knife-edges to sweep across the beam. By using tomographic reconstruction, mathematical processes reconstruct the laser beam size in different orientations to an image similar to the one produced by CCD cameras. The main advantage of this scanning method is that it is free from pixel size limitations (as in CCD cameras) and allows beam reconstructions with wavelengths not usable with existing CCD technology. Reconstruction is possible for beams in deep UV to far IR. D86 width The D86 width is defined as the diameter of the circle that is centered at the centroid of the beam profile and contains 86% of the beam power. The solution for D86 is found by computing the area of increasingly larger circles around the centroid until the area contains 0.86 of the total power. Unlike the previous beam width definitions, the D86 width is not derived from marginal distributions. The percentage of 86, rather than 50, 80, or 90, is chosen because a circular Gaussian beam profile integrated down to 1/e2 of its peak value contains 86% of its total power. The D86 width is often used in applications that are concerned with knowing exactly how much power is in a given area. For example, applications of high-energy laser weapons and lidars require precise knowledge of how much transmitted power actually illuminates the target. ISO11146 beam width for elliptic beams The definition given before holds for stigmatic (circular symmetric) beams only. For astigmatic beams, however, a more rigorous definition of the beam width has to be used: and This definition also incorporates information about x–y correlation , but for circular symmetric beams, both definitions are the same. Some new symbols appeared within the formulas, which are the first- and second-order moments: the beam power and Using this general definition, also the beam azimuthal angle can be expressed. It is the angle between the beam directions of minimal and maximal elongations, known as principal axes, and the laboratory system, being the and axes of the detector and given by Measurement International standard ISO 11146-1:2005 specifies methods for measuring beam widths (diameters), divergence angles and beam propagation ratios of laser beams (if the beam is stigmatic) and for general astigmatic beams ISO 11146-2 is applicable. The D4σ beam width is the ISO standard definition and the measurement of the M² beam quality parameter requires the measurement of the D4σ widths. The other definitions provide complementary information