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Is it possible to transform a light spherical wave front or another wave front with a known behaviour into a planar one?

Say I have the position of a point light source, and I can approximate it by an isotropic spherical model (just as an example), what kind of operations do I need to do to make it a planar wave. More specifically, if I take a plane perpendicular to the light axis from an unknown distance to the light, I want to simulate a constant lighting on that plane.

I know a spherical wave can be transformed to a planar (or almost planar) using different optics, however, I am not sure how/if this can be done analitically. Is it at all possible?

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2 Answers 2

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That's what a lens does. So if you take a look at the equations governing, say, a lens placed its focal length away from a point source, that will show you how a spherical wave emanating from the point source is transformed into an outgoing plane wave.

I hope that's what you're asking, since "mathematically transform" doesn't have any real meaning.

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  • $\begingroup$ I mean to transform it in a modelling environment. Say I have the position of a point light source, and I can approximate it by an isotropic spherical model (just as an example), what kind of operations do I need to do to make it a planar wave. More specifically, if I take a plane perpendicular to the light axis from an unknown distance to the light, I want to simulate a constant lighting on that plane. $\endgroup$
    – strangelyput
    Commented Jun 2, 2014 at 18:48
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    $\begingroup$ Then create a "lens function," as I suggested. $\endgroup$
    – Carl Witthoft
    Commented Jun 2, 2014 at 19:59
  • $\begingroup$ Thank you for the reply. Can you point me toward where I could find more information on the subject and on how I could create such function? $\endgroup$
    – strangelyput
    Commented Jun 4, 2014 at 14:22
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To add to Carl Witthoff's answer: a plane wave won't simply become spherical just by propagating. One piece of background you seem to be lacking is this: plane waves are eigenmodes of freespace (or of any homogeneous medium), meaning they do not change their form by propagation (aside from taking on a phase delay) in a homogeneous medium. So, if they are going to change their form in any way aside from simply being delayed, you have to have a specific piece of hardware comprising a non-homogeneous medium in mind to do the transformation. So, as Carl says, you need to imagine a specific lens and work out the transformation it makes.

Otherwise, if you're willing to accept a Gaussian beam with a huge waist parameter (see Wiki page "Gaussian Beam") as an approximation to a plane wave, you can let it propagate a huge distance, much greater than the Rayleigh distance for the Gaussian beam. Its wavefronts will then have a radius of curvature roughly equal to the propagated distance.

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