# Curved Fresnel Zone Plates

HEM87
Hi there,

I'm wondering if anyone has any analysis or sources to help me understand how a Fresnel zone plate can be implemented on a curved surface, and the corresponding diffractive efficiency and focal length??

Thanks!

That's an odd question. Is there a specific application you have in mind?

What are the plates supposed to achieve? Focus light? From a plane wave? Simply take the points on your curved surface that have a distance d to the focal point f that has fulfills
$$d \in \left[ \frac{(4n-1)\pi}{2 \lambda } ,\frac{(4n+1)\pi }{2 \lambda } \right], n \in \mathbb{N}$$
This will produce your Fresnell pattern. All light going through these points can interfere constructively in f. The complement will produce the same effect due to Babinet's principle.

HEM87
Hi,

I'm curious about using Fresbel zone plates implemented on contact lenses (RGP) for an alternative method of focusing.

So yes, I'm looking to focus light at a certain point from a plane wave, thanks deadbeef, that's useful!

Gold Member
Hi,

I'm curious about using Fresbel zone plates implemented on contact lenses (RGP) for an alternative method of focusing.

So yes, I'm looking to focus light at a certain point from a plane wave, thanks deadbeef, that's useful!

Wouldn't the liquid (tears) on the surface affect the optics?

HEM87
Wouldn't the liquid (tears) on the surface affect the optics?

The tear film lens effect behind the lens is pretty well understood (generally giving a +0.25 D addition per 0.05 mm difference between corneal curvature and back RGP lens curvature) and can be corrected for generally by providing an intrinsic correction in the lens.

Gold Member
That makes sense.
So the front of the fresnel lens is, in fact, smooth?

HEM87
That makes sense.
So the front of the fresnel lens is, in fact, smooth?

What do you mean by smooth? Planar?

Gold Member
I mean that freznel structures often have ridges in them (?). The tears would fill these up when you blink.

HEM87
I mean that freznel structures often have ridges in them (?). The tears would fill these up when you blink.

Oh yeah, it would be smooth, just a series of opaque and transparent sections on a smooth surface.