# Analysis on the Isostatic Bipod Mounts for the HERA Mission LIDAR
## 1 Introduction  
The HERA spacecraft includes several payload instruments, such as the Time-of-Flight (ToF) LIDAR that will measure the distances from the HERA spacecraft to the target. The measurement operations shall be performed at a distance from 500 m to 14 km, enabling operations such as fly-bys or landings. Previous space missions have deployed analogous instruments for specific requirements. One of the main challenges in those missions was the operational temperature range, since the LIDAR instruments were directly exposed to space and the required optical tolerances to maintain the instrument performance, i.e., internal alignment of optics and alignment between receiver and emitter. Each mission requires a specific LIDAR measurement range, operational temperature interval, radiation requirements and target objects, making the LIDAR design rather specific. The contribution of this paper is the design of isostatic bipod mounts for a small mirror of the LIDAR. Within the mirror, the reflecting coating, the substrate and the supports have to be validated over the thermal range of the mission. When the mirror is subjected to a thermal condition, maintaining the surface shape is critical. \"A temperature change induces a change in size which, for curving optical surfaces, produces a change in radius and hence a focus shift\" [1]; therefore, a large change in temperature can cause a distortion. Isostatic mounts, or flexures, are optomechanical components capable of compensating thermal and gravitational deformations in optical components. Isostatic bipod mounts areused to prevent deformations due to differences of thermal expansion coefficients, and to keep the mirror's optical axis in place [1]. Several design limitations occur due to the mission environmental requirements. An a-thermal design must be taken into consideration since critical components have a different Coefficient of Thermal Expansion (CTE). Usually, optical components have a low CTE compared to the mount, thus the a-thermal design is a critical aspect to the mount design [2]. [PERSON] [2] studied two different a-thermalization methods: one matching the bond thickness, and the second by applying elastic elements in the mount. The first approach is to adapt the thickness of the adhesive to compensate for the expansion of the optics and mounts. However, it resulted in the instability of the optical components, since it resulted in a thick bond line which does not work properly for strength and stiffness. The second approach included a tangential isostatic flexible element, a leaf spring. If well dimensioned, the mirror would be supported by three leaf springs, with a small bonding spot. The stability under inertial loads, such as gravity, is achieved by constraining with high stiffness the degree of freedom of the optical component, where \"only residual local stresses in the glass arises around the bond spots\" [2]. Following the second approach of [PERSON] [2], several designs were presented for several space missions, especially for mirrors with large aperture. There are two types of conformities that should be followed: radial compliance for axisymmetric mirrors to compensate for thermal expansion mismatch, and tangential compliance to prevent assembly stress from navigating towards the mirror surface. Lateral mirror supports on the edge of the mirror help in fulfilling these compliances [3; 4]. Isostatic mounts can be categorized according to the type of flexure element: simple blade flexures, that are used for tangential edge support for small axisymmetric mirrors, and a bipod flexure, which is a combination of two blade flexures forming a triangle [3; 4]. [PERSON] [3] presented a design for a lightweight primary mirror, with pockets in the back surface, and with three square bosses extruded at the edge of the mirror for isostatic mounting.