Abstract

Stimulated emission depletion (STED) microscopes, like all super-resolution methods, are sensitive to aberrations. Of particular importance are aberrations that affect the quality of the depletion focus, which requires a point of near-zero intensity surrounded by strong illumination. We present analysis, modeling, and experimental measurements that show the effects of coma aberrations on depletion patterns of two-dimensional (2D) and three-dimensional (3D) STED configurations. Specifically, we find that identical coma aberrations create focal shifts in opposite directions in 2D and 3D STED. This phenomenon could affect the precision of microscopic measurements and has ramifications for the efficacy of combined 2D/3D STED systems.

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Corrections

2 August 2016: A correction was made to Eq. 1.


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References

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2016 (2)

B. R. Patton, D. Burke, D. Owald, T. J. Gould, J. Bewersdorf, and M. J. Booth, Opt. Express 24, 8862 (2016).
[Crossref]

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

2015 (1)

B. R. Patton, D. Burke, R. Vrees, and M. J. Booth, Meth. Appl. Fluoresc. 3, 024002 (2015).
[Crossref]

2014 (1)

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

2013 (1)

2012 (1)

2011 (1)

M. R. Foreman and P. Török, J. Mod. Opt. 58, 339 (2011).
[Crossref]

2010 (1)

2009 (2)

2008 (2)

2007 (2)

2004 (2)

1994 (1)

1976 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

Allgeyer, E. S.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Auksorius, E.

Baddeley, D.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Bewersdorf, J.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

B. R. Patton, D. Burke, D. Owald, T. J. Gould, J. Bewersdorf, and M. J. Booth, Opt. Express 24, 8862 (2016).
[Crossref]

T. J. Gould, D. Burke, J. Bewersdorf, and M. J. Booth, Opt. Express 20, 20998 (2012).
[Crossref]

Booth, M.

Booth, M. J.

Boruah, B. R.

Bottanelli, F.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Brown, A. C. N.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

Burke, D.

Cheng, Y.

Clegg, J. H.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

J. H. Clegg and M. A. A. Neil, Opt. Lett. 38, 1043 (2013).
[Crossref]

Davis, D. M.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

Deng, S.

Dunsby, C.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

E. Auksorius, B. R. Boruah, C. Dunsby, P. M. P. Lanigan, G. Kennedy, M. A. A. Neil, and P. M. W. French, Opt. Lett. 33, 113 (2008).
[Crossref]

Erdmann, R. S.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Foreman, M. R.

M. R. Foreman and P. Török, J. Mod. Opt. 58, 339 (2011).
[Crossref]

French, P. M. W.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

E. Auksorius, B. R. Boruah, C. Dunsby, P. M. P. Lanigan, G. Kennedy, M. A. A. Neil, and P. M. W. French, Opt. Lett. 33, 113 (2008).
[Crossref]

Gould, T. J.

Harke, B.

B. Harke, C. K. Ullal, J. Keller, and S. W. Hell, Nano Lett. 8, 1309 (2008).
[Crossref]

Hell, S. W.

S. W. Hell, Nat. Methods 6, 24 (2009).
[Crossref]

B. Harke, C. K. Ullal, J. Keller, and S. W. Hell, Nano Lett. 8, 1309 (2008).
[Crossref]

J. Keller, A. Schönle, and S. W. Hell, Opt. Express 15, 3361 (2007).
[Crossref]

S. W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994).
[Crossref]

Keller, J.

B. Harke, C. K. Ullal, J. Keller, and S. W. Hell, Nano Lett. 8, 1309 (2008).
[Crossref]

J. Keller, A. Schönle, and S. W. Hell, Opt. Express 15, 3361 (2007).
[Crossref]

Kennedy, G.

Kromann, E. B.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Lanigan, P. M. P.

Lenz, M. O.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

Li, R.

Liu, L.

Munro, P. R. T.

Neil, M. A. A.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

J. H. Clegg and M. A. A. Neil, Opt. Lett. 38, 1043 (2013).
[Crossref]

E. Auksorius, B. R. Boruah, C. Dunsby, P. M. P. Lanigan, G. Kennedy, M. A. A. Neil, and P. M. W. French, Opt. Lett. 33, 113 (2008).
[Crossref]

Noll, R. J.

Owald, D.

Patton, B. R.

B. R. Patton, D. Burke, D. Owald, T. J. Gould, J. Bewersdorf, and M. J. Booth, Opt. Express 24, 8862 (2016).
[Crossref]

B. R. Patton, D. Burke, R. Vrees, and M. J. Booth, Meth. Appl. Fluoresc. 3, 024002 (2015).
[Crossref]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

Rothman, J. E.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Savell, A.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

Schepartz, A.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Schönle, A.

Schwertner, M.

Sinclair, H. G.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

Sirinakis, G.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Toomre, D. K.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Török, P.

M. R. Foreman and P. Török, J. Mod. Opt. 58, 339 (2011).
[Crossref]

P. Török and P. R. T. Munro, Opt. Express 12, 3605 (2004).
[Crossref]

Ullal, C. K.

B. Harke, C. K. Ullal, J. Keller, and S. W. Hell, Nano Lett. 8, 1309 (2008).
[Crossref]

Vrees, R.

B. R. Patton, D. Burke, R. Vrees, and M. J. Booth, Meth. Appl. Fluoresc. 3, 024002 (2015).
[Crossref]

Wichmann, J.

Wilson, T.

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

Wood Baguley, S.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Xu, Z.

J. Biophoton. (1)

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. N. Brown, D. M. Davis, C. Dunsby, M. A. A. Neil, and P. M. W. French, J. Biophoton. 7, 29 (2014).
[Crossref]

J. Mod. Opt. (1)

M. R. Foreman and P. Török, J. Mod. Opt. 58, 339 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

Meth. Appl. Fluoresc. (1)

B. R. Patton, D. Burke, R. Vrees, and M. J. Booth, Meth. Appl. Fluoresc. 3, 024002 (2015).
[Crossref]

Nano Lett. (1)

B. Harke, C. K. Ullal, J. Keller, and S. W. Hell, Nano Lett. 8, 1309 (2008).
[Crossref]

Nat. Commun. (1)

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, Nat. Commun. 7, 10778 (2016).

Nat. Methods (1)

S. W. Hell, Nat. Methods 6, 24 (2009).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

Philos. Trans. R. Soc. A (1)

M. J. Booth, Philos. Trans. R. Soc. A 365, 2829 (2007).
[Crossref]

Proc. R. Soc. London A (1)

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

(a)  x y cross sections of the 2D depletion focus measured by scanning a 150 nm gold bead for different values of the coma aberration c . The white vertical bars mark the center of each image ( 1.55    μm × 1.55    μm ). (b)  x y cross sections of the 3D depletion focus. Each image uses a different color map to enhance the contrast. (c) Shifts Δ x 2 (left) and Δ x 3 (right). Solid lines: shifts estimated from the data in (a) and (b). Dashed lines: shifts calculated using Eqs. (10) and (15).

Fig. 2.
Fig. 2.

Effect of coma aberration c on the normalized intensity cross sections of the 2D ( I 2 ), 3D ( I 3 ), and combined ( I c ) depletion foci. Each curve, obtained by numerically evaluating the integrals in Eq. (1), is normalized to the maximum of I c when c = 0 . For c = 0.4 , the vertical dashed bars denote the shifts Δ x 2 = 39    nm and Δ x 3 = 65    nm , according to Eqs. (10) and (15). The relative shift is 103 nm. For c = 0.8 , I 3 does not exhibit a well-defined zero.

Fig. 3.
Fig. 3.

Ratio between the minimum ( I min ) and maximum ( I max ) of the intensity cross section ( I c ) of the combined depletion foci as a function of the coma aberration c . The graph is obtained by numerically evaluating the integrals in Eq. (1).

Fig. 4.
Fig. 4.

Images of 100 nm crimson beads. (a) Confocal mode. (b)–(f) Combined 2D/3D STED. (c) and (d) Same sign coma aberration applied to the depletion beams. Lateral shifts are indicated by the arrows, and significant reduction in signal is seen. (e) and (f) Opposite coma aberrations are applied to the depletion beams. As the zeros move in the same direction, the signal reduction is less pronounced. Image size: 1    μm × 1    μm .

Equations (17)

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E ( x , y , z ) = 0 α 0 2 π e ( θ , φ ) T ( θ , φ ) exp [ i Φ ( θ , φ ) ] × exp [ i k ( x sin θ cos φ + y sin θ sin φ ) ] × exp [ i k z cos θ ] sin θ d φ d θ ,
e ( θ , φ ) = A ( θ ) cos θ [ cos θ + 1 + ( cos θ 1 ) e i 2 φ i ( cos θ + 1 ) i ( cos θ 1 ) e i 2 φ 2 sin θ e i φ ] ,
T 2 ( φ ) = e i φ T 3 ( θ ) = { 1 θ β    1 θ > β ,
Φ ( θ , φ ) = c f ( θ ) cos φ ,
E ( x ) = 0 α 0 2 π e ( θ , φ ) T ( θ , φ ) × exp [ i ( c f ( θ ) + k x sin θ ) cos φ ] sin θ d φ d θ .
exp [ i ( c f ( θ ) + k x sin θ ) cos φ ] 1 + i ( c f ( θ ) + k x sin θ ) cos φ .
E 2 ( x ) 0 α 0 2 π [ ( cos θ + 1 ) e i φ + ( cos θ 1 ) e i 3 φ i ( cos θ + 1 ) e i φ i ( cos θ 1 ) e i 3 φ 2 sin θ e i 2 φ ] × [ 1 + i ( c f ( θ ) + k x sin θ ) cos φ ] × A ( θ ) cos θ sin θ d φ d θ .
E 2 ( x ) 0 α [ i π ( cos θ + 1 ) ( c f ( θ ) + k x sin θ ) π ( cos θ + 1 ) ( c f ( θ ) + k x sin θ ) 0 ] × A ( θ ) cos θ sin θ d θ .
0 α ( cos θ + 1 ) ( c f ( θ ) + k x sin θ ) A ( θ ) cos θ sin θ d θ 0 ,
a 2 c + b 2 k Δ x 2 0 ,
a 2 = 0 α ( cos θ + 1 ) f ( θ ) A ( θ ) cos θ sin θ d θ b 2 = 0 α ( cos θ + 1 ) A ( θ ) cos θ ( sin θ ) 2 d θ .
E 3 ( x ) 0 α 0 2 π [ ( cos θ + 1 ) + ( cos θ 1 ) e i 2 φ i ( cos θ + 1 ) i ( cos θ 1 ) e i 2 φ 2 sin θ e i φ ] × [ 1 + i ( c f ( θ ) + k x sin θ ) cos φ ] × T 3 ( θ ) A ( θ ) cos θ sin θ d φ d θ .
E 3 ( x ) 0 α [ 2 π ( cos θ + 1 ) i 2 π ( cos θ + 1 ) i 2 π sin θ ( c f ( θ ) + k x sin θ ) ] × T 3 ( θ ) A ( θ ) cos θ sin θ d θ .
0 α ( c f ( θ ) + k x sin θ ) T 3 ( θ ) A ( θ ) cos θ ( sin θ ) 2 d θ 0 .
a 3 c + b 3 k Δ x 3 0 .
a 3 = 0 α f ( θ ) T 3 ( θ ) A ( θ ) cos θ ( sin θ ) 2 d θ b 3 = 0 α T 3 ( θ ) A ( θ ) cos θ ( sin θ ) 3 d θ .
Φ ( r , φ ) = c 8 ( 3 r 3 2 r ) cos φ ,

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