Abstract

A method, based on the reciprocity principle of radiative transfer, for using routinely collected field measurements of apparent optical properties in a water body to estimate the total return (time integrated) to an airborne or space borne lidar is presented. It will allow prediction of lidar returns using the databases of apparent optical properties assembled in support of ocean color remote sensing.

© 2009 Optical Society of America

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References

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  1. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, "Comparison of Numerical Models for Computing Underwater Light Fields," Appl. Opt.,  32, 7484-7504 (1993).
    [CrossRef]
  2. C. D. Mobley, Light and Water, (Academic Press, San Diego, CA, 1994) pp. 592.
  3. J. R. V. Zaneveld, E. Boss, and M. Behrenfeld, "LIDAR photon return calculation in a homogeneous optical medium," (Unpublished Report)
  4. K. M. Case, "Transfer Problems and the Reciprocity Principle," Rev. Mod. Phys. 29, 651-663 (1957).
    [CrossRef]
  5. H. Yang and H. R. Gordon, "Remote sensing of ocean color: Assessment of the water-leaving radiance bidirectional effects on the atmospheric diffuse transmittance," Appl. Opt. 36, 7887-7897 (1997).
    [CrossRef]
  6. H. R. Gordon, "Interpretation of airborne oceanic lidar: effects of multiple scattering," Appl. Opt. 212996-3001 (1982).
    [CrossRef] [PubMed]
  7. In Ref. [6], E (energy) is replaced by P (power), and ENInc is replaced by P0, the laser power; however, that was incorrect because the laser power was taken as P(t) = P0δ(t−t0) rather than the correct P(t) = E0δ(t−t0) so ∫P(t) dt = E0, not P0. In the Monte Carlo simulations that were carried out in [6], detected photon numbers were placed in time bins. Photon numbers correspond to energy not power.
  8. H. R. Gordon, "Can the Lambert-Beer Law Be Applied to the Diffuse Attenuation Coefficient of Ocean Water?," Limnol. Oceanogr. 34, 1389-1409 (1989).
    [CrossRef]
  9. D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
    [CrossRef]
  10. Scott McLean (Personal commun.)
  11. H. R. Gordon, "Contribution of Raman scattering to water-leaving radiance: A reexamination," Appl. Opt,  38, 3166-3174 (1999).
    [CrossRef]
  12. T. J. Petzold, "Volume scattering functions for selected ocean waters," SIO Ref. 72-78. (1972).
  13. http://seabass.gsfc.nasa.gov

1999 (1)

H. R. Gordon, "Contribution of Raman scattering to water-leaving radiance: A reexamination," Appl. Opt,  38, 3166-3174 (1999).
[CrossRef]

1997 (2)

H. Yang and H. R. Gordon, "Remote sensing of ocean color: Assessment of the water-leaving radiance bidirectional effects on the atmospheric diffuse transmittance," Appl. Opt. 36, 7887-7897 (1997).
[CrossRef]

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

1993 (1)

1989 (1)

H. R. Gordon, "Can the Lambert-Beer Law Be Applied to the Diffuse Attenuation Coefficient of Ocean Water?," Limnol. Oceanogr. 34, 1389-1409 (1989).
[CrossRef]

1982 (1)

1957 (1)

K. M. Case, "Transfer Problems and the Reciprocity Principle," Rev. Mod. Phys. 29, 651-663 (1957).
[CrossRef]

Broenkow, W.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

Case, K. M.

K. M. Case, "Transfer Problems and the Reciprocity Principle," Rev. Mod. Phys. 29, 651-663 (1957).
[CrossRef]

Clark, D. K.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

Ge, Y.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

Gentili, B.

Gordon, H. R.

H. R. Gordon, "Contribution of Raman scattering to water-leaving radiance: A reexamination," Appl. Opt,  38, 3166-3174 (1999).
[CrossRef]

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

H. Yang and H. R. Gordon, "Remote sensing of ocean color: Assessment of the water-leaving radiance bidirectional effects on the atmospheric diffuse transmittance," Appl. Opt. 36, 7887-7897 (1997).
[CrossRef]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, "Comparison of Numerical Models for Computing Underwater Light Fields," Appl. Opt.,  32, 7484-7504 (1993).
[CrossRef]

H. R. Gordon, "Can the Lambert-Beer Law Be Applied to the Diffuse Attenuation Coefficient of Ocean Water?," Limnol. Oceanogr. 34, 1389-1409 (1989).
[CrossRef]

H. R. Gordon, "Interpretation of airborne oceanic lidar: effects of multiple scattering," Appl. Opt. 212996-3001 (1982).
[CrossRef] [PubMed]

Jin, Z.

Kattawar, G. W.

Mobley, C. D.

Morel, A.

Reinersman, P.

Stamnes, K.

Stavn, R. H.

Trees, C.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

Voss, K. J.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

Yang, H.

Appl. Opt (1)

H. R. Gordon, "Contribution of Raman scattering to water-leaving radiance: A reexamination," Appl. Opt,  38, 3166-3174 (1999).
[CrossRef]

Appl. Opt. (3)

J. Geophys. Res. (1)

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, Validation of Atmospheric Correction over the Oceans, J. Geophys. Res. 102D, 17209-17217 (1997).
[CrossRef]

Limnol. Oceanogr. (1)

H. R. Gordon, "Can the Lambert-Beer Law Be Applied to the Diffuse Attenuation Coefficient of Ocean Water?," Limnol. Oceanogr. 34, 1389-1409 (1989).
[CrossRef]

Rev. Mod. Phys. (1)

K. M. Case, "Transfer Problems and the Reciprocity Principle," Rev. Mod. Phys. 29, 651-663 (1957).
[CrossRef]

Other (6)

In Ref. [6], E (energy) is replaced by P (power), and ENInc is replaced by P0, the laser power; however, that was incorrect because the laser power was taken as P(t) = P0δ(t−t0) rather than the correct P(t) = E0δ(t−t0) so ∫P(t) dt = E0, not P0. In the Monte Carlo simulations that were carried out in [6], detected photon numbers were placed in time bins. Photon numbers correspond to energy not power.

C. D. Mobley, Light and Water, (Academic Press, San Diego, CA, 1994) pp. 592.

J. R. V. Zaneveld, E. Boss, and M. Behrenfeld, "LIDAR photon return calculation in a homogeneous optical medium," (Unpublished Report)

Scott McLean (Personal commun.)

T. J. Petzold, "Volume scattering functions for selected ocean waters," SIO Ref. 72-78. (1972).

http://seabass.gsfc.nasa.gov

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Tables (1)

Tables Icon

Table 1: Expected number of photons received by a lidar system with a 0.05 J pulse energy and a 1 m aperture, operating at 600 km above the water surface at a wavelength of 532 nm in oligotrophic waters.

Equations (34)

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S d S ξ ̂ n ̂ < 0 ξ ̂ n ̂ L 1 ( ρ , ξ ̂ ) L 2 ( ρ , ξ ̂ ) d Ω ( ξ ̂ ) = S dS ξ ̂ n ̂ < 0 ξ ̂ n ̂ L 2 ( ρ , ξ ̂ ) L 1 ( ρ , ξ ̂ ) d Ω ( ξ ̂ ) ,
S F W ξ ̂ 0 n ̂ χ W ( x , y ) L N ( x , y , ξ ̂ 0 ) dx dy = S F N ξ ̂ 0 n ̂ χ N ( x , y ) L W ( x , y , ξ ̂ 0 ) dx dy .
F W ξ ̂ 0 n ̂ L N ( x , y , ξ ̂ 0 ) dx dy = L W ( ξ ̂ 0 ) S χ N ( x , y ) F N ξ ̂ 0 n ̂ dx dy ,
L N ( x , y , ξ ̂ 0 ) = d 2 P N ( x , y , ξ ̂ 0 ) dx dy d Ω ( ξ ̂ 0 ) ξ ̂ 0 n ̂ ,
ξ ̂ 0 n ̂ L N ( x , y , ξ ̂ 0 ) dx dy = P N ( ξ ̂ 0 ) ΔΩ ( ξ ̂ 0 ) ,
P N ( ξ ̂ 0 ) = P N Inc ΔΩ ( ξ ̂ 0 ) [ L W ( ξ ̂ 0 ) F W ] ,
P N ( ξ ̂ 0 ) = P N Inc ΔΩ ( ξ ̂ 0 ) I W ( ξ ̂ 0 ) ,
I W ( ξ ̂ 0 ) L W ( ξ ̂ 0 ) F W .
d N out ( t ) = N in ( t 0 ) f ( t t o ) dt
N out Total = t 0 d N out ( t ) = t 0 N in ( t 0 ) f ( t t 0 ) dt .
N out Total = 0 N in ( t 0 ) f ( τ ) = N in ( t 0 ) 0 f ( τ ) N in ( t 0 ) F .
d N out ( t ) = Δ N in f ( t t 0 ) dt + Δ N in f ( t t 0 Δ t 0 ) dt + Δ N in f ( t t 0 2 Δ t 0 ) dt +
= Δ N in dt i = 0 f ( t t 0 i Δ t 0 ) = Δ N in Δ t 0 dt i = 0 f ( t t 0 i Δ t 0 ) Δ t 0
Δ t 0 0 d N in d t 0 dt t f ( t t 0 ) d t 0
= d N in d t 0 dt 0 f ( τ ) = d N in d t 0 dt F .
d N out ( t ) dt = d N in d t 0 F ,
N out Total = N in ( t 0 ) F ,
P N = P N Inc ΔΩ ( ξ ̂ 0 ) I W ( ξ ̂ 0 ) ,
E N Total = E N Inc ΔΩ ( ξ ̂ 0 ) I W ( ξ ̂ 0 ) ,
d E ( t ) dt = C ν 2 m exp [ κν ( t t 0 ) / m ] ,
t 0 d E ( t ) dt dt = C 2 κ = E Total ,
d E ( t ) ( t , ξ ̂ 0 ) dt = ν m κ E Total exp [ κν ( t t 0 ) / m ] ,
= ν m κ E Inc ΔΩ ( ξ ̂ 0 ) I W ( ξ ̂ 0 ) exp [ κν ( t t 0 ) / m ] ,
d E ( z , ξ ̂ 0 ) dz = 2 κ ξ ̂ 0 n ̂ E Inc ΔΩ ( ξ ̂ 0 ) I W ( ξ ̂ 0 ) exp [ 2 κz / ξ ̂ 0 n ̂ ]
2 K d E Inc ΔΩ ( ξ ̂ 0 ) I W ( ξ ̂ 0 ) exp [ 2 K d z ] ,
I W = L W F 0 T f 2 L u m 2 E d ,
d E ( z , ξ ̂ 0 ) dz T A E Inc ΔΩ T f 2 L u m 2 E d 2 K d exp [ 2 K d z ]
E Total T A E Inc ΔΩ T f 2 L u m 2 E d .
E Total E Inc = 3.29 × 10 15
d E ( z ) E Inc dz = E Total E Inc 2 K d exp [ 2 K d z ] ,
ΔE ( z ) E Inc = 3.62 × 10 16 exp [ 0.11 z ] Δ z .
E Total T A 2 E Inc T f 2 A 2 m 2 H 2 β ( 180 ° ) κ ,
E Total E Inc = 4.3 × 10 15
E Total T A 2 E Inc T f 2 A 2 m 2 H 2 β ( 180 ° ) K d ,

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