Abstract

This Letter analyzes the imaging performance of Bessel beam microscopy (BBM), an imaging technique that places an axicon in the light path of a microscope. Like other superresolution imaging techniques that attempt to narrow the point spread function, in BBM there is a trade-off between spatial resolution and relative brightness of the images. The performance of BBM is analyzed using two parameters, gain and Strehl ratio, which measure the relative spatial resolution increase and relative brightness of the images, respectively. Analytical relationships for both of these parameters are provided and compared to results calculated from simulations. Finally, an optimized BBM system design is presented which has a gain of 0.7 and a Strehl ratio of 0.9.

© 2013 Optical Society of America

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References

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2013 (2)

C. Snoeyink and S. Wereley, Exp. Fluids 54, 1453 (2013).
[CrossRef]

C. Snoeyink and S. Wereley, Opt. Lett. 38, 625 (2013).
[CrossRef]

2012 (1)

2010 (1)

J. B. Arroyo and G. M. Niconoff, Spectrum 56, 159 (2010).

2009 (1)

B. Huang, M. Bates, and X. Zhuang, Annu. Rev. Biochem. 78, 993 (2009).
[CrossRef]

2007 (1)

S. W. Hell, Science 316, 1153 (2007).
[CrossRef]

2004 (1)

H. Ding, Q. Li, and W. Zou, Opt. Commun. 229, 117 (2004).
[CrossRef]

2003 (1)

2000 (1)

M. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 2457 (2000).

1997 (1)

1970 (1)

1954 (1)

1952 (1)

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426435 (1952).

Arroyo, J. B.

J. B. Arroyo and G. M. Niconoff, Spectrum 56, 159 (2010).

Bates, M.

B. Huang, M. Bates, and X. Zhuang, Annu. Rev. Biochem. 78, 993 (2009).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Cagigal, M. P.

Canales, V. F.

Collins, J.

De Juana, D. M.

Ding, H.

H. Ding, Q. Li, and W. Zou, Opt. Commun. 229, 117 (2004).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Co., 2004), p. 491.

Hell, S. W.

S. W. Hell, Science 316, 1153 (2007).
[CrossRef]

Huang, B.

B. Huang, M. Bates, and X. Zhuang, Annu. Rev. Biochem. 78, 993 (2009).
[CrossRef]

Juskaitis, R.

M. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 2457 (2000).

Laczik, Z. J.

M. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 2457 (2000).

Li, Q.

H. Ding, Q. Li, and W. Zou, Opt. Commun. 229, 117 (2004).
[CrossRef]

McLeod, J. H.

Morris, G. M.

Neil, M. A.

M. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 2457 (2000).

Niconoff, G. M.

J. B. Arroyo and G. M. Niconoff, Spectrum 56, 159 (2010).

Oti, J. E.

Pedrotti, F. J.

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1992), p. 672.

Pedrotti, L. S.

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1992), p. 672.

Sales, T. R.

Sarafis, V.

M. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 2457 (2000).

Snoeyink, C.

Toraldo di Francia, G.

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426435 (1952).

Wereley, S.

Wilson, T.

M. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 2457 (2000).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Zhuang, X.

B. Huang, M. Bates, and X. Zhuang, Annu. Rev. Biochem. 78, 993 (2009).
[CrossRef]

Zou, W.

H. Ding, Q. Li, and W. Zou, Opt. Commun. 229, 117 (2004).
[CrossRef]

Annu. Rev. Biochem. (1)

B. Huang, M. Bates, and X. Zhuang, Annu. Rev. Biochem. 78, 993 (2009).
[CrossRef]

Exp. Fluids (1)

C. Snoeyink and S. Wereley, Exp. Fluids 54, 1453 (2013).
[CrossRef]

J. Opt. Soc. Am. (2)

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426435 (1952).

Opt. Commun. (1)

H. Ding, Q. Li, and W. Zou, Opt. Commun. 229, 117 (2004).
[CrossRef]

Opt. Lett. (5)

Science (1)

S. W. Hell, Science 316, 1153 (2007).
[CrossRef]

Spectrum (1)

J. B. Arroyo and G. M. Niconoff, Spectrum 56, 159 (2010).

Other (3)

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1992), p. 672.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Co., 2004), p. 491.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of BBM attachment. Essential components are a refocusing lens placed its focal length from microscope imaging plane, an axicon, and any modifying optics placed between the camera and axicon.

Fig. 2.
Fig. 2.

Plot of gain from simulated microscope (α=0.5°, solid curve) and from Eq. (4) (dashed curve).

Fig. 3.
Fig. 3.

Plot of theoretical (dashed curve) and simulated (solid curve) values of Strehl ratio (thick curves) and gain (thin curves) for α=1.0°, D=1.0, and flens=150mm.

Fig. 4.
Fig. 4.

Plot of theoretical (dashed curve) and simulated (solid curve) values of Strehl ratio (thick curves) and side-lobe intensity ratio (thin curves) versus gain for a high-performance setup.

Equations (16)

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dmin=fobj2.405λD2πα(n1)C,
Cmax=w0Dα(n1),
dmin=0.3828λCNA,
G=0.6275C.
SIBBMIbase.
Ibase=P0πwb2λ2ftube2,
Eax(rax,θax)=eikα(n1)raxπ1/2waxU(raxwax),
Ei(ri,θi)=ikeikC2πCEax(rax,θax)×eik2C[Drax2+Ari22raxricos(θiθax)]rdθaxdrax,
Ei(ri,θi)=ikeikC2πCπ1/2waxU(raxwax)×eik2C[2Cα(n1)rax+Drax2+Ari22raxricos(θiθax)]rdθaxdrax.
2πJ0(x)=02πeixcos(ϕϕ0)dϕ,
Ei(ri,θi)=ikeikCCπ1/2waxU(raxwax)J0(kraxriC)×eik2C[2Cα(n1)rax+Drax2+Ari2]rdrax.
rp=Cα(n1)D.
Ei(ri,θi)=i2kCα2(n1)2wax2D3J02(kα(n1)riD)×U(Cα(n1)riDwax)2eik2C(32[Cα(n1)]2D).
IBBM=2kCα2(n1)2wax2D3U(Cα(n1)riDwax)2.
IBBM=C2kα(n1)waxD2U(C)2.
S=C8πα(n1)[Mag/NA]3kD2flens.

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