There are several ways to define the width of a beam. When measuring the beam parameter product and M2, one uses the
D4σ or "second moment" width of the beam to determine both the radius of the beam's waist and the divergence in the far field. The BPP can be easily measured by placing an
array detector or
scanning-slit profiler at multiple positions within the beam after focusing it with a
lens of high optical quality and known
focal length. To properly obtain the BPP and M2 the following steps must be followed: • Measure the D4σ widths at 5 axial positions near the beam waist (the location where the beam is narrowest). • Measure the D4σ widths at 5 axial positions at least one
Rayleigh length away from the waist. • Fit the 10 measured data points to W^2(z) = W_0^2 + M^4 \left(\frac{\lambda}{\pi W_0}\right)^2(z-z_0)^2 , where W(z) = 2\sigma(z) = \tfrac 1 2 \text{D4}\sigma(z) and \sigma^2(z) is the second moment of the distribution in the x or y direction (see ), and z_0 is the location of the beam waist with second moment width of \sigma_0 . Fitting the 10 data points yields M2, z_0 , and \sigma_0 . Siegman showed that all beam profiles—Gaussian,
flat top,
TEMxy, or any shape—must follow the equation above provided that the beam radius uses the D4σ definition of the beam width. Using other definitions of beam width does not work. In principle, one could use a single measurement at the waist to obtain the waist diameter, a single measurement in the far field to obtain the divergence, and then use these to calculate the BPP. The procedure above gives a more accurate result in practice, however. 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. ==See also==