How to model a complex Fresnel lens

Also available in 日本語

This article describes how to model complex Fresnel lenses, in which each groove may have different defining data. It is also a useful tutorial on defining complex objects in general.

Authored By Mark Nicholson

download example (.zip)

Introduction

Fresnel lenses break a normal lens into a set of concentric annular sections known as Fresnel zones. This design allows Fresnel lenses to be lighter and occupy less space than the equivalent spherical lens. As such, Fresnel lenses are especially useful for light collimation or focusing. Some examples of their uses are in lighthouses¹, in rear-projection TVs, and as solar concentrators. This article will give an overview of modeling both simple and complex Fresnel lenses.

Fresnel lens modelling

Shown below is a Fresnel lens alongside the spherical lens with equivalent properties.

The vast majority of practical Fresnel lenses can be modeled using the Non-Sequential Fresnel 1 object, which gives great control not only of optical properties but also of manufacturing parameters like pitch angle (the angle the inactive face makes to the lens body) and end caps. The sample file Fresnel lens radial structure.zmx in user data folder {Zemax}\Samples\Non-sequential\Fresnel Lenses is a good example. Stray light caused by total internal reflection from the inactive face can be clearly seen.

Now it is sometimes required to model more complex Fresnel objects, typically for applications like TIR lenses and other complex imaging applications:

Lenses like this can be easily made, using an Annular Aspheric Lens object for each Fresnel zone.

The Annular Aspheric Lens Object

For situations where precise control of the Fresnel is needed on a ring by ring basis, the Annular Aspheric Lens Object is ideal:

This object has the surface shape of an even aspheric surface (radius, conic, and even-polynomial aspheric coefficients up to r¹⁶) on both faces, plus user-definable maximum and minimum diameters and thickness. It is ideal for modeling complex Fresnel lenses.

Here is an example of a complex Fresnel, in which one face is a single even-aspheric surface and the other is a highly-aspheric set of five rings:

It is implemented using five Annular Aspheric Lens objects, like so:

The file is included in the article attachments. Note the following:

• The materials are picked up from the first object, so the rings are all made from the same material
• The maximum back aperture of object 2 picks up its value from the minimum back aperture of object 1, and so on through the list of objects, so that the radial height of any ring can be set directly, and the one below it will automatically adjust so that no rings overlap, and there is no gap between the rings
• The radius of curvature, conic constant and even aspheric coefficients on the front face of object 1 are picked up by the other Annular Aspheric Lens objects, so that a single smooth aspheric curve is used on this face. As this requires about 40 pick-up solves, see "How to set solves from ZPL" for a simple macro which can be used to simplify the process. 
• The radius of curvature, conic constant, thickness and even aspheric coefficients on the rear face of each object are set individually, to form the Fresnel grooves.

Because of the use of Pickup Solves to lock the objects together, only those things different between the rings must be entered. Also, object 1 is used as the reference object for the other four objects, and so when object 1 is moved the other four automatically move to remain in the same position relative to it. Therefore, the lens can be moved as a single unit by moving just this one object.

This example demonstrates one of the key advantages of the OpticStudio user interface: complex objects can be made by adding simple objects together, and the use of Pickup Solves and reference objects allows the more complex object be treated as if it were a single object.

The resulting object is fast to ray-trace, optimize, and tolerance. If you need to export it to a mechanical CAD package, use a Boolean Native object to make a single object, and then export that. In this example, the Annular Aspheric Lens objects were added together, and a Rectangular Volume object subtracted, so that a cross-section view would result:

The same approach can be used to produce slices and other unusual sections of the object. The article attachment contains all the files used in this article.

References

1. Britten, William A. 2010. The Fresnel Lens. http://lighthousegetaway.com/lights/fresnel.html

KA-01373