Published on 18 October 2005

This article demonstrates:

How to model an off-axis parabolic mirror according to the manufacturer's specifications.
How to center the image surface on the chief ray using the chief-ray solve.

The ZIP archive containing the sample file can be downloaded from the final page of the article.

Introduction

An off-axis parabolic mirror has the advantage of not having to obscure the input beam to access the image plane. ZEMAX can easily model any off-axis portion of a surface, parabolic or not. This tutorial will show you how to model an off-axis parabolic mirror. The concept shown here applies to any decentered surface and is not limited to off-axis parabolic mirrors.

We will model a commercially-available off-axis parabolic mirror. The goal of this exercise is to be able to tilt the mirror about the X axis at any point along the optical axis (Z axis). The specifications for the mirror, taken from the manufacturer's web site, are as following:

Off-axis distance = 150 mm
Focal length = 1000 mm
Component physical diameter = 203 mm
Back surface of the substrate is perpendicular to the optical axis

If you are not sure about any of the procedures used in this tutorial, please refer to the following articles first.

Designing A Singlet in ZEMAX
How to Tilt and Decenter a Sequential Optical Component

Entering the Basic Geometry

Set the following system parameters

System unit to mm (System > General > Units)
Wavelength to 0.550um (System > Wavelengths)
Set one field with values X=0 and Y=0 (System > Fields)
Set system aperture as Entrance Pupil Diameter of 100 mm (System > General > Aperture)

Enter the following surfaces in the Lens Data Editor. The image surface has a user-defined semi-diameter of 15 mm (U next to the column).

The "sag" or z-coordinate of the standard surface is given by:

where c is the curvature (the reciprocal of the radius), r is the radial coordinate in lens units and k is the conic constant. The conic constant is less than -1 for hyperbolas, -1 for parabolas, between -1 and 0 for ellipses, 0 for spheres, and greater than 0 for oblate ellipsoids. To make the mirror surface parabolic, enter the conic of -1.

Since the focal length of a mirror is half the radius of curvature, enter -2000 mm in the Radius column. The sign of the radius of curvature is negative since the center of curvature is to the left (toward -Z axis) of the mirror.

Since surface #1 and the image surface are co-located, we will choose not to draw the surface #1 in the layout so that we can see only the image surface at that location.

Set the following property in the surface property window.

To make the mirror substrate flat and orthogonal to the optical axis, choose the following options in the surface property window. We will chose the thickness of 40 mm since the manufacture does not specify the substrate thickness on their web site.

Open the 3D layout with the following settings.

Settings for 3D Layout

Add the off-axis Distance

Specify a Y decenter of -150 mm in the surface #2 property window.

From the manufacturer's specifications, the off-axis distance is 150 mm and the physical diameter of the mirror is 203 mm. Specify the correct aperture size and location.

Open the 3D layout

Note that the rays are moving away from the coordinate system. In order to center the image surface and make it orthogonal to the chief ray, insert a coordinate break surface before the image surface and place a chief-ray solve on the Y decenter and the X-tilt parameters. ZEMAX will automatically calculate the amount of decenter and tilt needed to make the chief ray hit at the center of this surface at normal incidence.

Update the layout.

Perfect!

Summary and References

This article has demonstrated how to model an off-axis parabolic mirror in sequential ZEMAX. In summary:

Surface and aperture decenter can be specified in the surface property window
The chief-ray solve can automatically center the coordinate system to the chief-ray.