Abstract

The index of refraction structure constant, Cn2 indicates how strongly the index of refraction varies in a region of the atmosphere. These variations usually arise through turbulent motions, creating an inhomogeneous distribution of species, density, temperature and pressure. Because the index of refraction also depends on wavelength, the measured value of Cn2 will depend on wavelength. This Cn2 difference generally becomes more pronounced as the difference in wavelength increases. This paper describes a technique for converting between measurements of Cn2 at different wavelengths, and gives an example for converting from centimeter to visible and near IR wavelengths.

© 2013 Optical Society of America

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  1. S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).
  2. S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).
  3. J. J. Cohen, “Demonstration and verification of a broad spectrum anomalous dispersion effects tool for index of refraction and optical turbulence calculations,” Master’s thesis, Air Force Institute of Technology (2009).
  4. F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy” Prog. Optics19, 283–387 (1981).
  5. V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).
  6. A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
    [CrossRef]
  7. M. Z. Jacobson, Fundamentals of Atmospheric Modeling, 2nd ed. (Cambridge University, 2005).
    [CrossRef]
  8. D. Bolton, “The computation of equivalent potential temperature,” Mon. Wea. Rev.108, 1046–1053 (1980).
    [CrossRef]
  9. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Optics35, 1566–1573 (1996).
    [CrossRef]
  10. M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

2012

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

2009

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

1998

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

1996

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Optics35, 1566–1573 (1996).
[CrossRef]

1981

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy” Prog. Optics19, 283–387 (1981).

1980

D. Bolton, “The computation of equivalent potential temperature,” Mon. Wea. Rev.108, 1046–1053 (1980).
[CrossRef]

Acharya, P.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Adler-Golden, S.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Anderson, G.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Bartell, R.

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

Bartell, R. J.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Berk, A.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Bernstein, L.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Bolton, D.

D. Bolton, “The computation of equivalent potential temperature,” Mon. Wea. Rev.108, 1046–1053 (1980).
[CrossRef]

Chetwynd, J.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Ciddor, P. E.

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Optics35, 1566–1573 (1996).
[CrossRef]

Cohen, J. J.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

J. J. Cohen, “Demonstration and verification of a broad spectrum anomalous dispersion effects tool for index of refraction and optical turbulence calculations,” Master’s thesis, Air Force Institute of Technology (2009).

Cusumano, S.

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

Cusumano, S. J.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Downs, A.

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

Fiorino, S.

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

Fiorino, S. T.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Jacobson, M. Z.

M. Z. Jacobson, Fundamentals of Atmospheric Modeling, 2nd ed. (Cambridge University, 2005).
[CrossRef]

Krizo, M.

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

Krizo, M. J.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Marchid, G.

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

McClung, B. T.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Nicolas, S.

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

Randall, R.

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

Randall, R. M.

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Riker, J.

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

Robertson, D.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Roddier, F.

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy” Prog. Optics19, 283–387 (1981).

Schwering, P.

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

Tatarskii, V.

V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

Velluet, M.-T.

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

Vorontsov, M.

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

Appl. Optics

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Optics35, 1566–1573 (1996).
[CrossRef]

J. Directed Energy

S. T. Fiorino, R. J. Bartell, M. J. Krizo, B. T. McClung, J. J. Cohen, R. M. Randall, and S. J. Cusumano, “Broad-spectrum optical turbulence assessments from climatological temperature, pressure, humidity, and wind,” J. Directed Energy3, 223–228 (2009).

Mon. Wea. Rev.

D. Bolton, “The computation of equivalent potential temperature,” Mon. Wea. Rev.108, 1046–1053 (1980).
[CrossRef]

Proc. SPIE

M.-T. Velluet, M. Vorontsov, P. Schwering, G. Marchid, S. Nicolas, and J. Riker, “Turbulence characterization and image processing data sets from a NATO RTO SET 165 trial in Dayton, Ohio, USA,” Proc. SPIE8380, 83800J (2012).

Prog. Optics

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy” Prog. Optics19, 283–387 (1981).

Remote Sens. Environ.

A. Berk, L. Bernstein, G. Anderson, P. Acharya, D. Robertson, J. Chetwynd, and S. Adler-Golden, “{MODTRAN} cloud and multiple scattering upgrades with application to {AVIRIS},” Remote Sens. Environ.65, 367–375 (1998).
[CrossRef]

Other

M. Z. Jacobson, Fundamentals of Atmospheric Modeling, 2nd ed. (Cambridge University, 2005).
[CrossRef]

V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

S. Fiorino, R. Randall, A. Downs, R. Bartell, M. Krizo, and S. Cusumano, “Three-dimensional optical turbulence assessments from doppler weather radar for laser applications,” in “6th DEPS Systems Symposium” (2011).

J. J. Cohen, “Demonstration and verification of a broad spectrum anomalous dispersion effects tool for index of refraction and optical turbulence calculations,” Master’s thesis, Air Force Institute of Technology (2009).

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Figures (2)

Fig. 1
Fig. 1

C n 2 vs. time. C n 2 values are from a 10 cm NEXRAD radar (black line), along with scintillometer measurements of the same air volume using an 880 nm scintillometer (blue dotted line), and the estimated measurements of an 880 nm device created from the radar measurements and GFS NWP data (magenta dashed-dotted line). Shaded areas indicate night-time. All times are local Eastern-Daylight Savings Time from October of 2011.

Fig. 2
Fig. 2

Computed C n 2 vs. time at wavelengths decreasing from 100 mm to 500 nm. The order, from top to bottom, in the legend corresponds to the relative C n 2 of each wavelength. Also included are the measured radar and scintillometer data. Shaded areas are for night, and portions of the plot are magnified so that the fine structure can be seen. Note that the original radar data and the data corrected to 10 cm match, as they should. Times are local EDT from October 2011.

Equations (23)

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D n ( r ) = C n 2 r 2 3 ,
C n 2 = a 2 α L 0 3 4 ( d n d z ) 2 .
C n , λ 1 2 C n , λ 2 2 = ( d n λ 1 / d z d n λ 2 / d z ) 2 .
d n λ d z θ n ( θ , p , q : λ ) Δ θ Δ z + q n ( θ , p , q : λ ) Δ q Δ z
d N d z f ( T , P , e v : N ) d T d z .
C n , λ 1 2 C n , λ 2 2 = ( f λ 1 ( T , P , e v ) f λ 2 ( T , P , e v ) ) 2 .
d N d z = N P d P d z + N T d T d z + N h d e v d z ,
d N d z = N P d P d T d T d z + N T d T d z + N e v e v T d T d z ,
d N d z = ( N P d P d T + N T + N e v e v T ) d T d z f ( T , P , e v ) d T d z .
d P d T = P T γ γ 1 = P T Γ .
e v = h e s = h 6.122 exp ( 17.67 T 273.15 T 29.65 ) .
d e v d T = e v 4355.655 ( T 29.65 ) 2 = e v β ( T ) .
d N d z = d T d z ( N T + Γ P T N P + β N e v ) .
N = 79 T ( P + 4800 e v T ) ,
d N d z = d T d z [ N T ( β 2 ) 79 P T β + 79 P T 2 ( Γ + 1 ) ] ,
N = ρ α N α s ρ α s + ρ w N w s ρ w s .
N = P M α Z R T ( 1 x w ) N α s ρ α s + P M w Z R T x w N w s ρ w s .
N = P Z T ( A + x w B ) .
d N d z = N [ Γ 1 T 1 Z ( Z T + Γ P T Z P ) ] d T d z .
Z = 1 P T [ a 0 + a 1 t + a 2 t 2 + ( b 0 + b 1 t ) x w + ( c 0 + c 1 t ) x w 2 ] + ( P T ) 2 ( d + e x w 2 ) .
Z P = Z 1 P + P T 2 ( d + e x w 2 ) ,
Z T = 1 Z T P 2 T 3 ( d + e x w 2 ) + P T [ a 1 + 2 a 2 t + x w ( b 1 + c 1 x w ) ] .
d N d z = N T Z { ( Γ 1 ) [ 1 + ( P T ) 2 ( d + e x w 2 ) ] P [ a 1 + 2 a 2 t + x w ( b 1 + c 1 x w ) ] } d T d z

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