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Faraday modulation spectroscopy: Theoretical description and experimental realization for detection of nitric oxide
Umeå University, Faculty of Science and Technology, Department of Physics. (Laser Physics Group)
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Faraday modulation spectroscopy (FAMOS) is a laser-based spectroscopic dispersion technique for detection of paramagnetic molecules in gas phase. This thesis presents both a new theoretical description of FAMOS and experimental results from the ultra-violet (UV) as well as the mid-infrared (MIR) regions. The theoretical description, which is given in terms of the integrated linestrength and Fourier coefficients of modulated dispersion and absorption lineshape functions, facilitates the description and the use of the technique considerably. It serves as an extension to the existing FAMOS model that thereby incorporates also the effects of lineshape asymmetries primarily originating from polarization imperfections. It is shown how the Fourier coefficients of modulated Lorentzian lineshape functions, applicable to the case with fully collisionally broadened transitions, can be expressed in terms of analytical functions. For the cases where also Doppler broadening needs to be included, resulting in lineshapes of Voigt type, the lineshape functions can be swiftly evaluated (orders of magnitude faster than previous procedures) by a newly developed method for rapid calculation of modulated Voigt lineshapes (the WWA-method). All this makes real-time curve fitting to FAMOS spectra feasible. Two experimental configurations for sensitive detection of nitric oxide (NO) by the FAMOS technique are considered and their optimum conditions are determined. The two configurations target transitions originating from the overlapping Q22(21=2) and QR12(21=2) transitions in the ultra-violet (UV) region (227nm) and the Q3=2(3=2)-transition in the fundamental rotational-vibrational band in the mid-infrared (MIR) region (5.33 µm). It is shown that the implementations of FAMOS in the UV- and MIR-region can provide detection limits in the low ppb range, which opens up the possibility for applications where high detection sensitivities of NO is required.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2013. , 152 p.
Keyword [en]
Faraday modulation spectroscopy (FAMOS), Westberg-Wang-Axner (WWA) method, Fourier coefficients, Lineshape asymmetries, Nitric oxide (NO)
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
URN: urn:nbn:se:umu:diva-68649ISBN: 978-91-7459-616-8 (print)OAI: oai:DiVA.org:umu-68649DiVA: diva2:617183
Public defence
2013-05-14, Naturvetarhuset, N420, Umeå universitet, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2013-04-23 Created: 2013-04-22 Last updated: 2013-04-23Bibliographically approved
List of papers
1. Quantitative description of Faraday modulation spectrometry in terms of the integrated linestrength and 1st Fourier coefficients of the modulated lineshape function
Open this publication in new window or tab >>Quantitative description of Faraday modulation spectrometry in terms of the integrated linestrength and 1st Fourier coefficients of the modulated lineshape function
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2010 (English)In: Journal of Quantitative Spectroscopy and Radiative Transfer, ISSN 0022-4073, E-ISSN 1879-1352, Vol. 111, no 16, 2415-2433 p.Article in journal (Refereed) Published
Abstract [en]

A quantitative description of the strength and shape of Faraday modulation spectrometry (FAMOS) signals is given. It is first shown how the signal can be expressed in terms of the integrated linestrength for the targeted transition, Si,j. Secondly, since the technique relies on a periodic modulation of the transition frequency induced by an alternating magnetic field, it is explicitly shown that it is possible to express the FAMOS signal concisely in terms of 1st Fourier coefficients of a magnetic-field-modulated dispersive lineshape function for left- and right-handed circularly polarized light. Expressions for the FAMOS signal in terms of the integrated linestrength and such Fourier coefficients are given for three cases: (i) for transitions between two arbitrary types of states, (ii) for transitions between two states that both belong to Hund’s coupling case (a), as is the case for rotational–vibrational transitions of NO, and finally (iii) for the commonly used Q-transitions between such states. It is finally shown that the FAMOS signal from a Q-transition can be expressed succinctly solely in terms of one 1st Fourier coefficient. A general analysis of FAMOS addressing an arbitrary Q-transition as well as the most sensitive Q3/2(3/2) transition in NO is given. The conditions for maximum signal are specifically identified.

Place, publisher, year, edition, pages
Elsevier, 2010
Keyword
FAMOS, Faraday rotation spectrometry, Magnetic rotation spectrometry, Integrated linestrength, Fourier coefficient; Nitric oxide (NO)
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-36153 (URN)10.1016/j.jqsrt.2010.06.017 (DOI)000282252500006 ()
Available from: 2010-09-20 Created: 2010-09-20 Last updated: 2013-04-23Bibliographically approved
2. Faraday modulation spectrometry of nitric oxide addressing its electronic X2Π − A2Σ+ band: I. theory
Open this publication in new window or tab >>Faraday modulation spectrometry of nitric oxide addressing its electronic X2Π − A2Σ+ band: I. theory
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2010 (English)In: Applied Optics, ISSN 0003-6935, E-ISSN 1539-4522, Vol. 49, no 29, 5597-5613 p.Article in journal (Refereed) Published
Abstract [en]

We give a simple two-transition model of Faraday modulation spectrometry (FAMOS) addressing the electronic X2Π(ν''=0) − A2Σ+(ν'=0) band in nitric oxide. The model is given in terms of the integrated line strength, S, and first Fourier coefficients for the magnetic-field-modulated dispersive line shape function. Although the two states addressed respond differently to the magnetic field (they adhere to the dissimilar Hund coupling cases), it is shown that the technique shares some properties with FAMOS when rotational-vibrational Q-transitions are targeted: the line shapes have a similar form and the signal strength has an analogous magnetic field and pressure dependence. The differences are that the maximum signal appears for larger magnetic field amplitudes and pressures, ∼1500 G and ∼200 Torr, respectively.

Place, publisher, year, edition, pages
OSA, The Optical Society, 2010
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-37867 (URN)10.1364/AO.49.005597 (DOI)000282685300012 ()
Available from: 2010-11-17 Created: 2010-11-17 Last updated: 2013-04-23Bibliographically approved
3. Faraday modulation spectrometry of nitric oxide addressing its electronic X2Π - A2Σ+ band: II. experiment
Open this publication in new window or tab >>Faraday modulation spectrometry of nitric oxide addressing its electronic X2Π - A2Σ+ band: II. experiment
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2010 (English)In: Applied Optics, ISSN 0003-6935, E-ISSN 1539-4522, Vol. 49, no 29, 5614-5625 p.Article in journal (Refereed) Published
Abstract [en]

A first demonstration of Faraday modulation spectrometry (FAMOS) of nitric oxide (NO) addressing its strong electronic X2Π(ν″=0)−A2Σ+=0) band is presented. The instrumentation was constructed around a fully diode-laser-based laser system producing mW powers of ultraviolet light targeting the overlapping Q22(21/2) and R12Q(21/2) transitions at ∼226.6nm. The work verifies a new two-transition model of FAMOS addressing the electronic transitions in NO given in an accompanying work. Although the experimental instrumentation could address neither the parameter space of the theory nor the optimum conditions, the line shapes and the pressure dependence could be verified under low-field conditions. NO could be detected down to a partial pressure of 13µTorr, roughly corresponding to 10ppb·m for an atmospheric pressure sample, which demonstrates the feasibility of FAMOS for sensitive detection of NO addressing its strong electronic band. A first demonstration of Faraday modulation spectrometry (FAMOS) of nitric oxide (NO) addressing its srtong electronic X2Π - A2Σ+ band is presented. The instrumentation was constructed around a fully diode-laser-based laser system producing mW powers of ultraviolet light targeting the overlapping Q22(21) and QR12(21) transitions at around 226.6 nm. The work verifies a new two-transition model of FAMOS addressing the electronic transitions in NO given in an accompanying work. Although the experimental instrumentation could address neither the parameter space of the theory nor the optimum conditions, the line shapes and the pressure dependence could be verified under low-field conditions. NO could be detected down to a partial pressure of 13 μTorr, roughly corresponding to 10 ppb · mfor an atmospheric pressure sample, which demonstrates the feasibility of FAMOS for sensitive detection of NO addressing its strong electronic band.

Place, publisher, year, edition, pages
OSA, The Optical Society of America, 2010
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-38881 (URN)10.1364/AO.49.005614 (DOI)000282685300013 ()
Available from: 2011-01-10 Created: 2011-01-07 Last updated: 2013-04-23Bibliographically approved
4. Faraday rotation spectrometer with sub-second response time for detection of nitric oxide using a cw DFB quantum cascade laser at 5.33 µm
Open this publication in new window or tab >>Faraday rotation spectrometer with sub-second response time for detection of nitric oxide using a cw DFB quantum cascade laser at 5.33 µm
2011 (English)In: Applied physics. B, Lasers and optics (Print), ISSN 0946-2171, E-ISSN 1432-0649, Vol. 103, no 2, 451-459 p.Article in journal (Refereed) Published
Abstract [en]

A Faraday modulation spectrometer for sensitive and fast detection of nitric oxide at 5.33 μm utilizing a room temperature continuous wave distributed feedback quantum cascade laser and a Peltier cooled MCT detector is presented. The magnetic field was modulated at 7.4 kHz whereas the laser wavelength was scanned at 20 Hz across the most favorable rotational-vibrational transition for FAMOS, Q3/2(3/2), at 5.33 μm. Using a 15 cm optical path and lineshape fitting, the spectrometer provides a detection limit of 4.5 ppb for a response time of 1 s. An Allan variance analysis demonstrates that the system has an excellent stability, up to several hours of operation.

Place, publisher, year, edition, pages
Springer, 2011
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-51793 (URN)10.1007/s00340-010-4336-8 (DOI)
Available from: 2012-02-08 Created: 2012-02-02 Last updated: 2017-12-08Bibliographically approved
5. Analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function
Open this publication in new window or tab >>Analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function
2011 (English)In: Journal of Quantitative Spectroscopy and Radiative Transfer, ISSN 0022-4073, E-ISSN 1879-1352, Vol. 112, no 9, 1443-1449 p.Article in journal (Refereed) Published
Abstract [en]

Modulated spectroscopic detection techniques that rely on dispersion, e.g. Faraday modulation/rotation spectroscopy and wavelength-modulated noise-immune cavity-enhanced optical heterodyne molecular spectroscopy, are often described in terms of Fourier coefficients of a modulated dispersion lineshape function. This work derives a non-complex analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function. The expression is easier to implement, and orders of magnitude faster to execute, than previous approaches involving numerical calculations of integrals. The first six Fourier coefficients are explicitly given and illustrated for their optimum modulation amplitudes, which are also given

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
Modulated Lorentzian dispersion lineshape, Fourier coefficient, Phase-sensitive detection, Faraday modulation/rotation spectrometry, FAMOS/FRS, NICE-OHMS
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-51808 (URN)10.1016/j.jqsrt.2011.02.007 (DOI)
Available from: 2012-02-07 Created: 2012-02-02 Last updated: 2017-12-08Bibliographically approved
6. Fast and non-approximate methodology for calculation of wavelength-modulated Voigt lineshape functions suitable for real-time curve fitting
Open this publication in new window or tab >>Fast and non-approximate methodology for calculation of wavelength-modulated Voigt lineshape functions suitable for real-time curve fitting
2012 (English)In: Journal of Quantitative Spectroscopy and Radiative Transfer, ISSN 0022-4073, E-ISSN 1879-1352, Vol. 113, no 16, 2049-2057 p.Article in journal (Refereed) Published
Abstract [en]

Wavelength modulation (WM) produces lock-in signals that are proportional to various Fourier coefficients of the modulated lineshape function of the molecular transition targeted. Unlike the case for the Lorentzian lineshape function, there is no known analytical expression for the Fourier coefficients of a modulated Voigt lineshape function; they consist of nested integrals that have to be solved numerically, which is often time-consuming and prevents real-time curve fitting. Previous attempts to overcome these limitations have so far consisted of approximations of the Voigt lineshape function, which brings in inaccuracies. In this paper we demonstrate a new means to calculate the lineshape of nf-WM absorption signals from a transition with a Voigt profile. It is shown that the signal can conveniently be expressed as a convolution of one or several Fourier coefficients of a modulated Lorentzian lineshape function, for which there are analytical expressions, and the Maxwell-Boltzmann velocity distribution for the system under study. Mathematically, the procedure involves no approximations, wherefore its accuracy is limited only by the numerical precision of the software used (in this case similar to 10(-16)) while the calculation time is reduced by roughly three orders of magnitude (10(-3)) as compared to the conventional methodology, i.e. typically from the second to the millisecond range. This makes feasible real-time curve fitting to lock-in output signals from modulated Voigt profiles. (C) 2012 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
Oxford: Elsevier, 2012
Keyword
Voigt lineshape, Wavelength modulation, 2f-signal, Convolution, TDLAS
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-61349 (URN)10.1016/j.jqsrt.2012.05.023 (DOI)000309574400009 ()
Available from: 2012-11-20 Created: 2012-11-12 Last updated: 2017-12-07Bibliographically approved
7. Lineshape asymmetries in Faraday modulation spectroscopy
Open this publication in new window or tab >>Lineshape asymmetries in Faraday modulation spectroscopy
2014 (English)In: Applied physics. B, Lasers and optics (Print), ISSN 0946-2171, E-ISSN 1432-0649, Vol. 116, no 2, 467-476 p.Article in journal (Refereed) Published
Abstract [en]

Faraday modulation/rotation spectroscopy (FAMOS/FRS) is a spectroscopic technique for detection of paramagnetic species in gas phase. Although the prevailing theoretical description predicts fully symmetrical lineshapes, experiments do not in general provide such. This work shows that asymmetries in FAMOS can have at least two origins; (i) a frequency dependent laser intensity and (ii) polarization imperfections, which both are scrutinized here. A general analytical description for the latter, derived under the assumption that both the polarization imperfections and the relative absorption are small, is presented, conveniently expressed in terms of 1st Fourier coefficients of modulated dispersion and absorption lineshape functions. The resulting expression, which is thus an extension to the conventional FAMOS expression, can thereby be swiftly evaluated and allows for on-line fitting to measured asymmetric FAMOS signals. Curve fits to experimentally obtained data from nitric oxide measured both in the ultra-violet and the mid-infrared region demonstrate the applicability of the methodology.

Place, publisher, year, edition, pages
Berlin/Heidelberg: Springer, 2014
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-68500 (URN)10.1007/s00340-013-5721-x (DOI)000339727000025 ()
Available from: 2013-04-22 Created: 2013-04-22 Last updated: 2017-12-06Bibliographically approved
8. Methodology for fast curve fitting to modulated Voigt dispersion lineshape functions
Open this publication in new window or tab >>Methodology for fast curve fitting to modulated Voigt dispersion lineshape functions
2014 (English)In: Journal of Quantitative Spectroscopy and Radiative Transfer, ISSN 0022-4073, E-ISSN 1879-1352, Vol. 133, 244-250 p.Article in journal (Refereed) Published
Abstract [en]

Faraday rotation spectroscopy (FAMOS) as well as other modulated techniques that rely on dispersion produce lock-in signals that are proportional to various Fourier coefficients of modulated dispersion lineshape functions of the molecular transition targeted. In order to enable real-time curve fitting to such signals a fast methodology for calculating the Fourier coefficients of modulated lineshape functions is needed. Although there exist an analytical expression for such Fourier coefficients of modulated Lorentzian absorption and dispersion lineshape functions, there is no corresponding expression for a modulated Voigt dispersion function. The conventional computational route of such Fourier coefficients has therefore so far either consisted of using various approximations to the modulated Voigt lineshape function or solving time-consuming integrals, which has precluded accurate real-time curve fitting. Here we present a new methodology to calculate Fourier coefficients of modulated Voigt dispersion lineshape functions that is significantly faster (several orders of magnitude) and more accurate than previous approximative calculation procedures, which allows for real-time curve fitting to FAMOS signals also in the Voigt regime.

Place, publisher, year, edition, pages
Elsevier, 2014
Keyword
Faraday rotation, Faraday modulation, Spectroscopy, Quantum cascade laser
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:umu:diva-68648 (URN)10.1016/j.jqsrt.2013.08.008 (DOI)
Available from: 2013-04-22 Created: 2013-04-22 Last updated: 2017-12-06Bibliographically approved

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