Abstract

The interrelation of various image parameters such as point-spread function, line-spread function, edge response, flux passing through hole, flux passing through slit, and the spatial-frequency response is demonstrated. These image parameters are computed from the point-spread function in presence of aberrations and diffraction. The point-spread function is first calculated for varying amounts of spherical aberration, coma, astigmatism, and coma+astigmatism using the Zernike-Nijboer theory and then the other parameters are computed. The data are obtained for different focal positions. A discussion of method of computation of all these integrals on a Univac-1105 computer is included along with an analysis of errors.

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  1. E. H. Selwyn, Phot. J. B88, 6, 46 (1948).
  2. O. H. Schade, Natl. Bur. Standards (U. S.) Circ. 526 (April 29, 1954).
  3. R. K. Luneberg, Mathematical Theory of Optics (Brown University, Providence, Rhode Island, 1944).
  4. P. M. Duffieux, "L'Integrale de Fourier et ses applications à l'optique," Rennes (1946).
  5. A. Marechal, Étude des effets combines de la diffraction et des aberrations geometriques sur l'image d'un point lumineux (Editions de la Revue d'Optique Theorique et Instrumentale, Paris, France, 1948).
  6. W. H. Steel, "Étude des effets combines des aberrations et d'une obturation centrale de la pupille sur le contraste des image optique," Rev. opt. 32, 4–26, 143–178, 269–306 (1953).
  7. O. H. Schade, RCA Rev. 9 (1948).
  8. O. H. Schade, "Optical Image Evaluation," Natl. Bur. Standards (U. S.), Circ. 526 (April 1954).
  9. "Image Evaluation Symposium," Institute of Optics, University of Rochester (1955).
  10. Proc. Summer School on "Optical Image Assessment Using Frequency Response Techniques," Imperial College, London (1958).
  11. E. L. O'Neill, Tech. Note 110, BUPRL (January 1954).
  12. G. B. Parrent, thesis, Boston University (1955).
  13. H. H. Hopkins, Proc. Roy. Soc. (London) A217, 408 (1953).
  14. M. De, Proc. Roy. Soc. (London) 233A, 91 (1955).
  15. L. R. Baker, Proc. Phys. Soc. (London) BLXVIII, 871 (1955).
  16. F. D. Smith, J. Opt. Soc. Am. 45, 408 (1955).
  17. F. Zernike, Physica 5, 785 (1938).
  18. H. H. Hopkins, Proc. Roy. Soc. (London) A28 (1951).
  19. E. Wolf, Proc. Roy. Soc. (London) A230 (1955).
  20. A. Marechal and P. Croce, Compt. rend. 237, 607 (1953).
  21. E. O. O'Neill, IRE Trans. of the Profess. Group on Inf. Theory IT-2, No. 2 (1956).
  22. R. V. Shack, J. Research Nall. Bur. Standards, 56, 245 (1956).
  23. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), pp. 488–489.
  24. (x0,y0) are coordinates normalized in such a way that both the object point and its Gaussian image may be specified by the same ordered pair of numbers (x0,y0).
  25. B. R. A. Nijboer, "The Diffraction Theory of Aberrations," thesis, University of Gronigen (1942).
  26. K. Nienhuis, "On the Influence of Diffraction on Image Formation in the Presence of Aberration," thesis, University of Gronigen (1948).
  27. E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, England, 1955).

1953 (1)

W. H. Steel, "Étude des effets combines des aberrations et d'une obturation centrale de la pupille sur le contraste des image optique," Rev. opt. 32, 4–26, 143–178, 269–306 (1953).

Baker, L. R.

L. R. Baker, Proc. Phys. Soc. (London) BLXVIII, 871 (1955).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), pp. 488–489.

Croce, P.

A. Marechal and P. Croce, Compt. rend. 237, 607 (1953).

De, M.

M. De, Proc. Roy. Soc. (London) 233A, 91 (1955).

Duffieux, P. M.

P. M. Duffieux, "L'Integrale de Fourier et ses applications à l'optique," Rennes (1946).

Hopkins, H. H.

H. H. Hopkins, Proc. Roy. Soc. (London) A217, 408 (1953).

H. H. Hopkins, Proc. Roy. Soc. (London) A28 (1951).

Linfoot, E. H.

E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, England, 1955).

Luneberg, R. K.

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

Marechal, A.

A. Marechal and P. Croce, Compt. rend. 237, 607 (1953).

A. Marechal, Étude des effets combines de la diffraction et des aberrations geometriques sur l'image d'un point lumineux (Editions de la Revue d'Optique Theorique et Instrumentale, Paris, France, 1948).

Nienhuis, K.

K. Nienhuis, "On the Influence of Diffraction on Image Formation in the Presence of Aberration," thesis, University of Gronigen (1948).

Nijboer, B. R. A.

B. R. A. Nijboer, "The Diffraction Theory of Aberrations," thesis, University of Gronigen (1942).

O’Neill, E. L.

E. L. O'Neill, Tech. Note 110, BUPRL (January 1954).

O’Neill, E. O.

E. O. O'Neill, IRE Trans. of the Profess. Group on Inf. Theory IT-2, No. 2 (1956).

Parrent, G. B.

G. B. Parrent, thesis, Boston University (1955).

Schade, O. H.

O. H. Schade, "Optical Image Evaluation," Natl. Bur. Standards (U. S.), Circ. 526 (April 1954).

O. H. Schade, RCA Rev. 9 (1948).

O. H. Schade, Natl. Bur. Standards (U. S.) Circ. 526 (April 29, 1954).

Selwyn, E. H.

E. H. Selwyn, Phot. J. B88, 6, 46 (1948).

Shack, R. V.

R. V. Shack, J. Research Nall. Bur. Standards, 56, 245 (1956).

Smith, F. D.

F. D. Smith, J. Opt. Soc. Am. 45, 408 (1955).

Steel, W. H.

W. H. Steel, "Étude des effets combines des aberrations et d'une obturation centrale de la pupille sur le contraste des image optique," Rev. opt. 32, 4–26, 143–178, 269–306 (1953).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), pp. 488–489.

E. Wolf, Proc. Roy. Soc. (London) A230 (1955).

Zernike, F.

F. Zernike, Physica 5, 785 (1938).

Natl. Bur. Standards (U. S.), Circ. (1)

O. H. Schade, "Optical Image Evaluation," Natl. Bur. Standards (U. S.), Circ. 526 (April 1954).

Rev. opt. (1)

W. H. Steel, "Étude des effets combines des aberrations et d'une obturation centrale de la pupille sur le contraste des image optique," Rev. opt. 32, 4–26, 143–178, 269–306 (1953).

Other (25)

O. H. Schade, RCA Rev. 9 (1948).

E. H. Selwyn, Phot. J. B88, 6, 46 (1948).

O. H. Schade, Natl. Bur. Standards (U. S.) Circ. 526 (April 29, 1954).

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

P. M. Duffieux, "L'Integrale de Fourier et ses applications à l'optique," Rennes (1946).

A. Marechal, Étude des effets combines de la diffraction et des aberrations geometriques sur l'image d'un point lumineux (Editions de la Revue d'Optique Theorique et Instrumentale, Paris, France, 1948).

"Image Evaluation Symposium," Institute of Optics, University of Rochester (1955).

Proc. Summer School on "Optical Image Assessment Using Frequency Response Techniques," Imperial College, London (1958).

E. L. O'Neill, Tech. Note 110, BUPRL (January 1954).

G. B. Parrent, thesis, Boston University (1955).

H. H. Hopkins, Proc. Roy. Soc. (London) A217, 408 (1953).

M. De, Proc. Roy. Soc. (London) 233A, 91 (1955).

L. R. Baker, Proc. Phys. Soc. (London) BLXVIII, 871 (1955).

F. D. Smith, J. Opt. Soc. Am. 45, 408 (1955).

F. Zernike, Physica 5, 785 (1938).

H. H. Hopkins, Proc. Roy. Soc. (London) A28 (1951).

E. Wolf, Proc. Roy. Soc. (London) A230 (1955).

A. Marechal and P. Croce, Compt. rend. 237, 607 (1953).

E. O. O'Neill, IRE Trans. of the Profess. Group on Inf. Theory IT-2, No. 2 (1956).

R. V. Shack, J. Research Nall. Bur. Standards, 56, 245 (1956).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), pp. 488–489.

(x0,y0) are coordinates normalized in such a way that both the object point and its Gaussian image may be specified by the same ordered pair of numbers (x0,y0).

B. R. A. Nijboer, "The Diffraction Theory of Aberrations," thesis, University of Gronigen (1942).

K. Nienhuis, "On the Influence of Diffraction on Image Formation in the Presence of Aberration," thesis, University of Gronigen (1948).

E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, England, 1955).

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