Kinematic evaluation of the whiffletree lateral support setup and its application for the mirror support of the TMT tertiary mirror

Abstract

With increasing size of the reflecting mirror apertures in telescopes, the lateral support is becoming more and more important. In order to find a setup satisfying the requirements for the TMT tertiary mirror, based on the classic three-point flexure support setup, a twelve-point lateral support setup was investigated its basic internal relations and properties were investigated. The virtual equivalent circle concept is then proposed to evaluate different potential setups. By studying the relationship between the virtual equivalent circle radius and the thermal deformation and resonant frequency, it can be concluded that a larger virtual equivalent circle radius results in a smaller the thermal deformation and a higher resonant frequency. Preliminary research results suggested that the TMT tertiary mirror surface figure error and thermal deformation requirements can easily be met. However, it was more difficult to obtain resonant frequencies higher than 15 Hz. Based on the virtual equivalent circle concept, the TMT tertiary mirror support setup was optimized, resulting in a resonant frequency of 17.7 Hz, which satisfies the requirements. The whiffletree lateral support setup can be applied to similar reflecting mirror support structures.