# Fraunhofer diffraction due to a rectangular aperture?

I have an aperture of length a and width b (sizes are comparable) How do I calculate the irradiance for a point on the screen? I know that I should calculate the electric field due to an element of area, then integrate over the whole area of the aperture, and then use the amplitude to calculate the irradiance. But I don't know how to express the optical path difference $\Delta$ between any element and the element at the center of the aperture. This is all I've been able to write down:

$dE = \frac{dE_{0}}{r_{0}+\Delta } e^{i[k(r_{0}+\Delta )-\omega t]}\simeq \frac{E_{A}dA}{r_{0}}e^{i[k(r_{0}+\Delta )-\omega t]}$

Where $dE_{0}$ is the amplitude of element dA at unit distance away, $E_{A}$ is amplitude per unit area at unit distance away, $r_{0}$ is the optical path of the central element, and $dA=dxdy$.

• We have the MathJax rendering engine active on the site explicitly to allow you to write clear and readable math in a LaTeX math-mode-alike language.. A picture or scan of a handwritten document is neither searchable nor something that a page reader can parse. This is something that you'll want to fix. Nov 23, 2016 at 20:04