Bowtie design for thermal expansion mimicry and mitigation

Abstract

A geometric bowtie design for the purpose of mimicking (matching) and/or mitigating (reducing) the thermal expansion effects between two laterally opposing structures is investigated. A bowtie design is that of two opposing overlapping triangles with farthest sides parallel. This design embodies thermal centering concepts which utilize the relationships of the trigonometric identity known as the law of sines for a triangle from which beneficial thermal properties can be engineered. For validation. The bowtie design is embodied using two separated Zerodur plane mirrors, symmetrically opposed, and each seated in Maxwell-style kinematic couplings of spheres and vee-groves. The vee-grooves form a wheel-like pattern on an aluminum baseplate. The intersection of the vee-grooves is the common overlapping thermal center of both mirror mounts. The refractive-index corrected interferometric measurement of the displacement between these two mirrors shows that even during non-isothermal non-equilibrium transitions and states, the nominal ∼90 μm thermally induced (13 °C) expansion of an aluminum baseplate can be mitigated, being reduced more than 98 % to ∼1.4 μm by mimicking the thermal expansion properties of the mirrors’ structural material. Engineering thermally-invariant kinematic bowtie designs using materials having higher thermal expansion coefficients is also described.