Abstract

Two novel superrresolving scanning microscopes, one of which uses coherent imaging and the other incoherent imaging, are described. The optical arrangement used in the coherent microscope is similar to that in a scanning confocal microscope with the detector pinhole replaced by a special holographic mask, a Fourier lens, and a pinhole. The incoherent design uses two intensity-transmittance masks, two integrating detectors, and an electronic subtractor. The design of the microscopes is based on the results of singular-system theory, and the mask forms are calculated by means of this analysis. These arrangements obviate the need for an array of detectors to implement singular-system processing, and in the coherent case direct phase measurement is no longer required. Experimental results are presented that demonstrate a significant resolution improvement for a one-dimensional low-numerical-aperture coherent microscope.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  2. G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscope with high aperture lenses,” J. Microsc. (Oxford) 117, 219–232 (1978).
    [CrossRef]
  3. M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
    [CrossRef]
  4. M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
    [CrossRef]
  5. M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
    [CrossRef]
  6. M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
    [CrossRef]
  7. D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–63 (1961).
  8. J. G. Walker, “Optical imaging with resolution exceeding the Rayleigh criterion,” Opt. Acta 30, 1197–1202 (1983).
    [CrossRef]
  9. M. Bertero, P. Brianzi, E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Probl. 3, 195–212 (1987).
    [CrossRef]
  10. M. Bertero, C. De Mol, E. R. Pike, “Analytic inversion formula for confocal scanning microscopy,” J. Opt. Soc. Am. A 4, 1748–1750 (1987).
    [CrossRef]
  11. M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d incoherent case,” in Digest of Conference on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), paper WD4.
  12. M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
    [CrossRef]
  13. E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
    [CrossRef]
  14. J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British Patent Application89/13129 (September1989).
  15. R. E. Davies, “Inverse problems in confocal scanning microscopy,” Ph.D. dissertation (University of London, London, 1990).

1990 (1)

E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
[CrossRef]

1989 (1)

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
[CrossRef]

1987 (2)

M. Bertero, P. Brianzi, E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Probl. 3, 195–212 (1987).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, “Analytic inversion formula for confocal scanning microscopy,” J. Opt. Soc. Am. A 4, 1748–1750 (1987).
[CrossRef]

1984 (2)

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

1983 (1)

J. G. Walker, “Optical imaging with resolution exceeding the Rayleigh criterion,” Opt. Acta 30, 1197–1202 (1983).
[CrossRef]

1982 (2)

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

1978 (1)

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscope with high aperture lenses,” J. Microsc. (Oxford) 117, 219–232 (1978).
[CrossRef]

1961 (1)

D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–63 (1961).

Barends, P.

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscope with high aperture lenses,” J. Microsc. (Oxford) 117, 219–232 (1978).
[CrossRef]

Bertero, M.

M. Bertero, P. Brianzi, E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Probl. 3, 195–212 (1987).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, “Analytic inversion formula for confocal scanning microscopy,” J. Opt. Soc. Am. A 4, 1748–1750 (1987).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British Patent Application89/13129 (September1989).

Blom, P.

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscope with high aperture lenses,” J. Microsc. (Oxford) 117, 219–232 (1978).
[CrossRef]

Boccacci, P.

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

Brakenhoff, G. J.

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscope with high aperture lenses,” J. Microsc. (Oxford) 117, 219–232 (1978).
[CrossRef]

Brianzi, P.

M. Bertero, P. Brianzi, E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Probl. 3, 195–212 (1987).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

Davies, R. E.

E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d incoherent case,” in Digest of Conference on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), paper WD4.

R. E. Davies, “Inverse problems in confocal scanning microscopy,” Ph.D. dissertation (University of London, London, 1990).

De Mol, C.

M. Bertero, C. De Mol, E. R. Pike, “Analytic inversion formula for confocal scanning microscopy,” J. Opt. Soc. Am. A 4, 1748–1750 (1987).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

Parker, P.

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

Pike, E. R.

E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, “Analytic inversion formula for confocal scanning microscopy,” J. Opt. Soc. Am. A 4, 1748–1750 (1987).
[CrossRef]

M. Bertero, P. Brianzi, E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Probl. 3, 195–212 (1987).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d incoherent case,” in Digest of Conference on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), paper WD4.

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British Patent Application89/13129 (September1989).

Pollak, H. O.

D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–63 (1961).

Sheppard, C. J. R.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Slepian, D.

D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–63 (1961).

Walker, J. G.

E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

J. G. Walker, “Optical imaging with resolution exceeding the Rayleigh criterion,” Opt. Acta 30, 1197–1202 (1983).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d incoherent case,” in Digest of Conference on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), paper WD4.

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British Patent Application89/13129 (September1989).

Wilson, T.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Young, M. R.

E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
[CrossRef]

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d incoherent case,” in Digest of Conference on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), paper WD4.

Bell Syst. Tech. J. (1)

D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–63 (1961).

Europhys. Lett. (1)

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d coherent case,” Europhys. Lett. 9, 773–778 (1989).
[CrossRef]

Inverse Probl. (1)

M. Bertero, P. Brianzi, E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Probl. 3, 195–212 (1987).
[CrossRef]

J. Microsc. (Oxford) (2)

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscope with high aperture lenses,” J. Microsc. (Oxford) 117, 219–232 (1978).
[CrossRef]

E. R. Pike, R. E. Davies, J. G. Walker, M. R. Young, “An introduction to singular systems with applications to confocal scanning microscopy,” J. Microsc. (Oxford) 160, 107–114 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (5)

J. G. Walker, “Optical imaging with resolution exceeding the Rayleigh criterion,” Opt. Acta 30, 1197–1202 (1983).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV The case of uncertain localisation of nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

Other (4)

M. R. Young, R. E. Davies, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: confirmation in the 1-d incoherent case,” in Digest of Conference on Signal Recovery and Synthesis 3 (Optical Society of America, Washington, D.C., 1989), paper WD4.

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British Patent Application89/13129 (September1989).

R. E. Davies, “Inverse problems in confocal scanning microscopy,” Ph.D. dissertation (University of London, London, 1990).

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

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.


Figures (3)

Fig. 1
Fig. 1

Superresolving coherent microscope. Illuminating lens L1 focuses laser light onto small region of object O. The object is scanned in two or three dimensions with respect to the focused light. An objective lens L2 images the illuminated region of the object onto a holographic mask, which multiplies the light amplitude by its complex amplitude transmittance. A lens L3 forms the Fourier transform of the amplitude distribution at the mask, and a pinhole selects the dc component. The operations of Fourier transformation and selection of the dc component are equivalent to a spatial integration of the complex amplitude in the plane of the mask and yield the superresolved signal to a detector behind the pinhole. Output from the detector is stored for subsequent display or analysis.

Fig. 2
Fig. 2

Superresolving incoherent microscope. An illuminating lens L1 focuses laser light onto a small region of an object O stained with a fluorescent material. The object is scanned in two or three dimensions with respect to the focused light. Fluorescent light from the object is focused by an objective lens L2 and divided by a beam splitter to form two identical incoherent images on two intensity masks M+ and M−. The intensity mask M+ performs the processing that corresponds to the positive portions of the complete mask function (the negative portions being opaque), and the mask M− performs the processing that corresponds to the modulus of the negative portions of the mask (the positive portions being opaque). A signal obtained from an integrating detector behind mask M− is electronically subtracted from that of mask M+ to produce a superresolved intensity signal, which is stored for subsequent display or analysis.

Fig. 3
Fig. 3

Experimental results. The circles show the measured point-spread function obtained with the mask removed; this point-spread function is equivalent to that of a conventional coherent microscope of the same numerical aperture. The diamonds show the point-spread function data obtained with the mask in position. The increase in resolution over the conventional microscope, by approximately a factor of 1.7–1.8, is evident.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

i ( y , Δ x ) = p c ( x ) o ( Δ x x ) p o ( y x ) d x , < y < ,
o ( Δ x x ) = n = 0 k u n ( x ) i ( y , Δ x ) υ n ( y ) d y α n ,
o ( Δ x ) = i ( y , Δ x ) h ( y ) d y , h ( y ) = n = 0 k u n ( 0 ) υ n ( y ) α n .
I ( y , Δ x ) = P c ( x ) O ( Δ x x ) P o ( y x ) d x , < y < ,
O ( Δ x x ) = n = 0 k U n ( x ) I ( y , Δ x ) V n ( y ) d y A n ,
O ( Δ x ) = I ( y , Δ x ) H ( y ) d y , H ( y ) = n = 0 k U n ( 0 ) V n ( y ) A n .
o ( Δ x ) = o ( Δ x x ) p c ( x ) p o ( y x ) h ( y ) d y d x .
o ( Δ x ) = o ( x ) { p c ( x ) [ p o ( x ) h ( x ) ] } .
p s ( x ) = p c ( x ) [ p o ( x ) h ( x ) ] ,
p s ( f ) = p c ( f ) [ p o ( f ) h ( f ) ] ,
P s ( x ) = P c ( x ) [ P o ( x ) H ( x ) ]
P s ( f ) = P c ( f ) [ P o ( f ) H ( f ) ] ,
p c ( x ) = p o ( x ) = sinc ( 2 π N x λ ) , sinc ( θ ) = sin ( θ ) θ .
h ( x ) = cos ( 2 π N x λ ) .
p s ( x ) = sinc ( 2 π N x λ ) [ sinc ( 2 π N x λ ) cos ( 2 π N x λ ) ] = sinc ( 4 π N x λ ) .

Metrics