Athermalization
Athermalization, in the field of optics, is the process of achieving optothermal stability in optomechanical systems.
[1][2] Optomechanical systems are typically made of several materials with different thermal properties.
Thermal expansion is the driving phenomena for the extensive and intensive property changes in an optomechanical system.
Extensive property changes, such as volume, alter the shape of optical and mechanical components.
Systems are geometrically optimized for optical performance and are sensitive to components changing shape and orientation.
While volume is a three dimensional parameter, thermal changes can be modeled in a single dimension with linear expansion, assuming an adequately small temperature range.
These equations describe how diameter, thickness, radius of curvature, and element spacing change as a function of temperature.
The dominant intensive property change, in terms of optical performance, is the index of refraction.
[4] There are multiple formulas that can be used to define the wavelength dependence, or dispersion, of a glass.
These coefficients can be found in glass catalogs provided from manufacturers and are usually valid from the near-ultraviolet to the near-infrared.
From the dispersion formula, the temperature dependence of refractive index can be written:[6][7] and Where
[8][9] To account for optical variations introduced by extensive and intensive property changes in materials, systems can be athermalized through material selection or feedback loops.
The simplest way to do this is to choose materials for the optics and mechanics which have low CTE and
This technique is not always possible as glass types are primarily chosen based on their refractive index and dispersion characteristics at operating temperature.
Alternatively, mechanical materials can be chosen which have CTE values complementary to the change in focus introduced by the optics.
[1][10] Negative thermal expansion materials have recently increased the range of potential CTEs available, expanding passive athermalization options.
[11] When optical designs do not permit the selection of materials based on their thermal characteristics, passive athermalization may not be a viable technique.
For example, the use of germanium in mid to long wave infrared systems is common because of its exceptional optical properties (high index of refraction and low dispersion).
[12] Because the primary aberration induced by temperature change is defocus, an optical element, group, or focal plane can be mechanically moved to refocus a system and account for thermal changes.
This affects each radius of curvature, therefor changing the optical power of the lens.
The radius of curvature change is a function of the temperature gradient in the optic.
Radial gradients are less predictable as they may cause the shape of curvature to change, making spherical surfaces aspherical.
Temperature gradients are determined by heat flow and can be a result of conduction, convection, or radiation.
Whether steady-state or transient solutions are adequate for an analysis is determined by operating requirements, system design, and the environment.
It can be beneficial to leverage the computational power of the finite element method to solve the applicable heat flow equations to determine the temperature gradients of optical and mechanical components.
