Abstract

A computational model to simulate the effects of boundary layer isotropic atmospheric turbulence on the radiative transfer process is presented. We perform a large number of simulations with stochastic ambient conditions to estimate the statistics necessary to predict the detection limit of a given trace gas. We find that the radiance and transmittance variability are primarily determined by the optical depth of the emitting atmosphere, and that the relative variability of the transmittance is an order of magnitude smaller than that of the radiance. We estimate that the atmospheric detection limit of a DMMP vapor cloud at 30 meters altitude for a ground-based observer ranges from 3.5 to 12 ppbm, depending on the horizontal range to the cloud. Addition of uncorrelated detector noise has a disproportionate effect on the detection limit over the spectrally correlated turbulence noise. These calculations appear to be the first predictions of vapor detection limits that explicitly incorporate the effects of turbulence.

© 2008 Optical Society of America

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References

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  1. E. R. Schildkraut, R. F. Connors, A. Ben-David, and A. Ifarraguerri, "An ultra-high sensitivity passive FTIR sensor (HiSPEC) and initial field results," Proc. SPIE 4574, 8-25 (2001).
  2. D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
    [CrossRef]
  3. J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
    [CrossRef]
  4. P. Ciotti, D. Solimini, and P. Basili, "Spectra of Atmospheric Variables as Deduced from Ground Based Radiometry," IEEE Trans. on Geosci.Elec. GE-17, 68-77 (1979)
    [CrossRef]
  5. A. Ben-David, S. K. Holland, G. Laufer, and J. D. Baker, "Measurements of atmospheric brightness temperature fluctuations and their implications on passive remote sensing," Opt. Express 13, 8781-8800 (2005).
    [CrossRef] [PubMed]
  6. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  7. R. R. Beland, "Propagation through atmospheric optical turbulence," in Infrared & Electro-Optical Systems Handbook, Volume 2: Atmospheric Propagation of Radiation, F. G. Smith, ed., (SPIE, 1999).
  8. G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London A 164, (1938).
  9. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. of Am. 609, 826-830 (1970).
    [CrossRef]
  10. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).
  11. M. C. Roggerman and B. M. Welsh, Imaging Through Turbulence (CRC 1996).
  12. A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
    [CrossRef]
  13. D. F. Flanigan, "Prediction of the limits of detection of hazardous vapors by passive infrared with the use of MODTRAN," Appl. Opt. 35, 6090-6098 (1996).
    [CrossRef] [PubMed]
  14. J. H. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change (Wiley, 1997).
  15. S. W. Sharpe, T. J. Johnson, R. L. Sams, P. M. Chu, G. C. Rhoderick, and P. A. Johnson, "Gas-phase databases for quantitative infrared spectroscopy," Appl. Spectrosc. 58, 1452-1461 (2004).
    [CrossRef] [PubMed]

2005 (2)

A. Ben-David, S. K. Holland, G. Laufer, and J. D. Baker, "Measurements of atmospheric brightness temperature fluctuations and their implications on passive remote sensing," Opt. Express 13, 8781-8800 (2005).
[CrossRef] [PubMed]

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

2004 (1)

2003 (1)

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

2001 (1)

E. R. Schildkraut, R. F. Connors, A. Ben-David, and A. Ifarraguerri, "An ultra-high sensitivity passive FTIR sensor (HiSPEC) and initial field results," Proc. SPIE 4574, 8-25 (2001).

1998 (1)

J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
[CrossRef]

1996 (1)

1979 (1)

P. Ciotti, D. Solimini, and P. Basili, "Spectra of Atmospheric Variables as Deduced from Ground Based Radiometry," IEEE Trans. on Geosci.Elec. GE-17, 68-77 (1979)
[CrossRef]

1970 (1)

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. of Am. 609, 826-830 (1970).
[CrossRef]

1938 (1)

G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London A 164, (1938).

Acharya, P. K.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Adler-Golden, S. M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Anderson, G. P.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Anderson, K. K.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Baker, J. D.

Ben-David, A.

A. Ben-David, S. K. Holland, G. Laufer, and J. D. Baker, "Measurements of atmospheric brightness temperature fluctuations and their implications on passive remote sensing," Opt. Express 13, 8781-8800 (2005).
[CrossRef] [PubMed]

E. R. Schildkraut, R. F. Connors, A. Ben-David, and A. Ifarraguerri, "An ultra-high sensitivity passive FTIR sensor (HiSPEC) and initial field results," Proc. SPIE 4574, 8-25 (2001).

Berk, A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Bernstein, L. S.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Blumberg, W. A.

J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
[CrossRef]

Brown, J. H.

J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
[CrossRef]

Chetwynd, J. H.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Chu, P. M.

Clifford, S. F.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. of Am. 609, 826-830 (1970).
[CrossRef]

Connors, R. F.

E. R. Schildkraut, R. F. Connors, A. Ben-David, and A. Ifarraguerri, "An ultra-high sensitivity passive FTIR sensor (HiSPEC) and initial field results," Proc. SPIE 4574, 8-25 (2001).

Cooley, T. W.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Duff, J. W.

J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
[CrossRef]

Flanigan, D. F.

Fox, M. J.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Gallagher, N. B.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Gardner, J. A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Gruninger, J. H.

J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
[CrossRef]

Hoke, M. L.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Holland, S. K.

Johnson, P. A.

Johnson, T. J.

Laufer, G.

Lawrence, R. S.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. of Am. 609, 826-830 (1970).
[CrossRef]

Lee, J.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Lockwood, R. B.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Muratov, L.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Ochs, G. R.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. of Am. 609, 826-830 (1970).
[CrossRef]

Rhoderick, G. C.

Sams, R. L.

Schildkraut, E. R.

E. R. Schildkraut, R. F. Connors, A. Ben-David, and A. Ifarraguerri, "An ultra-high sensitivity passive FTIR sensor (HiSPEC) and initial field results," Proc. SPIE 4574, 8-25 (2001).

Schultz, J. F.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Sharpe, S. W.

S. W. Sharpe, T. J. Johnson, R. L. Sams, P. M. Chu, G. C. Rhoderick, and P. A. Johnson, "Gas-phase databases for quantitative infrared spectroscopy," Appl. Spectrosc. 58, 1452-1461 (2004).
[CrossRef] [PubMed]

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Sheen, D. M.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Taylor, G. I.

G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London A 164, (1938).

Appl. Opt. (1)

Appl. Spectrosc. (1)

Elec. (1)

P. Ciotti, D. Solimini, and P. Basili, "Spectra of Atmospheric Variables as Deduced from Ground Based Radiometry," IEEE Trans. on Geosci.Elec. GE-17, 68-77 (1979)
[CrossRef]

J. Opt. Soc. of Am. (1)

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. of Am. 609, 826-830 (1970).
[CrossRef]

Opt. Express (1)

Proc SPIE (2)

J. H. Gruninger, J. W. Duff, J. H. Brown, and W. A. Blumberg, "Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence," Proc SPIE 3495, 122-135 (1998).
[CrossRef]

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. J. Fox, S. M. Adler-Golden, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, T. W. Cooley, and J. A. Gardner, "MODTRAN5: A Reformulated Atmospheric Band Model with Auxiliary Species and Practical Multiple Scattering Options," Proc SPIE 5655, 88-95 (2005).
[CrossRef]

Proc. R. Soc. London A (1)

G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London A 164, (1938).

Proc. SPIE (2)

E. R. Schildkraut, R. F. Connors, A. Ben-David, and A. Ifarraguerri, "An ultra-high sensitivity passive FTIR sensor (HiSPEC) and initial field results," Proc. SPIE 4574, 8-25 (2001).

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Schultz, "Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity," Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Other (5)

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

R. R. Beland, "Propagation through atmospheric optical turbulence," in Infrared & Electro-Optical Systems Handbook, Volume 2: Atmospheric Propagation of Radiation, F. G. Smith, ed., (SPIE, 1999).

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).

M. C. Roggerman and B. M. Welsh, Imaging Through Turbulence (CRC 1996).

J. H. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change (Wiley, 1997).

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Figures (8)

Fig. 1.
Fig. 1.

(a). Average radiance and radiance standard deviation as a function of wavenumber as seen by a nadir observer at 1000 meters above the ground; (b) average transmittance and transmittance standard deviation for the same geometry.

Fig. 2.
Fig. 2.

Dependence of path radiance (a), path radiance variability (b), path transmittance (c) and path transmittance variability (d) on altitude of the observer.

Fig. 3.
Fig. 3.

Up-looking geometry used for our simulation, where elevation angle and horizontal range are varied but the 30m target altitude is set.

Fig. 4.
Fig. 4.

(a). Average path radiance and radiance standard deviation as a function of wavenumber as seen by an observer standing at 1 meter above the ground and looking into space at an elevation angle of 1.7° towards a target 30 m above the ground; (b) average foreground transmittance and transmittance standard deviation for the same geometry.

Fig. 5.
Fig. 5.

Dependence of path radiance (a), path radiance variability (b), transmittance (c) and transmittance variability (d) on the elevation of the line of sight.

Fig. 6.
Fig. 6.

Dependence of the radiance variability on the value of the temperature structure function at 1 meter above the ground. The elevation angle is 1.7°.

Fig. 7.
Fig. 7.

Absorption coefficient spectrum of DMMP.

Fig. 8.
Fig. 8.

Detection limit estimates for DMMP as a function of horizontal range (see Fig. 3). The solid lines represent a least squares best fit to the data points. The added noise has a NESR of 10-10 W/cm2/sr/cm-1.

Tables (1)

Tables Icon

Table 1. Layers of the reference (nominal) atmosphere. The values are interpolated from the 1976 U.S. Standard Atmosphere. Layers above 1km use the MODTRAN default values.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

D T ( Δ x ) E { ( T ( x ) T ( x + Δ x ) ) 2 } = C T 2 Δ x 2 3
C T 2 = α 2 P 2 T 4 C n 2
α = α dry [ 1 + 7.53 × 10 1 λ 2 7733 q T ] α dry [ 1 7733 q T ]
C n 2 ( z ) = C n 2 ( z 0 ) ( z z 0 ) 4 3
L = L f + t f [ ( 1 t v ) B ( T ) + t v L b ]
t f = L f + b L f L b .
t v = 1 k c
ρ ̂ = ρ + r
H 0 : ρ ̂ = r , r N ( 0 , σ 0 2 )
vs .
H 1 : ρ ̂ = ρ + r , r N ( 0 , σ ρ 2 )
P f ( γ ) = 1 F ( γ σ 0 )
and
P d ( γ ρ ) = 1 F ( γ ρ σ ρ )
ρ DL = σ 0 F 1 ( 1 P f ) σ ρ F 1 ( 1 P d ) .
σ ̂ ρ = 1 N i = 1 N ( ρ ̂ i ρ i ) 2
σ ̂ 0 = 1 N i = 1 N ρ ̂ i 2
ρ ̂ i = b 0 + j = 1 M b j L i ( λ j )
ρ ̂ ' i = b 0 + j = 1 M b j [ L i ( λ j ) + n i ( λ j ) ] .
σ ρ , n 2 = j = 1 M b j 2 σ n 2 ( λ j ) .
ρ ̂ DL ( noise ) = ( σ n j = 1 M b j 2 ) [ F 1 ( 1 P f ) F 1 ( 1 P d ) ] .
ρ DL 2 ( total ) = ρ DL 2 ( atmosphere ) + ρ DL 2 ( noise ) + ρ DL 2 ( algorithm )
σ L 2 ( λ ) = φ ( λ ) D T ( C T 2 , u , Δ t )
χ 2 ( N ) = N σ ̂ i 2 σ i 2
σ ̂ i σ i = χ 2 ( N ) N
re ( α ) = 100 × ( σ ̂ i σ i 1 ) = 100 × ( χ 2 ( N , α ) N 1 )

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