In the aerospace industry, CubeSats have emerged as a low-cost, easily manufacturable solution for space-based optical systems. They offer a unique opportunity to develop a production line approach for a space-based product through the manufacture of a constellation of smaller, more affordable systems.

Companies that manufacture CubeSat optical systems need an accurate and reliable method for developing an optical design, opto-mechanically packaging the system, as well as modeling structural and thermal impacts that the system will experience in-orbit.  This article series will walk through the high-level development of a CubeSat system by leveraging the Zemax and Ansys software suites. We will illustrate how an integrated software toolset can streamline the design and analysis workflow.

By: Jordan Teich & Flurin Herren

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Introduction

For decades, optical systems have been developed for operation in low, medium, and high Earth orbit. For many optical systems, the packaging form factor and the opto-mechanics that stemmed from this form factor were designed on a system-by-system basis. CubeSats are a class of lightweight nanosatellite that can house optical systems for applications ranging from laser communications to earth imaging. They are unique in that they use a standardized size and form factor.

For this article series, the paper Optical Design of a Reflecting Telescope for CubeSat¹ was used as a reference for developing the CubeSat optical design.

In Part 4 of this series, we will cover how to bring FEA data from Ansys Mechanical into STAR and use the data as part of a STOP (Structural, Thermal, Optical Performance) analysis. We will analyze the effect of FEA data on optical performance and derive insights that will be used to revise the nominal CubeSat design.

Using the STAR Module for STOP Analysis

Structural deformation datasets for the primary and secondary mirrors have now been generated at three temperatures within the operating range of the optics (12C, 15C, and 18C).

This deformation data will be directly compared to performance data from the original model in OpticStudio. Before running any FEA, Ansys Mechanical assumes that the opto-mechanics and optics are soaked in a room-temperature environment with no stress applied to the optics. Because of this, we can assume that the original sequential model simulates the performance of the optical system at ambient temperature and pressure.

The STAR module can read FEA data directly into the Sequential optical model. Upon doing so, the entire suite of analysis tools can be used to analyze impacts on system performance due to the loads and boundary conditions applied during FEA. We can use the Sequential model to interpret results since the only change made in Non-Sequential was creating a cut-out at the bottom of the primary mirror. In Sequential mode, this cut-out technically does not exist, but due to the nature of sequential ray tracing, rays passing through the bottom of the mirror do not interact optically with the surface.

A few steps need to be taken to properly load FEA data into STAR.  First the Load FEA Data tool can be used to import the text files. This tool will bring up a window where structural and/or thermal datasets can be loaded and assigned to the corresponding optical surfaces. For this example, structural data for both mirrors at 12C have been loaded into STAR.

Figure 1: Loading Data into STAR

Once the data is prepared, the FEA data can be fit. Using the Fit Assessment tool, the fit parameters for the data can be adjusted independently for each optical surface until an accurate fit is achieved. Figure 2 displays the default settings for how the structural deformation data was fit to the primary mirror. With this tool, the RMS and PV Fit Error can be viewed, and the Fit Parameters can be adjusted to minimize this error.

Figure 2: STAR Fit Assessment 

By increasing the Grid 1 and Grid 2 fit parameters, the STAR fitting algorithm will consult more neighboring points during the fitting process, resulting in an overall smoother fit. These parameters can be increased for finer sampling until the desired accuracy is achieved. For this design, an acceptable fitting of the data was reached with Grid 1 and Grid 2 set to 3.

Figure 3: Primary Mirror Fit Assessment with Correct Settings

Figure 4: Secondary Mirror Fit Assessment with Correct Settings

We can now analyze the optical performance of the system at all operating temperatures with the structural deformation datasets applied. All structural FEA datasets can be viewed in the Structural Data Summary tool located in the STAR tab. From here, the datasets can be toggled on or off to examine structural deformation effects from any surfaces of interest.

Figure 5: Structural Data Tab

For the following plots, the 12C FEA dataset was used since it results in the CubeSat having the largest performance difference from nominal. The following Spot Diagram and FFT MTF charts showcase the negative impact on performance when structural deformation data is applied.

Figure 6: System Performance at 21C vs 12C

With the ability to interchangeably apply FEA data to a Sequential OpticStudio model, impacts on performance can easily be accounted for. By applying specific FEA datasets to the model, further insights can be gained. In Figure 7, only the structural deformation data for the secondary mirror is applied.  Applying this data and looking at the FFT MTF plot confirms that degradation in system performance mainly results from the primary mirror for this design.

Figure 7: MTF Performance with Secondary Mirror Data

While the FFT MTF and Spot Diagram analyses have been highlighted here, any of the analyses available in Sequential mode can be used to examine potential performance impacts. Analyzing how system performance is affected by in-orbit conditions is key to understanding if any iterations should be made to a design before proceeding to manufacturing. 

Iterating the Optical Design Based on STAR Results

From these insights, we’ve learned that the system fails performance specifications within the operating temperature range. At 12C, the system no longer has a diffraction limited spot and the MTF is lowered to below 0.25 at 80 cycles/mm.

To move forward with the design, adjustments need to be made to recover performance.  One change that can be considered is an adjustment of the image plane’s best focus position. For the nominal system, the position of the detector was determined through an optimization for best focus. This optimization placed the detector 7.018mm behind the primary mirror. However, the nominal model is assumed to be soaked at room temperature, or 21C. Once the CubeSat is put into orbit, the optical design will operate at a slightly cooler temperature of 15C +/- 3C. Per the results from STAR, when the design is placed into operating temperature conditions, the system’s best focus position shifts. With the detector currently positioned at best focus for a condition of 21C, the detector is not optimally positioned for in-orbit temperature conditions.

To recover performance, the detector’s best focus position can be changed based on STAR results. This involves defocusing the detector from its best focus position at 21C during the alignment phase on Earth. If defocused properly, the system will self-correct for focus in-orbit when it is soaked in the operating temperature range. In a manufacturing environment, this defocus could be implemented by adjusting the thickness of the detector shim. Another design option could be to add suitable mechanics for a focus adjustment mechanism. Such a focus mechanism could move the detector along the Z-axis to recover performance in orbit. However, this method can lead to more intensive testing and increased cost in manufacturing. For this CubeSat design, we have assumed that adjustment of a camera shim is the only path available for recovering system performance in-orbit.

To optimize the detector position for in-orbit conditions, the FEA datasets for all three operating temperatures must first be loaded into OpticStudio via STAR. After an FEA dataset is loaded, a Quick Focus optimization for the Spot Size Radial can be run to adjust the back focal distance such that the image plane is located at best focus. The Quick Focus routine only adjusts the thickness of the surface prior to the image plane, but for this example the detector location will be referenced with respect to the back of the primary mirror. For all three-operating temperatures, the results were as follows:

Operating Temperature	Best Focus Position after Quick Focus (With respect to the back of the primary mirror)
12C	6.758mm
15C	6.845mm
18C	6.932mm

 

This illustrates that the best focus position for the detector behaves linearly with temperature. To achieve best performance on orbit, the detector can be positioned such that it lies 6.845mm behind the primary mirror. This equates to a movement of -0.173mm from the 21C best focus position.

To implement this design change, the thickness of Surface 6 can be adjusted. After this adjustment, note how best performance is no longer achieved at 21C before STAR data is applied.

Figure 8: Performance Data at 21C (Defocused System)

The Sequential design is now being simulated with an intentional defocus at 21C. Surface 6 has a thickness of -0.155mm to place the detector in the correct location for in-orbit focus correction. If we re-apply the FEA data at all three operating temperatures, system performance can be analyzed with this implemented design change.

Figure 9: FFT MTF Performance for Updated Design

Re-applying the FEA data for all three operating temperatures illustrates that the MTF requirement of 0.25 at 80 cycles/mm can now be obtained in-orbit. Looking at the spot size data showcases that this design change also allows for a diffraction limited spot at each temperature condition.

This is one example of how analyzing STAR data with OpticStudio’s sequential analysis tools can aid engineering decisions when iterating on a design. To achieve best performance under operating conditions, another example workflow could be to define a merit function that optimizes specific system parameters while STAR data is applied. While this example specifically utilizes structural deformation datasets, note that thermal datasets can also be applied at the same time.

Iterating the Mechanical Design Based on STAR Results

Using STAR data, insights can also be gained on the state of the opto-mechanical design under operating conditions.

As visible on Figures 3 and 4, the distribution of the deformation magnitude across the primary and secondary mirrors are shown to be in opposite directions from each other (the bottom left of the primary mirror and bottom right of the secondary mirror). To keep the deformation of the two mirrors relative to each other and preserve the balance of the deformation load, a mechanical design improvement was implemented to adjust the mechanical stop surface (mirror surface where the mirror lays on the retainer) onto the other bottom corner of the mirror. By implementing this change, both mirrors can now have a load distribution that goes in same direction relative to each other. This is indicated on the graphic below (Figure 10) with the red marked coordinate system.

Figure 10: Primary Mirror Retaining System

After implementing this mechanical design change, we can re-run the FEA analysis in Ansys Mechanical and import the new set of FEA data into OpticStudio. After importing the new set of data, we can observe the change in load distribution on the secondary mirror in the Fit Assessment tool. In Figure 11, the load distribution on the secondary mirror now goes in the same direction relative to the primary mirror.

Figure 11: FEA Data Fit to Secondary Mirror (Post Mechanical Design Update) 

Another method for brainstorming improvements to the opto-mechanical design is through investigation of the mesh grid created by Ansys Mechanical. This mesh grid is created before an FEA analysis can be run. In the bottom image of the figure below (Figure 12) one of the metering rods is fully enclosed throughout the whole length of the primary mirror retainer. This could lead to an over-constrained connection of the two components.

 

 

Figure 12: Ansys Mechanical Deformation Mesh View on Primary Mirror Retainer

To solve this, the design was updated such that this metering rod was only fully enclosed by the mirror retainer for a shorter distance.  By carving out some of the material on the primary mirror retainer, the hole surrounding the metering rod was adjusted to be the same thickness as the holes for other three metering rods. This update can be observed in Figure 10, where it is indicated with a red arrow.

Conclusion

By leveraging the Ansys Zemax software suite, we’ve demonstrated how to take a 3U CubeSat optical system and bring it through a few stages of the design process. With this integrated toolset, an optical design can be created with OpticStudio and easily exported to OpticsBuilder for the purpose of creating opto-mechanical structures. The full opto-mechanical design can then be exported from OpticsBuilder to FEA software for running the finite element analysis. And with OpticStudio’s STAR module, it is now effortless to import structural and thermal data from FEA software into OpticStudio for analyzing system performance. While this article series highlighted how the development of a CubeSat system can benefit from the Ansys Zemax workflow, this chain of software can provide engineers a complete workflow for designing other types of space-based products that require STOP analysis. This type of workflow empowers engineers to use their time more effectively during the design process.

References

1. Jin H, Lim J, Kim Y, Kim S. Optical Design of a Reflecting Telescope for CubeSat. J Opt Soc Korea. 2013;17(6):533-537. doi:10.3807/josk.2013.17.6.533