Abstract

Various definitions of depth of field in the microscope are discussed. The variation in the integrated intensity in the image of a point object outside the focal plane shows how the microscope discriminates against such objects. The power diffusely scattered by a translucent object is also considered. A Type-2 scanning microscope is found to have a much reduced depth of field according to these criteria, which makes it useful for studying thick biological slices. These results do not contradict the claim that depth of field may be much increased in such a microscope by using lenses with annular pupil functions.

© 1978 Optical Society of America

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References

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  1. C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
    [CrossRef]
  2. C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
    [CrossRef]
  3. M. Minsky, U. S. Patent3,013,467, Microscopy Apparatus (Dec.19, 1961; filed Nov. 7, 1957).
  4. P. Davidovits, M. D. Egger, Appl. Opt. 10, 1615 (1971).
    [CrossRef] [PubMed]
  5. C. J. R. Sheppard, Optik 48, 329 (1977).
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).
  7. M. Abromawitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
  8. C. J. R. Sheppard, T. Wilson, J. Microsc. (Oxford), to be published.

1978

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

1977

C. J. R. Sheppard, Optik 48, 329 (1977).

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

1971

Abromawitz, M.

M. Abromawitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Choudhury, A.

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

Davidovits, P.

Egger, M. D.

Minsky, M.

M. Minsky, U. S. Patent3,013,467, Microscopy Apparatus (Dec.19, 1961; filed Nov. 7, 1957).

Sheppard, C. J. R.

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

C. J. R. Sheppard, Optik 48, 329 (1977).

C. J. R. Sheppard, T. Wilson, J. Microsc. (Oxford), to be published.

Stegun, I. A.

M. Abromawitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Wilson, T.

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

C. J. R. Sheppard, T. Wilson, J. Microsc. (Oxford), to be published.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Appl. Opt.

Opt. Acta

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

Optik

C. J. R. Sheppard, Optik 48, 329 (1977).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

M. Abromawitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

C. J. R. Sheppard, T. Wilson, J. Microsc. (Oxford), to be published.

M. Minsky, U. S. Patent3,013,467, Microscopy Apparatus (Dec.19, 1961; filed Nov. 7, 1957).

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Figures (1)

Fig. 1
Fig. 1

The variation in the integrated intensity in the image of a single-point normalized distance u from the focal plane of the microscope for a scanning microscope of Type 1 and for scanning microscopes of Type 2 with two circular pupils, and with one circular and one annular pupil.

Equations (13)

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I ( u , v ) = h 1 ( u , v ) 2 ,
I ( u , 0 ) = ( sin u u ) 2 .
I ( u , v ) = h 1 ( u , v ) h 2 ( u , v ) 2 .
I ( u , 0 ) = ( sin u u ) 4 ,
I int ( u ) = 0 I ( u , v ) v d v .
I int ( 0 ) = 0 J 1 2 ( v ) v d v = 1 2 ,
I int ( u ) = 0 | 0 1 J 0 ( v ρ ) × exp ( - 1 2 j u ρ 2 ) ρ d ρ | 4 d v ,
C ( u , v ) = 0 1 J 0 ( v ρ ) cos ( 1 2 u ρ 2 ) ρ d ρ S ( u , v ) = 0 1 J 0 ( v ρ ) sin ( 1 2 u ρ 2 ) ρ d ρ } ,
I int ( u ) = 0 ( C 2 + S 2 ) 2 v d v .
I int ( u ) = 0 | 0 1 J 0 ( v ρ ) exp ( - 1 2 j u ρ 2 ) ρ d ρ | 2 × J 0 2 ( v ) v d v ,
0 J 1 4 ( x ) d x x 3 = 0.0575 ,
0 J 1 2 ( x ) J 0 2 ( x ) x d x = 0.1486.
I diff = const [ h 1 2 ( x / M , y / M ) S ( x , y ) ] × [ h 2 2 ( x / M , y / M ) D ( x , y ) ] d x d y ,

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