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Corrections

E. A. Trabka, "Erratum: Wiener Spectrum of Scans Obtained from an Isotropic Two-Dimensional Random Field," J. Opt. Soc. Am. 55, 1699-1699 (1965)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-55-12-1699

References

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961), Chap. I.
  2. R. C. Jones, J. Opt. Soc. Am. 48, 934 (1958).
    [CrossRef]
  3. R. C. Jones, J. Opt. Soc. Am. 35, 151 (1945).
  4. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1963), p. 111.
  5. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, England, 1962), p. 417.
  6. E. W. H. Selwyn, Proc. Phys. Soc. (London) 55 (Part 4) 287 (July1943).
  7. See Ref. 5, p. 328.
  8. G. H. Godfrey, Austr. J. Sci. Res. (Series A) 1, 1 (1948).
  9. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, Inc., New York, 1959), p. 120.

1958 (1)

1948 (1)

G. H. Godfrey, Austr. J. Sci. Res. (Series A) 1, 1 (1948).

1945 (1)

R. C. Jones, J. Opt. Soc. Am. 35, 151 (1945).

1943 (1)

E. W. H. Selwyn, Proc. Phys. Soc. (London) 55 (Part 4) 287 (July1943).

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, Inc., New York, 1959), p. 120.

Godfrey, G. H.

G. H. Godfrey, Austr. J. Sci. Res. (Series A) 1, 1 (1948).

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 48, 934 (1958).
[CrossRef]

R. C. Jones, J. Opt. Soc. Am. 35, 151 (1945).

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1963), p. 111.

Selwyn, E. W. H.

E. W. H. Selwyn, Proc. Phys. Soc. (London) 55 (Part 4) 287 (July1943).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961), Chap. I.

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, Inc., New York, 1959), p. 120.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, England, 1962), p. 417.

Austr. J. Sci. Res. (Series A) (1)

G. H. Godfrey, Austr. J. Sci. Res. (Series A) 1, 1 (1948).

J. Opt. Soc. Am. (2)

R. C. Jones, J. Opt. Soc. Am. 48, 934 (1958).
[CrossRef]

R. C. Jones, J. Opt. Soc. Am. 35, 151 (1945).

Proc. Phys. Soc. (London) (1)

E. W. H. Selwyn, Proc. Phys. Soc. (London) 55 (Part 4) 287 (July1943).

Other (5)

See Ref. 5, p. 328.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, Inc., New York, 1959), p. 120.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1963), p. 111.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, England, 1962), p. 417.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961), Chap. I.

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Figures (2)

Fig. 1
Fig. 1

Normalized Wiener spectrum of transmittance fluctuations obtained with a circular aperture of radius r0 as a function of a normalized radian spatial “frequency” r0κ; note scale change at r0κ=3.

Fig. 2
Fig. 2

Normalized integrated Wiener spectrum of transmittance fluctuations obtained with a circular aperture of radius r0 as a function of a normalized cutoff radian spatial “frequency” r0κ0; λ fraction of total noise “power” outside radian frequency interval (−κ0, κ0); note linear approximation indicated by dashed line.

Equations (9)

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r ( τ ) = R ( τ , 0 ) .
σ 1 2 = r ( 0 ) = R ( 0 , 0 ) = σ 2 2 .
ϕ ( κ ) = 1 π κ Φ ( ω ) ω ( ω 2 - κ 2 ) 1 2 d ω .
Φ ( ω ) = - 2 d d ω 0 ϕ ( κ ) ω κ ( κ 2 - ω 2 ) 1 2 d κ .
ϕ ( κ ) = 1 π κ Φ i ( ω ) A ( ω ) 2 ω ( ω 2 - κ 2 ) 1 2 d ω ,
Φ i ( ω ) = N 0 ;             A ( ω ) = ( k / ω ) J 1 ( r 0 ω ) ,
ϕ ( κ ) = k 2 N 0 r 0 2 π · H 1 ( 2 r 0 κ ) ( r 0 κ ) 2 ,
λ = 1 - 2 { π - 1 0 r 0 κ 0 z - 2 H 1 ( 2 z ) d z } .
λ = 1 - ( r 0 κ 0 / 1.85 ) .