Abstract

The Earth’s atmosphere has significant effects on the propagation of electromagnetic (EM) radiation and accordingly degrades the performance of electro-optical systems. These effects are attributed to atmospheric turbulence and to absorption and scattering of EM waves by atmospheric molecules and aerosols. In this paper we develop a detailed model of the effects of absorption and scattering on the optical radiation propagating from the object plane to an imaging system based on the classical theory of EM scattering. Scattering has the effect of de-correlating the light leaving the target from the unscattered light reaching the imaging system, and scattering has the effect of broadening the angle at which the scattered light arrives at the receiver compared to the unscattered light. Absorption has the effect of reducing the amount of power available for the image. Both of these effects depend upon the atmospheric species present, their EM properties, and wavelength. We use this detailed model to compute the average point spread function (PSF) of an imaging system that properly accounts for the effects of the diffraction and scattering, and the appropriate optical power level of both the unscattered and the scattered radiation arriving at the pupil of the imaging system. Since the scattered radiation is temporally and spatially de-correlated from the unscattered radiation, we model the effects of the unscattered radiation and the radiation scattered from the various species as additive in the image plane. The key result of this study is the significant effect of atmospheric scattering on the contrast and spatial resolution of images acquired by imaging systems, due to the increased level of the scattered radiation PSF and the reduced level of the direct radiation PSF, upon increasing the atmospheric optical depth.

© 2014 Optical Society of America

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References

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  2. I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
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  3. B. Ben Dor, A. D. Devir, G. Shaviv, P. Bruscaglioni, P. Donelli, and A. Ismaelli, “Atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am. A 14, 1329–1337 (1997).
    [CrossRef]
  4. L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
    [CrossRef]
  5. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).
  6. E. P. Shettle and R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1979), www.dtic.mil .
  7. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).
  8. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
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    [CrossRef]
  10. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).
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  12. S. G. Gathman, “Optical properties of the marine aerosol as predicted by the Navy aerosol model,” Opt. Eng. 22, 220157 (1983).
    [CrossRef]
  13. E. P. Shettle, D. R. Longtin, J. R. Hummel, and J. D. Pryce, “A wind dependent desert aerosol model: radiative properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .
  14. K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).
  15. R. G. Grainger, “Some Useful Formulae for Aerosol Size Distributions and Optical Properties,” Lecture Notes (University of Oxford, 2012).
  16. M. T. Eismann and D. A. LeMaster, “Aerosol modulation transfer function model for passive long-range imaging over a nonuniform atmospheric path,” Opt. Eng. 52, 046201 (2013).
    [CrossRef]
  17. E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

2013 (1)

M. T. Eismann and D. A. LeMaster, “Aerosol modulation transfer function model for passive long-range imaging over a nonuniform atmospheric path,” Opt. Eng. 52, 046201 (2013).
[CrossRef]

1999 (1)

N. S. Kopeika and D. Arbel, “Imaging through the atmosphere: an overview,” Proc. SPIE 3609, 78–89 (1999).
[CrossRef]

1997 (1)

1995 (1)

1992 (1)

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

1983 (1)

S. G. Gathman, “Optical properties of the marine aerosol as predicted by the Navy aerosol model,” Opt. Eng. 22, 220157 (1983).
[CrossRef]

1980 (1)

Abreu, L. W.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Anderson, G. P.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Arbel, D.

N. S. Kopeika and D. Arbel, “Imaging through the atmosphere: an overview,” Proc. SPIE 3609, 78–89 (1999).
[CrossRef]

Ben Dor, B.

Bissonnette, L. R.

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

Bruscaglioni, P.

Chetwynd, J. H.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Clough, S. A.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).

Devir, A. D.

Donelli, P.

Dror, I.

Eismann, M. T.

M. T. Eismann and D. A. LeMaster, “Aerosol modulation transfer function model for passive long-range imaging over a nonuniform atmospheric path,” Opt. Eng. 52, 046201 (2013).
[CrossRef]

Fenn, R. W.

E. P. Shettle and R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1979), www.dtic.mil .

Gallery, W. O.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Gathman, S. G.

S. G. Gathman, “Optical properties of the marine aerosol as predicted by the Navy aerosol model,” Opt. Eng. 22, 220157 (1983).
[CrossRef]

Grainger, R. G.

R. G. Grainger, “Some Useful Formulae for Aerosol Size Distributions and Optical Properties,” Lecture Notes (University of Oxford, 2012).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

Hummel, J. R.

E. P. Shettle, D. R. Longtin, J. R. Hummel, and J. D. Pryce, “A wind dependent desert aerosol model: radiative properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

Ismaelli, A.

Kneizys, F. X.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Kopeika, N. S.

LeMaster, D. A.

M. T. Eismann and D. A. LeMaster, “Aerosol modulation transfer function model for passive long-range imaging over a nonuniform atmospheric path,” Opt. Eng. 52, 046201 (2013).
[CrossRef]

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

Longtin, D. R.

E. P. Shettle, D. R. Longtin, J. R. Hummel, and J. D. Pryce, “A wind dependent desert aerosol model: radiative properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Pryce, J. D.

E. P. Shettle, D. R. Longtin, J. R. Hummel, and J. D. Pryce, “A wind dependent desert aerosol model: radiative properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Selby, J. E. A.

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Shaviv, G.

Shettle, E. P.

E. P. Shettle and R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1979), www.dtic.mil .

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

E. P. Shettle, D. R. Longtin, J. R. Hummel, and J. D. Pryce, “A wind dependent desert aerosol model: radiative properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

Shirkey, R. C.

R. C. Shirkey and D. H. Tofsted, “High resolution electro-optical aerosol phase function database PFNDAT2006,” (U.S. Army Research Laboratory, White Sands Missile Range, 2008), www.dtic.mil .

Tofsted, D. H.

R. C. Shirkey and D. H. Tofsted, “High resolution electro-optical aerosol phase function database PFNDAT2006,” (U.S. Army Research Laboratory, White Sands Missile Range, 2008), www.dtic.mil .

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Wiscombe, W. J.

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Opt. Eng. (3)

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

S. G. Gathman, “Optical properties of the marine aerosol as predicted by the Navy aerosol model,” Opt. Eng. 22, 220157 (1983).
[CrossRef]

M. T. Eismann and D. A. LeMaster, “Aerosol modulation transfer function model for passive long-range imaging over a nonuniform atmospheric path,” Opt. Eng. 52, 046201 (2013).
[CrossRef]

Proc. SPIE (1)

N. S. Kopeika and D. Arbel, “Imaging through the atmosphere: an overview,” Proc. SPIE 3609, 78–89 (1999).
[CrossRef]

Other (10)

E. P. Shettle, F. X. Kneizys, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “User’s guide to LOWTRAN 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).

R. C. Shirkey and D. H. Tofsted, “High resolution electro-optical aerosol phase function database PFNDAT2006,” (U.S. Army Research Laboratory, White Sands Missile Range, 2008), www.dtic.mil .

E. P. Shettle, D. R. Longtin, J. R. Hummel, and J. D. Pryce, “A wind dependent desert aerosol model: radiative properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1988), www.dtic.mil .

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

R. G. Grainger, “Some Useful Formulae for Aerosol Size Distributions and Optical Properties,” Lecture Notes (University of Oxford, 2012).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

E. P. Shettle and R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts, 1979), www.dtic.mil .

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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Figures (7)

Fig. 1.
Fig. 1.

Qext, Qsca, and Qabs versus size parameter x for a spherical particle with m=1.33, and various m values, at visible wavelength. (a) Extinction efficiency factor Qext. (b) Scattering efficiency factor Qsca. (c) Absorption efficiency factor Qabs.

Fig. 2.
Fig. 2.

Qext, Qsca, and Qabs versus size parameter x for a spherical particle with m=0.1, and various m values, at visible wavelength. (a) Extinction efficiency factor Qext. (b) Scattering efficiency factor Qsca. (c) Absorption efficiency factor Qabs.

Fig. 3.
Fig. 3.

Single-scattering phase function, P(θ), for differently sized particles with refractive index m=1.33+i108, at visible wavelength.

Fig. 4.
Fig. 4.

Optical properties of haze aerosol models in accordance with the parameters listed in Table 1. (a) Extinction coefficient kext[km1]. (b) Scattering coefficient ksca[km1]. (c) Absorption coefficient kabs[km1].

Fig. 5.
Fig. 5.

Optical properties of fog aerosol models in accordance with the parameters listed in Table 2. (a) Extinction coefficient kext[km1]. (b) Scattering coefficient ksca[km1]. (c) Absorption coefficient kabs[km1].

Fig. 6.
Fig. 6.

Phase function for tropospheric haze, moderate radiation fog, and heavy advection fog aerosol models.

Fig. 7.
Fig. 7.

Angular distribution of the detected PSFs for fog aerosol models in accordance with the data listed in Table 3. (a) Direct (coherent) PSF. (b) Scattered (incoherent) PSF. (c) Normalized total PSF.

Tables (3)

Tables Icon

Table 1. Haze Aerosol Models’ Characteristic Parameters: Bimodal Lognormal Size Distribution Function [6,11]

Tables Icon

Table 2. Fog Aerosol Models’ Characteristic Parameters: Modified Gamma Size Distribution Function [6,11]

Tables Icon

Table 3. Calculated Optical Parameters of Fog Atmospheric Aerosol Models for Various Meteorological Range (M) Values

Equations (24)

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

Qext=2x2n=1(2n+1)Re(an+bn),Qsca=2x2n=1(2n+1)(|an|2+|bn|2),Qabs=QextQsca,
ωo=σscaσext.
P(θ)=|S1(θ)|2+|S2(θ)|22πx2Qsca,
S1(θ)=n=1(2n+1)n(n+1)[anπn(cosθ)+bnτn(cosθ)]
S2(θ)=n=1(2n+1)n(n+1)[anτn(cosθ)+bnπn(cosθ)],
g=cosθ=4πP(θ)cosθdΩ,
g=4x2Qscan=1[n(n+2)n+1Re(anan+1*+bnbn+1*)+2n+1n(n+1)Re(anbn*)].
n(r)=i=1k[Ni2πln(10)rσi]exp[(log10rlog10rgi)22σi2],
n(r)=Arαexp(Brγ),
τ(λ)=kext(λ,z)dz,
kext(λ)=ksca(λ)+kabs(λ),
kext(λ)=0σext(λ,r)n(r)dr,
ksca(λ)=0σsca(λ,r)n(r)dr,
kabs(λ)=0σabs(λ,r)n(r)dr.
ωot(λ)=ksca(λ)kext(λ),
P(λ,θ)=1ksca(λ)0σsca(λ,r)P(λ,r,θ)n(r)dr,
g(λ)=1ksca(λ)0σsca(λ,r)g(λ,r)n(r)dr.
PSFt(β)=PSFdir(β)+PSFsca(β),
PSFdir(β)=eτ(D2fβ)2J12(kDβ2),
PSFsca(β)=(D2ρi)2exp[τ(1ωot)(fβρi)2],
ρi=0.26(ρAiryDρo),
ρo=1.04amodekscaz,
PSFt(β)=D24{(eτf2β2)J12(kDβ2)+(1ρi2)exp[τ(1ωot)(fβρi)2]}.
PSFn(β)=PSFdir(β)+PSFsca(β)PSFdir(0)+PSFsca(0).

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