mathar_2007#

R. J. Mathar, “Refractive index of humid air in the infrared: model fits”, J. Opt. A: Pure Appl. Opt. 9, 470 (2007)

Source record · Catalogue · Review register

Source kind: fit

Recorded technique: Least-squares fits of polynomials to a line-by-line calculation of the refractive index of humid air (mathar_2004’s method, with the HITRAN 2004 list updated to August 2006): chi_m of each species from its line intensities (Eq. 2), combined by Lorentz-Lorenz (Eq. 4), with virial densities and temperature-dependent line strengths, for 10-25 degrees C, 500-1023 hPa and 5-60 % relative humidity at a fixed 370 ppm CO2; fitted by a fifth-degree polynomial in wavenumber in each of five infrared windows with coefficients quadratic in 1/T, p and H (Eqs. 5-6, Tables 1-5; pp. 470-475).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes#

Identity VALIDATED. Journal pages 470-476 = pdf pages 2-8 (pdf page 1 is the publisher’s cover sheet). Nothing is extracted: the fits are of moist air, which is not a curated species, and their coefficients are not refractive-index data of a species (TC-722).

THE CALCULATION (Section 2, pp. 470-471). chi_m(omega) = 2 N_m c^2 sum_l (S_ml / omega_0ml) [1/(omega + omega_0ml - i Gamma/2) - 1/(omega - omega_0ml - i Gamma/2)] (Eq. 2), S_ml the line intensities, for N2, O2, Ar, Ne, CO2, H2O, O3, CH4 and CO; the macroscopic chi = sum chi_m / (1 - sum chi_m / 3) (Eq. 4, Lorentz-Lorenz, about 2e-8 in n); real-gas densities (second virials of N2 about -7.5e-6 and O2 about -1.9e-5 m^3/mol at 12 degrees C: 2e-4 in density and refractivity; water from Wagner and Pruss); line strengths scaled line by line with temperature (changes below 2e-9 in c_0ref, below 3e-5 K in c_0T); widths left at HITRAN’s 1 atm values; O2’s magnetic-dipole lines included; volume susceptibility of dry air about 3.7e-7 at 1013 hPa. The relative accuracy of the calculated susceptibility is estimated at 2e-4 (p. 470).

THE FITS (Eqs. 5-6, p. 471; Tables 1-5, pp. 472-473). n - 1 = sum_{j=0..5} c_j(T, p, H) (sigma - sigma_ref)^j, sigma in cm^-1, with c_j = c_jref + c_jT (1/T - 1/T_ref) + c_jTT (1/T - 1/T_ref)^2 + c_jH (H - H_ref) + c_jHH (H - H_ref)^2 + c_jp (p - p_ref) + c_jpp (p - p_ref)^2 + c_jTH (1/T - 1/T_ref)(H - H_ref) + c_jTp (1/T - 1/T_ref)(p - p_ref) + c_jHp (H - H_ref)(p - p_ref); T_ref = 290.65 K (17.5 degrees C), p_ref = 75,000 Pa, H_ref = 10 % relative humidity. Windows and sigma_ref (vacuum wavelength 1e4/sigma_ref um): Table 1, 1.3-2.5 um, 2.25; Table 2, 2.8-4.2 um, 3.4; Table 3, 4.35-5.2 um, 4.8; Table 4, 7.5-14.1 um, 10.1; Table 5, 16-24 um, 20. Printed c_0ref (n - 1 at the reference conditions and sigma_ref): 0.200192e-3, 0.200049e-3, 0.200020e-3, 0.199885e-3, 0.199436e-3 (Tables 1-5, cells checked against tbl_07ea871716f6, tbl_fcbe84f7dc81, tbl_593b3ec40c45, tbl_2bdb93f28b56, tbl_e82d13934a0a; the library’s text rendering attaches no caption to Tables 3 and 5, whose captions and sigma_ref were checked on the page). The CO2 fraction is fixed at 370 ppm and enters no coefficient: no term gives CO2’s (or water’s) contribution on its own.

ON POLES (p. 473): the polynomial has ‘artificial wiggles’; at any fixed (T, p, H) ‘a Sellmeier format with two resonances’ (Peck 1983) fits the raw data better, but expanding its five parameters in T, p and H ‘did not achieve competitive stability’, so it is not given.

COMPARISONS STATED (Section 4, pp. 473-475). The raw theory lies about 4e-8 above dry air measured in the visible and near infrared (Peck and Reeder; Fig. 1), about 0.8e-8 of it from the temperature scale and 1e-8 from Peck and Reeder’s lower CO2 (300 ppm); Table 4’s pressure coefficient at 10.57 um and 23 degrees C (0.2618e-8 per Pa) is 6e-3 below Marchetti and Simili’s 0.2633e-8 per Pa, within their 5e-3; within 3.5e-8 of Bonsch and Potulski’s humid air at 508.7 and 644 nm (Fig. 2); about 1e-8 from Matsumoto’s water vapour and moist air at 3.4 um (Figs. 3, 4).

CHECK (computed 2026-09-29, a comparison, not a reproduction). Tables 1-5 at 17.5 degrees C, 750 hPa and H = 0 (a linear extrapolation from the fitted 5-60 %), against optmat’s dry air: the stored fits of the CIPM-2007 constituents (picard_2008) with CO2 set to 370 ppm, combined by Lorentz-Lorenz at CoolProp’s density of air. Level: Mathar’s n - 1 is higher by 5.4e-8 (2.7e-4 relative) over 1.3-2.5 um, 5.1e-8 at 3.5 um, 6.2e-8 at 4.8 um, 7.8e-8 at 10.8 um and 16e-8 at 20 um; at 15 degrees C and 1013.25 hPa (outside the fitted pressures) 5.0e-8 at 1.3-1.7 um, where the same optmat sum lies 3.0e-8 below Edlen’s 1966 standard air (edlen_1966, whose level is uncertain by +-5e-8). Dispersion within each window (n - 1 relative to its value at sigma_ref): agrees within 0.23e-8 over 1.3-2.5 um and 0.34e-8 over 4.49-5.2 um, within 1.4e-8 over 3.0-4.0 um; it departs by 1.9e-8 at 2.8 um, 3.4e-8 at 4.2 um and 2.1e-8 at 4.35 um (the edges of the 2.7 and 4.3 um bands), from -1.25e-8 at 7.5 um to +2.4e-8 at 14.1 um, and by -3.4e-8 to +7.1e-8 over 16-24 um (next to CO2’s 15 um band). At 370 ppm CO2’s own infrared term is 1e-9 to 6e-8 of n - 1 inside the windows (optmat: -1.0e-9 at 1.5 um, -1.4e-8 at 3.5 um, +3.0e-8 at 4.8 um, +1.9e-9 at 10.1 um, -4.5e-8 at 14.1 um) and 1.5-2.2e-7 at 4.35 and 4.2 um (4.2 um, 2381 cm^-1, lies inside the 4.3 um band’s R branch): the fits test optmat’s CO2 bands only to about 1e-8, and not at the band edges, where the polynomials’ wiggles and the one pole per band both fail.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

No datasets are recorded.

Formulas#

No formulas are recorded.

Corrections#

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.