Abstract

The basic laws of photometry are derived from the theory of partial coherence by considering a generalized form of the Van Cittert–Zernike theorem.

© 1968 Optical Society of America

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References

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  1. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Inc., Englewood Cliffs, N. J., 1964).
  2. See A. Walther, Am. J. Phys. 36, 808 (1967), where further references may be found.
    [Crossref]
  3. A. Walther, J. Opt. Soc. Am. 57, 639 (1967).
    [Crossref]
  4. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964).
  5. P. H. van Cittert, Physica 1, 201 (1934).
    [Crossref]
  6. F. Zernike, Physica 5, 785 (1938).
    [Crossref]
  7. The reader well versed in quantum mechanics will not fail to notice the suggestive similarity with the Wigner distribution.
  8. A. Sommerfeld, Optics (Academic Press Inc., New York, 1954).
  9. G. Sarfatt, Nuovo Cimento 27, 119 (1963).
    [Crossref]

1967 (2)

See A. Walther, Am. J. Phys. 36, 808 (1967), where further references may be found.
[Crossref]

A. Walther, J. Opt. Soc. Am. 57, 639 (1967).
[Crossref]

1963 (1)

G. Sarfatt, Nuovo Cimento 27, 119 (1963).
[Crossref]

1938 (1)

F. Zernike, Physica 5, 785 (1938).
[Crossref]

1934 (1)

P. H. van Cittert, Physica 1, 201 (1934).
[Crossref]

Beran, M. J.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Inc., Englewood Cliffs, N. J., 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964).

Parrent, G. B.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Inc., Englewood Cliffs, N. J., 1964).

Sarfatt, G.

G. Sarfatt, Nuovo Cimento 27, 119 (1963).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954).

van Cittert, P. H.

P. H. van Cittert, Physica 1, 201 (1934).
[Crossref]

Walther, A.

A. Walther, J. Opt. Soc. Am. 57, 639 (1967).
[Crossref]

See A. Walther, Am. J. Phys. 36, 808 (1967), where further references may be found.
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964).

Zernike, F.

F. Zernike, Physica 5, 785 (1938).
[Crossref]

Am. J. Phys. (1)

See A. Walther, Am. J. Phys. 36, 808 (1967), where further references may be found.
[Crossref]

J. Opt. Soc. Am. (1)

Nuovo Cimento (1)

G. Sarfatt, Nuovo Cimento 27, 119 (1963).
[Crossref]

Physica (2)

P. H. van Cittert, Physica 1, 201 (1934).
[Crossref]

F. Zernike, Physica 5, 785 (1938).
[Crossref]

Other (4)

The reader well versed in quantum mechanics will not fail to notice the suggestive similarity with the Wigner distribution.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954).

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Inc., Englewood Cliffs, N. J., 1964).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964).

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Figures (1)

Fig. 1
Fig. 1

Flux from radiating surface, at obliquity angle θ.

Equations (32)

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u ( x , y , z ) = u ˆ ( L , M ) exp i k ( L x + M y + N z ) d L d M , N = + ( 1 - L 2 - M 2 ) 1 2 .
ϕ = N u ˆ ( L , M ) 2 d L d M .
Γ ( x 1 , y 1 , z 1 , x 2 , y 2 , z 2 ) = Γ ˆ ( L 1 , M 1 , L 2 , M 2 ) × exp i k [ L 1 x 1 + M 1 y 1 + N 1 z 1 - L 2 x 2 - M 2 y 2 - N 2 z 2 ] d L 1 d M 1 d L 2 d M 2 .
Γ ( x 1 , y 1 , z 1 , x 2 , y 2 , z 2 ) = u ( x 1 , y 1 , z 1 ) u * ( x 2 , y 2 , z 2 ) ,
Γ ˆ ( L 1 , M 1 , L 2 , M 2 ) = u ˆ ( L 1 , M 1 ) u ˆ * ( L 2 , M 2 ) .
ϕ = N Γ ˆ ( L , M , L , M ) d L d M .
x a = 1 2 ( x 1 + x 2 ) ,             x d = x 1 - x 2 ,
L a = 1 2 ( L 1 + L 2 ) ,             L d = L 1 - L 2 ,
i k [ L 1 x 1 + M 1 y 1 - L 2 x 2 - M 2 y 2 ] = i k [ L d x a + M d y a + L a x d + M a y d ] .
Γ ( x a , y a , x d , y d ) = Γ a ( x a , y a ) Γ d ( x d , y d ) .
Γ ˆ ( L a , M a , L d , M d ) = Γ ˆ a ( L a , M a ) Γ ˆ d ( L d , M d ) ,
Γ a ( x a , y a ) Γ ˆ d ( L d , M d )
Γ d ( x d , y d ) Γ ˆ a ( L a , M a ) .
ϕ = B d A d Ω cos θ ,
ϕ = N Γ ˆ ( L , M , L , M ) d L d M .
ϕ = N a Γ ˆ ( L a , M a , 0 , 0 ) d Ω cos θ ,
Γ ˆ ( L a , M a , L d , M d ) = 1 λ 2 Γ ( L a , M a , x a , y a ) × exp - i k [ L a x a + M a y a ] d x a d y a ,
Γ ˆ ( L a , M a , 0 , 0 ) = 1 λ 2 Γ ( L a , M a , x a , y a ) d x a d y a .
ϕ = 1 λ 2 N a Γ ( L a , M a , x a , y a ) d x a d y a d Ω cos θ ,
B = ( 1 / λ 2 ) Γ ( L a , M a , x a , y a ) .
B = N 1 λ 2 Γ ( x + 1 2 ξ , y + 1 2 η , x - 1 2 ξ , y - 1 2 η ) × exp - i k [ L ξ + M η ] d ξ d η ,
B = N Γ ˆ ( L + 1 2 p , M + 1 2 q , L - 1 2 p , M - 1 2 q ) × exp i k [ p x + q y ] d p d q .
exp i k ( N 1 - N 2 ) z .
N 1 , 2 = [ 1 - ( L ± 1 2 p ) 2 - ( M ± 1 2 q ) 2 ] 1 2 .
N 1 - N 2 - ( 1 / N ) ( p L + q M ) z .
B = N Γ ˆ ( L + 1 2 p , M + 1 2 q , L - 1 2 p , M - 1 2 q ) × exp i k [ p ( x - L N z ) + q ( y - M N z ) ] d p d q .
x = x 0 + ( L / N ) z ,             y = y 0 + ( M / N ) z .
B = N 1 λ 2 Γ ( ξ , η ) exp - i k ( L ξ + M η ) d ξ d η .
L ( ξ , η ) = 1 N B exp i k ( L ξ + M η ) d L d M .
Γ ( ξ , η ) = 2 π B ( sin k p / k p ) ,
B ~ cos θ .
Γ ( ξ , η ) ~ [ 2 J 1 ( k p ) / k p ] ,