Abstract

The functional relationship between the total illuminance and transfer function is obtained for systems having rotationally symmetric aberrations. It is shown that the behavior of the transfer function at zero spatial frequency determines the asymptotic behavior of the total illuminance. In addition, the moments of the transfer function determine the behavior of the total illuminance in the vicinity of the origin. Typical numerical results are presented.

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  1. R. Barakat, J. Opt. Soc. Am. 52, 985 (1962).
  2. R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).
  3. R. Barakat and M. V. Morello, "Computation of the Total Illuminance of an Optical System from the Design Data for Rotationally Symmetric Aberrations" (to be published).
  4. E. L. O'Neill, Selected Topics in Optics and Communication Theory (Boston University Physical Research Laboratory, Boston, 1959).
  5. H. S. Carelaw, Introduction to the Theory of Fourier's Series and Integrals (Dover Publications, Inc., New York, 1956), 3rd ed., p. 219.
  6. B. van der Pol and H. Bremmer, Operational Calculus Based on the Two-Sided Laplace Transform (Cambridge University Press, Cambridge, England, 1950), Chap. 7.
  7. H. F. Willis, Phil. Mag. 39, 455 (1948). We had derived these relations independently although in a somewhat less satisfactory manner than Willis.
  8. R. Barakat, J. Opt. Soc. Am. 51, 152 (1961).
  9. Lord Rayleigh (J. W. Strutt), Phil. Mag. 11, 214 (1881).
  10. T. J. Bromwich, An Introduction to the Theory of Infinite Series (Macmillan and Company Ltd., New York, 1955), 2nd ed., p. 338.
  11. R. K. Luneberg, Mathematical Theory of Optics (Brown University, Providence, Rhode Island, 1944).
  12. R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).
  13. R. Barakat and L. Riseberg, "On the Theory of Aberration Balancing" (to be published).
  14. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London, 1959), Chap. 9.

Barakat, R.

R. Barakat, J. Opt. Soc. Am. 52, 985 (1962).

R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

R. Barakat and M. V. Morello, "Computation of the Total Illuminance of an Optical System from the Design Data for Rotationally Symmetric Aberrations" (to be published).

R. Barakat, J. Opt. Soc. Am. 51, 152 (1961).

R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).

R. Barakat and L. Riseberg, "On the Theory of Aberration Balancing" (to be published).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London, 1959), Chap. 9.

Bremmer, H.

B. van der Pol and H. Bremmer, Operational Calculus Based on the Two-Sided Laplace Transform (Cambridge University Press, Cambridge, England, 1950), Chap. 7.

Bromwich, T. J.

T. J. Bromwich, An Introduction to the Theory of Infinite Series (Macmillan and Company Ltd., New York, 1955), 2nd ed., p. 338.

Carelaw, H. S.

H. S. Carelaw, Introduction to the Theory of Fourier's Series and Integrals (Dover Publications, Inc., New York, 1956), 3rd ed., p. 219.

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (Brown University, Providence, Rhode Island, 1944).

Morello, M. V.

R. Barakat and M. V. Morello, "Computation of the Total Illuminance of an Optical System from the Design Data for Rotationally Symmetric Aberrations" (to be published).

R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

O’Neill, E. L.

E. L. O'Neill, Selected Topics in Optics and Communication Theory (Boston University Physical Research Laboratory, Boston, 1959).

Rayleigh, Lord

Lord Rayleigh (J. W. Strutt), Phil. Mag. 11, 214 (1881).

Riseberg, L.

R. Barakat and L. Riseberg, "On the Theory of Aberration Balancing" (to be published).

van der Pol, B.

B. van der Pol and H. Bremmer, Operational Calculus Based on the Two-Sided Laplace Transform (Cambridge University Press, Cambridge, England, 1950), Chap. 7.

Willis, H. F.

H. F. Willis, Phil. Mag. 39, 455 (1948). We had derived these relations independently although in a somewhat less satisfactory manner than Willis.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London, 1959), Chap. 9.

Other

R. Barakat, J. Opt. Soc. Am. 52, 985 (1962).

R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

R. Barakat and M. V. Morello, "Computation of the Total Illuminance of an Optical System from the Design Data for Rotationally Symmetric Aberrations" (to be published).

E. L. O'Neill, Selected Topics in Optics and Communication Theory (Boston University Physical Research Laboratory, Boston, 1959).

H. S. Carelaw, Introduction to the Theory of Fourier's Series and Integrals (Dover Publications, Inc., New York, 1956), 3rd ed., p. 219.

B. van der Pol and H. Bremmer, Operational Calculus Based on the Two-Sided Laplace Transform (Cambridge University Press, Cambridge, England, 1950), Chap. 7.

H. F. Willis, Phil. Mag. 39, 455 (1948). We had derived these relations independently although in a somewhat less satisfactory manner than Willis.

R. Barakat, J. Opt. Soc. Am. 51, 152 (1961).

Lord Rayleigh (J. W. Strutt), Phil. Mag. 11, 214 (1881).

T. J. Bromwich, An Introduction to the Theory of Infinite Series (Macmillan and Company Ltd., New York, 1955), 2nd ed., p. 338.

R. K. Luneberg, Mathematical Theory of Optics (Brown University, Providence, Rhode Island, 1944).

R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).

R. Barakat and L. Riseberg, "On the Theory of Aberration Balancing" (to be published).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London, 1959), Chap. 9.

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