Abstract

Radiation sources that have apertures and dimensions that are comparable to those of the receivers cannot be considered as point sources when they are close to the receivers. This paper presents a method of calculating the collection efficiency of a receiver for the case in which the receiver and source are closely spaced coaxial disks. The calculations consider sources with uniform and Gaussian brightness distribution; they also consider sources and receivers whose elements have both spherically symmetrical and Lambert’s law response patterns.

© 1963 Optical Society of America

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References

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  1. W. T. Walsh, Proc. Phys. Soc. (London) 32, 59 (1919–1920).
    [Crossref]
  2. C. S. Williams, J. Opt. Soc. Am. 51, 564 (1961).
    [Crossref]
  3. E. Berne, Rev. Sci. Instr. 22, 509 (1951).
    [Crossref]
  4. J. H. Smith and M. L. Storm, J. Appl. Phys. 25, 519 (1954).
    [Crossref]
  5. A. H. Jaffey, Rev. Sci. Instr. 25, 349 (1954).
    [Crossref]
  6. R. J. Keyes and T. M. Quist, Proc. IRE 50, 1822 (1962).
    [Crossref]

1962 (1)

R. J. Keyes and T. M. Quist, Proc. IRE 50, 1822 (1962).
[Crossref]

1961 (1)

1954 (2)

J. H. Smith and M. L. Storm, J. Appl. Phys. 25, 519 (1954).
[Crossref]

A. H. Jaffey, Rev. Sci. Instr. 25, 349 (1954).
[Crossref]

1951 (1)

E. Berne, Rev. Sci. Instr. 22, 509 (1951).
[Crossref]

Berne, E.

E. Berne, Rev. Sci. Instr. 22, 509 (1951).
[Crossref]

Jaffey, A. H.

A. H. Jaffey, Rev. Sci. Instr. 25, 349 (1954).
[Crossref]

Keyes, R. J.

R. J. Keyes and T. M. Quist, Proc. IRE 50, 1822 (1962).
[Crossref]

Quist, T. M.

R. J. Keyes and T. M. Quist, Proc. IRE 50, 1822 (1962).
[Crossref]

Smith, J. H.

J. H. Smith and M. L. Storm, J. Appl. Phys. 25, 519 (1954).
[Crossref]

Storm, M. L.

J. H. Smith and M. L. Storm, J. Appl. Phys. 25, 519 (1954).
[Crossref]

Walsh, W. T.

W. T. Walsh, Proc. Phys. Soc. (London) 32, 59 (1919–1920).
[Crossref]

Williams, C. S.

J. Appl. Phys. (1)

J. H. Smith and M. L. Storm, J. Appl. Phys. 25, 519 (1954).
[Crossref]

J. Opt. Soc. Am. (1)

Proc. IRE (1)

R. J. Keyes and T. M. Quist, Proc. IRE 50, 1822 (1962).
[Crossref]

Proc. Phys. Soc. (London) (1)

W. T. Walsh, Proc. Phys. Soc. (London) 32, 59 (1919–1920).
[Crossref]

Rev. Sci. Instr. (2)

E. Berne, Rev. Sci. Instr. 22, 509 (1951).
[Crossref]

A. H. Jaffey, Rev. Sci. Instr. 25, 349 (1954).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Source-receiver geometry.

Fig. 2
Fig. 2

Collection efficiency as a function of source–receiver separation.

Tables (1)

Tables Icon

Table I Collection efficiencies for various receiver diameters and source–receiver separations.

Equations (11)

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d 4 P = N ( b ) f ( α ) b d θ d b d 2 ω .
d 2 ω = ( 1 / r 2 ) a cos α d ϕ d a ,
d 4 P n = [ N ( b ) a b cos n α / r 2 ] d a d b d θ d ϕ ,
n = 1 , spherical source and spherical receiver ; n = 2 , Lambert’s law source and spherical receiver or , spherical source and Lambert’s law receiver ; n = 3 , Lambert’s law source and Lambert’s law receiver .
β = θ - ϕ x = ( a / h ) L a = ( R a / h ) , η = θ + ϕ y = ( b / h ) L b = ( R b / h ) ,
d 4 P n = h 2 N ( y ) x y ( 1 + x 2 + y 2 - 2 x y cos β ) [ ( n / 2 ) + 1 ] d x d y d η d β .
P n = 4 π h 2 0 π 0 L b 0 L a N ( y ) x y ( 1 + x 2 + y 2 - 2 x y cos β ) [ ( n / 2 ) + 1 ] × d x d y d β .
P L = π 2 h 2 L b 2 N 0 ,
P S = 2 π 2 h 2 L b 2 N 0 .
E S ( n ) = ( P n / P S ) ( where n = 1 , 2 ) ; E L ( n ) = ( P n / P L ) ( where n = 2 , 3 ) .
N ( y ) = 2.3026 N 0 e ( - 2.3026 y 2 / L b 2 ) .