Application One: Diffraction¶
Problem Introduction¶
what is diffraction: inteference patterns that light makes passing through apertures
how to make:
light from a distant source, which means the aperture plain is a wavefront i.e. wave have the same phase at all points of the aperture
plain with apertures
image plain at some distance
assumptions:
light is an oscollating E/M field
light is monochromatic (only one frequency)
light of the aperture plain as:
where
Near-Field vs. Far-Field¶
Distance between the aperture plain and the image plain (measured relative to the wavelength) determines diffraction
near-field Fresnel diffraction
far-field Fraunhofer diffraction
Huygens Principle¶
Each point on a wavefront can be regarded as a source i.e. all the sources on the wavefront will be integrated
Question: what is the strength of the wave on point

Solutioin¶
After introducing coordinates on the aperture plain, it is clear that the main
effect in light going from
therefore the total field is the integral over the aperture:
where
with Fraunhofer approximation:

The integral can be re-written as:
where axillary variable
Conclusion: for far-field diffraction, the intensity of the light is the magnitude of the inverse Fourier transform of the aperture function.
Back to Fourier Transform.