Abstract

A modified version of the differential optical absorption spectroscopy (DOAS) method is presented. The technique is called orthogonal optical absorption spectroscopy (OOAS). A widespread variant of DOAS with smoothing of the registered spectrum and absorption cross sections being made employing a polynomial regression is a particular case of OOAS. The concept of OOAS provides a variety of new possibilities for constructing computational schemes and analyzing the influence of different error sources on calculated concentrations.

© 2014 Optical Society of America

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  1. L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
    [CrossRef]
  2. L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
    [CrossRef]
  3. L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
    [CrossRef]
  4. L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.
  5. A. M. Liudchik, “An advanced theory for the multi-wave open path optical absorption spectroscopy measurements,” Int. J. Remote Sens. 34, 1194–1206 (2013).
    [CrossRef]
  6. A. M. Liudchik, “Multiwavelength technique for open-path measurements of the concentrations of atmospheric constituents,” J. Appl. Spectrosc. 79, 477–483 (2012).
    [CrossRef]
  7. U. Platt and D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. A. Killinger and A. Mooradien, eds. (Springer Verlag, 1983), pp. 95–105.
  8. U. Platt, “Differential optical absorption spectroscopy (DOAS),” Chem. Anal. Series 127, 27–83 (1994).
  9. J. Stutz and U. Platt, “Numerical analysis and estimation of the statistical error of differential optical absorption spectroscopy measurements with least-squares methods,” Appl. Opt. 35, 6041–6053 (1996).
    [CrossRef]
  10. U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy: Principles and Applications (Springer-Verlag, 2008).
  11. S. Kraus, DOASIS. A Framework Design for DOAS (Shaker Verlag, 2006).
  12. R. W. Hamming, Digital Filters (Prentice-Hall, 1997).
  13. WMO, “Handbook for Dobson ozone data re-evaluation,” (1993).
  14. J. B. Kerr, C. T. McElroy, and R. A. Olafson, “Measurements of total ozone with the Brewer spectrophotometer,” in Proceedings of the Quadrennial International Ozone Symposium, J. London, ed. (National Center for Atmospheric Research, 1981), pp. 74–79.
  15. R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, 1960).
  16. F. R. Gantmacher, The Theory of Matrices (AMS Chelsea, 2000).

2013

A. M. Liudchik, “An advanced theory for the multi-wave open path optical absorption spectroscopy measurements,” Int. J. Remote Sens. 34, 1194–1206 (2013).
[CrossRef]

2012

A. M. Liudchik, “Multiwavelength technique for open-path measurements of the concentrations of atmospheric constituents,” J. Appl. Spectrosc. 79, 477–483 (2012).
[CrossRef]

2010

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

2008

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

2005

L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
[CrossRef]

1996

1994

U. Platt, “Differential optical absorption spectroscopy (DOAS),” Chem. Anal. Series 127, 27–83 (1994).

Balatsko, L.

L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.

Balatsko, L. M.

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

Bellman, R.

R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, 1960).

Bolot’ko, L. M.

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
[CrossRef]

Demin, V. S.

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

Dziomin, V.

L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.

Dziomin, V. S.

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

Gantmacher, F. R.

F. R. Gantmacher, The Theory of Matrices (AMS Chelsea, 2000).

Hamming, R. W.

R. W. Hamming, Digital Filters (Prentice-Hall, 1997).

Kerr, J. B.

J. B. Kerr, C. T. McElroy, and R. A. Olafson, “Measurements of total ozone with the Brewer spectrophotometer,” in Proceedings of the Quadrennial International Ozone Symposium, J. London, ed. (National Center for Atmospheric Research, 1981), pp. 74–79.

Krasouski, A.

L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.

Krasouski, A. N.

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

Krasovskii, A. N.

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
[CrossRef]

Kraus, S.

S. Kraus, DOASIS. A Framework Design for DOAS (Shaker Verlag, 2006).

Liudchik, A.

L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.

Liudchik, A. M.

A. M. Liudchik, “An advanced theory for the multi-wave open path optical absorption spectroscopy measurements,” Int. J. Remote Sens. 34, 1194–1206 (2013).
[CrossRef]

A. M. Liudchik, “Multiwavelength technique for open-path measurements of the concentrations of atmospheric constituents,” J. Appl. Spectrosc. 79, 477–483 (2012).
[CrossRef]

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

Lyudchik, A. M.

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
[CrossRef]

McElroy, C. T.

J. B. Kerr, C. T. McElroy, and R. A. Olafson, “Measurements of total ozone with the Brewer spectrophotometer,” in Proceedings of the Quadrennial International Ozone Symposium, J. London, ed. (National Center for Atmospheric Research, 1981), pp. 74–79.

Olafson, R. A.

J. B. Kerr, C. T. McElroy, and R. A. Olafson, “Measurements of total ozone with the Brewer spectrophotometer,” in Proceedings of the Quadrennial International Ozone Symposium, J. London, ed. (National Center for Atmospheric Research, 1981), pp. 74–79.

Pakatashkin, V.

L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.

Pakatashkin, V. I.

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

Perner, D.

U. Platt and D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. A. Killinger and A. Mooradien, eds. (Springer Verlag, 1983), pp. 95–105.

Platt, U.

J. Stutz and U. Platt, “Numerical analysis and estimation of the statistical error of differential optical absorption spectroscopy measurements with least-squares methods,” Appl. Opt. 35, 6041–6053 (1996).
[CrossRef]

U. Platt, “Differential optical absorption spectroscopy (DOAS),” Chem. Anal. Series 127, 27–83 (1994).

U. Platt and D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. A. Killinger and A. Mooradien, eds. (Springer Verlag, 1983), pp. 95–105.

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy: Principles and Applications (Springer-Verlag, 2008).

Pokatashkin, V. I.

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
[CrossRef]

Stutz, J.

Appl. Opt.

Chem. Anal. Series

U. Platt, “Differential optical absorption spectroscopy (DOAS),” Chem. Anal. Series 127, 27–83 (1994).

Int. J. Remote Sens.

A. M. Liudchik, “An advanced theory for the multi-wave open path optical absorption spectroscopy measurements,” Int. J. Remote Sens. 34, 1194–1206 (2013).
[CrossRef]

L. M. Balatsko, V. S. Dziomin, A. N. Krasouski, A. M. Liudchik, and V. I. Pakatashkin, “Theory of multiwave differential optical absorption spectroscopy surface ozone measurement with open path meters,” Int. J. Remote Sens. 31, 523–529 (2010).
[CrossRef]

J. Appl. Spectrosc.

L. M. Bolot’ko, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Measurement of the terrestrial ozone concentration by absorption UV spectroscopy,” J. Appl. Spectrosc. 72, 911–916 (2005).
[CrossRef]

L. M. Bolot’ko, V. S. Demin, A. N. Krasovskii, A. M. Lyudchik, and V. I. Pokatashkin, “Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system,” J. Appl. Spectrosc. 75, 268–274 (2008).
[CrossRef]

A. M. Liudchik, “Multiwavelength technique for open-path measurements of the concentrations of atmospheric constituents,” J. Appl. Spectrosc. 79, 477–483 (2012).
[CrossRef]

Other

U. Platt and D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. A. Killinger and A. Mooradien, eds. (Springer Verlag, 1983), pp. 95–105.

L. Balatsko, V. Dziomin, A. Krasouski, A. Liudchik, and V. Pakatashkin, “Multi-wave differential optical absorption spectroscopy surface ozone measurement with open path meters,” in Advances in Measurement Systems, M. Kr. Sharma, ed. (InTech, 2010), pp. 538–560.

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy: Principles and Applications (Springer-Verlag, 2008).

S. Kraus, DOASIS. A Framework Design for DOAS (Shaker Verlag, 2006).

R. W. Hamming, Digital Filters (Prentice-Hall, 1997).

WMO, “Handbook for Dobson ozone data re-evaluation,” (1993).

J. B. Kerr, C. T. McElroy, and R. A. Olafson, “Measurements of total ozone with the Brewer spectrophotometer,” in Proceedings of the Quadrennial International Ozone Symposium, J. London, ed. (National Center for Atmospheric Research, 1981), pp. 74–79.

R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, 1960).

F. R. Gantmacher, The Theory of Matrices (AMS Chelsea, 2000).

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Equations (52)

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I(λ)=I0(λ)exp[τ(λ)].
S(λ)=γ(λ)I0(λ)exp[τp(λ)τx(λ)].
τx(λ)=i=1MCi(λ)Xi
Z(λ)=lnS(λ),
R^Z(λ)=R^(lnγ(λ))+R^(lnI0(λ))R^τp(λ)R^τx(λ).
τd(λ)R^τx(λ)=τx(λ)τx(λ)
τd(λ)=X˜Cd(λ)=X˜[R^C(λ)]=X˜[C(λ)C(λ)].
(A·B)n=1NA(λn)B(λn),
Z(λ)=lnγ(λ)+lnI0(λ)τp(λ)X˜C(λ).
C(λ)=Cs(λ)+Co(λ),
Q(λ)=lnγ(λ)+lnI0(λ)τp(λ).
Z(λ)=Q(λ)X˜Cs(λ)X˜Co(λ).
Q(λ)=k=1Kakψk(λ).
Q(λ)=k=1Kakψk(λ)+δQ(λ),
Z(λ)=k=1Kakψk(λ)X˜Cs(λ)X˜Co(λ).
Skl=(ψk·ψl).
Cio(λ)=Ci(λ)k,l=1K(ψk·Ci)Skl1ψl(λ).
(Cio·ψm)=(Ci·ψm)k,l=1K(ψk·Ci)Skl1(ψl·ψm)=(Ci·ψm)k,l=1K(ψk·Ci)Skl1Slm=(Ci·ψm)k=1K(ψk·Ci)δkm=(Ci·ψm)(Ci·ψm)=0.
(Cis·Cjo)0.
(Z·Cio)=j=1M(Cio·Cjo)Xj,
Z=DX,
D=(Co·C˜o),
Z=n=1NZ(λn)Co(λn)=(Z·Co).
X=D1Z.
δX=D1δQ,
δQ(λ)=Xy[Cy(λ)k,l=1N(ψk·Cy)Skl1ψl(λ)],
A(λ)=l=1K(A·φl)sl1φl(λ).
A(λ)=l,m=1K(A·ψl)Slm1ψm(λ),
A(λ)=lzK(A·φl)sl1φl(λ).
Skl+=mzKVmksm1Vml,
Zc(λ)=k,l=1K(ψk·Z)Skl1ψl(λ)X˜Co(λ),
ΔZ(λ)=Z(λ)Zc(λ).
δZ(λ)=ε(λ),
δX=D1δZ,
Zc(λ)=Zc(λ)+k,lK(ψk·δZ)Skl1ψl(λ)C˜o(λ)D1δZ.
ΔZ(λ)=Z(λ)Zc(λ)=δZ(λ)k,lK(ψk·δZ)Skl1ψl(λ)+C˜o(λ)D1(δZ·Co).
σΔZ2=(1/N)(ΔZ·ΔZ)=(1/N)(δZ·δZ)(1/N)δZ˜D1δZ(1/N)k,lK(δZ·ψk)Skl1(δZ·ψl).
UZ(λ)2=[δZ(λ)]2¯,
UZ(λ)2=u2(λ),
UXi2=δXi2¯=k,lKDik1Dil1δZkδZl¯.
UZ(λ)2=UZ2=const(λ),
δZkδZl¯=n,mNδZ(λn)δZ(λm)¯Cko(λn)Clo(λm)=nNδZ(λn)2¯Cko(λn)Clo(λn)=UZ2(Cko·Clo)=DklUZ2.
UXi2=Dii1UZ2.
UΔZ2=σΔZ2¯=N(M+K)NUZ20.
δX=D1[δZδDX],
δD(δCo·C˜o)(Co·δC˜o),δZ=(Z·δCo).
δCio(λ)=δCi(λ)k,l=1K(ψk·δCi)Skl1ψl(λ).
δDX(δCo·C˜o)X(Co·δC˜o)X.
δZ=([X˜Co]·δCo).
δX=D1([X˜δCo]·Co).
ΔZ(λ)={Z(λ)k,l=1K(ψk·Z)Skl1ψl(λ)+X˜Co(λ)}+X˜δCo(λ)+δX˜Co(λ),
ΔZ(λ)=X˜δCo(λ)+δX˜Co(λ)=X˜δCo(λ)+([X˜δCo]·C˜o)D1Co(λ).

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