Abstract

Methods of using cw and pulsed electromagnetic sources are compared for determination of the coefficients of the Legendre polynomial expansion of the single-scattering phase function from measurements of the multiply scattered radiance emerging from the surfaces of the atmosphere. Quadrature formulas are presented with which to calculate the angular moments of the radiance needed for the methods.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).
  2. N. J. McCormick, J. Math. Phys. 20, 1504 (1979).
    [CrossRef]
  3. N. J. McCormick, R. Sanchez, J. Math. Phys. 22, 199 (1981).
    [CrossRef]
  4. R. Sanchez, N. J. McCormick, J. Quant. Spectrosc. Radiat. Transfer 28, 169 (1982).
    [CrossRef]
  5. N. J. McCormick, J. Opt. Soc. Am. 72, 756 (1982).
    [CrossRef]

1982

R. Sanchez, N. J. McCormick, J. Quant. Spectrosc. Radiat. Transfer 28, 169 (1982).
[CrossRef]

N. J. McCormick, J. Opt. Soc. Am. 72, 756 (1982).
[CrossRef]

1981

N. J. McCormick, R. Sanchez, J. Math. Phys. 22, 199 (1981).
[CrossRef]

1979

N. J. McCormick, J. Math. Phys. 20, 1504 (1979).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).

McCormick, N. J.

R. Sanchez, N. J. McCormick, J. Quant. Spectrosc. Radiat. Transfer 28, 169 (1982).
[CrossRef]

N. J. McCormick, J. Opt. Soc. Am. 72, 756 (1982).
[CrossRef]

N. J. McCormick, R. Sanchez, J. Math. Phys. 22, 199 (1981).
[CrossRef]

N. J. McCormick, J. Math. Phys. 20, 1504 (1979).
[CrossRef]

Sanchez, R.

R. Sanchez, N. J. McCormick, J. Quant. Spectrosc. Radiat. Transfer 28, 169 (1982).
[CrossRef]

N. J. McCormick, R. Sanchez, J. Math. Phys. 22, 199 (1981).
[CrossRef]

J. Math. Phys.

N. J. McCormick, J. Math. Phys. 20, 1504 (1979).
[CrossRef]

N. J. McCormick, R. Sanchez, J. Math. Phys. 22, 199 (1981).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

R. Sanchez, N. J. McCormick, J. Quant. Spectrosc. Radiat. Transfer 28, 169 (1982).
[CrossRef]

Other

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (19)

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

σ ( β ) / α = ( 4 π ) 1 n = 0 N ( 2 n + 1 ) f n P n ( β ) ,
( c 1 t + μ z + α ) L ( z , μ , ϕ , t ) = 0 2 π d ϕ 1 1 d μ σ ( β ) L ( z , μ , ϕ , t ) .
[ ( α c ) 1 t + μ x + 1 ] L ( x , μ , ϕ , t ) = ( 4 π ) 1 n = 0 N ( 2 n + 1 ) f n 0 2 π d ϕ 1 1 d μ P n ( β ) L ( x , μ , ϕ , t ) .
L m ( x , μ , t ) = ( 2 π ) 1 0 2 π cos m ϕ L ( x , μ , ϕ , t ) d ϕ ; x = x , x + ; m = 0 to N .
[ ( α c ) 1 t + μ x + 1 ] L m ( x , μ , t ) = ½ n = m N ( 2 n + 1 ) f n P n m ( μ ) 1 1 P n m ( μ ) L m ( x , μ , t ) d μ ,
( n + 1 m ) P n + 1 m ( μ ) ( 2 n + 1 ) μ P n m ( μ ) + ( n + m ) P n 1 m ( μ ) = 0 , n m ,
P m 1 m ( μ ) = 0 , P m m ( μ ) = ( 1 μ 2 ) m / 2 n = 0 m 1 ( 2 n + 1 ) , m 1 .
L m ( x , μ , s ) = 0 exp ( s t ) L m ( x , μ , t ) d t .
( μ τ + 1 ) L m ( τ , μ , s ) = ½ n = m N ( 2 n + 1 ) f n P n m ( μ ) × 1 1 P n m ( μ ) L m ( τ , μ , s ) d μ , τ τ τ + ,
n = m N A mn 0 f n = S m 0 , m = 0 to N ,
n = m N A mn 1 f n / ( 1 f n ) = S m 1 , m = 0 to N ,
A mn k = ( 1 ) n m α n m [ 1 1 μ k P n m ( μ ) L m ( τ , μ , s ) d μ ] 2 τ τ + , S m k = 4 0 1 μ 2 k L m ( τ , μ , s ) L m ( τ , μ , s ) d μ τ τ + .
( α c ) est = [ s 0 f n ( s 0 ) s f n ( s ) ] / [ f n ( s ) f n ( s 0 ) ] , n = 0 to N * .
f n = ( s s 0 ) f n ( s ) f n ( s 0 ) s f n ( s ) s 0 f n ( s 0 ) , n = 0 to N * .
1 f m = ( α c ) 1 t 2 t 1 ln [ ( t 1 t 2 ) 3 / 2 L m ( x , μ , t 1 ) L m ( x , μ , t 2 ) ] , 0 μ 1 , m = 0 to N * ,
L m ( x , μ , t ) = i = 0 N * w i m L ( x , μ , ϕ i , t ) , m = 0 to N * ,
i = 0 N * w i m cos m ϕ i = δ mm / ( 2 δ m 0 ) , m = 0 to N * , m = 0 to N * .
1 1 μ k P n m ( μ ) L m ( τ , μ , s ) d μ = j = 0 N * a j μ j k P n m ( μ j ) L m ( τ , μ j , s ) ,
a j = [ k = 0 k j N * ( μ j μ k ) ] 1 1 1 k = 0 k j N * ( μ μ k ) d μ , j = 0 to N * .

Metrics