Abstract

We present a new family of pupil masks to control the axial component of the intensity distribution in the focal region of tightly focused light fields. The filters, which consist of a circular clear pupil with a single shaded ring, allow to control the width of the central lobe of the axial spot together with the residual sidelobes energy. The filters can be applied to improve the optical sectioning capacity of different scanning microscopes.

© 2003 Optical Society of America

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References

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Appl. Opt. (2)

Appl. Phys. Lett. (3)

C. M. Blanca, J. Bewersdorf and S. W. Hell, �??Single sharp spot in fluorescence microscopy of two opposing lenses,�?? Appl. Phys. Lett. 79, 2321-2323 (2001)
[CrossRef]

D. Ganic, J. W. M. Chon and M. Gu, �??Effect of numerical aperture on the splitting feature near phase singularities of focused waves,�?? Appl. Phys. Lett. 82, 1527-1528 (2003).
[CrossRef]

J. W. M. Chon, X. Gan and M. Gu, �??Splitting of the focal spot of a high-numerical objective in free space,�?? Appl. Phys. Lett. 81, 1576-1579 (2002).
[CrossRef]

Atti Fond. Giorgio Ronchi (1)

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

Bioimaging (1)

C. J. R. Sheppard and P. Török, �??An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,�?? Bioimaging 5, 205-218 (1997).
[CrossRef]

J. Microsc. (2)

P. D. Higdon, P. Török and T. Wilson, �??Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,�?? J. Microsc. 193, 127-141 (1998).
[CrossRef]

K. Bahlman and S. W. Hell, �??Electric field depolarization in high aperture focusing with emphasis on annular apertures,�?? J. Microsc. 200, 59-67 (2000).
[CrossRef]

J. Mod. Opt. (1)

J. Campos, J. C. Escalera, C. J. R. Sheppard and M. J. Yzuel, �??Axially invariant pupil filters,�?? J. Mod. Opt. 47, 57-68 (2000).

J. Opt. Soc. Am. A (4)

Opt. Express (2)

Opt. Lett. (6)

Optik (2)

G. Boyer and V. Sarafis, "Two pinhole superresolution using spatial filters," Optik 112, 177-179 (2001).
[CrossRef]

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

Phys. Rev. E (1)

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, 1-9 (2001).
[CrossRef]

Proc. Roy. Soc. (London) A (1)

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

Other (3)

P. Török and F. J. Kao (eds.) Optical Imaging and Microscopy: Techniques and Advanced Systems, (Springer, Heidelberg, 2003).

J. Pawley (ed.), Handbook of Biological Confocal Microscopy (Plenun, New York, 1995).
[CrossRef]

A. Diaspro (ed.) Confocal and Two-Photon Microscopy. Foundations, Applications and Advances (Wiley, New York, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Mapped transmittance of a SR filter (black curve). The SR filter is composed by a DR filter (green curve) and a shaded ring (red curve); (b) Amplitude PSF of the SR filter (black curve) which is calculated as the sum of two amplitude PSF’s: the one of the DR filter and that of the shaded ring; (c) Intensity PSF of the SR filter, as compared with the PSF of the nonapodized objective. The parameters for the calculation were µ=0.75, η=0.68.

Fig. 2.
Fig. 2.

(a) SLPR values for families of SR filters with the same axial gain; (b) Numerically evaluated 3D PSF (pseudo-colored) of a confocal instrument with two circular pupils; (c) Same as (b) but with the selected SR filter in illumination. The parameters for the calculation where: φ=π/2, λill =350 nm, λdet =440 nm (Coumarin 400) and NA=1.2 (water).

Fig. 3.
Fig. 3.

(a) SLPR2p values for families of SR filters with the same axial gain; (b) Numerically evaluated 3D PSF (pseudo-colored) of a TPE scanning microscope with circular pupil (bottom) or with the selected SR filter (top); (c) Comparison of axial PSF’s corresponding to different kind of filters. The parameters for the calculation where: φ=π/2, λill =700 nm, and NA=1.2.

Equations (10)

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E ( r , z , φ ; λ ) = [ I 0 ( r , z ; λ ) + I 2 ( r , z ; λ ) cos φ ] i + I 2 ( r , z ; λ ) sin 2 φ j 2 I 1 ( r , z ; λ ) cos φ k ,
E ( r = 0 , z , φ ; λ ) = i I 0 ( r = 0 , z ; λ ) = i 0 α P ( θ ) ( 1 + cos θ ) exp ( i 2 π n cos θ λ z ) sin θ d θ ,
ζ = cos θ cos α 1 cos α 0.5 ; Q ( ζ ) = ( 1 + cos θ ) P ( θ ) .
E ( r = 0 , z , φ ; λ ) = E o ( z N ) = ( 1 cos α ) exp ( i π 1 + cos α 1 cos α z N ) 0.5 0.5 Q ( ζ ) exp ( i 2 π ζ z N ) d ζ ,
G A = ( 1 η μ 3 ) ( 1 η μ ) ,
PSF ( r , z , φ ; λ ill , λ det ) = PSF ill ( r , z , φ ; λ ill ) PSF det ( r , z ; λ ill ε ) =
= E ill ( r , z , φ ; λ ill ) 2 E det ( r , z , φ ; λ ill ε ) 2 φ ,
SLPR = z p + E ill ( r = 0 , z , φ ; λ ill ) 2 d z 0 z p E ill ( r = 0 , z , φ ; λ ill ) 2 d z ,
PSF 2 p ( r , z , φ ; λ ill ) = E ill ( r , z , φ ; λ ill ) 4 .
SLPR 2 p = z p + E ill ( r = 0 , z , φ ; λ ill ) 4 d z 0 z p E ill ( r = 0 , z , φ ; λ ill ) 4 d z .

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