Abstract

Monte Carlo techniques are used to simulate atmospheric point-spread functions (PSF’s) that are appropriate for the viewing geometries typical of the Airborne Visible–Infrared Imaging Spectrometer (AVIRIS). A model sensor is located at an altitude of 20 km and views a Lambertian surface through a horizontally homogeneous and vertically stratified atmosphere. Simulations show the effects on the PSF of variation of the aerosol phase function, the aerosol optical thickness, the sensor viewing angle, and the wavelength. An algorithm that uses the PSF to correct high-contrast images for adjacency effects is developed and applied to an AVIRIS image of Big Pine Key in the Florida Keys. A method to approximate the atmospheric PSF’s without the need to resort to a Monte Carlo simulation is described. Correction of the AVIRIS image through the use of the approximated PSF is consistent with a previous correction. Error analysis is difficult and scene dependent; however, the correction algorithm is shown to be capable of indicating regions of high-contrast images in which conventional estimates of surface-leaving radiance are likely to be unreliable due to adjacency effects.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. H. Gordon, “Ship perturbation of irradiance measurements at sea. 1: Monte Carlo simulations,” Appl. Opt. 24, 4172–4182 (1985).
    [CrossRef] [PubMed]
  18. C. Mobley, B. Gentili, H. Gordon, Z. Jin, G. Kattawar, A. Morel, T. G. Floppini, K. Stamnes, R. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
    [CrossRef] [PubMed]
  19. H. Gordon, J. Brown, R. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862–871 (1988).
    [CrossRef] [PubMed]
  20. H. Gordon, D. Castano, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
    [CrossRef] [PubMed]
  21. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” Rep. AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).
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    [CrossRef] [PubMed]
  23. G. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
    [CrossRef]

1994 (1)

1993 (2)

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

C. Mobley, B. Gentili, H. Gordon, Z. Jin, G. Kattawar, A. Morel, T. G. Floppini, K. Stamnes, R. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

1992 (1)

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

1991 (1)

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

1989 (1)

1988 (1)

1987 (1)

1986 (2)

1985 (1)

1984 (1)

1983 (1)

1982 (1)

1981 (2)

1980 (1)

1979 (2)

1978 (1)

1975 (1)

G. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

Bissonnette, L.

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

Broenkow, W.

Brown, J.

Brown, O.

Bruscaglioni, P.

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

Carder, K.

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

Carswell, A.

Castano, D.

Chen, R.

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

Clark, D.

Davis, C.

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

de Leffe, A.

Deschamps, P.

Donelli, P.

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

Elterman, L.

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” Rep. AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).

Evans, R.

Floppini, T. G.

Fraser, R.

Gencay, Y.

Gentili, B.

Gordon, H.

Hamilton, M.

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

Herman, M.

Ishimaru, A.

Ismaelli, A.

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Jin, Z.

Kaestner, M.

Kattawar, G.

Kaufman, Y.

Kopeika, N.

Kuga, Y.

Mobley, C.

Morel, A.

Muller-Karger, F.

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

Otterman, J.

Pearce, W.

Quenzel, H.

Reinersman, P.

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

Ryan, J.

Solomon, S.

Stamnes, K.

Stavn, R.

Tanre, D.

Wang, M.

Zaccanti, G.

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

Appl. Opt. (14)

J. Otterman, R. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979).
[CrossRef] [PubMed]

D. Tanre, M. Herman, P. Deschamps, A. de Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18, 3587–3594 (1979).
[CrossRef] [PubMed]

H. Quenzel, M. Kaestner, “Optical properties of the atmosphere: calculated variability and application to satellite remote sensing of phytoplankton,” Appl. Opt. 19, 1338–1344 (1980).
[CrossRef] [PubMed]

D. Tanre, M. Herman, P. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981).
[CrossRef] [PubMed]

H. Gordon, D. Clark, J. Brown, O. Brown, R. Evans, W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

Y. Kaufman, “Atmospheric effect on spatial resolution of surface imagery: errata,” Appl. Opt. 23, 4164–4172 (1984).
[CrossRef] [PubMed]

H. Gordon, “Ship perturbation of irradiance measurements at sea. 1: Monte Carlo simulations,” Appl. Opt. 24, 4172–4182 (1985).
[CrossRef] [PubMed]

W. Pearce, “Monte Carlo study of the atmospheric spread function,” Appl. Opt. 25, 438–447 (1986).
[CrossRef] [PubMed]

Y. Kuga, A. Ishimaru, “Modulation transfer function of layered inhomogeneous random media using the small-angle approximation,” Appl. Opt. 25, 4382–4385 (1986).
[CrossRef] [PubMed]

H. Gordon, J. Brown, R. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862–871 (1988).
[CrossRef] [PubMed]

H. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
[CrossRef] [PubMed]

H. Gordon, D. Castano, “Coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

H. Gordon, D. Castano, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
[CrossRef] [PubMed]

C. Mobley, B. Gentili, H. Gordon, Z. Jin, G. Kattawar, A. Morel, T. G. Floppini, K. Stamnes, R. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Quant. Spectrosc. Radiat. Transfer (1)

G. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

Opt. Eng. (1)

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

Remote Sensing Environ. (1)

K. Carder, P. Reinersman, R. Chen, F. Muller-Karger, C. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sensing Environ. 44, 205–216 (1993).
[CrossRef]

Other (2)

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” Rep. AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

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Figures (29)

Fig. 1
Fig. 1

Viewing geometry for the simulation of P[θ(i); k, l]. The sensor is located over the center column of the AVIRIS image and is viewing a pixel in column i of the AVIRIS image. The PSF image is centered on the target pixel. The viewing plane is perpendicular to the surface and contains the viewing path. The half-plane beyond the viewing path lies to the right of column i.

Fig. 2
Fig. 2

Aerosol phase functions used in this study. The solid curve represents the marine aerosol, the dashed curve, haze L, and the dotted curve, modified haze C.

Fig. 3
Fig. 3

PSF weight of 20-m-wide annuluses that are centered on target. The solid curve represents the marine aerosol (MA), the dashed curve, haze L (HL), and the dotted curve, modified haze C (MHC).

Fig. 4
Fig. 4

PSF weight of the circular regions centered on the target plotted as function of the radius R. The PSF’s were calculated by summation of individual annulus weights for annuluses with an outer radius of rR. The solid curve represents the marine aerosol (MA), the dashed curve is haze L (HL), and the dotted curve, modified haze C (MHC).

Fig. 5
Fig. 5

Nadir-viewing PSF near-target-pixel weights tallied by means of the scattering history at (a) 400 nm and (b) 800 nm. The data were taken from an 11-pixel span of the PSF-image row that was centered on the target pixel.

Fig. 6
Fig. 6

PSF near-target-pixel weight. The data were taken from an 11-pixel span of the PSF-image row that was centered on the target pixel. The solid curve represents a nadir viewing angle, the dashed curve a viewing angle of 20°, and the dotted curve a viewing angle of 40° at (a) 400 nm and (b) 800 nm.

Fig. 7
Fig. 7

PSF weights of the half-planes versus the viewing angle for (a) 400 nm and (b) 800 nm. Half-planes are defined by the line passing through the target pixel perpendicular to the viewing plane. The upper curve of each pair (solid, dashed, etc.) represents half-plane beneath the viewing path; the lower curve represents the half-plane beyond the viewing path. The solid curves represent the total PSF weight; the dashed curves are PSF weights solely from aerosol scattering; the dashed–dotted curves are the PSF weights solely from Rayleigh scattering; the dotted curves are the PSF weights from Rayleigh–aerosol interaction scattering.

Fig. 8
Fig. 8

Transmittances versus the viewing angle at (a) 400 nm and (b) 800 nm. The solid curves are as follows: out is the total PSF weight arising from the region beyond the boundary of the PSF image; in is the total PSF weight of the PSF image; t b is the beam transmittance given by Eq. (5); t d = t b + in + out. The dotted curve represents the diffuse transmittance obtained with Eq. (3).

Fig. 9
Fig. 9

PSF weights of the circular regions centered on the target pixel for four aerosol optical thicknesses. τ r = 0.093 and τ0 = 0.011 for all curves; the curve labeled for τ a = 0.244 corresponds to the 550-nm atmosphere from Elterman.21

Fig. 10
Fig. 10

Transmittances for the atmospheres simulated for Fig. 8; t d and t b were calculated as for Fig. 7. The dashed–dotted curve represents contribution t d , solely from aerosol scattering; the dashed curve represents contribution t d , solely from Rayleigh scattering; the dotted curve represents contribution t d , from the Rayleigh–aerosol interaction scattering.

Fig. 11
Fig. 11

Sum of the Rayleigh-scattering and the Rayleigh–aerosol interaction-scattering contributions to the PSF weight of the circular regions that are centered on the target pixel for two of the atmospheres simulated for Fig. 8: the Solid curve is τ a = 0.971 and the dotted curve, τ a = 0.032.

Fig. 12
Fig. 12

PSF weights of 20-m-wide annuluses that are centered on the target pixel for the atmospheres simulated for Fig. 8 and tallied by their scattering histories: (a) τ a = 0.032, (b) τ a = 0.244, (c) τ a = 0.486, and (d) τ a = 0.971.

Fig. 13
Fig. 13

Nadir-viewing PSF near-target pixel weights. The data were taken from an 11-pixel span of the PSF-image row. The left-most pixel is the target. The solid curves represent 550 nm; dashed curves, 400 nm; and dotted curves, 800 nm.

Fig. 14
Fig. 14

PSF weights of the circular regions centered on the target pixel for 400 nm (solid curve), 550 nm (dashed curve), and 800 nm (dotted curve).

Fig. 15
Fig. 15

PSF weights of the circular regions centered on the target pixel and tallied by their scattering histories. The upper three curves show the weights that are due solely to aerosol scattering; the lower three curves show the sum of the weights that are due to Rayleigh and Rayleigh–aerosol interaction scattering. The solid curves represent 550 nm; dashed curves, 400 nm; and dotted curves, 800 nm.

Fig. 16
Fig. 16

Transmittances versus wavelengths: t d is from Eq. (3) and t b is from Eq. (5) with Elterman’s 550-nn atmosphere.21 The crosses indicate values derived from Monte Carlo simulations at 400, 550, and 800 nm with Eq. (6).

Fig. 17
Fig. 17

Relative positions of the AVIRIS surface image and the PSF image when the arbitrary pixel (i, j) is corrected.

Fig. 18
Fig. 18

PSF weight per unit surface area for regions beyond the PSF image.

Fig. 19
Fig. 19

Fractional error in the PSF target-pixel weight estimation resulting from approximation with Eqs. (14), (16a), and (16b).

Fig. 20
Fig. 20

Trimmed AVIRIS image of Pine Key in the Florida Keys: the image was acquired from an altitude of 20 km at 800 nm.

Fig. 21
Fig. 21

Positive correction image of Fig. 20: The positive values of Cor7 were scaled to 256 gray levels, and the negative values set to 0. The brightest areas correspond to the largest additive image corrections resulting from the PSF-correction algorithm.

Fig. 22
Fig. 22

Negative correction image of Fig. 20: The negative values of Cor7 were scaled to 256 gray levels, and the positive values set to 0. The brightest areas correspond to the largest subtractive image corrections resulting from the PSF-correction algorithm.

Fig. 23
Fig. 23

Transect A surface-leaving radiance values: The distance scale begins at the lower end of the transect. The dotted curve represents radiance before correction for the adjacency effect and the solid curve radiance after correction for adjacency effect through the use of the PSF generated with the Monte Carlo technique.

Fig. 24
Fig. 24

Correction for the adjacency effect along transect A. The curve shown represents the difference between the solid and dotted curves from Fig. 22.

Fig. 25
Fig. 25

Correction for the adjacency effect along transect B. The curve shown represents the difference between the solid and dotted curves from Fig. 24.

Fig. 26
Fig. 26

Correction for the adjacency effect along Transect C.

Fig. 27
Fig. 27

PSF weight of the circular regions centered on the target pixel for 400, 550, and 800 nm. The solid curves are the results of the Monte Carlo simulation; the dotted–dashed lines are the results of calculations with Eq. (22).

Fig. 28
Fig. 28

Nadir-viewing PSF near-target pixel weight at 800 nm for Pine Key. The solid curve is the result of the Monte Carlo simulation; the dotted curve is the approximated PSF resulting from calculations with Eqs. (22) and (23).

Fig. 29
Fig. 29

Corrections for the adjacency effect along Transect A. The solid curve is the correction resulting from a PSF generated with the Monte Carlo technique and is shown also in Fig. 23; the dotted curve is the correction resulting from the application of the approximated PSF.

Tables (3)

Tables Icon

Table 1 Defining Aerosol-Parameter Values

Tables Icon

Table 2 Simulation Parameters

Tables Icon

Table 3 Convergence of the Iterative Correction for the PSF’sa

Equations (24)

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L t = L r + L a + L ra + L g + t d L s ,
L t - L r - L a - L ra = t d L s L v ,
t d = exp [ - ( 0.5 τ r + τ a ( 1 - w a F ) + τ 0 ) / cos ( θ ) ] ,
L v ( i , j ) = t b ( i , j ) L s ( i , j ) + k l P ( i , j ; k , l ) L s ( i + k , j + l ) .
t b ( i , j ) = exp [ - ( τ r + τ a + τ 0 ) / cos ( θ ) ] .
t d ( i , j ) = t b ( i , j ) + k l P ( i , j ; k , l ) .
P r ( θ ) = ( 3 / 16 π ) ( 1 + cos 2 ( θ ) ) ,
P a ( θ ) = α F ( θ , g 1 ) + ( 1 - α ) F ( θ , g 2 ) ,
F ( θ , g ) = ( 1 / 4 π ) ( 1 - g 2 ) ( 1 + g 2 - 2 g cos ( θ ) ) - 1.5 .
L s ( i , j ) = { L v ( i , j ) - k l ( L s + L s ( i + k , j + l ) ) × P ( θ ( i ) ; k , l ) } / t b ( θ ( i ) ) .
L s ( i , j ) = L s ( i , j ) - L s .
P ( θ ( i ) , IN ) + P ( θ ( i ) , OUT ) = t d ( θ ( i ) ) - t b ( θ ( i ) ) .
L s ( i , j ) = { L v ( i , j ) - L s [ t d ( θ ( i ) ) - t b ( θ ( i ) ) ] - k l L s ( i + k , j + l ) ) P ( θ ( i ) ; k , l ) } / t b ( θ ( i ) ) .
P ( θ ( i ) ; k , l ) = n ( θ ( i ) ) P 0 ( k , l ) ,
L s ( i , j ) = { L v ( i , j ) - L s [ t d ( θ ( i ) ) - t b ( θ ( i ) ) ] - n ( θ ( i ) ) × k l L s ( i + k , j + l ) ) P 0 ( k , l ) } / t b ( θ ( i ) ) .
n ( θ ( i ) ) = cos ( θ ( i ) ) ,
P 0 ( k , l ) = P ( θ = 0 ; k , l ) ,
Cor n ( i , j ) = L s n ( i , j ) - L s 0 ( i , j ) .
t aer = t d exp ( - 0.5 τ ray ) - t b ,
t rra = t d - t b - t aer .
cum aer ( R ) = t aer [ 1 - 0.326 exp ( - 0.234 R ) - 0.674 exp ( - 3.1 R ) ] ,
cum rra ( R ) = t rra [ 1 - 0.084 exp ( - 0.51 R ) - 0.916 exp ( - 0.0821 R ) ] ,
cum ( R ) = cum aer ( R ) + cum rra ( R ) .
PSF dens = [ 1 / ( 2 π R × 10 - 6 ) ] d d R [ cum ( R ) ] ,

Metrics