mathar_2004 =========== R\. J\. Mathar, "Calculated refractivity of water vapor and moist air in the atmospheric window at 10 um", Appl\. Opt\. 43, 928 \(2004\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/ao\.43\.000928 `__ **Source kind:** theory **Recorded technique:** Line\-by\-line calculation of the dielectric function of water vapour and moist air\: a linear superposition of independent Lorentz oscillators, Eq\. \(1\), eps = 1 \+ \(e^2 / m eps0\) sum\_m N\_m sum\_l f\_ml / \(2 omega\_0ml\) \[1/\(omega \+ omega\_0ml \- i Gamma/2\) \- 1/\(omega \- omega\_0ml \- i Gamma/2\)\], n = sqrt\(eps\), with the oscillator strengths from HITRAN 2000's squared transition moments, f = 2 m c omega\_0 R^2 / \(3 hbar e^2\) \(Eq\. 2\), and the ultraviolet from pseudospectra and measured oscillator\-strength distributions; no fitted parameter \(pp\. 928\-931\)\. **Materials in structured entries:** None recorded. **Dataset quantities:** None recorded. **Contents:** 0 datasets; 0 formulas. Curation notes -------------- Identity VALIDATED\_WITH\_WARNINGS by the library \(no DOI printed; found by title, author and year\); the first page reads Applied Optics, received 30 July 2003, footer 0003\-6935/04/040928\-05\. Journal pages 928\-932 = pdf pages 1\-5\. Nothing is extracted\: the results are figures of air and water vapour \(not curated species\), and this record is cited for method \(TC\-721\)\. THE LINES \(p\. 929\)\. Water\: 31,646 HITRAN lines between 441 nm and 24\.96 mm; CO2\: 27,123 lines between 1\.036 and 22\.6 um \(HITRAN 2000; the 2001 edition's 31,683 water lines differ 'indiscernibly'\)\. Fig\. 1 shows the dispersion of water \(1e23 m^\-3\) with and without CO2 \(7\.076e21 m^\-3\), the only place CO2's infrared contribution appears on its own \(a figure, not digitised\)\. The line list alone leaves out the electronic spectrum; adding Margoliash and Meath's ten water pseudo\-oscillators \(margoliash\_1978, all below 178\.1 nm\) lifts n by about 9e\-7 at 1e23 m^\-3 and brings it to Matsumoto's 3\.4 and 10\.6 um cell data \(Fig\. 2\)\. The HITRAN\-only calculation is valid only beyond about 2\.5 um \(p\. 931\)\. THE AIR MODEL \(Section 4, pp\. 930\-931\)\. N2, O2, H2O and CH4 with ten pseudospectral lines each \(Margoliash and Meath\); CO2 with Padial et al\.'s discrete and continuum transitions; Ar with Eggarter's two lines \(11\.62, 11\.83 eV\), 12 lines of Chan et al\. \(13\.864\-15\.188 eV\) and 450 histogram bins to 500 eV, S\(0\) about 13\.3; Ne from Hibbert et al\. and Chan et al\.; densities of the Very Large Telescope site \(Fig\. 3\: N2 1\.49e25, O2 3\.84e24, Ar 1\.1786e23, CO2 7\.076e21, Ne 3\.44e20, CH4 3\.06e19, O3 2\.23e18, CO 1\.91e18 m^\-3, 746\.64 hPa of dry air\)\. He, N2O, Kr and NH3 add at most 1\.3e\-10, 1\.05e\-10, 3e\-10 and 1e\-10 \(p\. 931\)\. No Lorentz\-Lorenz local field\: eps is linear in the densities, and the author states that the response is linear at all wavelengths\. STATED COMPARISONS\. At 10 um the dry components fall about 1\.6e\-6 below Ciddor's \(1996\) formula at 752\.9 hPa and 1\.5e\-7 below it at 746\.64 hPa \(p\. 931\)\. The 311 and 337 um water refractivities \(\+2\.61e\-5, \+2\.12e\-5\) are within 4 % and 6 % of Bradley and Gebbie's after density scaling \(p\. 929\)\. At 28 um the calculated humid air \(833\.3 hPa, 26 degrees C\) lies about 0\.25e\-4 below Bradley and Gebbie's \(2\.3 \+\- 0\.1\)e\-4, unexplained \(p\. 931\); their pure N2 value 2\.26e\-4 'fits rather well' with the calculated 2\.31e\-4 at 833\.3 hPa\. Check \(2026\-09\-29\)\: fit/N2 gives 2\.2050e\-4 at 28 um, 833\.3 hPa and 26 degrees C, and 2\.3135e\-4 at 12 degrees C \(the temperature of the paper's Fig\. 2\)\: the calculated 2\.31e\-4 matches 12, not 26, degrees C; the paper does not state the temperature of that comparison\. The paper gives no compact representation of the infrared terms\. Its successor, mathar\_2007, adds Lorentz\-Lorenz, virial densities and temperature\-dependent line strengths and publishes polynomial fits\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. 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 :doc:`review register ` for the checks and decisions.