Abstract

The principle of equivalence between the imaging properties of scanning and conventional imaging systems has been proven in the past by assuming scalar sources of radiation and isotropic media. We prove here its general validity for optical systems with vector, electromagnetic sources of radiation and any optically nonactive media.

© 1977 Optical Society of America

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References

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  1. W. T. Welford, Optics in Metrology, edited by P. Mollet (Pergamon, London, 1960), pp. 85–91.
  2. E. Zeitler and M. G. R. Thomson, “Scanning transmission electron Microscopy I & II,” Optic 31, 258–280, 353–366 (1970).
  3. Dorian Kermisch, “Partially coherent image processing by laser scanning,” J. Opt. Soc. Am. 65, 887–801 (1975).
    [Crossref]
  4. M. E. Barnett, “The reciprocity theorem and the equivalence of conventional and transmission microscopes,” Optik 38, 585–588 (1973).
  5. See, for example, D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 59–65.
  6. See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 387–389.

1975 (1)

1973 (1)

M. E. Barnett, “The reciprocity theorem and the equivalence of conventional and transmission microscopes,” Optik 38, 585–588 (1973).

1970 (1)

E. Zeitler and M. G. R. Thomson, “Scanning transmission electron Microscopy I & II,” Optic 31, 258–280, 353–366 (1970).

Barnett, M. E.

M. E. Barnett, “The reciprocity theorem and the equivalence of conventional and transmission microscopes,” Optik 38, 585–588 (1973).

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 387–389.

Jones, D. S.

See, for example, D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 59–65.

Kermisch, Dorian

Thomson, M. G. R.

E. Zeitler and M. G. R. Thomson, “Scanning transmission electron Microscopy I & II,” Optic 31, 258–280, 353–366 (1970).

Welford, W. T.

W. T. Welford, Optics in Metrology, edited by P. Mollet (Pergamon, London, 1960), pp. 85–91.

Wolf, E.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 387–389.

Zeitler, E.

E. Zeitler and M. G. R. Thomson, “Scanning transmission electron Microscopy I & II,” Optic 31, 258–280, 353–366 (1970).

J. Opt. Soc. Am. (1)

Optic (1)

E. Zeitler and M. G. R. Thomson, “Scanning transmission electron Microscopy I & II,” Optic 31, 258–280, 353–366 (1970).

Optik (1)

M. E. Barnett, “The reciprocity theorem and the equivalence of conventional and transmission microscopes,” Optik 38, 585–588 (1973).

Other (3)

See, for example, D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 59–65.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 387–389.

W. T. Welford, Optics in Metrology, edited by P. Mollet (Pergamon, London, 1960), pp. 85–91.

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Figures (3)

FIG. 1
FIG. 1

Generalized representation of a scanning imaging system.

FIG. 2
FIG. 2

Representation of a flat Lambertian radiating source.

FIG. 3
FIG. 3

Generalized representation of a laser scanning imaging system.

Equations (10)

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[ E ( r 2 ) ] = [ G ( r 1 , r 2 ) ] [ A ( r 1 ) ] ,
[ E ( r ) ] = [ E 1 ( r ) E 2 ( r ) E 3 ( r ) ] , [ A ( r ) ] = [ A 1 ( r ) A 2 ( r ) A 3 ( r ) ] , and [ G ( r 1 , r 2 ) ] = [ G 11 ( r 1 , r 2 ) G 12 ( r 1 , r 2 ) G 13 ( r 1 , r 2 ) G 21 ( r 1 , r 2 ) G 22 ( r 1 , r 2 ) G 23 ( r 1 , r 2 ) G 31 ( r 1 , r 2 ) G 32 ( r 1 , r 2 ) G 33 ( r 1 , r 2 ) ] .
E i j ( r 2 ) = G i j ( r 1 , r 2 ) A i ( r 1 ) .
G i j ( r 1 , r 2 ) = G j i ( r 2 , r 1 ) .
a E ( r 1 ) = b E ( r 2 ) .
[ E ( r 1 ) ] = [ G ( r 1 , r 2 ) ] [ A ( r 2 ) ] ,
G i 3 ( r 1 , r 2 ) G 3 i ( r 1 , r 2 ) 0 ,
Q = | A 1 ( r 1 ) | 2 = | A 2 ( r 1 ) | 2 .
d [ | E i ( r 2 ) | 2 ] = j = 1 2 [ | G i j ( r 1 , r 2 ) | 2 | A j ( r 1 ) | 2 ] d r 1 .
I D = Q i = 1 2 j = 1 2 S D | G i j ( r 1 , r 2 ) | 2 d r 1 d r 2 .