Abstract

A correction is presented to a quantitative study [J. Opt. Soc. Am. 55, 572 (1965)] of Rayleigh’s criterion for allowable wave-front amplitude aberration. Also, for comparison, Maréchal’s alternative root-mean-square criterion is evaluated under the same conditions.

© 1999 Optical Society of America

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References

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  1. R. Barakat, “Rayleigh wavefront criterion,” J. Opt. Soc. Am. 55, 572–573 (1965).
    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).
  3. A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–277 (1947).
  4. M. R. Schroeder, “Synthesis of low-peak-factor signals and binary sequences with low autocorrelation,” IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
    [CrossRef]
  5. A. van den Bos, “A new method for synthesis of low-peak-factor signals,” IEEE Trans. Acoustics, Speech, Signal Process. ASSP-35, 120–122 (1987).
    [CrossRef]

1987

A. van den Bos, “A new method for synthesis of low-peak-factor signals,” IEEE Trans. Acoustics, Speech, Signal Process. ASSP-35, 120–122 (1987).
[CrossRef]

1970

M. R. Schroeder, “Synthesis of low-peak-factor signals and binary sequences with low autocorrelation,” IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
[CrossRef]

1965

1947

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–277 (1947).

Barakat, R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

Maréchal, A.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–277 (1947).

Schroeder, M. R.

M. R. Schroeder, “Synthesis of low-peak-factor signals and binary sequences with low autocorrelation,” IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
[CrossRef]

van den Bos, A.

A. van den Bos, “A new method for synthesis of low-peak-factor signals,” IEEE Trans. Acoustics, Speech, Signal Process. ASSP-35, 120–122 (1987).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

IEEE Trans. Acoustics, Speech, Signal Process.

A. van den Bos, “A new method for synthesis of low-peak-factor signals,” IEEE Trans. Acoustics, Speech, Signal Process. ASSP-35, 120–122 (1987).
[CrossRef]

IEEE Trans. Inf. Theory

M. R. Schroeder, “Synthesis of low-peak-factor signals and binary sequences with low autocorrelation,” IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
[CrossRef]

J. Opt. Soc. Am.

Rev. Opt. Theor. Instrum.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–277 (1947).

Other

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

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Figures (4)

Fig. 1
Fig. 1

Legendre polynomial of order 20.

Fig. 2
Fig. 2

Optical transfer function for a slit aperture as a function of the normalized spatial frequency. The aperture wave-front aberration is shaped like the Legendre polynomial of Fig. 1 and has an amplitude range of a quarter-wavelength. The triangular aberration-free optical transfer function is also shown.

Fig. 3
Fig. 3

High peak-factor function.

Fig. 4
Fig. 4

Low peak-factor function with the same rms value and Fourier amplitude content as the function of Fig. 3.

Tables (1)

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Table 1 Strehl Ratios

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