Athermal design and analysis using numerical methods


Maintaining the optical performance of a remote sensing payload in extreme temperature differences when orbiting the earth, from eclipse to the sunlit part of the orbit 15 times a day, is a major challenge. These temperature differences will result in the expansion and contraction of the optical elements and parts that will have a direct impact on the relative alignment and ultimately the optical performance. This article will explain the approach used to achieve an athermal design for Simera Sense’s remote sensing payload using numerical and experimental methods.

Two evaluation methodologies are considered to predict the behaviour of the optical system when it is subjected to isothermal loads. The first methodology is used to correlate the optical performance of the payload using Zemax and finite element analysis (FEA). To establish the spacing required to achieve an athermal design, the optical components are subjected to an isothermal load case in Zemax. The software computes the required effective coefficient of thermal expansion (CTE) between components to achieve an athermal design. The effective CTEs are used to drive the mechanical design, regarding spacing and material selection.

Once the mechanical design is completed, FEA is used to determine the numerical correlation between the predicted Zemax results and the mechanical design when it is subjected to isothermal loads. The finite element (FE) displacement results are used to extract the surface deformation and relative translation and rotation of the optical components. These results are then processed into a format that is compatible with Zemax where the optical performance of the payload is determined. This methodology is followed until acceptable correlation is obtained between the predicted Zemax effective CTE and the mechanical design. This approach therefore allows for two independent numerical procedures that can be used to correlate the optical performance and mechanical design.

This procedure is only useful for numerical correlation but does not capture the influence of the payload within the CubeSat structure and does not relate to the experimental testing of orbit conditions. Also, when working with optical payloads, it is necessary to keep in mind that the precision and accuracy require to maintain optical performance is usually within micro meters. Considering the sensitivity of such a system, the influence of each interface should be determined. Since Zemax cannot include the complexity of mechanical interfaces, such as the payload assembled within the CubeSat structure, it must be established using alternative methods.

Therefore, the second evaluation methodology is used to determine the optical performance of the payload when it is mounted within the CubeSat structure while it is subjected to isothermal loads and vacuum conditions. At Simera the thermal response of the optical payload, when it is fully integrated with the attitude determination and control system (ADCS) and 3U CubeSat frame assembly, is placed within a vacuum chamber that can be heated or cooled to the desired temperature. To develop an estimate of the predicted mechanical behaviour, a FE model of the test set-up is developed.

The FE results are used to extract the surface deformation, relative translation, and rotation of the optical components. These results are then processed into a format that is compatible with Zemax. Here the optical performance of the payload is evaluated once again. This methodology is used to refine the mechanical design until the desired results are achieved.

Although the main purpose of the analyses is to achieve an athermal design, the effect of gravitational acceleration during ground testing and alignment is also considered during FEA where it is applicable. An example of the FE displacement of the payload during 1 g acceleration applied in the negative Z-axis and isothermal load of 10 °C is shown in Figure 1 and Figure 3, respectively. A scatter plot of the surface deformation extracted from the respective FE results the entrance lens is shown in Figure 3 and Figure 4:

Figure 1: Numerical displacement at 1 g applied in the negative Z-axis.

Figure 2: Numerical displacement at 30 °C isothermal load (delta of 10 °C increase).

Figure 3: Scatter plot of entrance lens surface deformation subject to 1g load.

Figure 4: Scatter plot of the entrance lens surface deformation subject to 10 °C increase in temperature.

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