Implementing Curved Fresnel Zone Plates: Analysis and Efficiency

[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!

 

[Andy Resnick]

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

 

[0xDEADBEEF]

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!

 

[sophiecentaur]

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.

 

[sophiecentaur]

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?

 

[sophiecentaur]

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.

 

[0xDEADBEEF]

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

That's a Fresnel lens. IT is similar but not the same as the zone plates. And a Fresnel lens would really hurt your eyes.