A LightTools add-on to compute first order properties of a compound lens, such as equivalent/back/front focal length. Written in VB .NET using Visual Studio 2022
Let's assume we use LightTools (LT) illumination optics design software by Keysight (previously, by Synopsys) to create optics for collimating the light from an LED (imaging it into infinity), using two positive lenses because a single one is not strong enough. The diameter d of the LED approximates the far field angle alpha of the beam via focal length f: alpha = d / f. Therefore, we're interested in the focal length of the compound lens (our two lenses combined)
But while LT does tell you the focal length of each individual lens, it does not directly tell you the focal length of the compound lens. If you have licensed the imaging path module, you can easily create an imaging path through the two lenses and find the desired values (and much more), but if you don't, you would have to resort to trial and error. You would maybe trace a ray fan from the LED edge, see where it goes, adjust the LED position to make the outgoing fan parallel and measure its angle -- too tedious. So I thought it would be nice if there were an easy way to find such parameters with standard LT.
LT offers an API for external client software, using programming languages like Visual Basic .NET, C# .NET, Excel VBA or any other programming environment that can communicate through Windows COM. LT comes with a utility library (Tools -> Utility Library...) that consists of a collection of external executables written in Visual Basic .NET (or C# .NET) - a set of useful demonstrations what can be done this way. LT also allows the user to define her or his own add-ons: Executables that talk back to LT through COM. Here, I'm using this approach to write this add-on to compute first-order properties of a compound lens.
The starting point for the add-on is the set of currently selected surfaces. The add-on finds those surfaces in the selection that are a SIGNCURV_SURFACE. Spherical, Conic, Polynomial Asphere, and a few more qualify as a SIGNCURV_SURFACE (a surface with signed curvature). The add-on verifies that the vertices of all selected SIGNCURV_SURFACEs are collinear (on an optical axis). If so, the two outermost vertices are determined: These form the boundary of the compound lens.
Now, I'm ready to find the front and back foci and principal points via ray tracing. I trace rays through the compound lens that start out parallel to the axis and find (i) the foci: where the rays would intersect the optical axis after traversing the compound lens, and (ii) the principal points: where the first (axis-parallel) and the last (focus-intersecting) ray segments intersect when extended to long straight lines.
This is executed when you click the "Compute lens properties" button. Results and error messages are displayed in the LT Macro Output tab (typically at the bottom, right next to the Message Log tab).
If I could neglect roundoff error, I could trace one forward and one backward ray truly paraxial ray through the system, parallel to and infinitesimally close to the optical axis. But I cannot, I must trace such rays at a small but finite distance. To mitigate the error introduced by the finite ray height, I first estimate a good value for the finite ray height. I look at each SIGNCURV_SURFACE's curvature radius and half width, and determine the smallest such value, let's call it R. My finite ray height is 0.001 R. Experiments showed that this is large enough to avoid roundoff error, but not small enough to avoid spherical aberration: The ray-axis intersection point is on the axis (by definition) but it is not the true paraxial focus. However, the on-axis distance of the ray-axis intersection point to the true paraxial focus is an even function of ray height due to symmetry (its Taylor polynomial expansion has only even powers). So I trace two such rays from each side: One at 0.001 R, and the second at 0.002 R. Then, I assume a quadratic dependence (neglecting O(4)), which allows me to extrapolate to ray height = 0. Experiments show that this approach typically gets the focal length right to about seven decimal digits, way beyond any manufacturing accuracy.
The add-on offers check boxes to draw properly named focal points and planes as well as principal points and planes.
If you have Visual Studio 2022 installed: Open the FirstOrderLensProperties.sln solution in Visual Studio 2022 and build the FirstOrderLensProperties project to obtain the FirstOrderLensProperties.exe executable, in the LT_FirstOrderLensProperties\bin\Release\net8.0-windows subdirectory of your local copy.
In the LT_FirstOrderLensProperties/FirstOrderLensProperties_Setup/Release/ subdirectory, run the setup.exe program. It will install the add-on in C:\Program Files\JMO\FirstOrderLensProperties.
- In 3D view, click Tools->Addins.
- In the "Customize User Tools Menu", click Add.
- Enter your "Menu Text" (e.g. "First order lens properties"
- For "Command", click on the three little dots and navigate to the folder where FirstOrderLensProperties.exe resides. Select FirstOrderLensProperties.exe and confirm by clicking "Open".
- Leave "Agruments" empty
- Use any Initial Directory; the default LTUser folder is fine. The add-in doesn't read or write any files.
In LightTools, make sure all desired lens surfaces are included in the current selection. Then, click Tools->First order lens properties (or whatever name you gave in the Menu Text entry). The add-on window should open. Click the large button, "Compute lens properties". The add-on will do its work and display the result in the Macro Output tab (typically, at the bottom of the LightTools window, next to the Message Log tab)