See 2D Fourier Transform, Fourier Transform
Derivation Fresnel Diffraction
Recall Fresnel Diffraction, which will be our starting point.
being signficantly larger than the other distances allows a useful approximation for the denominator of the Spherical Wave However, small changes in
will lead to big changes in the exponential function of the equation so we can’t apply the approximation there. Instead, Overall we end up with Equation 1
Let
, Allowed due to assumption See 2D Fourier Transform Equation 2
Examples
Fraunhofer Diffraction from a Slit
Fraunhofer Diffraction from a slit is just the Fourier Transform of the
function, which is the sinc function. The Irradiance is Also, through a square hole, would just be the same idea, but for
and