Why 16/84 clip levels are chosen for determining laser beam diameter by knife edge technique (ISO 11146)? In ISO 11146 pt.3 (https://www.iso.org/obp/ui/#iso:std:iso:tr:11146:-3:ed-1:v1:en) - the standard committee determines the clip level at 16% and 84% power levels but, unfortunately, I wasn't able to find any explanation of this.
At the end of this standard linked the paper by A. E. Siegman, M. W. Sasnett and T. F. Johnston, "Choice of clip levels for beam width measurements using knife-edge techniques," doi: 10.1109/3.83346. Which consist authors recommendations is to choose the clip level somewhere between 8.5% and 11.6%, because, as they show, it allows to compare beams with different beam quality.
Besides I can find those 16/84 numbers only in the ISO 11146 standard and some user manuals for beam measurement devices, which, of course, referenced me on the standard itself. I'm a little bit stuck and confused. Please help me to figure it out.
 A: If we assume a Gaussian beam, we have the intensity
$$
I(\rho) = \frac{2P_{tot}}{\pi w^2} e^{-2 \rho^2/w^2}
\Rightarrow 
\frac{I(\rho)}{I_0} = \frac{w_0^2}{w^2} e^{-2 \rho^2/w^2}
$$
The knife edge integrates the intensity in one direction, while limiting it in the perpendicular direction. Further note that the exponential has the form of the normal distribution (with a prefactor), if we substitute $w = 2\sigma$. This motivates the second integration limit of integration,
$\int_{-\infty}^\infty dx \int_{-w/2}^{w/2} dy \; I(\rho) = ... = erf(1/\sqrt{2}) \approx 68\%$. This means that we have 16% on either side outside the interval,
\begin{align}
\int_{-\infty}^\infty dx \int_{-\infty}^{-w/2} dy \; I(\rho) &\approx  16\%
\\
\int_{-\infty}^\infty dx \int_{-\infty}^{w/2} dy \; I(\rho) &\approx 1-0.16 = 84\%
\end{align}
Please note that I am not using the same symbols as in the ISO norm. I once had to define the laser beam and specify measurement conditions according to the ISO norm. I remember that I had a hard time, because of the notation difference. In the end I took one hour and expressed each equation of the ISO norm in my standard notation.
