Soon, we will launch a new and updated customer portal, which is an important step toward providing our customers with one place to learn, interact, and get help.

How to model a Fresnel lens in OpticStudio

This article provides a summary of the ideal and real Fresnel lens models available in OpticStudio.
Sandrine Auriol
01/26/2018
OpticStudio

A Fresnel lens is a concave or convex lens that has been clasped in the z-direction. The profile is discontinuous and has grooves that minimize its thickness, but it is otherwise identical to a curved surface.

Figure 1: A convex lens and an equivalent Fresnel lens.

Because the Fresnel lens is thin, there’s minimal light loss due to absorption at the expense of image quality.

Fresnel lenses are used in lighthouse projectors, rear-projection televisions, and as solar concentrators, among several other uses.

Summary of the Fresnel lens models:
 Mode Object Type of model Sequential Fresnel Ideal Generalized Fresnel Ideal Extended Fresnel Ideal Cylinder Fresnel Ideal Non-Sequential Fresnel 1 Real Fresnel 2 Ideal Tabulated Fresnel Radial Real Tabulated Faceted Radial Real

To describe the different Fresnel lens models, we use the following definitions:
• Zs – The sag of the substrate. It’s used to calculate the ray intercept with the surface.
• Zf – The sag of the Fresnel surface. It’s used to calculate the ray refraction or reflection.

Fresnel models available in sequential mode

Note that all models are ideal, which means that the software idealizes the grooves to be of infinitesimal height. OpticStudio traces rays to the surface, ignoring the presence of the grooves, and then refracts rays as though the grooves truly exist. The substrate of a Fresnel surface can be flat or curved.
Important: Non-plane substrate Fresnel surfaces do not support calculations that require OPD data—such as OPD fans, MTF, and Zernike coefficients—because there’s no reliable way to compute the phase through a Fresnel surface that isn’t a plane.

Fresnel

The Fresnel surface is modeled as a flat surface. Once the ray has intercepted the plane surface, the ray reflects or refracts as if the surface had a shape described by an even asphere.
 Ray intercept Ray refraction or reflection Zs = Flat surface Zf = Even asphere to the 16th order
Figure 2: On the left, rays intercepting Zs the sag of substrate of the Fresnel Surface. On the right, rays after refraction by Zf the sag of the Even Asphere of the Fresnel Surface.

The Fresnel surface can be used for Fresnel lenses with fine grooves (the groove depth is shallow compared to the aperture).
Sample file: <documents>\Zemax\Samples\Short course\Archive\sc_fresnel1.ZMX

Generalized Fresnel

The Generalized Fresnel surface uses a polynomial aspheric substrate model, identical to the Even Aspheric surface. After the ray has intercepted the surface, the ray reflects or refracts as if the surface had a shape described by an extended polynomial.
 Ray intercept Ray refraction or reflection Zs = Even asphere to the 16th order Zf =
Figure 3: On the left, rays intercepting Zs the sag of the Even Asphere of the Generalized Fresnel Surface. On the right, rays after refraction by Zf the sag of the Extended Polynomial of the Generalized Fresnel Surface.

The Generalized Fresnel surface can be used to model faceted surfaces. For example, a flat substrate may consist of a series of small faceted planes, which would reflect or refract the light as though the surface was tilted. This can be simulated using a flat substrate and a linear x or y tilt term in the polynomial coefficients.

Figure 4: The surface of this non-sequential lens is made of a series of small faceted planes.
It could be modeled in sequential mode with the Generalized Fresnel surface.

Extended Fresnel

In the Extended Fresnel surface, the surface sag is identical to the Even Asphere surface and the sag is used for the ray-surface intercept. The refraction or reflection of the surface is determined by the local slope of the Fresnel facets, which is impacted by the Fresnel facet shape expression for Zf and the substrate shape expression for Zs. The refraction at the surface accounts for both the substrate sag and the Fresnel sag, while the ray-surface intercept depends only on the substrate sag.
 Ray intercept Ray refraction or reflection Zs = Even asphere to the 16th order Zf + Zs Zf = Even asphere to the 16th order Local slope of the Fresnel facets = Fresnel facet shape expression for Zf + the substrate shape expression for Zs
Figure 5: On the left, rays intercepting Zs the sag of the Even Asphere of the Extended Fresnel Surface. On the right, rays after refraction by Zs + Zf of the Extended Fresnel Surface.

The Extended Fresnel surface can be used to model a Fresnel lens with fine grooves (the groove depth is shallow compared to the aperture) on a curved substrate.

Cylinder Fresnel

In the Cylinder Fresnel surface, the surface sag is identical to the Even cylindrical Asphere surface (in y) and it is used for the ray-surface intercept. The refraction or reflection of the surface is determined by an another even cylindrical asphere sag equation. The refraction at the surface accounts for the Fresnel sag, while the ray-surface intercept depends on the substrate sag.
 Ray intercept Ray refraction or reflection Zs = Even cylindrical asphere to the 16th order in y Zf = Even cylindrical asphere to the 16th order in y

Note: Zs and Zf have independent coefficients.

The Cylinder Fresnel surface can be used to model cylindrical Fresnel lenses with fine grooves (the groove depth is shallow compared to the aperture) on a cylindrical substrate.

Fresnel models available in non-sequential mode

Models in non-sequential mode can be ideal or real. Ideal models are based on the same approximation as the sequential case (the grooves are of infinitesimal height). Real models define the exact profile shape.

Fresnel 1

In the Fresnel 1 surface, the profile is made of radially flat faces. The endpoints of the faces follow the equation of the Even Asphere surface.
 Ray intercept Ray refraction or reflection Zs = Radially flat or rectangular faces whose endpoints are defined by a sag expression identical to the Even Asphere surface. The size of the groove is defined by the +Depth/-Frequency parameter. The Pitch (degrees) is the angle of the “inactive” faces. Zf = Zs

Figure 6: Two Fresnel 1 lenses.
Figure 7: Explanation of the profile of the Fresnel 1 lens.
Sample files:
• <documents>\Zemax\Samples\Non-sequential\Fresnel Lenses\Fresnel lens cylinder structure.zmx
• <documents>\Zemax\Samples\Non-sequential\Fresnel Lenses\Fresnel lens radial structure.zmx

Fresnel 2

The Fresnel 2 is an idealized Fresnel lens. This object works as the sequential Fresnel surface.
 Ray intercept Ray refraction or reflection Zs = Flat surface Zf = Even asphere to the 16th order   If the “Is Cylinder?” parameter = 1 then Zf = Even cylindrical asphere to the 16th order in y
Figure 8: On the left, rays intercepting Zs the sag of the flat surface of the Fresnel 2 Lens. On the right, rays after refraction by Zf the Even Asphere of the Fresnel 2 Surface.

Sample file: <documents>\Zemax\Samples\Non-sequential\Fresnel Lenses\Fresnel lens ideal.zmx

The Tabulated Fresnel Radial is a tabulated object based on YZ sag coordinates defined in a TOB file. A TOB file contains two columns of data: the first column represents the local Y coordinate, and the second column represents the local Z coordinate. A figure of revolution around the local Z axis is generated by replicating the YZ curve over a specific angular range. The radially symmetric faces that result are smooth.
 Ray intercept Ray refraction or reflection Zs = Tabulated Fresnel Radial Zf = Zs

Figure 9: On the left, the shaded model of a Tabulated Fresnel Radial Lens and on the right a YZ cross section of that lens.
Sample file: <documents>\Zemax\Samples\Non-sequential\Fresnel Lenses\Fresnel lens from table.zmx

The Tabulated Faceted Radial object is nearly identical to the Tabulated Fresnel Radial object. The key difference is that the radially symmetric faces are not smooth in this object, as opposed to the Tabulated Fresnel Radial described above.
 Ray intercept Ray refraction or reflection Zs = Tabulated Faceted Radial Zf = Zs

Figure 10: Comparison of a Tabulated Fresnel Radial Lens (Left) and a Tabulated Faceted Radial Lens (Right).
Sample file: <documents>\Zemax\Samples\Non-sequential\Fresnel Lenses\Fresnel lens unfaceted table.ZMX

Other Fresnel lenses

When working in non-sequential mode, there are several solutions to resolve instances when any of the built-in objects are not appropriate to describe a Fresnel lens. For example, a Fresnel lens can be built from a series of annular aspheric lenses (learn how).
If none of the models listed above are sufficient to model the Fresnel lens in your system, you can construct your own DLL model.