Since beams typically do not have sharp edges, the diameter can be defined in many different ways.
A beam may, for example, have an elliptical cross section, in which case the orientation of the beam diameter must be specified, for example with respect to the major or minor axis of the elliptical cross section.
An obvious choice for this fraction is 1/2 (−3 dB), in which case the diameter obtained is the full width of the beam at half its maximum intensity (FWHM).
The 1/e2 width is equal to the distance between the two points on the marginal distribution that are 1/e2 = 0.135 times the maximum value.
In many cases, it makes more sense to take the distance between points where the intensity falls to 1/e2 = 0.135 times the maximum value.
The 1/e2 width is important in the mathematics of Gaussian beams, in which the intensity profile is described by
The American National Standard Z136.1-2007 for Safe Use of Lasers (p. 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.
In addition, the Federal Aviation Administration also uses the 1/e definition for laser safety calculations in FAA Order JO 7400.2, Para.
For an ideal single-mode Gaussian beam, the D4σ, D86 and 1/e2 width measurements would give the same value.
The baseline is easily measured by recording the average value for each pixel when the sensor is not illuminated.
The D4σ width, unlike the FWHM and 1/e2 widths, is meaningful for multimodal marginal distributions — that is, beam profiles with multiple peaks — but requires careful subtraction of the baseline for accurate results.
The width of the beam is defined as the distance between the points of the measured curve that are 10% and 90% (or 20% and 80%) of the maximum value.
On the other hand, the D4σ, 1/e2, and FWHM widths encompass fractions of power that are beam-shape dependent.
Most CCD beam profiler's software can compute the knife-edge width numerically.
The main drawback of the knife-edge technique is that the measured value is displayed only on the scanning direction, minimizing the amount of relevant beam information.
[4] By mechanically moving the knife edge across the beam, the amount of energy impinging the detector area is determined by the obstruction.
The profile is then measured from the knife-edge velocity and its relation to the detector's energy reading.
Unlike other systems, a unique scanning technique uses several different oriented knife-edges to sweep across the beam.
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.
For example, applications of high-energy laser weapons and lidars require precise knowledge of how much transmitted power actually illuminates the target.
It is the angle between the beam directions of minimal and maximal elongations, known as principal axes, and the laboratory system, being the