When sequential surfaces and non-sequential objects are exported to CAD programs, OpticStudio describes them as NURBS (Non-Uniform Rational B-Splines). This article shows the range of OpticStudio surfaces and objects than can be exactly defined using CAD export file formats, and gives an example of exporting high-order aspheres and testing the accuracy of the export.

**Authored By Mark Nicholson, Kristen Norton**

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## Introduction

OpticStudio describes surfaces and objects exported to separate CAD programs as Non-Uniform Rational B-Splines (NURBS). NURBS are very useful to optical engineers as they are able to exactly represent spheres, ellipses, parabolas, and hyperbolas. However, rational b-splines do have their limitations, and are only able to represent higher-order optics (such as polynomial aspheres) with limited accuracy. Thus, some objects that can be modeled with extreme accuracy in OpticStudio may be reduced in resolution in a CAD export, resulting in inconsistent analyses.

In this article, we discuss what objects can be modelled exactly in a CAD export, and will provide an example through the use of a high-order asphere.

## How accurate is the CAD exchange?

A very useful property of the rational b-spline is that conic aspheres are represented exactly by NURBS. Therefore spheres, ellipses, parabolas and hyperbolas can be represented exactly by the NURBS surface form. This is great news for optical engineers, of course, because these shapes are so commonly used in optical design.

However, NURBS cannot model arbitrary surfaces to arbitrary precision. Just as circles cannot be modeled exactly using a finite number of straight lines, NURBS will model other surfaces only to finite accuracy. Higher-order aspheres, like polynomial aspheres, are approximated by using multiple segmented splines, which is in general a piece-wise fit over the whole optical surface using multiple lower-order polynomials. Typically, multiple third or fourth order polynomials are used to approximate the surface. This is adequate for mechanical design, but should be carefully tested for optical precision ray tracing, where surfaces may be needed to be known to fractions of the wavelength of light.

This problem often arises when a high optical precision surface is modeled in OpticStudio, then exported as a CAD file to have mechanical sections added, and then imported as a CAD file for subsequent ray tracing. The optical precision of non-conic asphere parts is reduced upon exporting the high-precision, native object from OpticStudio as a NURBS surface form. For non-imaging optics, the precision of the CAD representation is usually adequate, but for imaging systems, care must be taken to verify that the imported CAD part is a suitably accurate description of the desired shape. OpticStudio uses a relative internal optical precision of about 10^{-12} for ray tracing. Most CAD representations of objects are many orders of magnitude courser.

## An example

The best way to test is to repeat the ray-trace analysis using the NURBS component. For example, consider an even-aspheric lens, consisting of a surface with a conic asphere with added r^{4} and r^{6} terms. This is a very common aspheric element:

As you can see from the Spot Diagram analysis, the lens is clearly diffraction limited. The Ray Fan analysis shows balancing focus, spherical, and higher-order spherical, and unbalanced r^{8} higher-order spherical:

Now that we have some baseline measurements, we can export the lens using **File...CAD Files** tool:

Use the default settings:

The default settings are that 32 spline segments are used to represent non-conic asphere surfaces, and the approximate accuracy of the export is 10^{-4} lens units. Since lens units in this file were millimeters, the approximate accuracy is 0.1 micron. This number should be compared to the manufacturing method used to make the component, and is normally reduced only if the manufacturing method employed justifies it.

The resulting STEP file yields the following optical performance:

The Spot Diagram analysis now shows a slightly larger distribution of rays, and the scale of the Ray Fan analysis increased to +/-0.5 um. Therefore, the 32 low-order splines do not fully describe the shape of the r^{6} order asphere. Increasing the precision of the export settings can reduce the differences between the system with the native object and the CAD file, but only to a certain extent. The NURBS representation is only exact for conic aspheres, so there will be some unavoidable differences between higher order aspheric surfaces and their exported CAD representation. In addition, the tolerance and spline export settings should not be set tighter than the manufacturing method can provide.

However, we must not fall into the trap of thinking that just because we can see a difference in performance, the difference must be important and must be eliminated! The engineer(s) responsible for meeting specification should decide whether this difference is significant or not. In this asphere example, the Ray Fan and Spot Diagram analyses are very sensitive ways to demonstrate the differences between the native Even Asphere lens and the STEP file. Other analyses, which may be more meaningful to the system specifications, may not be so sensitive. For example, the PSF results are extremely similar for the native object and the STEP file, because both are well within the diffraction-limited performance range.

The MTF performance is similarly unaffected by the use of the CAD object.

The quality of the CAD export should always be assessed using the real-world, physically-significant performance criteria for your optical system, and not just the more sensitive tests that will show any differences.

## Direct comparison

The asphere example shown above assesses the export quality using sequential analyses in Mixed Mode, but it can also be useful to directly compare the sag of the native object with its NURBS equivalent in Non-Sequential Mode. This is done by tracing a non-sequential ray to each of the objects, and comparing the point at which the rays intersect.

The file "CAD_Testing.zmx" in the article attachments compares a native object In OpticStudio (highlighted in orange, below) with its STEP equivalent.

One source ray is traced to each object. The Merit Function reports the z-coordinates of the intersection points, and then calculates the difference in z-coordinate between the two objects.

The DIFF operand is then used in the Universal Plot. The source rays are scanned along the Y axis from 0 to 30 mm, and the Universal Plot reports the difference in intersection points as a function of position.

Generally, this difference should be small compared to the Tolerance setting used in the Export CAD File dialog box. If it is not, then increase the number of splines used until satisfactory accuracy is achieved.

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