Abstract

An optical technique is described which is capable of compensating the effects of imperfect spatial coherent illumination on the performance of a modified Mach-Zehnder spectrum analyzer. Methods for experimentally determining the complex mutual coherence function of the illumination using the analyzer are also described. The addition to the system of a calibrated phase shifter controlled by a minicomputer is proposed, which permits the spectral amplitude and phase to be determined automatically in real time.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Gardner, P. Ransom, W. Atkins, J. Opt. Soc. Am. 68, 909 (1978).
    [Crossref]
  2. L. M. Frantz, A. A. Sawchuk, W. von der Ohe, Appl. Opt. 18, 3301 (1979).
    [Crossref] [PubMed]
  3. M. J. Dentino, C. W. Barnes, J. Opt. Soc. Am. 60, 420 (1970).
    [Crossref]
  4. R. Mittra, P. Ransom, in Proceedings, Symposium on Modern Optics,J. Fox, Ed. (Polytechnic Press, Brooklyn, 1967), pp. 619–647.
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 83.
  6. P. L. Ransom, Appl. Opt. 11, 2554 (1972).
    [Crossref] [PubMed]

1979 (1)

1978 (1)

1972 (1)

1970 (1)

Atkins, W.

Barnes, C. W.

Dentino, M. J.

Frantz, L. M.

Gardner, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 83.

Mittra, R.

R. Mittra, P. Ransom, in Proceedings, Symposium on Modern Optics,J. Fox, Ed. (Polytechnic Press, Brooklyn, 1967), pp. 619–647.

Ransom, P.

C. Gardner, P. Ransom, W. Atkins, J. Opt. Soc. Am. 68, 909 (1978).
[Crossref]

R. Mittra, P. Ransom, in Proceedings, Symposium on Modern Optics,J. Fox, Ed. (Polytechnic Press, Brooklyn, 1967), pp. 619–647.

Ransom, P. L.

Sawchuk, A. A.

von der Ohe, W.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Other (2)

R. Mittra, P. Ransom, in Proceedings, Symposium on Modern Optics,J. Fox, Ed. (Polytechnic Press, Brooklyn, 1967), pp. 619–647.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 83.

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 (2)

Fig. 1
Fig. 1

Mach-Zehnder spectrum analyzer.

Fig. 2
Fig. 2

Modified spectrum analyzer with pupil transparency to provide optical compensation for illumination with imperfect spatial coherence.

Equations (31)

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

u ( ρ ) = a ( ρ ) + { a ( ρ i ) b ( ρ i ) } ,
B ( κ ) = α ( κ ) exp [ i θ ( κ ) ] = { b ( ρ i ) } ,
I ( ρ ) = | u ( ρ ) | 2 = I R + I S + I I ,
Γ ( ρ i ) = a ( ρ i + ρ i ) a * ( ρ i ) ,
Φ ( κ ) = [ Γ ( ρ i ) ] .
I R ( ρ ) = Γ ( 0 ) 1 .
I S ( ρ ) = Φ ( κ ) * α 2 ( κ ) | ρ = λ f κ .
I I ( ρ ) = 2 Re { Φ ( κ ) exp ( i 2 ρ κ ρ ) * B ( κ ) } | ρ = λ f κ ,
I I ( ρ ) = 2 Re { Γ ( ρ ) * [ b ( ρ ) exp ( i 2 π κ ρ ) ] } | ρ = λ f κ .
I S ( λ f κ ) = α 2 ( κ ) , I I ( λ f κ ) = 2 α ( κ ) cos [ θ ( κ ) ] .
α ( κ ) = [ I S ( λ f κ ) ] 1 / 2 ,
θ ( κ ) = ± cos 1 { I I ( λ f κ ) / 2 [ I S ( λ f κ ) ] 1 / 2 } .
g ( ρ ) = d 2 ρ l ψ f ( ρ ρ l ) ψ f * ( ρ l ) p ( ρ l ) × d 2 ρ i ψ f ( ρ l ρ i ) a ( ρ i ) b ( ρ i ) ,
ψ z ( ρ ) = i λ z exp ( i π λ z | ρ | 2 ) ,
g ( ρ ) = d 2 ρ i a ( ρ i ) b ( ρ i ) × d 2 ρ l p ( ρ l ) ψ f * ( ρ l ) ψ f ( ρ ρ l ) ψ f ( ρ l ρ i ) .
ψ f * ( ρ l ) ψ f ( ρ ρ l ) ψ f ( ρ l ρ i ) = exp ( i 2 π ρ ρ i / λ f ) ψ f ( ρ + ρ i ρ l ) .
g ( ρ ) = d 2 ρ i exp ( i 2 π ρ ρ i / λ f ) a ( ρ i ) b ( ρ i ) h ( ρ + ρ i ) ,
h ( ρ + ρ i ) = d 2 ρ l ψ f ( ρ + ρ i ρ l ) p ( ρ l ) .
u ( ρ ) = a ( ρ ) + g ( ρ ) ,
I ( ρ ) = | a ( ρ ) | 2 + | g ( ρ ) | 2 + 2 Re g ( ρ ) a * ( ρ ) .
I C ( ρ ) = g ( ρ ) a * ( ρ ) .
I C ( λ f κ ) = d 2 ρ i exp ( i 2 π κ ρ i ) b ( ρ i ) h ( ρ i + λ f κ ) a ( ρ i ) a * ( λ f κ ) .
I C ( λ f κ ) = d 2 ρ i exp ( i 2 π κ ρ i ) b ( ρ i ) h ( ρ i + λ f κ ) Γ ( ρ i + λ f κ ) ,
h ( ρ ) = 1 / Γ ( ρ ) ,
I C ( λ f κ ) = B ( κ ) ,
p ( ρ l ) = ψ f * ( ρ l ) * 1 / Γ ( ρ l ) ,
I ( ρ ) = | a ( ρ ) + a ( ρ ) | 2 ,
I ( ρ ) = 2 + 2 Re [ Γ ( 2 ρ ) ] ,
I ( ρ ) = | a ( ρ ) | 2 + | g ( ρ ) | 2 + 2 Re [ B ( ρ ) exp ( i θ 0 ) ] .
α ( ρ ) = ( I max I min ) / 4 ,
θ ( ρ ) = { [ θ 0 ] max or π [ θ 0 ] min .

Metrics