Abstract
We present a compact, uniform generalized Sellmeier-equation (GSE) description of air refraction and its dispersion that remains highly accurate within an ultrabroad spectral range from the ultraviolet to the long-wavelength infrared. While the standard Sellmeier equation (SSE) for atmospheric air is not intended for the description of air refractivity in the mid-infrared and long-wavelength infrared, failing beyond, roughly 2.5 μm, our generalization of this equation is shown to agree remarkably well with full-scale air-refractivity calculations involving over half a million atmospheric absorption lines, providing a highly accurate description of air refractivity in the range of wavelengths from 0.3 to 13 μm. With its validity range being substantially broader than the applicability range of the SSE and its accuracy being at least an order of magnitude higher than the accuracy that the SSE can provide even within its validity range, the GSE-based approach offers a powerful analytical tool for the rapidly progressing mid- and long-wavelength-infrared optics of the atmosphere.
Highlights
We present a compact, uniform generalized Sellmeier-equation (GSE) description of air refraction and its dispersion that remains highly accurate within an ultrabroad spectral range from the ultraviolet to the long-wavelength infrared
With its validity range being substantially broader than the applicability range of the standard Sellmeier equation (SSE) and its accuracy being at least an order of magnitude higher than the accuracy that the SSE can provide even within its validity range, the GSE-based approach offers a powerful analytical tool for the rapidly progressing mid- and long-wavelength-infrared optics of the atmosphere
To quantify the accuracy of the GSE approximation of Eq (5), we introduce the approximation errors η = nGSE − nFMA and ζ = (k2)GSE − (k2)full-model analysis (FMA) where nGSE and (k2)GSE are the refractive index and the group-velocity dispersion (GVD) calculated with the use of the GSE of Eq (5) and nFMA and (k2)FMA are the refractive index and the GVD calculated with the FMA of Eq (1) including the entire manifold of a total of about 650,000 high-resolution transmission molecular absorption (HITRAN)-database atomic and molecular transitions in atmospheric air
Summary
The Sellmeier equation of the form of Eq (2) including only two UV resonant terms with B1 = 0.05792105 μm−2, B2 = 0.00167917 μm−2, C1 = 238.0185 μm−2, and C2 = 57.362 μm−2 is known to provide a highly accurate description of the refractive index of atmospheric air[11,12,13,14,15] This equation with temperature- and humidity-dependent coefficients has been generally accepted and approved (e.g., by the Joint Commission for Spectroscopy, the Advisory Committee for the Definition of Metre, and the Commission of the International Astronomical Union) as a standard for high-precision spectroscopy and interferometry in atmospheric air, as well as for geodetic surveying.
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