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 `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/1464\-4258/9/5/008 `__ **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. 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