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An example is laser surgery. [6] Power-in-the-bucket and Strehl ratio are two other attempts to define beam quality. Both these methods use a laser beam profiler to measure how much power is delivered to a given area. There is also no simple conversion between M 2, power-in-the-bucket, and Strehl ratio.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
This definition assumes either flat-top profile of the laser beam inside the laser, or some effective gain, averaged across the beam cross-section. The amplification coefficient K {\displaystyle ~K~} can be defined as ratio of the output power P o u t {\displaystyle ~P_{\rm {out}}} to the input power P i n {\displaystyle ~P_{\rm {in}}} :
6) defines the beam diameter as the distance between diametrically opposed points in that cross-section of a beam where the power per unit area is 1/e (0.368) times that of the peak power per unit area. This is the beam diameter definition that is used for computing the maximum permissible exposure to a laser beam.
For example, a helium-neon laser (633 nm) with 1 mm beam diameter would focus to a 317 μm spot with a 500 mm lens. A laser beam profiler with a 5.6 μm pixel size would adequately sample the spot at 56 locations.
High-power lasers, such as those used in laser welding and cutting are typically measured by using a beamsplitter to sample the beam. The sampled beam has much lower intensity and can be measured by a scanning-slit or knife-edge profiler. Good beam quality is very important in laser welding and cutting operations. [5]
M 2 is useful because it reflects how well a collimated laser beam can be focused to a small spot, or how well a divergent laser source can be collimated. It is a better guide to beam quality than Gaussian appearance because there are many cases in which a beam can look Gaussian, yet have an M 2 value far from unity. [1]
The observation of sub-wavelength structures with microscopes is difficult because of the Abbe diffraction limit.Ernst Abbe found in 1873, [2] and expressed as a formula in 1882, [3] that light with wavelength , traveling in a medium with refractive index and converging to a spot with half-angle will have a minimum resolvable distance of