Abstract

Most optical systems have rotational symmetry. For such systems, we establish a method of finding (a) the maximum attainable modulation transfer function (MTF) at arbitrary frequency ω<sub>o</sub>; and (b) the required pupil function <i>U</i>(ω<sub>0</sub>; ρ). Physically, the latter are absorbing films in the pupil of diffraction-limited optics. The method of solution is numerical and iterative, based upon the Newton-Raphson algorithm. Solutions (a) and (b) are established at frequencies ω<sub>0</sub>=0.1, 0.2, ..., 0.9 (× optical cutoff). The computed (a) are correct to ±0.0001 over all ω<sub>0</sub> indicated. Quantities (b) have an average error over each pupil of ±0.002 for frequencies ω<sub>0</sub>≤0.5. With 0.6≤ω<sub>0</sub>≤0.9, the error is ±0.01. The curve of maximum MTF(ω<sub>0</sub>) seems sufficiently smooth to allow for accurate interpolation. Solutions (a) and (b) were also found over the finer subdivision ω<sub>0</sub>=0.05, 0.1, 0.15, …, 0.8 with slightly less accuracy than above, in order to allow for interpolation of pupils <i>U</i>(ω<sub>0</sub>; ρ) over values ω<sub>0</sub>. This seems possible for 0.05≤ω<sub>0</sub>≤0.40. The maximum MTF(ω<sub>0</sub>) shows appreciable gain (e.g., 8% at ω<sub>0</sub>=0.2) over the MTF for uncoated, diffraction-limited optics at all ω<sub>0</sub> except in the intermediate region 0.4≤ω<sub>0</sub>≤0.6. However, in the high-frequency band 0.5≤ω<sub>0</sub>≤1.0, the maximum MTF(ω<sub>0</sub>) shows little gain over the MTF due to an uncoated, diffraction-limited pupil with the proper central obstruction. The light loss due to each <i>U</i>(ω<sub>0</sub>; ρ) may be measured by the total energy transmittance and the Strehl flux ratio. These are plotted against ω<sub>0</sub>, and indicate moderate light loss.

PDF Article

References

  • View by:
  • |
  • |

  1. Limitations of this method are discussed by P. G. Roetling, E. A. Trabka, and R. E. Kinzly, J. Opt. Soc. Am. 58, 342 (1968).
  2. B. R. Frieden, J. Opt. Soc. Am. 58, 1107 (1968).
  3. J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).
  4. W. Lukosz, J. Opt. Soc. Am. 52, 827 (1962).
  5. B. P. Hildebrand, J. Opt. Soc. Am. 56, 12 (1966).
  6. E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publ. Co., Reading, Mass., 1963).
  7. R. Barakat J. Opt. Soc. Am. 54, 920 (1964).
  8. F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill Book Co., New York, 1956), p. 343.
  9. P. Jacquinot and B. Roizen-Dossier, in Progress in Optics III, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1964).

Barakat, R.

R. Barakat J. Opt. Soc. Am. 54, 920 (1964).

Frieden, B. R.

B. R. Frieden, J. Opt. Soc. Am. 58, 1107 (1968).

Hildebrand, B. P.

B. P. Hildebrand, J. Opt. Soc. Am. 56, 12 (1966).

Hildebrand, F. B.

F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill Book Co., New York, 1956), p. 343.

Jacquinot, P.

P. Jacquinot and B. Roizen-Dossier, in Progress in Optics III, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1964).

Kinzly, R. E.

Limitations of this method are discussed by P. G. Roetling, E. A. Trabka, and R. E. Kinzly, J. Opt. Soc. Am. 58, 342 (1968).

Lukosz, W.

W. Lukosz, J. Opt. Soc. Am. 52, 827 (1962).

MacDonald, J. A.

J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).

O’Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publ. Co., Reading, Mass., 1963).

Roetling, P. G.

Limitations of this method are discussed by P. G. Roetling, E. A. Trabka, and R. E. Kinzly, J. Opt. Soc. Am. 58, 342 (1968).

Roizen-Dossier, B.

P. Jacquinot and B. Roizen-Dossier, in Progress in Optics III, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1964).

Trabka, E. A.

Limitations of this method are discussed by P. G. Roetling, E. A. Trabka, and R. E. Kinzly, J. Opt. Soc. Am. 58, 342 (1968).

Other (9)

Limitations of this method are discussed by P. G. Roetling, E. A. Trabka, and R. E. Kinzly, J. Opt. Soc. Am. 58, 342 (1968).

B. R. Frieden, J. Opt. Soc. Am. 58, 1107 (1968).

J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).

W. Lukosz, J. Opt. Soc. Am. 52, 827 (1962).

B. P. Hildebrand, J. Opt. Soc. Am. 56, 12 (1966).

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publ. Co., Reading, Mass., 1963).

R. Barakat J. Opt. Soc. Am. 54, 920 (1964).

F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill Book Co., New York, 1956), p. 343.

P. Jacquinot and B. Roizen-Dossier, in Progress in Optics III, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1964).

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.