Sellmeierligningene

Sellmeierligningene is a set of empirical equations used to describe the wavelength dependence of the refractive index in transparent materials, particularly optical glasses and crystals. Named after the German physicist Wolfgang Sellmeier, these equations provide a mathematical model to accurately predict how light propagates through various substances across different wavelengths.

The Sellmeier equations are typically expressed as a sum of terms involving resonant wavelengths, which correspond to the material’s electronic and vibrational absorption bands. The most common form of the Sellmeier equation is:

n²(λ) = 1 + (B₁λ²) / (λ² - C₁) + (B₂λ²) / (λ² - C₂) + (B₃λ²) / (λ² - C₃)

where n(λ) is the refractive index at wavelength λ, and B₁, B₂, B₃, C₁, C₂, C₃ are material-specific coefficients determined experimentally.

Sellmeier coefficients are obtained through precise measurements of refractive indices at various wavelengths, allowing for the creation of accurate dispersion models over wide spectral ranges. These models are essential in designing optical systems such as lenses, prisms, and other optical components, where knowing the refractive index behavior is crucial for managing chromatic aberration and optimizing performance.

The Sellmeier equations are favored over simpler models because they provide a more accurate description of dispersion, especially near absorption bands. They serve as a standard tool in optics research and engineering, facilitating the selection of appropriate materials for specific applications and wavelengths.