Abstract

An analysis of the Strehl ratio and the optical transfer function as imaging quality parameters of optical elements with enhanced focal length is carried out by employing the Wigner distribution function. To this end, we use four different pupil functions: a full circular aperture, a hyper-Gaussian aperture, a quartic phase plate, and a logarithmic phase mask. A comparison is performed between the quality parameters and test images formed by these pupil functions at different defocus distances.

© 2000 Optical Society of America

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1998 (2)

1997 (1)

G. Saavedra, W. D. Furlan, E. Silvestre, E. E. Sicre, “Analysis of the irradiance along different paths in the image space using the Wigner distribution function,” Opt. Commun. 139, 11–16 (1997).
[CrossRef]

1995 (2)

E. R. Dowsky, W. Thomas Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
[CrossRef]

D. Zalvidea, M. Lehman, S. Granieri, E. E. Sicre, “Analysis of the Strehl ratio using the Wigner distribution function,” Opt. Commun. 118, 207–214 (1995).
[CrossRef]

1992 (1)

1991 (1)

1990 (1)

1988 (1)

1987 (1)

1986 (1)

1984 (1)

1983 (1)

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

1979 (2)

M. J. Bastiaans, “The Wigner distribution function and Hamilton characteristics of a geometric-optical system,” Opt. Commun. 30, 321–326 (1979).
[CrossRef]

M. J. Yzuel, F. Calvo, “A study of the possibility of image optimization by apodization filters in optical systems of residual aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

1978 (1)

M. J. Bastiaans, “The Wigner distribution function applied to optical signal and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

1974 (1)

1972 (1)

G. Häusler, “A method to increase the depth of focus by two steps image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

1971 (2)

1966 (1)

H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
[CrossRef]

1960 (1)

1957 (1)

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
[CrossRef]

1879 (1)

Lord Raleigh, “Investigations in optics with special reference to the spectroscopy,” Philos. Mag. 8, 261 (1879).
[CrossRef]

Andrés, P.

Bará, S.

Bartelt, H.

Bastiaans, M. J.

M. J. Bastiaans, “The Wigner distribution function and Hamilton characteristics of a geometric-optical system,” Opt. Commun. 30, 321–326 (1979).
[CrossRef]

M. J. Bastiaans, “The Wigner distribution function applied to optical signal and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Berriel-Valdós, L. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989), pp. 460–464.

Brenner, K. H.

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

Calvo, F.

M. J. Yzuel, F. Calvo, “A study of the possibility of image optimization by apodization filters in optical systems of residual aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

Cathey, W. Thomas

Davidson, N.

Di´az, A.

Dowsky, E. R.

Duffieux, P. M.

P. M. Duffieux, L’intégrale de Fourier et ses Applications à l’Optique (Imprimeries Oberthur, Rennes, France, 1946).

Friesem, A. A.

Furlan, W. D.

G. Saavedra, W. D. Furlan, E. Silvestre, E. E. Sicre, “Analysis of the irradiance along different paths in the image space using the Wigner distribution function,” Opt. Commun. 139, 11–16 (1997).
[CrossRef]

Granieri, S.

D. Zalvidea, M. Lehman, S. Granieri, E. E. Sicre, “Analysis of the Strehl ratio using the Wigner distribution function,” Opt. Commun. 118, 207–214 (1995).
[CrossRef]

Hasman, E.

Häusler, G.

G. Häusler, “A method to increase the depth of focus by two steps image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
[CrossRef]

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
[CrossRef]

Jaroszewicz, Z.

Kolodziejczyck, A.

Lehman, M.

D. Zalvidea, M. Lehman, S. Granieri, E. E. Sicre, “Analysis of the Strehl ratio using the Wigner distribution function,” Opt. Commun. 118, 207–214 (1995).
[CrossRef]

Lohmann, A. W.

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

Maréchal, A.

A. Maréchal, Ph.D. thesis (University of Paris, Paris, 1948).

McCrickerd, J. T.

Mino, M.

Montes, E.

Morales, J.

Ojeda-Castañeda, J.

Okano, Y.

Papoulis, A.

Pons, A.

Raleigh, Lord

Lord Raleigh, “Investigations in optics with special reference to the spectroscopy,” Philos. Mag. 8, 261 (1879).
[CrossRef]

Saavedra, G.

G. Saavedra, W. D. Furlan, E. Silvestre, E. E. Sicre, “Analysis of the irradiance along different paths in the image space using the Wigner distribution function,” Opt. Commun. 139, 11–16 (1997).
[CrossRef]

Sicre, E. E.

D. Zalvidea, E. E. Sicre, “Phase pupil functions for focal depth enhancement derived from a Wigner distribution function,” Appl. Opt. 37, 3623–3627 (1998).
[CrossRef]

G. Saavedra, W. D. Furlan, E. Silvestre, E. E. Sicre, “Analysis of the irradiance along different paths in the image space using the Wigner distribution function,” Opt. Commun. 139, 11–16 (1997).
[CrossRef]

D. Zalvidea, M. Lehman, S. Granieri, E. E. Sicre, “Analysis of the Strehl ratio using the Wigner distribution function,” Opt. Commun. 118, 207–214 (1995).
[CrossRef]

H. Bartelt, J. Ojeda-Castañeda, E. E. Sicre, “Misfocus tolerance seen by simple inspection of the ambiguity function,” Appl. Opt. 23, 2693–2696 (1984).
[CrossRef] [PubMed]

Silvestre, E.

G. Saavedra, W. D. Furlan, E. Silvestre, E. E. Sicre, “Analysis of the irradiance along different paths in the image space using the Wigner distribution function,” Opt. Commun. 139, 11–16 (1997).
[CrossRef]

Sochacki, J.

Soroko, L. M.

L. M. Soroko, “Axicons and meso-optical imaging devices,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1989), Vol. 27, pp. 109–160.

Tepichin, E.

Welford, W. T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989), pp. 460–464.

Yzuel, M. J.

M. J. Yzuel, F. Calvo, “A study of the possibility of image optimization by apodization filters in optical systems of residual aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

Zalvidea, D.

D. Zalvidea, E. E. Sicre, “Phase pupil functions for focal depth enhancement derived from a Wigner distribution function,” Appl. Opt. 37, 3623–3627 (1998).
[CrossRef]

D. Zalvidea, M. Lehman, S. Granieri, E. E. Sicre, “Analysis of the Strehl ratio using the Wigner distribution function,” Opt. Commun. 118, 207–214 (1995).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Acta (2)

H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
[CrossRef]

M. J. Yzuel, F. Calvo, “A study of the possibility of image optimization by apodization filters in optical systems of residual aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

Opt. Commun. (6)

G. Häusler, “A method to increase the depth of focus by two steps image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

M. J. Bastiaans, “The Wigner distribution function applied to optical signal and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

M. J. Bastiaans, “The Wigner distribution function and Hamilton characteristics of a geometric-optical system,” Opt. Commun. 30, 321–326 (1979).
[CrossRef]

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

D. Zalvidea, M. Lehman, S. Granieri, E. E. Sicre, “Analysis of the Strehl ratio using the Wigner distribution function,” Opt. Commun. 118, 207–214 (1995).
[CrossRef]

G. Saavedra, W. D. Furlan, E. Silvestre, E. E. Sicre, “Analysis of the irradiance along different paths in the image space using the Wigner distribution function,” Opt. Commun. 139, 11–16 (1997).
[CrossRef]

Opt. Lett. (3)

Philos. Mag. (1)

Lord Raleigh, “Investigations in optics with special reference to the spectroscopy,” Philos. Mag. 8, 261 (1879).
[CrossRef]

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

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
[CrossRef]

Other (4)

L. M. Soroko, “Axicons and meso-optical imaging devices,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1989), Vol. 27, pp. 109–160.

A. Maréchal, Ph.D. thesis (University of Paris, Paris, 1948).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989), pp. 460–464.

P. M. Duffieux, L’intégrale de Fourier et ses Applications à l’Optique (Imprimeries Oberthur, Rennes, France, 1946).

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