Implementing Curved Fresnel Zone Plates: Analysis and Efficiency

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    Fresnel Plates
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Discussion Overview

The discussion revolves around the implementation of Fresnel zone plates on curved surfaces, focusing on their diffractive efficiency and focal length. Participants explore theoretical aspects, potential applications, and practical considerations related to optics, particularly in the context of contact lenses.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the analysis and sources for implementing Fresnel zone plates on curved surfaces, specifically regarding diffractive efficiency and focal length.
  • Another participant questions the specific application of the Fresnel zone plates, suggesting a focus on light from a plane wave.
  • A mathematical expression is provided by a participant, indicating how to determine points on the curved surface that contribute to the Fresnel pattern.
  • One participant expresses interest in using Fresnel zone plates in contact lenses as an alternative focusing method.
  • Concerns are raised about the effect of the tear film on the optics of the contact lenses, with references to known corrections for curvature differences.
  • Participants discuss the nature of Fresnel structures, questioning whether they are smooth or have ridges, and how tears might interact with these structures.
  • A distinction is made between Fresnel lenses and Fresnel zone plates, with a warning about the potential discomfort of using Fresnel lenses in the eye.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the implementation and effects of Fresnel zone plates, with no consensus reached on the best approach or the implications of using them in contact lenses.

Contextual Notes

Participants mention the need for further analysis regarding the interaction of the tear film with Fresnel structures, as well as the mathematical conditions for achieving the desired optical effects, which remain unresolved.

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

What do you mean by smooth? Planar?
 
I mean that freznel structures often have ridges in them (?). The tears would fill these up when you blink.
 
  • #10
sophiecentaur said:
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.
 
  • #11
sophiecentaur said:
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.
 

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