# Fresnel lens/kinoform: How to model diffraction at the edges of zones?

I would like to find the intensity distribution of light due to the diffraction at the edges of zones on Fresnel lenses or kinoforms. (That is, location of orders, heights of maxima, etc.)

I can't seem to apply Huygens' principle since there is no obvious aperture or opening. (See images below.)

How does one go about deriving this information? ## 1 Answer

Huygens' principle is linear superposition of spherical wavelets, hence it can be applied to every single wavelet individually that taken together form the incident plane wave, i.e., the propagation is applied to its Fourier transform. After they have propagated through the glass (plastic) you can sum (integrate) again and you get the far-field behavior of the lens.

• Having not had much background in Fourier optics, I'm not sure I fully understand. Firstly, do you mean that the Fourier transform of the plane wave ($\exp(ikx-i\omega{}t)$) gives you the individual wavelets? And secondly, I know that I can sum over the individual wavelets after they have propagated through the medium, but how do I get an expression for the post-lens wave for even just one of the wavelets? (I know it depends almost entirely on the geometry of the lens, but is there an equation or method which has geometry as an input, and resulting wave as an output?) – nivk Dec 17 '14 at 23:11