Abstract

The use of pupil-plane filters in microscopes has been proposed as a method of producing superresolution. Here it is shown that pupil-plane filters cannot increase the support of the transfer function for a large class of optical systems, implying that resolution cannot be improved solely by adding pupil-plane filters to an instrument. However, pupil filters can improve signal-to-noise performance and modify transfer-function zero crossing positions, as demonstrated through a confocal fluorescence example.

© 2004 Optical Society of America

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References

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Atti Fond. Giorgio

G. Toraldo di Francia, �??Nuovo pupille superresolventi,�?? Atti Fond. Giorgio 7, 366-372 (1952).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

M. Nagorni and S.W. Hell, �??Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts,�?? J. Opt. Soc. Am. A 18, 36-48 (2001).
[CrossRef]

S. Hell and E.H.K. Stelzer, �??Properties of a 4Pi confocal fluorescence microscope,�?? J. Opt. Soc. Am. A 9, 2159-2166 (1992).
[CrossRef]

C.J.R. Sheppard, M. Gu, Y. Kawata and S. Kawata, �??Three-dimensional transfer functions for high-aperture systems,�?? J. Opt. Soc. Am. A 11, 593-598 (1994).
[CrossRef]

M. Gu and C.J.R. Sheppard, �??Three-dimensional transfer functions in 4Pi confocal microscopes,�?? J. Opt. Soc. Am. A 11, 1619-1627 (1994).
[CrossRef]

S. Grill and E.H.K. Stelzer, �??Method to calculate lateral and axial gain factors of optical setups with a large solid angle,�?? J. Opt. Soc. Am. A 16, 2658-2665 (1999).
[CrossRef]

C.J.R. Sheppard and Z.S. Hegedus, �??Axial behavior of pupil-plane filters,�?? J. Opt. Soc. Am. A 5, 643-647 (1988).
[CrossRef]

M. Gu and C.J.R. Sheppard, �??Confocal fluorescent microscopy with a finite-sized circular detector,�?? J. Opt. Soc. Am. A 9, 151-153 (1992).
[CrossRef]

R. Heintzmann, T.M. Jovin and C. Cremer, �??Saturated patterned excitation microscopy �?? a concept for optical resolution improvement,�?? J. Opt. Soc. Am. A 19, 1599-1609 (2002).
[CrossRef]

C.W. McCutchen, �??Generalized aperture and the three-dimensional diffraction image: erratum,�?? J. Opt. Soc. Am. A 19, 1721 (2002).
[CrossRef]

A. Schonle and S.W. Hell, �??Calculation of vectorial three-dimensional transfer functions in large-angle focusing systems,�?? J. Opt. Soc. Am. A 19, 2121-2126 (2002).
[CrossRef]

D.M. de Juana, J.E. Oti, V.F. Canales and M.P. Cagigal, �??Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters,�?? J. Opt. Soc. Am. A 20, 2172-2178 (2003).
[CrossRef]

Opt. Commun.

M.R. Arnison and C.J.R. Sheppard, �??A 3D vectorial optics transfer function suitable for arbitrary pupil functions,�?? Opt. Commun. 211, 53-63 (2002).
[CrossRef]

Opt. Express

Optik

C.J.R. Sheppard, �??The spatial frequency cut-off in three-dimensional imaging,�?? Optik 72, 131-133 (1986).

C.J.R. Sheppard, �??The spatial frequency cut-off in three-dimensional imaging II,�?? Optik 74, 128-129 (1986).

C.J.R. Sheppard, �??Leaky annular pupils for improved axial imaging,�?? Optik 99, 32-34 (1995).

Phys. Lett. A

D. Mugnai, A. Ranfagni and R. Ruggeri, �??Pupils with super-resolution,�?? Phys. Lett. A 311, 77-81 (2003).
[CrossRef]

Phys. Rev. E

T.A. Klar, E. Engel and S.W. Hell, �??Breaking Abbe�??s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,�?? Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Proc. Roy. Soc. A

B. Richards and E. Wolf, �??Electromagnetic diffraction in optical systems II: Structure of the image field in an aplanatic system,�?? Proc. Roy. Soc. A (London) 253, 358-379 (1959).
[CrossRef]

Science

W. Denk, J.H. Strickler and W.W. Webb, �??Two-photon laser scanning fluorescence microscopy,�?? Science 248, 73-76 (1990).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Graphical representation of the three-dimensional Fourier transform of the amplitude PSF of an aplanatic lens. The maximum collection angle for this plot is 65°.

Fig. 2.
Fig. 2.

Lateral and axial profiles along the axes for the confocal fluorescence point spread functions. One system is aplanatic while the other uses a shaded-ring pupil filter for the excitation. Note that the lateral profiles are too similar to distinguish.

Fig. 3.
Fig. 3.

Lateral and axial profiles along the axes for the confocal fluorescence transfer functions. One system is aplanatic while the other uses a shaded-ring pupil filter for the excitation.

Fig. 4.
Fig. 4.

Axial profiles along the z axis for the confocal fluorescence transfer functions when a large detector pinhole is used. One system is aplanatic while the other uses a shaded-ring pupil filter for the excitation.

Equations (5)

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

d ( r ) = o ( r ) * h ( r ) D ( k ) = H ( k ) O ( k )
S P = { k : P ( k ) 0 }
= { k : k = 2 π n λ , θ sin 1 ( NA n ) }
h ( r ) = p ex ( r ) 2 p det ( r ) 2
H ( k ) = [ P ex ( k ) P ex ( k ) ] * [ P det ( k ) P det ( k ) ]

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