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When analyzing structural deformation impact on optical performance, Optical Engineers often need to separate the effect of Rigid-Body Motions (RBMs) and higher-order deformations because they affect different aspects of the system performance. In this article we demonstrate how to use the Active RBMs feature in STAR and how it can help us gain better understanding of structural impact on optical performance. This feature enables users to look at just RBMs or just the higher-order effects, analyze sensitivities, and compensate the effect individually.
Authored By Hui Chen
Introduction
STAR (Structural & Thermal Analysis and Results) is a tool Ansys Zemax OpticStudio Enterprise. STAR supports loading, fitting, and analyzing Finite Element Analysis (FEA) data natively in OpticStudio. Users can load structural and thermal data obtained from FEA software into OpticStudio and perform structural, thermal, optical performance (STOP) analysis of their designs. STAR is directly integrated inside of OpticStudio and accepts data from any FEA package. This enables it to easily integrate into existing workflows and provides important design insights. The full STAR functionality can also be accessed using the STAR-API allowing for full automation of common workflows between OpticStudio and any finite element platform. Our Knowledgebase provides extensions to help data export from some FEA software.
Structural Deformation
When applying structural deformation using STAR module, the deformed surface sag includes Rigid-Body Motions (RBM) as well as higher-order surface deformation. With the Active RBM feature users can investigate these two effects separately, meaning the optical performance can be analyzed with just the effects of RBM, or just the surface deformation, or both.
This is very important because optical engineers treat RBMs and higher-order errors differently. RBMs primarily affect the boresight/line-of-sight error budget, whereas the higher-order deformations affect the performance error budget. The two budgets are linked through the allowed tolerance, (the amount of lens shift and tip tilt, for example). But the sensitivities are different for these two effects. Therefore, engineers will want to determine the sensitivities separately, look at just RBMs, or look at just higher-order effects.
Access the RBM feature
Under the STAR...Structural Data Summary, it lists which surface has structural data loaded and what data file is being used. Checking or unchecking the Status boxes will enable or disable the different structural data components on a given surface. User can make the following four selections, RBM only, Surface deformation only, Both RBM and surface deformation, or None. When the structural deformation is first loaded into your system, STAR performs an initial fitting to calculate the amount of rigid body motions, shifts and tilts, for a given surface so the structural deformation can be separated into two groups. By using the check box in Structural Data Summary one can choose which structural effect to enable.
Alternatively, you could also do so via the added Structural Options menu. Clicking the button will drop down a list for you to make selections of Use all deformation data, Use Deformation without RBMS, Use only RBMs, or Disregard deformation effects. Selections made via the Structural Options menu will reflect itself in the Structural Data Summary editor and will have an impact on ray trace results depending on which part of the structural deformation data is turned on.
Example for Decoupling RBMs and Higher-order Surface Deformation
In this section we’ll demonstrate how this Active RBMs feature works using an example. The demo system is a singlet lens focusing an incoming collimated beam. In the nominal system, after optimization the RMS spot radius is 6.2 um, which is on the same order of the Airy radius of 3.6 um. The RMS wavefront error is 0.19 waves. The performance is close to diffraction limited. The spot is centered on the image surface vertex. Below we show the 3D Layout, the Spot Diagram and the Wavefront Map of the nominal system.
Next let’s apply one set of structural deformation data on the front of the singlet lens using the Load FEA Data tool. This artificial dataset is created to introduce a small tilt motion to the front face of the singlet to simulate wedging effect, as well as additional surface curvature to deform the front spherical surface to aspheric shape. In other words, this structural deformation dataset consists of both rigid-body motion and higher-order surface deformation.
There are two tools you can use to examine and visualize the deformation introduced by the structural dataset. One is the FEA Data Viewer and the other is the System Viewer. You can find both tools under the STAR tab. The FEA Data Viewer enables users to view the FEA dataset without assigning to an optical surface in the system. This allows the opportunity to verify the correct file before assigning to an optical surface and performing a numeric fit. The viewer also displays pertinent information about the FEA dataset such as the number of data points, Median, Max/Min of positional information, and Median, Max/Min of deformation and temperature data. The System Viewer displays a system-wide view of the deformations and changes in optical properties due to the fitted FEA data. This data is overlaid on the entire optical system in a single window. In the screenshot below I enabled vector display in both analyses and assigned a scale factor of 10 to enlarge the displayed vectors for easy viewing in the layout window. Surface deformation can be represented using deformation vector which shows the magnitude and direction of the deformation. In the plot below the deformation vector arrows indicate a clear tilt motion about the X axis of the front surface.
In addition to these two analyses, you can also use Surface Sag analysis to display the sag of the deformed front surface of this singlet. If you open the Surface Sag analysis and choose to Remove Base Sag which removes the nominal sag of the underlying surface, you will be able to view the deformed sag introduced by STAR FEA dataset.
When the structural deformation dataset is first loaded onto the surface using Load FEA Data tool, the added deformation contains both rigid-body motions as well as higher-order surface deformation. STAR performs fitting internally to compute the amount of rigid-body motions, ΔX, ΔY, ΔZ, Theta X, Thera Y, Thera Z. You can find this RBM information reported in the Structural Data Summary under the Surface Properties\RBMs tab.
Now let’s take a look at the ray trace results. The first thing noticeable is that after the deformation data is loaded onto the front surface of the lens, the spot is shifted upward and no longer centered on the image surface vertex. This can be seen both in 3D Layout and the Spot Diagram. We’ll also open a Surface Sag analysis and select Remove Base Sag to view only the deformed sag on this surface 3. Here the sag plot displays a dominating surface tilt. Let’s also open the Spot Diagram and the Wavefront Map analyses to look at imaging performance. The RMS spot radius has increased to 17.2 um and the RMS wavefront error increased to 0.587 waves. These results suggest the system performance has worsened due to structural deformation and is no longer diffraction limited.
Fitted Deformation Only
In the Structural Data Summary editor, you’ll see the last two columns labeled as “Fitted Deformation” and “Extracted RBMs”. Users have the option to separately turn on higher-order deformation or calculated RBMs. If we choose to keep only the higher-order surface deformation by unchecking the RBMs box, you can see the spot now moves back to image surface center, and the sag profile only displays a rotationally symmetric aspheric deformation. The RMS spot radius remains large at 17.3 um and the RMS wavefront error at 0.583 waves.
RBM Only
We could also try keeping only the rigid-body motion and ignoring the higher-order deformation by unchecking the Fitted Deformation box, you’ll see the RMS spot size drops back to 7.3 um, and RMS wavefront error down to 0.24 waves. These numbers are still worse than the nominal system with a RMS spot 6.2um and RMS wavefront error 0.19 waves but are not very far from it.
Discussion
The above results suggest that in this simple system that consists of only one lens, the RBM motion of the lens front surface has relatively small impact on the imaging performance of the lens comparing to the higher-order deformation. The spot size and the wavefront error haven’t degraded too much. However, the chief ray angle and position do shift significantly which means large boresight/line-of-sight error is the main impact of the rigid-body motion of the lens front surface. This example shows us how this Active RBMs feature works and how we can use this feature to separate the RBMs from the higher-order deformation and analyze their performance impact respectively.
Conclusion
In this article we have demonstrated how to use the Active RBMs feature and how it can help us gain better understanding of structural impact on optical performance. Rigid-body motions and higher-order deformation affect different aspects of the system performance. They also have different sensitivities and belong to different error budget groups. With the Active RBMs feature in STAR, Optical Engineers are now able to separate these two structural effects, to look at just RBMs or just the higher-order effects, test their sensitivities, and compensate individually.