41 is determined by matching the Gaussian approximation and the actual intensity at both the peak and the exp[—1] points (Welsh and Gardner, 1989). When this is done we find... 

Figure 6. Comparison of the (a) Airy disc (oscillating) and Gaussian (monotonically decreasing) distributions, and (b) sinc (oscillating) and Gaussian (monotonically decreasing) distributions.

Instead of FC-region values. As mentioned above, this approximation enables one to obtain a qualitative description of the distribution. The good quantitative agreement with experiment obtained in the paper shows that asymptotic and FC region vibrational frequencies and bond lengths do not differ significantly. In this calculation the Airy function was used to describe the translational dependence. As noted by Freed and Band (2), the use of the uniform semiclassical approximation... 

Airy formula, intensity distribution of the Fraunhofer diffraction pattern, 148... 

Figure 1.4 Intensity distribution of two Airy disks with a distance. Ii indicates the maximum intensity of each point and I2 represents overlap intensity.

Thus, any solution to Eq. (4.24) that also fits the boundary conditions will be the elastic solution to the problem being sought. Conversely, mathematical functions that satisfy Eq. (4.23) are often studied to find the associated elastic problem. The function x is called the Airy stress function and Eq. (4.24) is called the Biharmonic equation This latter equation does not require any elastic constants for its solution, indicating the stress distributions are independent of the elastic properties. If, however, the strains are needed, the elastic constants appear once Hooke s Law is introduced. 

Since the laser resonator is a Fabry-Perot interferometer, the spectral distribution of the transmitted intensity follows the Airy formula (4.57). According to (4.53b), the halfwidth Avr of the resonances, expressed in terms of the free spectral range 5y, is Avr = Sy/F. If diffraction losses can be neglected, the finesse F is mainly determined by the reflectivity R of the mirrors, therefore the halfwidth of the resonance becomes... 

Figure 3. A) and B) Intensity distributions in the image of a luminous point a) Image plane b) Lens c) Objects plane C) Computed intensity distribution D) Airy disk...

In the axial direction, intensity distribution is similar in shape to the Airy disk in the lateral direction. As for lateral resolution, axial resolution defines the minimum distance that can be separated in the z-axis. It is described by the distance between the maximum intensity of the central bright region and the first point of minimum intensity along the z-axis, and is given by... 

The smallest resolvable structure or the smallest distance between two separately imaged points is dictated by the wave nature of light. In the course of imaging a diffraction pattern is generated as shown in Fig. 8.2 for a point source. The corresponding intensity distribution is represented by an Airy function. 

For TPA, the SLI, fi, is directly related to the photopolymerization rate. A near-focus SLI distribution is shown in Fig. 18. The light intensity in the focal plane was assumed to follow a formula due to Airy [126] ... 

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