Athermalization, in the field of optics, is the process of achieving optothermal stability in optomechanical systems. This is done by minimizing variations in optical performance over a range of temperatures.
Optomechanical systems are typically made of several materials with different thermal properties. These materials compose the optics (refractive or reflective elements) and the mechanics (optical mounts and system housing). As the temperature of these materials change, the volume and index of refraction will change as well, increasing strain and aberration content (primarily defocus). Compensating for optical variations over a temperature range is known as athermalizing a system in optical engineering.
Material property changes
Thermal expansion is the driving phenomena for the extensive and intensive property changes in an optomechanical system.
Extensive properties
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. For examples, glass manufacturer Schott provides the coefficient of linear thermal expansion for a temperature range of -30 C to 70 C. The change in length of a material is a function of the change in temperature with respect to the standard measurement temperature, . This temperature is typically room temperature or 22 degrees Celsius.
Where is the length of a material at temperature , is the length of the material at temperature , is the change in temperature, and is the coefficient of thermal expansion. These equations describe how diameter, thickness, radius of curvature, and element spacing change as a function of temperature.
Intensive properties
The dominant intensive property change, in terms of optical performance, is the index of refraction. The refractive index of glass is a function of wavelength and temperature. There are multiple formulas that can be used to define the wavelength dependence, or dispersion, of a glass. Following the notation from Schott, the empirical Sellmeier equation is shown below.
Where is wavelength and , , , , , and are the Sellmeier coefficients. These coefficients can be found in glass catalogs provided from manufacturers and are usually valid from the near-ultraviolet to the near-infrared. For wavelengths beyond this range, it is necessary to know the material's transmittance with respect to wavelength. From the dispersion formula, the temperature dependence of refractive index can be written:
and
Where , , , , , and are glass-dependent constants for an optic in vacuum. The power of an optic as a function of temperature can be written from the equations for extensive and intensive property changes, in addition to the lensmaker's equation.
Where is optical power, is the radius of curvature, is the thickness of the lens. These equations assume spherical surfaces of curvature. If a system is not in vacuum, the index of refraction for air will vary with temperature and pressure according to the Ciddor equation, a modified version of the Edlén equation.
Athermalization techniques
To account for optical variations introduced by extensive and intensive property changes in materials, systems can be athermalized through material selection or feedback loops.
Passive athermalization
Passive athermalization works by choosing materials for a system that will compensate the overall change in system performance. The simplest way to do this is to choose materials for the optics and mechanics which have low CTE and values. 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. A material with the preferred CTE is not always available, so two materials can be used in conjunction to effectively get the desired CTE value. Negative thermal expansion materials have recently increased the range of potential CTEs available, expanding passive athermalization options.