Abstract

New generalizations of the basic radiometric concepts of radiance, radiant emittance, and radiant intensity to fields generated by a two-dimensional stationary partially coherent source are made. It is explicitly shown how they are related to the cross-spectral density of the source. Such new definitions are consistent with the postulates of traditional radiometry.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).
  2. A. Walther, “Radiometry and coherence,”J. Opt. Soc. Am. 58, 1256–1259 (1968); “Radiometry and coherence,” J. Opt. Soc. Am. 63, 1622–1623 (1973).
    [CrossRef]
  3. E. W. Marchand, E. Wolf, “Radiometry with sources of any state of coherence,”J. Opt. Soc. Am. 64, 1219–1226 (1974).
    [CrossRef]
  4. E. W. Marchand, E. Wolf, “Angular correlation and the far-zone behavior of partially coeherent fields,”J. Opt. Soc. Am. 62, 379–385 (1972).
    [CrossRef]
  5. H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 187–336.
    [CrossRef]
  6. E. Wolf, “New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources,”J. Opt. Soc. Am. 72, 343–351 (1982).
    [CrossRef]
  7. R. Martínez-Herrero, “Expansion of the complex degree of coherence,” Nuovo Cimento B 54, 205–210 (1979); R. Martinez-Herrero, P. M. Mejías, “Relation between the expansions of the correlation function at the object and image planes for partially coherent illumination,” Opt. Commun. 37, 234–238 (1981).
    [CrossRef]
  8. P. P. Zabreyko, Integral Equations (Noordhoff, Leiden, The Netherlands, 1975), Chap. III.
  9. E. Wolf, “Coherence and radiometry,”J. Opt. Soc. Am. 68, 6–17(1978).
    [CrossRef]
  10. R. Martínez-Herrero, P. M. Mejías, “Characterization and reconstruction of planar sources that generate identical intensity distributions in the Fraunhofer zone,” Opt. Lett. 6, 607–609 (1981); “Relation among planar sources that generate the same radiant intensity at the output of a general optical system,”J. Opt. Soc. Am. 72, 765–769 (1982).
    [CrossRef] [PubMed]

1982 (1)

1981 (1)

1979 (1)

R. Martínez-Herrero, “Expansion of the complex degree of coherence,” Nuovo Cimento B 54, 205–210 (1979); R. Martinez-Herrero, P. M. Mejías, “Relation between the expansions of the correlation function at the object and image planes for partially coherent illumination,” Opt. Commun. 37, 234–238 (1981).
[CrossRef]

1978 (1)

1974 (1)

1972 (1)

1968 (1)

Gamo, H.

H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 187–336.
[CrossRef]

Marathay, A. S.

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).

Marchand, E. W.

Martínez-Herrero, R.

R. Martínez-Herrero, P. M. Mejías, “Characterization and reconstruction of planar sources that generate identical intensity distributions in the Fraunhofer zone,” Opt. Lett. 6, 607–609 (1981); “Relation among planar sources that generate the same radiant intensity at the output of a general optical system,”J. Opt. Soc. Am. 72, 765–769 (1982).
[CrossRef] [PubMed]

R. Martínez-Herrero, “Expansion of the complex degree of coherence,” Nuovo Cimento B 54, 205–210 (1979); R. Martinez-Herrero, P. M. Mejías, “Relation between the expansions of the correlation function at the object and image planes for partially coherent illumination,” Opt. Commun. 37, 234–238 (1981).
[CrossRef]

Mejías, P. M.

Walther, A.

Wolf, E.

Zabreyko, P. P.

P. P. Zabreyko, Integral Equations (Noordhoff, Leiden, The Netherlands, 1975), Chap. III.

J. Opt. Soc. Am. (5)

Nuovo Cimento B (1)

R. Martínez-Herrero, “Expansion of the complex degree of coherence,” Nuovo Cimento B 54, 205–210 (1979); R. Martinez-Herrero, P. M. Mejías, “Relation between the expansions of the correlation function at the object and image planes for partially coherent illumination,” Opt. Commun. 37, 234–238 (1981).
[CrossRef]

Opt. Lett. (1)

Other (3)

P. P. Zabreyko, Integral Equations (Noordhoff, Leiden, The Netherlands, 1975), Chap. III.

H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 187–336.
[CrossRef]

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).

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.


Figures (1)

Fig. 1
Fig. 1

Illustration of the notation used in this work.

Equations (15)

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

F ( ν ) ~ ( k 2 π ) 2 ( 2 π ) d Ω cos 2 θ D D exp [ i k s ^ ( r 2 - r 1 ) ] × Γ ¯ ( r 1 , r 2 , ν ) d 2 r 1 d 2 r 2 ,
Γ ¯ ( r 1 , r 2 , ν ) = n λ n 2 ( ν ) G n * ( r 1 , ν ) G n ( r 2 , ν ) ,
G ( r , r , ν ) = χ D ( r ) = n λ n ( ν ) G n ( r , ν ) G n * ( r , ν ) ,
Γ ¯ ( r 1 , r 2 , ν ) = D G * ( r 1 , r , ν ) G ( r 2 , r , ν ) d 2 r .
F ( ν ) ~ ( 2 π ) d Ω cos θ D B ( r , s ^ , ν ) d 2 r ,
B ( r , s ^ , ν ) = ( k 2 π ) 2 cos θ | D exp ( i k s ^ · r ) G ( r , r , ν ) d 2 r | 2 .
B ( r , s ^ , ν ) 0 ,
B ( r , s ^ , ν ) = 0             when             r D .
F ( ν ) = D E ( r , ν ) d 2 r
F ( ν ) = D J ( s ^ , ν ) d Ω ,
E ( r , ν ) = ( 2 π ) B ( r , s ^ , ν ) cos θ d Ω
J ( s ^ , ν ) cos θ D B ( r , s ^ , ν ) d 2 r ,
E ( r , ν ) 0
E ( r , ν ) = 0             when             r D ,
J ( s ^ , ν ) = ( k 2 π ) 2 cos 2 θ D D D exp [ i k s ^ · ( r 2 - r 1 ) ] × G * ( r 1 , r , ν ) G ( r 2 , r , ν ) d 2 r 1 d 2 r 2 d 2 r = ( k 2 π ) 2 cos θ D D exp [ i k s ^ · ( r 2 - r 1 ) ] × Γ ¯ ( r 1 , r 2 , ν ) d 2 r 1 d 2 r 2 ,

Metrics