How to model an ellipse using the Conjugate Surface

This article explains how to model an elliptical surface in OpticStudio using the Conjugate Surface in Sequential Mode. It presents an elliptical mirror example which perfectly focuses light from one focal point to the other.

Authored By Nam-Hyong Kim


Article Attachments


An elliptical mirror can image light from one focal point to the other without aberration. To model this in Sequential Mode, a Standard Surface or a Conjugate Surface can be used. If the foci locations of the ellipse are known, the Conjugate Surface is the superior method. Rather than having to compute the necessary radius of curvature and conic constant from these points, the Conjugate Surface allows them to be input directly as (x,y,z) coordinates. An example is available in the Article Attachments.

For more information on modeling an ellipse with the Standard Surface, refer to the OpticStudio Help Files at, "The Setup Tab...Editors Group...Lens Data Editor...Sequential Surfaces (lens data editor)...Standard."

Before getting started

Before continuing with this article, ensure that you are familiar with the basic operations in Sequential Mode, as well as how to tilt and decenter optical components. If you are unfamiliar with these concepts, see the following articles:

If you are comfortable with both of these operations, proceed to the next section.

Using the Conjugate Surface

The diagram below shows a finite-conjugate imaging system in which the object and the image surfaces are co-located with the foci of the elliptical mirror. The object and the image surfaces are centered on, and orthogonal to, the Chief Ray. Also note that like any other surface in OpticStudio, the vertex of the Conjugate Surface defines the local coordinate origin, which means that the foci locations are specified with respect to the surface vertex. 

This elliptical mirror can be constructed using the Standard Surface but as we will see shortly, it is much easier to use the Conjugate Surface instead.


From the Article Attachments, open the file "conjugate surface start.zar." This file represents a simple fold mirror that reflects rays from a point source through 90 degrees, as shown below. The STOP surface is located on a dummy surface (Surface 1) positioned immediately before the fold mirror.



We will make Surface 2 a Conjugate Surface type with the appropriate parameters to perfectly image the object to the image surface. Navigate to Surface 2 Properties...Type and change Surface Type: Conjugate. Then, select Make Surface Global Coordinate Reference to define the local axis of Surface 2 as the Global Coordinate Reference point.


Update the 3D Layout.


The Conjugate Surface requires the XYZ coordinates of both foci; the OBJECT and IMAGE Surface locations in this case. The object and image coordinates, as referenced to the mirror vertex, can be obtained from the Prescription Data report. Open the Prescription Data under Analyze...Reports...Prescription Data and open the Settings. Click Clear All to remove all of the data from the report. Now, we can select only the setting we are interested in: Global Vertex


With "Global Vertex" selected, the global object and image coordinate are reported in the Prescription Data report. Since the Conjugate Surface is the Global Coordinate Reference, the reported XYZ coordinates are referenced to the vertex of the Conjugate Surface.


Enter the coordinates in the Lens Data Editor.


Update the 3D Layout to see the result!




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