Illumination Gaussian beam

Novotny, L., Sanchez, E. J., and Xie, X. S. 1998. Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams. Ultramicrosc. 71 21-29. 

In order to relate the lateral dimensions of the laser-generated cavities to the laser spot size, a lateral extension parameter q can be defined. It is the ratio between the measured cross-sectional area of the ablation crater and the area illuminated by a Gaussian beam defined according to Eq. 1. When ablation is limited to the area with F(x,y)[Pg.266]

The above formalism is quite general, and can be used to study the effects of doing transmission EXAFS on non-uniform samples and particles of all sorts. However, the mathematics quickly become forbidding if one looks at a realistic situation such as a particle illuminated by a Gaussian beam. Such situations require numerical methods. For a simple, analytically accessible example, imagine a uniform foil with a hole in it such that a fraction/of the beam goes through the hole. Then, we have... 

Gaussian Beam Illumination The Gaussian beam intensity distribution is... 

Later in the chapter we shall consider illumination by Gaussian and uniform beams. The Gaussian beam has an infinite width, and the radial distribution and... 

Fig. 20-2 (a) Coordinates for describing the fields of the beam incident on the endface and (b) the fraction of total power of a Gaussian beam entering the modes of an infinite parabolic-profile fiber as a function of the tilt angle 0.. The orientation of the Gaussian beam is shown for (c) on-axis, (d) tilted and (e) offset illumination. 

This profile is the simplest example for determining the physical attributes of Gaussian-beam illumination [5-7], and is defined by... 

In this case the Gaussian beam is incident normally on the endface, but the center of the beam is shifted a distance along the x-axis in Fig. 20-2(e). Thus the fiber is illuminated asymmetrically, so less power enters the fundamental mode, and higher-order modes will be excited. In this situation, it is clear from Eqs. (20-7a) and (20-9) that on the... 

Many optical particle sizing instruments and particle characterization methods are based on scattering by particles illuminated with laser beams. A laser beam has a Gaussian intensity distribution and the often used appellation Gaussian beam appears justified. A mathematical description of a Gaussian beam relies on Davis approximations [45]. An nth Davis beam corresponds to the first n terms in the series expansion of the exact solution to the Maxwell equations in power of the beam parameter s,... 

Fig. 3.8. Variation of the normalized differential scattering cross-sections with the axial position of a prolate spheroid illuminated by a Gaussian beam...

E.E.M. Khaled, S.C. Hill, P.W. Barber, Scattered an internal intensity of a sphere illuminated with a Gaussian beam. IEEE Trans. Antennas Propagat. 41, 295 (1993)... 

A critical difference between the transient and CW measurements is that while the CW probe source uniformly illuminates the sample, both the transient pump and probe beams have Gaussian distributions. Equation (7.7) can be rewritten for the transient case as ... 

Figure 9.6. The point spread function of a circular aperture for 4 different values of the edge taper with Gaussian illumination. The four curves are for uniform illumination or 0 db taper, 9, 18 and 27 db taper. The sidelobe level decreases with increasing taper, while the width of the main beam increases slightly.

FIG. 21-12 Particles illuminated by a gaussian-shaped laser beam and its corresponding diffraction pattern show a fine structure. 

In the experiment above the light was collimated with a lens. Therefore, the Gaussian shaped beam profile introduced weaker illumination of the camera at the edges than in the center. Figure 6b shows the reference profile fin for this geometry. For optimum performance the reference hne should be positioned in close proximity to the LVF hue. 

In order to obtain minimum losses, the collimated light through the SLM has to illuminate the maximum quantity of pixels. As its intensity distribution has a Gaussian profile, it is sufficient that l/e beam bandwidth illuminates the SLM aperture. According to optical Gaussian laws, the following condition is reached ... 

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