Abstract

The existence of partially coherent planar sources with different states of coherence that generate identical radiant intensity distributions after light goes through a general optical system has been investigated. The relationship that must be satisfied by the cross-spectral density functions of all such sources has been derived. A general procedure for obtaining the common part of these sources from measurable radiant intensity data is presented. Also, the possibility of the existence of planar sources producing both identical optical intensity distributions at the output plane of the system and the same radiant intensity in the far zone has been analyzed. The general functional relationship among the cross-spectral density functions of all these sources has been determined.

© 1982 Optical Society of America

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References

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  1. E. W. Marchand and E. Wolf, "Radiometry with sources of any state of coherence," J. Opt. Soc. Am. 64, 1219–1226 (1974).
  2. E. Wolf, "Coherence and radiometry," J. Opt. Soc. Am. 68, 6–17 (1978).
  3. E. Wolf, "The radiant intensity from planar sources of any state of coherence," J. Opt. Soc. Am. 68, 1597–1605 (1978).
  4. E. Collet and E. Wolf, "Is complete spatial coherence necessary for the generation of highly directional light beams?" Opt. Lett. 2, 27–29 (1978).
  5. E. Collet and E. Wolf, "New equivalence theorems for planar sources that generate the same distributions of radiant intensity," J. Opt. Soc. Am. 69, 942–950 (1979).
  6. R. Martínez-Herrero and P. M. Mejías, "Characterization and reconstruction of planar sources that generate identical intensity distributions in the Fraunhofer zone," Opt. Lett. 6, 607–609 (1981).
  7. R. Martínez-Herrero and P. M. Mejías, "Relation between planar sources that generate the same intensity distribution at the output plane," J. Opt. Soc. Am. 72, 131–135 (1982).
  8. See, for example, J. Perina, Coherence of Light (Van Nostrand, London, 1971).
  9. L. Mandel and E. Wolf, "Spectral coherence and the concept of cross-spectral purity," J. Opt. Soc. Am. 66, 529–535 (1976).
  10. R. Martínez-Herrero, "Object reconstruction for the "Fourier transform optical system: uniqueness and characterization of data," Opt. Commun. 36, 261–264 (1981).
  11. A. C. Zaanen, Linear Analysis (North-Holland, Amsterdam, 1960).
  12. qi ∈ ker AÂ′AÂ⇒ AÂ′AÂqi = 0 ⇒ (AÂ′AÂqi,qi)L2(Ω×Ω) = 0 = (AÂqi, AÂqi)L2(Ω¯) AÂqi = 0.
  13. If we write C(R′) = ΣCnbn(RV), where Cn, and bn (R′) are defined in Eqs. (15) and (13), respectively, then Eq. (14) can easily be proved by taking into account Eqs. (13) and by using the fact that AÂ is linear and continuous and q ∊ ker AÂ.
  14. Condition (2) guarantees that operator -1 exists (see also Appendix A and Ref. 7).

1982

1981

R. Martínez-Herrero and P. M. Mejías, "Characterization and reconstruction of planar sources that generate identical intensity distributions in the Fraunhofer zone," Opt. Lett. 6, 607–609 (1981).

R. Martínez-Herrero, "Object reconstruction for the "Fourier transform optical system: uniqueness and characterization of data," Opt. Commun. 36, 261–264 (1981).

1979

1978

1976

1974

Collet, E.

Mandel, L.

Marchand, E. W.

Martínez-Herrero, R.

Mejías, P. M.

Perina, J.

See, for example, J. Perina, Coherence of Light (Van Nostrand, London, 1971).

Wolf, E.

Zaanen, A. C.

A. C. Zaanen, Linear Analysis (North-Holland, Amsterdam, 1960).

J. Opt. Soc. Am.

Opt. Commun.

R. Martínez-Herrero, "Object reconstruction for the "Fourier transform optical system: uniqueness and characterization of data," Opt. Commun. 36, 261–264 (1981).

Opt. Lett.

Other

See, for example, J. Perina, Coherence of Light (Van Nostrand, London, 1971).

A. C. Zaanen, Linear Analysis (North-Holland, Amsterdam, 1960).

qi ∈ ker AÂ′AÂ⇒ AÂ′AÂqi = 0 ⇒ (AÂ′AÂqi,qi)L2(Ω×Ω) = 0 = (AÂqi, AÂqi)L2(Ω¯) AÂqi = 0.

If we write C(R′) = ΣCnbn(RV), where Cn, and bn (R′) are defined in Eqs. (15) and (13), respectively, then Eq. (14) can easily be proved by taking into account Eqs. (13) and by using the fact that AÂ is linear and continuous and q ∊ ker AÂ.

Condition (2) guarantees that operator -1 exists (see also Appendix A and Ref. 7).

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