Abstract

Recent results of research in circuit theory and optics are combined to show both upper and lower bounds on the modulus of the transfer function of incoherent optical systems. The results are shown in the form of graphs. The upper bound is the best possible, but the lower has not been shown to be the greatest lower bound.

© 1966 Optical Society of America

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References

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  1. Armen H. Zemanian and Nelson Chang, IEEE Trans. Circuit Theory CT-10, 252 (1963).
    [Crossref]
  2. R. P. Boas and M. Kac, Duke Math. J. 12, 189 (1945).
    [Crossref]
  3. W. Lukosz, Opt. Acta 9, 335 (1962).
    [Crossref]

1963 (1)

Armen H. Zemanian and Nelson Chang, IEEE Trans. Circuit Theory CT-10, 252 (1963).
[Crossref]

1962 (1)

W. Lukosz, Opt. Acta 9, 335 (1962).
[Crossref]

1945 (1)

R. P. Boas and M. Kac, Duke Math. J. 12, 189 (1945).
[Crossref]

Boas, R. P.

R. P. Boas and M. Kac, Duke Math. J. 12, 189 (1945).
[Crossref]

Chang, Nelson

Armen H. Zemanian and Nelson Chang, IEEE Trans. Circuit Theory CT-10, 252 (1963).
[Crossref]

Kac, M.

R. P. Boas and M. Kac, Duke Math. J. 12, 189 (1945).
[Crossref]

Lukosz, W.

W. Lukosz, Opt. Acta 9, 335 (1962).
[Crossref]

Zemanian, Armen H.

Armen H. Zemanian and Nelson Chang, IEEE Trans. Circuit Theory CT-10, 252 (1963).
[Crossref]

Duke Math. J. (1)

R. P. Boas and M. Kac, Duke Math. J. 12, 189 (1945).
[Crossref]

IEEE Trans. Circuit Theory (1)

Armen H. Zemanian and Nelson Chang, IEEE Trans. Circuit Theory CT-10, 252 (1963).
[Crossref]

Opt. Acta (1)

W. Lukosz, Opt. Acta 9, 335 (1962).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Lower bound on the modulus of the transfer function as a function of δ.

Fig. 2
Fig. 2

Upper bound on the modulus of the transfer function as a function of ω.

Fig. 3
Fig. 3

Upper and lower bounds on the modulus of the transfer function at the second harmonic.

Fig. 4
Fig. 4

Upper and lower bounds on the modulus of the transfer function at the third harmonic.

Equations (2)

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H ( n ω ) 2 / H ( 0 ) 2 ( 1 / Q 2 ) ( 1 - Q 0 - Q 4 - Q 6 - Q 2 N - δ ) ,
H ( ω ) H ( 0 ) cos { π / [ ( W / ω ) + 1 ] } ,