In laser science, the parameter M2, also known as the beam propagation ratio or beam quality factor is a measure of laser beam quality. It represents the degree of variation of a beam from an ideal Gaussian beam. It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same wavelength. It relates the beam divergence of a laser beam to the minimum focussed spot size that can be achieved. For a single mode TEM00 (Gaussian) laser beam, M2 is exactly one. Unlike the beam parameter product, M2 is unitless and does not vary with wavelength. The M2 value for a laser beam is widely used in the laser industry as a specification, and its method of measurement is regulated as an ISO Standard. Measurement 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. M2 can be 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 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 , Here is half of the beam width and is the location of the beam waist with width . Fitting the 10 data points yields M2, , and . 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 M2. The procedure above gives a more accurate result in practice, however. Utility M2 is useful because it reflects how well a collimated laser beam can be