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Measurements of the 1/e<sup>2</sup> width only depend on three points on the marginal distribution, unlike D4σ and knife-edge widths that depend on the integral of the marginal distribution. 1/e<sup>2</sup> width measurements are noisier than D4σ width measurements. For [[transverse mode|multimodal]] marginal distributions (a beam profile with multiple peaks), the 1/e<sup>2</sup> width usually does not yield a meaningful value and can grossly underestimate the inherent width of the beam. For multimodal distributions, the D4σ width is a better choice. For an ideal single-mode Gaussian beam, the D4σ, D86 and 1/e<sup>2</sup> width measurements would give the same value.
For a Gaussian beam, the relationship between the 1/e<sup>2</sup> width and the full width at half maximum is <math>2w = \frac{\sqrt 2\ \mathrm{FWHM}}{\sqrt{\ln 2}} = 1.699 \times \mathrm{FWHM}</math>, where <math>2w</math> is the full width of the beam at 1/e<sup>2</sup>.<ref name=zemax>{{cite web |url=http://
How to
=== D4σ or second moment width ===
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