Abstract

The approximation to the defocused optical transfer function for an aberration-free system of circular aperture leads to an approximation to the corresponding three-dimensional optical transfer function. Although the former approximation is in good agreement with exact calculations, there is considerable discrepancy for the latter.

© 1991 Optical Society of America

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References

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  1. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
    [CrossRef]
  2. P. A. Stockseth, “Properties of a defocused optical system,”J. Opt. Soc. Am. 59, 1314–1321 (1969).
    [CrossRef]
  3. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  4. B. R. Frieden, “Optical transfer of the three-dimensional object,”J. Opt. Soc. Am. 57, 56–67 (1967).
    [CrossRef]
  5. A. Erhardt, G. Zinser, D. Komitowski, J. Bille, “Reconstructing 3-D light-microscopic images by digital image processing,” Appl. Opt. 24, 194–200 (1985).
    [CrossRef] [PubMed]
  6. S. Kimura, C. Munakata, “Calculation of three-dimensional optical transfer function for confocal scanning fluorescent microscope,” J. Opt. Soc. Am. A 6, 1015–1019 (1989).
    [CrossRef]
  7. S. Kimura, C. Munakata, “Three-dimensional optical transfer function for the fluorescent scanning optical microscope with a slit,” Appl. Opt. 29, 1004–1007 (1990).
    [CrossRef] [PubMed]
  8. M. M. Agrest, M. S. Maksimov, Theory of Incomplete Cylindrical Functions and Their Applications (Springer, New York, 1971).
    [CrossRef]

1990 (1)

1989 (1)

1985 (1)

1969 (1)

1967 (1)

1955 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Agrest, M. M.

M. M. Agrest, M. S. Maksimov, Theory of Incomplete Cylindrical Functions and Their Applications (Springer, New York, 1971).
[CrossRef]

Bille, J.

Erhardt, A.

Frieden, B. R.

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Kimura, S.

Komitowski, D.

Maksimov, M. S.

M. M. Agrest, M. S. Maksimov, Theory of Incomplete Cylindrical Functions and Their Applications (Springer, New York, 1971).
[CrossRef]

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Munakata, C.

Stockseth, P. A.

Zinser, G.

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Figures (5)

Fig. 1
Fig. 1

Contours of the three-dimensional OTF, with m the radial and r the axial normalized spatial frequencies: (a) exact theory, (b) approximate theory.

Fig. 2
Fig. 2

Three-dimensional OTF as a surface in three dimensions: (a) exact theory, (b) approximate theory.

Fig. 3
Fig. 3

Sections through the OTF for r = 0: (a) exact theory, (b) approximate theory.

Fig. 4
Fig. 4

Sections through the OTF for r = 1/4: (a) exact theory, (b) approximate theory.

Fig. 5
Fig. 5

Section: through the OTF for m = 1: (a) exact-theory, (b) approximate theeory.

Equations (8)

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C 2 ( m , 0 ; u ) = Λ ( m ) { 2 J 1 [ u m ( 1 - m / 2 ) ] u m ( 1 - m / 2 ) } ,             m 2 ,
u = 4 k z sin 2 ( α / 2 ) ,
Λ ( m ) = 2 π [ cos - 1 ( m 2 ) - m 2 ( 1 - m 2 ) 1 / 2 ] ,
C 3 ( m , 0 , r ) = Λ ( m ) m ( 1 - m / 2 ) Re ( { 1 - [ r m ( 1 - m / 2 ) ] 2 } 1 / 2 ) ,
C 3 ( m , 0 , r ) = 1 m Re { [ 1 - ( r m + m 2 ) 2 ] 1 / 2 } .
r = m ( 1 - m / 2 ) .
C 2 ( m , 0 ; u ) = 1 m 0 m ( 1 - m / 2 ) [ 1 - ( r m + m 2 ) 2 ] 1 / 2 × cos ( u r ) d r ,
C 2 ( m , 0 ; u ) = m / 2 1 ( 1 - l 2 ) 1 / 2 cos [ u m ( l - m 2 ) ] d l .

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