artmenlope / Fraunhofer-pattern

Use a Matplotlib gridspec to plot the Fraunhofer pattern of a 2 rectangle aperture.

Fraunhofer-pattern

Problem

Use a Matplotlib gridspec to plot the Fraunhofer pattern of a 2 rectangle aperture.

Solution

The used solution is

$$ u_z(x_z, y_z)\propto \exp\left(j\frac{\pi}{\lambda Z}(x_z^2+y_z^2)\right) 4hw \mbox{ sinc}\left(\dfrac{2 x_z w}{\lambda Z} \right) \cos\left(\dfrac{2\pi x_z d}{\lambda Z}\right) \mbox{sinc}\left(\dfrac{y_z h}{\lambda Z} \right) $$

where $x_z$ and $y_z$ are the coordinates on the screen, $Z$ is the distance from the object to the screen and $\lambda$ is the wavelength of the light.

Plot

The plotted pattern will be given by

$$ I_z (x_z, y_z) \propto \left| u_z(x_z, y_z) \right|^2 $$

When executed, the Python 3 script Fraunhofer-difraction.py will produce the following output:

 

The parameters used in this case are:

$$ \begin{array}{rcr} Z&=&1\mbox{ m},\\ w&=&0.1\times 10^{-3}\mbox{ m},\\ h&=&5\times 10^{-3}\mbox{ m},\\ d&=&0.7\times 10^{-3}\mbox{ m},\\ \lambda&=&500\times 10^{-9}\mbox{ m}.\\ \end{array} $$