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Setting up realistic optomechanical tolerances in Zemax can be complex, involving Coordinate Breaks, custom operands, and nested group rules. We introduce NEST (Nested Elements and Systems Tolerancing) to streamline this process by letting users define lens groups, assign mechanical pivot points, and model hierarchical relationships through an intuitive interface. NEST then automatically generates the necessary Coordinate Breaks and operands for correctly handling nested tilts and decenters. Using an unobscured Gregorian telescope, we show how NEST simplifies practical optomechanical tolerancing.
Note: This feature is only available in Ansys Zemax OpticStudio Premium/Enterprise.
Authored by Mojtaba Falahati
Introduction
Accurate optical system design requires not only optimizing the ideal prescription but also understanding how real manufacturing and assembly misalignments affect performance. Mechanical errors such as tilts, decenters, and axial shifts can significantly degrade image quality if not properly modeled. Correctly defining mechanical pivot points, often located away from optical axes and determined by the mount design, is essential for realistic misalignment simulation. Modern systems also include nested mechanical structures, where misalignments in one assembly propagate through others, making hierarchical modeling critical. Historically, setting up such tolerances in Zemax required manually defining complex operand structures, prone to errors and inefficiency.
By automating the most error-prone and labor-intensive parts of the tolerancing setup, NEST helps users build a complete and accurate tolerance portfolio directly in the Tolerance Data Editor, without relying on manual operand configuration or external scripting. This improves both the efficiency and reliability of tolerance analysis and shortens the path from design to manufacturable product.
Example: Tolerancing Setup with NEST
We present a practical example using an unobscured Gregorian telescope which is a two-mirror optical system designed to eliminate central obstruction and the diffraction artifacts it causes. Unlike the traditional Gregorian configuration, the unobscured variant employs an off-axis optical geometry. The primary mirror, typically a concave paraboloid, collects light and directs it toward a concave ellipsoidal secondary mirror positioned beyond the primary focus. Both mirrors are tilted and decentered relative to the system’s optical axis.
Mechanically, the two mirrors are mounted on distinct but kinematically related structures that define the system’s alignment and rigidity. The primary mirror is typically secured to a rigid base cell connected to the telescope’s foundation structure, establishing the global optical reference. The secondary mirror is supported by an independent off-axis assembly, such as a truss, that enables controlled adjustment of tip, tilt, and decenter degrees of freedom.
In most implementations, both mirrors are integrated into a common mirror group that can pivot about a defined mechanical node near the primary mirror’s vertex (preserving conjugate alignment while compensating for structural flexure or thermal drift). This kinematic hierarchy provides an ideal framework for NEST’s tolerancing methodology, where each optical and mechanical component is represented as a nested subsystem with its own local coordinate frame, pivot definition, and coupling to the telescope base.
Optical layout of Gregorian telescope (from J. Störkle, “Dynamic Simulation and Control of Optical Systems,” Ph.D. dissertation, Universität Stuttgart, 2020).
Open the “Unobscured Gregorian.zmx” file from the attachment
NEST can be accessed through the Tolerance tab along with other Tolerancing tools. By clicking NEST tab you may open the NEST window to set up your nesting groups and corresponding pivot points.
As shown in below, the left panel presents the groups list, where each entry represents a defined optical or mechanical subgroup, organized automatically by NEST according to their nesting relationships. The central table functions as the standard Lens Data Editor, listing all optical surfaces in the model. Users can select one or multiple surfaces and assign them to a group using the Add Group command. Once defined, NEST identifies parent–child relationships among groups and displays them in a hierarchical structure. The right panel provides detailed group properties, including user-defined pivot points and tolerance parameters for decenter and tilt.
A real-time layout view illustrates the optical configuration, where selected groups and their associated pivot points are highlighted to assist with spatial visualization and alignment validation.
In the unobscured Gregorian telescope example, each mirror is defined as an individual group within NEST, with both nested under a higher-level Group A representing the complete mirror assembly. The primary and secondary mirrors each have pivot points located at their respective rear vertices, which can be selected from the default options in the Pivot Point menu.
The nesting group (Group A), which encompasses both mirrors, is assigned a user-defined pivot point positioned at the mechanical node near the rear vertex of the primary mirror, serving as the central reference for group motion and alignment analysis. Because the primary mirror features a decentered (off-axis) aperture, the Referenced to Decentered Aperture Coordinates option can be enabled to define the pivot point within the mirror local off-axis coordinate system (See this: Known Issue in NEST (2025 R2.04); User-Defined Pivot Points Not Applied Correctly | Zemax Community.).
Tolerances of tilt/decenter for each group can be either manually specified by the user or selected from predefined precision levels, ranging from commercial to high-precision standards, enabling rapid yet flexible definition of alignment sensitivities across nested subsystems. This configuration accurately reflects the kinematic relationships of the telescope structure, allowing NEST to model how nested assemblies pivot, tilt, and decenter relative to realistic mechanical constraints.
After the grouping and pivot point definitions are completed, the user can select OK to automatically generate the corresponding tolerance data. NEST creates a comprehensive tolerance portfolio for all defined groups and pivot points, using standard tilt (TUTX, TUTY, TUTZ), decenter (TUDX, TUDY, TUDZ), and thickness (TTHI) operands within the OpticStudio Tolerance Data Editor.
Each operand is automatically linked to its associated group and axis of motion, ensuring that the hierarchical relationships defined in NEST are accurately reflected in the tolerancing model. This structured output allows users to perform Monte Carlo simulations directly, evaluating system performance sensitivity under realistic manufacturing and alignment variations.
The Monte Carlo file, accessible through the toolbar icon highlighted in the figure below, provides an immediate preview of the NESTed system streamlining the transition from optical modeling to tolerancing analysis within a single workflow.
The generated Monte Carlo file includes an updated Lens Data Editor, in which all pivot point definitions and group relationships established by NEST are automatically inserted. NEST uses coordinate break surfaces to define the appropriate pivot locations, tilts, and decenters exactly as specified by the user in the NEST window. Each coordinate break is clearly labeled with a short comment tag indicating the associated group and transformation type (e.g., ToPP, FromPP, TiltXYZ, DecXYZ), allowing users to trace the mechanical and optical hierarchy directly within the model. This annotation makes the structural organization of the optical system explicit and easy to validate. Users can further verify NEST’s performance by manually adjusting the tilt or decenter values within the Lens Data Editor and observing the corresponding changes in the layout view, confirming that each mirror and nested group pivots correctly about its assigned mechanical reference point.
For example, when the mirror groups in the unobscured Gregorian telescope model are tilted by –5° about the X-axis (as defined in line 6 of the Lens Data Editor), the resulting optical geometry can be visualized in the 3D Layout as shown below. The layout illustrates the response of the entire system to the applied mechanical perturbation, demonstrating how both mirrors pivot about their respective defined pivot points while maintaining the nested kinematic hierarchy established in NEST. The light paths remain continuous and correctly referenced, verifying that the coordinate breaks inserted by NEST accurately reproduce the intended motion of each mirror group.
Once the mirror groups and their pivot definitions are established through NEST, user can execute the tolerancing analysis just like any standard OpticStudio tolerancing task, with all NEST-defined coordinate breaks and hierarchy relationships automatically carried into the workflow.
Conclusion
In modern optical system design, accurate modeling of real-world assembly conditions is critical to ensuring system performance and manufacturability. Mechanical misalignments such as tilts, shifts, and decenters, especially in complex multi-element systems, can introduce significant performance degradation if not properly accounted for during the tolerancing phase. Traditional methods in OpticStudio often required manual operand configurations and custom scripting, which made the process error-prone, time-consuming, and difficult to scale for systems with nested mechanical structures.
The NEST (Nested Elements and Systems Tolerancing) tool addresses these challenges by introducing an intuitive, structured approach to defining mechanical relationships, pivot points, and hierarchical assemblies. Through a practical demonstration using a three-mirror reflective telescope, we have shown how NEST simplifies the setup of optomechanical tolerancing, reduces the potential for user error, and enhances both the efficiency and accuracy of tolerance analysis.
By integrating NEST into the standard OpticStudio workflow, optical engineers gain a powerful tool for bridging the gap between ideal optical design and real-world mechanical implementation. This ultimately leads to more robust designs, fewer iteration cycles, and a smoother transition from concept to production-ready optical systems.
Additional resources
How to perform a sequential tolerance analysis – Ansys Optics
Optomechanical Tolerancing and Systems Engineering - Mechanical Pivot Points – Ansys Optics
References
J. Störkle, Dynamic Simulation and Control of Optical Systems, Ph.D. dissertation, Universität Stuttgart, 2020.