# Curved Fresnel Zone Plates

1. Mar 11, 2010

### 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!

2. Mar 11, 2010

### Andy Resnick

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

3. Mar 11, 2010

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.

4. Mar 12, 2010

### 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!

5. Mar 12, 2010

### sophiecentaur

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

6. Mar 12, 2010

### HEM87

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.

7. Mar 12, 2010

### sophiecentaur

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

8. Mar 12, 2010

### HEM87

What do you mean by smooth? Planar?

9. Mar 12, 2010

### sophiecentaur

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

10. Mar 12, 2010

### HEM87

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

11. Mar 15, 2010