A Gaussian Point Spread Function $($PSF$)$ is used to describe the spatial distribution of light in an

optical system. The PSF can be represented by the following Gaussian function:

$I(x)=I_0{e}^{-\frac{x^2}{2{}^2}}$

where $I(x)$ is the intensity at position $x,I_0$ is the peak intensity, and $$ is the standard deviation

of the Gaussian distribution.

A$.$ Calculate the Full Width at Half Maximum $($FWHM$)$ of the Gaussian PSF given that the

standard deviation $$ is $2$ units.

B$.$ If the peak intensity $I_0$ of the Gaussian PSF is $100$ units, what is the intensity at the FWHM

of the PSF$?$