Interference in transmission spectra of overlapping Lorentzian lines |
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| Affiliation: | 1. School of Material Science and Engineering, University of Jinan, Jinan 250022, China;2. School of Material Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China;3. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China;1. Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of the Free State, 9300, Bloemfontein, South Africa;2. Moulay University of Meknes, Ismail Faculty of Sciences and Technology, Department de Mathematics B.P. 509, Boutalamine, Errachidia, Morocco |
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| Abstract: | The effect of line overlap on the integrated area between a transmission spectrum and baseline of a system with multiple Lorentzian cross section absorbers has been found to resemble classical optical interference. A generalized analytical expression for the magnitude of the interference effect has been derived and applied to a symmetric doublet system. Results from this particular case illustrate the level of interference with variation of species concentration and ratio of energy separation to line width. In this special case, the interference can be expressed in terms of polynomials based on a phase angle determined solely by the energy separation to linewidth ratio. The coefficients for these polynomial representations of the interference exhibit some interesting mathematical properties and lead to series representations for the symmetric Lorentzian doublet transmission integral and for Mersenne numbers. |
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