Gaussian intensity distribution

The crater surfaces obtained in the LA-TOF-MS experiment on the TiN-TiAlN-Fe sample were remarkably smooth and clearly demonstrated the Gaussian intensity distribution of the laser beam. Fig. 4.45 shows an SEM image of the crater after 100 laser pulses (fluence 0.35 J cm ). The crater is symmetrical and bell-shaped. There is no significant distortion of the single layers. Fig. 4.45 is an excellent demonstration of the potential of femtosecond laser ablation, if the laser beam had a flat-top, rather than Gaussian, intensity profile. 

For a single fluorescent species undergoing Brownian motion with a translational diffusion coefficient Dt (see Chapter 8, Section 8.1), the autocorrelation function, in the case of Gaussian intensity distribution in the x, y plane and infinite dimension in the z-direction, is given by... 

For a finite volume element with a Gaussian intensity distribution in three dimensions, the autocorrelation can be written as... 

Initially the signals were displayed on a fast storage oscilloscope, and a typical particle scattering trace for 8°, 6°, and 12 is shown in Figure 4. A nearly Gaussian intensity distribution was always observed, and the particle velocity can be estimated from the known beam width divided by the measmed transit time. 

The dependence of the sample volume size on the particle s apparent diameter since larger particles have a larger effective sample volume due to the Gaussian intensity distribution of the laser beam. 

The light intensity scattered by statistically fluctuating particles can generally be described by a Gaussian intensity distribution [938]... 

As proved by Siegert [939] for optical fields with a Gaussian intensity distribution (7.60), the second-order correlation function G x) is related to G x) by the Siegert relation... 

Figure 12.11 shows the CCD images of the lens at three voltage states V=0, 23, and 35 Vrms- At V = 0, the observed He-Ne laser beam is not very uniform due to its Gaussian intensity distribution. The peak intensity is -6x10 arbitrary units. As the voltage reaches 23 Vi. ,s... 

In the theories presented in Rll and R12 the Gaussian intensity distribution of the laser beam was replaced by a rectangular shape. Khoo et presented... 

The intensity distribution in the sample plane was scanned with a pinhole of 5 jum diameter mounted on a linear stage, which could be moved across the beam with an accuracy of 0.2 m. In all cases we got a nearly Gaussian intensity distribution. Some examples are given in Figure 3. 

The 3-line spectrum for VAc was simulated, assigning hyperfine splitting constants of 22.0, 21.0, and 9.0 G to the a-proton, one p-proton, and the other p-proton, respectively, and assuming a Gaussian intensity distribution with a linewidth of 14.0 G (Fig. 26 a). 

From a series of simulation snapshots, artificial images, similar to those created in actual experiments, have been created. The script used for the generation of these images, overlays a Gaussian intensity distribution function I x,y,z) as function of the particle diameter dp for every particle, whose exact position (Xi,yi,Zi) is known from the DPM simulation ... 

Figure 24.16 Gaussian intensity distribution of waveiength emerging from the monochromator. The spectrai bandwidth is defined by the red boundaries and 2sb- The spectrai siit width is depicted by the biue boundaries and Assw...

Scheme 1 Fitting functions for FCS analysis. Basic fitting functions and scheme for particle diffusion through the focal volume. Many experimental situations require combinations of the presented models. The complexity of a model to be applied is limited by the signal-to-noise ratio of recorded fluorescence fluctuations and the number of well-known parameters that can be fixed prior to analysis. The grey shading of the focus indicates the extension of and the Gaussian intensity distribution of the laser light within the focus...

Measuring Volume. Measurements take place in the intersection between the two incident laser beams, and the measuring volume is defined as the volume within which the modulation depth is higher than e times the peak core value. Due to the Gaussian intensity distribution in the beams, the measuring... 

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,... 

One necessary input for ealeulating the heat source term is the laser intensity Ix=o that reaehes the joining plane. This is determined experimentally as deseribed above for the motionless laser beam (Vscan= Om/s). Over the y-axis and in the direction in which the laser beam moves (z-direction), this corresponds to a Gaussian intensity distribution. Assuming that the Lambert-Bouger law is vahd, the thermal source term works out at (Eqn. 2) ... 

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