Abstract

We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and “log after averaging”, or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of “averaging before log”.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011

K. Numata, J. R. Chen, S. T. Wu, J. B. Abshire, and M. A. Krainak, “Frequency stabilization of distributed-feedback laser diodes at 1572 nm for lidar measurements of atmospheric carbon dioxide,” Appl. Opt.50(7), 1047–1056 (2011).
[CrossRef] [PubMed]

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

2010

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt.49(25), 4801–4807 (2010).
[CrossRef] [PubMed]

2009

J. Caron and Y. Durand, “Operating wavelengths optimization for a spaceborne lidar measuring atmospheric CO2.,” Appl. Opt.48(28), 5413–5422 (2009).
[CrossRef] [PubMed]

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

J. Caron, Y. Durand, J. L. Bezy, and R. Meynart, “Performance modeling for A-SCOPE, a spaceborne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E-1 (2009).
[CrossRef]

2008

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

2005

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

2004

1999

1990

N. Z. Hakim, B. E. A. Saleh, and M. C. Teich, “Generalized excess noise factor for avalanche photodiodes of arbitrary structure,” IEEE Trans. Electron. Dev.37(3), 599–610 (1990).
[CrossRef]

1989

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol.7(7), 1071–1082 (1989).
[CrossRef]

1988

F. Koyama and K. Oga, “Frequency chirping in external modulators,” J. Lightwave Technol.6(1), 87–93 (1988).
[CrossRef]

1987

1982

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A26(1), 12–18 (1982).
[CrossRef]

W. B. Grant, “Effect of differential spectral reflectance on DIAL measurements using topographic targets,” Appl. Opt.21(13), 2390–2394 (1982).
[CrossRef] [PubMed]

1981

R. N. Clark, “Water frost and ice: the near-infrared spectral reflectance 0.65–2.5 μm,” J. Geophys. Res.86(B4), 3087–3096 (1981).
[CrossRef]

1974

L. Mandel, “Interpretation of instantaneous frequency,” Am. J. Phys.42(10), 840–846 (1974).
[CrossRef]

1959

L. Mandel, “Fluctuations of photon beams: the distribution of the photo-electrons,” Proc. Phys. Soc.74(3), 233–243 (1959).
[CrossRef]

Abshire, J. B.

K. Numata, J. R. Chen, S. T. Wu, J. B. Abshire, and M. A. Krainak, “Frequency stabilization of distributed-feedback laser diodes at 1572 nm for lidar measurements of atmospheric carbon dioxide,” Appl. Opt.50(7), 1047–1056 (2011).
[CrossRef] [PubMed]

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Allan, G. R.

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Alpers, M.

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

Amediek, A.

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

Arnaud, Y.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Beck, J. D.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Besnard, P.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

Bezy, J. L.

J. Caron, Y. Durand, J. L. Bezy, and R. Meynart, “Performance modeling for A-SCOPE, a spaceborne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E-1 (2009).
[CrossRef]

Biraud, S.

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Blin, S.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

Brissaud, O.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Caron, J.

J. Caron and Y. Durand, “Operating wavelengths optimization for a spaceborne lidar measuring atmospheric CO2.,” Appl. Opt.48(28), 5413–5422 (2009).
[CrossRef] [PubMed]

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

J. Caron, Y. Durand, J. L. Bezy, and R. Meynart, “Performance modeling for A-SCOPE, a spaceborne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E-1 (2009).
[CrossRef]

Chen, J. R.

Clark, R. N.

R. N. Clark, “Water frost and ice: the near-infrared spectral reflectance 0.65–2.5 μm,” J. Geophys. Res.86(B4), 3087–3096 (1981).
[CrossRef]

Collatz, G. J.

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

Deniel, C.

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

Di Domenico, G.

Dumont, M.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Durand, Y.

J. Caron, Y. Durand, J. L. Bezy, and R. Meynart, “Performance modeling for A-SCOPE, a spaceborne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E-1 (2009).
[CrossRef]

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

J. Caron and Y. Durand, “Operating wavelengths optimization for a spaceborne lidar measuring atmospheric CO2.,” Appl. Opt.48(28), 5413–5422 (2009).
[CrossRef] [PubMed]

Ehret, G.

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

Elliott, D. S.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A26(1), 12–18 (1982).
[CrossRef]

Fix, A.

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

Flamant, P.

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

Gallet, J. C.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Gleckler, A. D.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Grant, W. B.

Gudimetla, V. S. R.

Hakim, N. Z.

N. Z. Hakim, B. E. A. Saleh, and M. C. Teich, “Generalized excess noise factor for avalanche photodiodes of arbitrary structure,” IEEE Trans. Electron. Dev.37(3), 599–610 (1990).
[CrossRef]

Hasselbrack, W. E.

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Houweling, S.

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

Kavaya, M. J.

Kawa, S. R.

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

J. Mao and S. R. Kawa, “Sensitivity studies for space-based measurement of atmospheric total column carbon dioxide by reflected sunlight,” Appl. Opt.43(4), 914–927 (2004).
[CrossRef] [PubMed]

Kiemle, C.

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

Koyama, F.

F. Koyama and K. Oga, “Frequency chirping in external modulators,” J. Lightwave Technol.6(1), 87–93 (1988).
[CrossRef]

Krainak, M. A.

Mandel, L.

L. Mandel, “Interpretation of instantaneous frequency,” Am. J. Phys.42(10), 840–846 (1974).
[CrossRef]

L. Mandel, “Fluctuations of photon beams: the distribution of the photo-electrons,” Proc. Phys. Soc.74(3), 233–243 (1959).
[CrossRef]

Mao, J.

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

J. Mao and S. R. Kawa, “Sensitivity studies for space-based measurement of atmospheric total column carbon dioxide by reflected sunlight,” Appl. Opt.43(4), 914–927 (2004).
[CrossRef] [PubMed]

Martin, R. J.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Meynart, R.

J. Caron, Y. Durand, J. L. Bezy, and R. Meynart, “Performance modeling for A-SCOPE, a spaceborne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E-1 (2009).
[CrossRef]

Millet, B.

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

Milton, M. J. T.

Mitra, P.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Numata, K.

Oga, K.

F. Koyama and K. Oga, “Frequency chirping in external modulators,” J. Lightwave Technol.6(1), 87–93 (1988).
[CrossRef]

Olsson, N. A.

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol.7(7), 1071–1082 (1989).
[CrossRef]

Picard, G.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Riris, H.

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Roy, R.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A26(1), 12–18 (1982).
[CrossRef]

Saleh, B. E. A.

N. Z. Hakim, B. E. A. Saleh, and M. C. Teich, “Generalized excess noise factor for avalanche photodiodes of arbitrary structure,” IEEE Trans. Electron. Dev.37(3), 599–610 (1990).
[CrossRef]

Schilt, S.

Schmitt, B.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Scritchfield, R.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Smith, S. J.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A26(1), 12–18 (1982).
[CrossRef]

Stephan, C.

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

Stéphan, G. M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

Strittmatter, R.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Sullivan, W.

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

Sun, X.

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

Tam, T. T.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

Teich, M. C.

N. Z. Hakim, B. E. A. Saleh, and M. C. Teich, “Generalized excess noise factor for avalanche photodiodes of arbitrary structure,” IEEE Trans. Electron. Dev.37(3), 599–610 (1990).
[CrossRef]

Têtu, M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

Thomann, P.

Weaver, C. J.

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Wirth, M.

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

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Wu, S. T.

Am. J. Phys.

L. Mandel, “Interpretation of instantaneous frequency,” Am. J. Phys.42(10), 840–846 (1974).
[CrossRef]

Appl. Opt.

Appl. Phys. B

G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B90(3-4), 593–608 (2008).
[CrossRef]

Atmos. Chem. Phys. Discuss.

M. Dumont, O. Brissaud, G. Picard, B. Schmitt, J. C. Gallet, and Y. Arnaud, “High-accuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths – comparison with modeling results,” Atmos. Chem. Phys. Discuss.9(5), 19279–19311 (2009).
[CrossRef]

Atmos. Meas. Tech.

A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO2,” Atmos. Meas. Tech.2(2), 755–772 (2009).
[CrossRef]

IEEE Trans. Electron. Dev.

N. Z. Hakim, B. E. A. Saleh, and M. C. Teich, “Generalized excess noise factor for avalanche photodiodes of arbitrary structure,” IEEE Trans. Electron. Dev.37(3), 599–610 (1990).
[CrossRef]

J. Geophys. Res.

R. N. Clark, “Water frost and ice: the near-infrared spectral reflectance 0.65–2.5 μm,” J. Geophys. Res.86(B4), 3087–3096 (1981).
[CrossRef]

J. Lightwave Technol.

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol.7(7), 1071–1082 (1989).
[CrossRef]

F. Koyama and K. Oga, “Frequency chirping in external modulators,” J. Lightwave Technol.6(1), 87–93 (1988).
[CrossRef]

Phys. Rev. A

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A26(1), 12–18 (1982).
[CrossRef]

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A71(4), 043809 (2005).
[CrossRef]

Proc. Phys. Soc.

L. Mandel, “Fluctuations of photon beams: the distribution of the photo-electrons,” Proc. Phys. Soc.74(3), 233–243 (1959).
[CrossRef]

Proc. SPIE

J. D. Beck, R. Scritchfield, P. Mitra, W. Sullivan, A. D. Gleckler, R. Strittmatter, and R. J. Martin, “Linear-mode photon counting with the noiseless gain HgCdTe e-APD,” Proc. SPIE8033, 80330N, 80330N–15 (2011).
[CrossRef]

J. Caron, Y. Durand, J. L. Bezy, and R. Meynart, “Performance modeling for A-SCOPE, a spaceborne lidar measuring atmospheric CO2,” Proc. SPIE7479, 74790E-1 (2009).
[CrossRef]

C. Stephan, M. Alpers, B. Millet, G. Ehret, P. Flamant, and C. Deniel, “MERLIN: a space-based methane monitor,” Proc. SPIE8159, 815908, 815908–815915 (2011).
[CrossRef]

Tellus Ser. B, Chem. Phys. Meteorol.

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 759–769 (2010).
[CrossRef]

J. B. Abshire, H. Riris, G. R. Allan, C. J. Weaver, J. Mao, X. Sun, W. E. Hasselbrack, S. R. Kawa, and S. Biraud, “Pulsed airborne lidar measurements of atmospheric CO2 column absorption,” Tellus Ser. B, Chem. Phys. Meteorol.62(5), 770–783 (2010).
[CrossRef]

Other

J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).

J. B. Abshire, H. Riris, G. Allan, X. Sun, S. R. Kawa, J. Mao, M. Stephen, E. Wilson, and M. A. Krainak, “Laser sounder for global measurement of CO2 concentrations in the troposphere from space,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (CD) (Optical Society of America, 2008), paper LMA4.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).

C. Weitkamp, Lidar: Range Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005).

Space Studies Board, National Research Council, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond (National Academies Press, 2007).

“A-SCOPE—advanced space carbon and climate observation of planet earth, report for assessment,” ESA-SP1313/1(European Space Agency, 2008), http://esamultimedia.esa.int/docs/SP1313-1_ASCOPE.pdf .

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Figures (6)

Fig. 1
Fig. 1

The laser transmitter provides the wavelength-stepped pulse train (left) to repeatedly measure at 8 points across the 1572.335 nm CO2 absorption line (right).

Fig. 2
Fig. 2

The nominal laser frequency noise PSD S δν (f)= h 1 /f+ h 0 (solid red) is suppressed to S δν (f)|H(f )| 2 (dotted blue) by averaging within a 1-μs top-hat pulse and further reduced to S δν (f)|H(f )| 2 W avn (f) (dashed black) by averaging across 1000 identical pulses separated by a period of 1 ms.

Fig. 3
Fig. 3

(left) The standard deviation of the absolute frequency of the slave laser and frequency offset between the slave and master lasers measured within a gating time from 1 μs to 1 ms; (right) Both frequencies were also measured periodically within a 1-µs gating time with a 1-ms period and averaged across multiple measurements. The standard deviation of each averaged frequency, computed from 100 averaged samples, is plotted as a function of the number of measurements being averaged.

Fig. 4
Fig. 4

Relative errors for atmospheric CO2 DAOD measurements: (left) (Δτ - Δτ0)/Δτ0 due to the finite linewidth 1/Δt of a top-hat pulse shape (calculated from Eqs. (5) and (6)); (right) laser line-center frequency noise contributions to the RRE for σ(δνnon) = 0.1 MHz (dashed red, calculated from Eq. (21)), and RSE ln(Rb)/Δτ for σ(δν1) = 10 MHz (dotted blue, from Eq. (18)) as functions of the online laser frequency offset from the absorption line center. The two-way optical depth τ (solid green) is also plotted, with blue dots marking the same online and absorption line-center frequency points used on the left.

Fig. 5
Fig. 5

The RRE σ(ΔτSNK2_av) /Δτ for atmospheric CO2 DAOD measurement (solid black) as a function of the two-way optical depth, computed from Eqs. (29) and (30) using parameters listed in Table 2. The blue dots mark the three online frequency points used in Fig. 4. Also plotted are partial contributions to this RRE from the shot noise (solid grey), frequency noise (dashed red), solar background (dotted brown), receiver circuitry noise (dash-dotted green), and detector dark count (long-dashed blue). The standard deviation of the effective frequency noise σ(δνnon) averaged in 10 s is 0.23 MHz for the above calculations. When it is increased to 1 MHz, the RRE (dotted black) rises above the 0.1% target (dashed black).

Fig. 6
Fig. 6

(left) Relative surface reflectance: measured data (grey) and its running average over a length of 50 m (blue), courtesy of A. Amediek of Deutsches Zentrum für Luft- und Raumfahrt (DLR); (right) ln( R A ) calculated from surface reflectance data for the worst case. For each online wavelength channel, two ln( R A ) are calculated from both offline sum i=0 n1 A s off (i) for 1-s averaging time and the average is plotted (blue dot). An average of 10 consecutive ln( R A ) values, each computed as above over 0.1 s averaging time, is also plotted (red square).

Tables (3)

Tables Icon

Table 1 RRE Targets, Relevant Parameters, and Resulting Effective Laser Frequency Noise Requirement for Atmospheric CO2 DAOD Measurement

Tables Icon

Table 2 Parameters Used to Evaluate the RRE of Δτ as a Function of τ

Tables Icon

Table 3 Parameters Used for Evaluation of the Impact of Surface Reflectance Variation

Equations (43)

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u(t)=a(t t 0 )exp( j[2π ν ¯ t+ϕ(t)] ).
ν c ( t 0 ) 0 ν F L N ( ν F )d ν F = ν(t)h(t t 0 )dt .
S δν1 (f)= S δν (f) | H(f) | 2 ,
dL( ν F ,l)=L( ν F ,l) σ 0 ( ν F ,l)N(l)dl.
E(l)=E(0)exp[ τ( ν c ,l) ], τ( ν c ,l) 0 l σ eff ( ν c ,l')N(l')dl' .
σ eff ( ν c ,l) 0 σ 0 ( ν F ,l) L N ( ν F ,l)d ν F = 0 σ 0 ( ν F ,l)T( ν F ,l)L( ν F ,0)d ν F 0 T( ν F ,l)L( ν F ,0)d ν F , T( ν F ,l)exp[ τ 0 ( ν F ,l) ], τ 0 ( ν F ,l) 0 l σ 0 ( ν F ,l')N(l')dl' .
W s = E s A s exp[ τ( ν c ,2 r G ) ],
K ¯ =α W ¯ ,
σ 2 (K)= F e K ¯ + α 2 σ 2 (W).
W s = E s A s exp[ τ( ν ¯ ,2 r G ) ][ 1(dτ/d ν c ) δ ν1 ( t 0 )+b δ ν1 2 ( t 0 ) ],
K s ¯ =α W s ¯ =α E s A s exp[ τ( ν ¯ ,2 r G ) ][ 1+b σ 2 ( δ ν1 ) ],
σ 2 ( K s )= F e K s ¯ + α 2 σ 2 ( W s )= F e K s ¯ + ( K s ¯ ) 2 ( dτ/d ν c ) 2 σ 2 ( δ ν1 ),
S NE1 i=0 n1 W s (i) E s (i) =exp[ τ( ν ¯ ,2 r G ) ]( i=0 n1 A s (i) )[ 1 dτ d ν c δ νn (t)+b Q n (t) ], Q n (t) 1 i=0 n1 A s (i) i=0 n1 [ A s (i) δ ν1 2 (t+i× t p ) ] ,
δ νn (t) 1 i=0 n1 A s (i) i=0 n1 [ A s (i) δ ν1 (t+i× t p ) ] .
S NE1 ¯ =exp[ τ( ν ¯ ,2 r G ) ]( i=0 n1 A s (i) )( 1+b σ 2 ( δ ν1 ) ),
σ 2 ( S NE1 )= ( S NE1 ¯ ) 2 ( dτ / d ν c ) 2 σ 2 ( δ νn ).
σ 2 ( S NK1 )= F e S NNK1 ¯ + α 2 σ 2 ( S NE1 ), S NNK1 i=0 n1 K s (i) E s 2 (i) S NK1 / E sav S K / E sav 2 .
Δτ=ln( S NK1 on ¯ S NK1 off ¯ )+ln( R A )+ln( R b ),
Δ τ SNK1 ln( S NK1 on S NK1 off ).
b Δτ_SNK1 ln( R A )ln( R b )+ F e 2 ( S NNK1 on ¯ S NK1 on ¯ 2 S NNK1 off ¯ S NK1 off ¯ 2 )+ 1 2 ( dτ d ν c ) on 2 σ 2 ( δ νn on ),
σ 2 (Δ τ SNK1 ) σ 2 ( S NK1 on ) S NK1 on ¯ 2 + σ 2 ( S NK1 off ) S NK1 off ¯ 2 F e S K off ¯ [1+exp(Δτ)]+ ( dτ d ν c ) on 2 σ 2 ( δ νn on ).
S δνn (f)= S δν (f)|H(f )| 2 W avn (f), W avn (f) | 1 i=0 n1 A s (i) i=0 n1 A s (i)exp(j2πf t p ×i) | 2 .
< W avn >= i=0 n1 A s 2 (i) / ( i=0 n1 A s (i) ) 2 .
σ 2 ( K T )= I δ i Δt/ ( M e e ) 2 , I δi S δ i (f) sinc 2 (fΔt)Δtdf,
σ 2 (K ' s ) F e K s ¯ + α 2 σ 2 ( W s )+ λ bgd Δt, λ bgd [ 2α N bgd B o F e + F d λ d + I δi / ( M e e ) 2 ]( 1+1/β ).
σ 2 ( S NK2 ) ( S NK2 ¯ ) 2 F e S NNK2 ¯ ( S NK2 ¯ ) 2 + ( dτ d ν c ) 2 σ 2 ( δ νn )+ S NN2 ¯ ( S NK2 ¯ ) 2 λ bgd Δt,
Δ τ SNK2 ln( S NK2 on S NK2 off )+ C Δτ_SNK2 , C Δτ_SNK2 F e 2 ( S NNK2 off S NK2 off 2 S NNK2 on S NK2 on 2 )+ λ bgd Δt 2 ( S NN2 off S NK2 off 2 S NN2 on S NK2 on 2 ).
b Δτ_SNK2 ln( R A )ln( R b )+ ( dτ/d ν c ) on 2 σ 2 ( δ νn on )/2+ b C_Δτ_SNK2 , b C_Δτ_SNK2 1 2 ( F e / S K' on ¯ ) 2 [ 1exp(2Δτ) ] 3 2 F e n λ bgd Δt[ 1exp(3Δτ) ]/ S K' on ¯ 3 ,
σ 2 (Δ τ SNK2 ) σ ΔτDET 2 + ( dτ/d ν c ) on 2 σ 2 ( δ νn on ), σ ΔτDET 2 F e [1+exp(Δτ)]/ S K' off ¯ +n λ bgd Δt[1+exp(2Δτ)]/ S K' off ¯ 2 .
Δ τ SNK2_av 1 m k=0 m1 Δ τ SNK2 (k) .
1/ A z (i)exp(2 σ eff NΔz)/exp[2 σ eff N z 0 (i)]( 12 σ eff N δ z (i)+2 [ σ eff N δ z (i)] 2 ),
b Δτ_SNK3 = b Δτ_SNK2 + b Δτz , b Δτz 2 σ eff ( ν ¯ on , r G )N( r G )Δz2 [ σ eff ( ν ¯ on , r G )N( r G ) σ z ] 2 (1< W avn >),
σ 2 (Δ τ SNK3 )= σ 2 (Δ τ SNK2 )+ σ Δτz 2 , σ Δτz 2 [ 2 σ eff ( ν ¯ on , r G )N( r G ) σ z ] 2 < W avn >.
B L 2 0 [ ν F ν c ( t 0 ) ] 2 L N ( ν F )d ν F = B LF 2 + B LA 2 , B LF 2 [ ν(t) ν c ( t 0 ) ] 2 h(t t 0 )dt , B LA 2 f 2 |A(f) | 2 df |A(f) | 2 df = 1 4 π 2 [ da(t) / dt ] 2 dt a 2 (t)dt .
B LF 2 ¯ = [ δ ν (t)] 2 ¯ [ δ ν1 ( t 0 )] 2 ¯ = S δν (f)[ 1|H(f) | 2 ]df .
R u ( t D ) u*(t)u(t+ t D ) dt= a(t')a(t'+ t D )exp(j2π ν ¯ t D )exp(jΔϕ) dt',
L 0 (Δ ν F ) ¯ = [ a(t')a(t'+ t D ) exp( j[Δϕ2π δ ν1 ( t 0 ) t D ] ) ¯ dt' ]exp(j2πΔ ν F t D )d t D .
exp( j[Δϕ2π δ ν1 ( t 0 ) t D ] ) ¯ =exp[ 1 2 ( Δϕ2π δ ν1 ( t 0 ) t D ) 2 ¯ ].
L 0 (Δ ν F ) ¯ = R 0 ( t D )exp(j2πΔ ν F t D )d t D , R 0 ( t D ) a(t')a(t'+ t D )exp[ 2 π 2 t D 2 S δν (f) | sinc(f t D )H(f)exp[ j2πf( t'+ t D /2 ) ] | 2 df ] dt'.
σ 2 ( K sn )= ( Δt/2 Δt/2 α P sn (t)dt ) 2 ¯ =Δt Tri( ξ Δt )Γ(ξ)dξ = I sn Δt, I sn S sn (f) sinc 2 (fΔt)Δtdf.
σ 2 ( K nn )= K nn ¯ ( F e + δ c ), δ c = K nn ¯ /(2 B o Δt N MM )=αN / ASE N MM .
b ΔτE N ASE N MM ( 1 E sav on 1 E sav off )( 2< W avn > ),
σ ΔτE 2 2 N ASE N MM ( 1 E sav on + 1 E sav off )< W avn >.

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