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.

Authored By Jordan Teich

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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 1 of this series, we will explain the standardized CubeSat form factor and cover the background details on building a CubeSat optical system in OpticStudio’s Sequential mode.

CubeSat Design Background

The CubeSat form factor is based on a standard that was originally developed as a collaboration effort between California Polytechnic State University and Stanford University’s Space Systems Development Laboratory (SSDL)².

The building blocks for standard CubeSat systems are in 1U, or “one unit”, cubes that measure 10x10x10cm. While a 1U CubeSat is the base size, CubeSats can be built to a larger form factor through the addition of more 1U building blocks. The following graphic from NASA provides an illustration of standardized CubeSat sizes.

Figure 1: Standardized CubeSat Sizes per NASA³

The CubeSat optical design referenced in this article series is an off-axis segmented, reflective telescope of the Ritchy-Chretian type. The design is meant to fit into a standardized 3U CubeSat form factor, or 10cm x 10cm x 30cm. To maximize the field of view, the design consists of two hyperbolic mirrors that are rectangular in shape. The primary mirror and secondary mirrors have dimensions of 80mm x 80mm and 41mm x 24mm, respectively.

This design is meant to function as a high-resolution earth-imager in Low Earth Orbit at 700km. The design has an effective focal length of 685mm and is designed to work in the visible spectrum. At the primary wavelength, the design has a ground resolving distance of 9.11m which allows system to image two distinct objects that are at least that distance apart. The ground resolving distance can be calculated with the following equation:

As designed in OpticStudio, the CubeSat is assumed to operate at room temperature, but in-orbit, the optics are expected to perform at an operating temperature of 15C + 3C. The detector for this system has an active array of 1280 x 800 pixels with each pixel being 3um x 3um. This allows for a total imaging area of 3.84mm x 2.4mm.

The main performance metrics for this design are to achieve a diffraction limited spot size at every field point and to achieve an MTF of 0.25 at 80 cycles/mm. These metrics were referenced from the same paper on which this design was based.

Designing the Optics in Sequential Mode

To begin the design process, the optics were modeled in sequential mode. Based off the design prescription, global system parameters were set in the System Explorer and the optic were inserted with the proper specifications in the lens data editor.

Figure 2: Initial Optical Prescription

Even though the final design contains mirrors with rectangular apertures, the first stage of the design had the mirrors retain a circular shape. Retaining the circular shape of the mirrors prevents the optimization from being over constrained at the start of the process. To position both mirrors off-axis, the two mirrors have been de-centered with respect to the global optical axis. Because of this, even though rays are focusing to the correct location, the image plane is offset from the rays. At this stage, the image plane is floating near the top of the primary mirror and is aligned with the global optical axis of the coordinate system.

Figure 3: Incorrect Image Plane Location

To be brought to the correct location, the image plane needs to be decentered with a coordinate break surface. This decenter was implemented by using a chief ray solve on the Decenter Y parameter of the coordinate break. This solve adjusts the Decenter Y value such that the coordinate break surface is aligned with the real chief ray. With the coordinate break now aligned to the chief ray, the image plane is properly positioned.

Figure 4: Chief Ray Solve

With the basic layout finalized, optimization can now begin. To preserve the system’s F/# of 12.455, an EFFL operand was used in the merit function to target 685mm in conjunction with an RMS spot size default merit function. Multiple optimization runs were conducted where the radii of each surface and the thicknesses were iteratively optimized. Since space is limited in a CubeSat system, it is critical to pay close attention to the total track length of the system as well as areas where rays can be vignetted. The total track length for this design is 19.5cm with 2U’s of space devoted to the optics. The remaining 1U of space is devoted to the system electronics. The total track length can be monitored via the merit function by using a thickness (TTHI) operand between the STOP and the image plane.

After verifying that the design would fit within the size constraints of a 3U CubeSat and ensuring that performance was as expected after optimization, the mirrors were adjusted to be rectangular. The mirrors were adjusted to the proper shape using the Aperture setting in the Object Properties tab for each mirror.

Figure 5: Rectangular Aperture

The X-Half Width and Y-Half Width settings were used to adjust each mirror to the proper size while the Aperture Y-Decenter setting was used to apply additional decenter to the optics. Each mirror was decentered to capture the entirety of the incoming beam.

After adjustment of the aperture settings, it was discovered that the secondary mirror was partially clipping the incoming ray bundle. With further decentering of the secondary mirror aperture, the results were favorable. After adjustment, the footprint diagram was used to verify that the full beam footprint reaches every critical surface of the system.

Figure 6: Clipping of the Beam

Figure 7: Footprint Diagram of Mirror 1 (Left) and Mirror 2 (Right)

At this stage, the design has been laid out in OpticStudio, optimized, and adjusted such that it fits within a 3U CubeSat form factor. The following spot size and MTF performance was achieved:

Figure 8: Nominal System Performance

The spot size is diffraction limited at all field points and the MTF meets the specification of 0.25 at 80 cycles/mm. With the optical performance meeting requirements, the mirror thicknesses were increased as a final update to the base model. If the mirrors remain as thin as 5mm, this could cause issues down the road when applying a temperature condition across the optics. In the Draw tab of the Object Properties menu, the thickness was adjusted to 18mm and 15mm for the primary and secondary mirrors respectively.

Conclusion

In this article, we have covered what a CubeSat is and the standardized form factors that exist for developing CubeSat optical systems. We walked through the background details and specifications for the 3U CubeSat telescope that will be expanded upon throughout the rest of this article series. We then walked through an example design process for creating a CubeSat telescope in OpticStudio’s sequential mode.

Special Thanks

Ansys Zemax would like to give a special thanks to Trenton Brendel from the University of Arizona for collaborating on the selection of design candidates for this article series.

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
2. About — CubeSat. CubeSat. https://www.cubesat.org/about. Accessed February 13, 2022.
3. Mabrouk E. Cubesat Form Factors.; 2015. https://www.nasa.gov/content/what-are-smallsats-and-cubesats. Accessed February 13, 2022.