Abstract

We implement wave front sensor-less adaptive optics in a structured illumination microscope. We investigate how the image formation process in this type of microscope is affected by aberrations. It is found that aberrations can be classified into two groups, those that affect imaging of the illumination pattern and those that have no influence on this pattern. We derive a set of aberration modes ideally suited to this application and use these modes as the basis for an efficient aberration correction scheme. Each mode is corrected independently through the sequential optimisation of an image quality metric. Aberration corrected imaging is demonstrated using fixed fluorescent specimens. Images are further improved using differential aberration imaging for reduction of background fluorescence.

© 2008 Optical Society of America

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References

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  1. J. B. Pawley, ed., Handbook of Biological Confocal Microscopy, 3rd Edition (Springer, New York, 2006).
    [CrossRef]
  2. J. A. Conchello and J. W. Lichtman, "Optical sectioning microscopy," Nature Methods 2(12), 920-931 (2005).
    [CrossRef] [PubMed]
  3. M. A. A. Neil, R. Juškaitis, and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
    [CrossRef]
  4. M. J. Booth, "Adaptive optics in microscopy," Philos. Transact. A Math. Phys. Eng. Sci. 365, 2829-2843 (2007).
    [CrossRef] [PubMed]
  5. M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Nat. Acad. Sci. 99, 5788-5792 (2002).
    [CrossRef] [PubMed]
  6. D. Débarre, M. J. Booth, and T. Wilson, "Image based adaptive optics through optimisation of low spatial frequencies," Opt. Express 15, 8176-8190 (2007).
    [CrossRef] [PubMed]
  7. H. Hopkins, "The use of diffraction-based criteria of image quality in automatic optical design," Opt. Acta 13, 343-69 (1966).
    [CrossRef]
  8. D. Karadagli?? and T. Wilson, "Image formation in structured illumination wide-field fluorescence microscopy," Micron (2008, in press).
    [CrossRef] [PubMed]
  9. E. W. Weisstein, CRC Concise Encyclopedia of Mathematics (Chapman and Hall/CRC, 2003).
  10. M. A. A. Neil, M. J. Booth, and T. Wilson, "New modal wavefront sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107, (2000).
    [CrossRef]
  11. M. J. Booth, T. Wilson, H.-B. Sun, T. Ota, and S. Kawata, "Methods for the characterisation of deformable membrane mirrors," Appl. Opt. 44(24), 5131-5139 (2005).
    [CrossRef] [PubMed]
  12. A. Leray and J. Mertz, "Rejection of two-photon fluorescence background in thick tissue by differential aberration imaging," Opt. Express 14, 10,565-10,573 (2006).
    [CrossRef]

2008

D. Karadagli?? and T. Wilson, "Image formation in structured illumination wide-field fluorescence microscopy," Micron (2008, in press).
[CrossRef] [PubMed]

2007

2006

A. Leray and J. Mertz, "Rejection of two-photon fluorescence background in thick tissue by differential aberration imaging," Opt. Express 14, 10,565-10,573 (2006).
[CrossRef]

2005

2002

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Nat. Acad. Sci. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

2000

1997

1966

H. Hopkins, "The use of diffraction-based criteria of image quality in automatic optical design," Opt. Acta 13, 343-69 (1966).
[CrossRef]

Booth, M. J.

Conchello, J. A.

J. A. Conchello and J. W. Lichtman, "Optical sectioning microscopy," Nature Methods 2(12), 920-931 (2005).
[CrossRef] [PubMed]

Débarre, D.

Hopkins, H.

H. Hopkins, "The use of diffraction-based criteria of image quality in automatic optical design," Opt. Acta 13, 343-69 (1966).
[CrossRef]

Juškaitis, R.

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Nat. Acad. Sci. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, R. Juškaitis, and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
[CrossRef]

Karadagli??, D.

D. Karadagli?? and T. Wilson, "Image formation in structured illumination wide-field fluorescence microscopy," Micron (2008, in press).
[CrossRef] [PubMed]

Kawata, S.

Leray, A.

A. Leray and J. Mertz, "Rejection of two-photon fluorescence background in thick tissue by differential aberration imaging," Opt. Express 14, 10,565-10,573 (2006).
[CrossRef]

Lichtman, J. W.

J. A. Conchello and J. W. Lichtman, "Optical sectioning microscopy," Nature Methods 2(12), 920-931 (2005).
[CrossRef] [PubMed]

Mertz, J.

A. Leray and J. Mertz, "Rejection of two-photon fluorescence background in thick tissue by differential aberration imaging," Opt. Express 14, 10,565-10,573 (2006).
[CrossRef]

Neil, M. A. A.

Ota, T.

Sun, H.-B.

Wilson, T.

Appl. Opt.

J. Opt. Soc. Am. A

Micron

D. Karadagli?? and T. Wilson, "Image formation in structured illumination wide-field fluorescence microscopy," Micron (2008, in press).
[CrossRef] [PubMed]

Nature Methods

J. A. Conchello and J. W. Lichtman, "Optical sectioning microscopy," Nature Methods 2(12), 920-931 (2005).
[CrossRef] [PubMed]

Opt. Acta

H. Hopkins, "The use of diffraction-based criteria of image quality in automatic optical design," Opt. Acta 13, 343-69 (1966).
[CrossRef]

Opt. Express

D. Débarre, M. J. Booth, and T. Wilson, "Image based adaptive optics through optimisation of low spatial frequencies," Opt. Express 15, 8176-8190 (2007).
[CrossRef] [PubMed]

A. Leray and J. Mertz, "Rejection of two-photon fluorescence background in thick tissue by differential aberration imaging," Opt. Express 14, 10,565-10,573 (2006).
[CrossRef]

Opt. Lett.

Philos. Transact. A Math. Phys. Eng. Sci.

M. J. Booth, "Adaptive optics in microscopy," Philos. Transact. A Math. Phys. Eng. Sci. 365, 2829-2843 (2007).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci.

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Nat. Acad. Sci. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Other

J. B. Pawley, ed., Handbook of Biological Confocal Microscopy, 3rd Edition (Springer, New York, 2006).
[CrossRef]

E. W. Weisstein, CRC Concise Encyclopedia of Mathematics (Chapman and Hall/CRC, 2003).

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Figures (7)

Fig. 1.
Fig. 1.

Illustration of the effects of grid modes and non-grid modes: (a1-3) the pupil function P(r) showing zero phase aberration, an example grid mode, and an example non-grid mode, respectively. The latter two aberrations have a rms phase of 1 rad. (b1) the geometry used for calculating the OTF, showing the two pupil functions offset by the grid frequency g; in (b2) the overlap region shows ΔΦ≠0 for the grid mode; in (b3) the overlap region shows ΔΦ=0 for the non-grid mode. (c1-3) show the corresponding OTFs; g is indicated by the green dots. (d1-3) simulated images of a checkerboard pattern for one grid position. (e1-3) corresponding sectioned images derived using Eq. (8).

Fig. 2.
Fig. 2.

Experimental determination of aberration modes. (a), the metric M is plotted as a function of the aberrated phase Φ(r) for a number of basis modes (here 3 Zernike modes: coma (z=7) and trefoil (z=9 and z=10)), and the resulting curves are fitted to a multidimensional ellipsoid. (b), the fitting parameters are used to construct the experimental A matrix and determine the new set of modes {Yi (r)}. (c), a similar plot of the metric M, derived using the new set of modes. The main axes of the fitted ellipsoid now correspond to pure {Yi (r)} modes. (d), the experimental A matrix for the new modes is diagonal, confirming that the cross-talk between the modes has been cancelled. Although only three modes are shown here, this principle can be extended to an arbitrary number.

Fig. 3.
Fig. 3.

Set of modes used for aberration correction. (a), set of modes determined experimentally and theoretically using an initial set of 11 Zernike modes (z=5 to 15). The modes are ordered by decreasing eigenvalue. The last two modes have no influence on the imaging of the grid. All the modes have a root mean square (rms) phase amplitude of 1 rad. (b), Influence of the modes on the metric M, determined theoretically using the mode eigenvalues, and experimentally as the FWHM of the curve of M as a function of aberration amplitude in a single mode. The last two modes influence only the sample frequency spectrum, and hence their eigenvalues depend on the sample and cannot be determined theoretically.

Fig. 4.
Fig. 4.

Schematic of the structured illumination microscope with aberration correction. WLS, white light source. DM, deformable mirror. DBS, dichroic beamsplitter. BSC, beam-splitter cube. S, sample. The blue rays mark the illumination path; the detection path is shown in yellow. The green path represents the Mach Zehnder interferometer used to characterise the deformable mirror - this is not used during the imaging experiments.

Fig. 5.
Fig. 5.

Aberration correction in SI microscopy. A fluorescent mouse intestine sample was imaged before (a) and after (b) aberration correction. The two images are displayed with the same color table. Insert, phase induced by the mirror in the pupil plane of the objective. The rms phase after correction is 0.61 rad. (c), profile along the lines drawn on the images. Both profiles have been normalized so that their mean value is identical. As a result of the resolution improvement, the contrast of small sample features (blue arrows) are better defined after (red solid line) rather than before (black dotted line) correction. The imaging depth was approximately 10µm. The coverslip thickness was 170µm.

Fig. 6.
Fig. 6.

Aberration correction and out-of-focus fluorescence rejection in SI microscopy. Axially sectioned images of a pollen grain without (a) and with (b) aberration correction, and with large induced aberration (c). The phase induced by the mirror is shown as an insert. In (c), the phase was a combination of the first 4 aberration modes in Fig. 3 with total rms amplitude of 3 radians. Background-free images were obtained by subtracting the highly aberrated image (c) from the images obtained before and after aberration correction, giving (d) and (e) respectively. (f), profiles obtained along the line drawn in (b) for images (a),(b),(d) and (e): aberration correction increases the intensity of the structures while background subtraction improves the contrast. The imaging depth was approximately 30µm. The coverslip thickness was 170µm.

Fig. 7.
Fig. 7.

Correction variation with imaging depth. Pollen grain images after background subtraction, at the top of the grain (a,b and c) and around the equator 20µm below (d,e and f). The images were acquired without aberration correction (a and d), with the correction optimised for the top of the grain (b and e), and for the equator (c and f). Images in the same row are displayed with the same color code and the phase induced by the DM is shown as an insert. The appropriate correction settings for one plane (b and f) clearly deteriorate the image quality in another plane (c and e). The rms phase after correction is 0.37 rad in (b) and 0.63 rad in (c). The imaging depth was approximately 30–50µm. The coverslip thickness was 170µm.

Equations (55)

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I ( n ) = h ( n ) * f ( n ) ,
I ( n ) = F T 1 [ H ( m ) F ( m ) ] ,
H ( m ) = P ( r ) P * ( r ) = 1 A D ( m ) P ( r m ) P * ( r ) d A ,
H ( m ) = 1 π D ( m ) exp [ j Δ Φ ( m , r ) ] d r
Δ Φ ( m , r ) = Φ ( r m ) Φ ( r ) .
I exc ( n ) = H exc ( 0 ) + H exc ( g ) e ( j ψ + j g . n ) 2 + H exc ( g ) e ( j ψ + j g . n ) 2 ,
I i ( n ) = [ f ( n ) I exc , i ( n ) ] * h em ( n ) ,
I sect ( n ) = i j ( I i I j ) 2 .
I sect ( n ) = 3 2 H ( g ) F T 1 [ F ( m ) H ( g + m ) ] .
M = M 0 i x i 2 ,
M M 0 i j α ij a i a j = M 0 a T A a ,
A = VBV T ,
M M 0 a T VBV T a = M 0 b T Bb = M 0 i β i b i 2 ,
M = + I sect 2 ( n ) d n .
M = S F ( m ) 2 H ( g ) H ( g + m ) 2 d m ,
M = ( S F ( m ) 2 d m ) H ( g ) 4 + 1 2 ( S F ( m ) 2 m 2 d m ) H ( g ) 2 2 ( H ( g ) 2 ) ,
M = F 0 H ( g ) 4 + F 1 H ( g ) 2 2 ( H ( g ) 2 ) ,
H ( m ) = 1 π D ( m ) d r + j π D ( m ) Δ Φ ( m , r ) d r 1 2 π D ( m ) [ Δ Φ ( m , r ) ] 2 d r .
M = F 0 H 0 ( g ) + j π D ( g ) Δ Φ ( g , r ) d r 1 2 π D ( g ) Δ Φ 2 ( g , r ) d r 4 ,
M = F 0 { H 0 4 2 H 0 2 [ H 0 π D ( g ) [ Δ Φ ( g , r ) ] 2 d r ( 1 π D ( g ) Δ Φ ( g , r ) d r ) 2 ] }
M = F 0 { H 0 4 2 H 0 2 i j a i a j [ H 0 π D ( g ) Δ X i Δ X j d r 1 π 2 D ( g ) Δ X i d r D ( g ) Δ X j d r ] } ,
M = M 0 i j a i a j X i , X j ,
X i , X j grid = 2 F 0 H 0 2 [ H 0 π D ( g ) X i X j d r 1 π 2 D ( g ) X i d r D ( g ) X j d r ] .
X i , X j non grid = F 1 [ H 0 π D ( g ) X i X j d r 1 π 2 D ( g ) X i d r D ( g ) X j d r ] ,
Φ ( r , θ ) = γ cos θ X i ( r ) + γ sin θ X j ( r ) ,
i , j α ij a i a j = c
H ( m , z ) = 1 π D ( g ) exp [ j Δ Φ ( g , r ) + j Δ Φ d ( g , r , z ) ] d r ,
I exc , i ( n , z ) = H ( 0 , z ) + H ( g , z ) e ( j ψ i + j g . n ) 2 + H ( g , z ) e ( j ψ i + j g . n ) 2
I i ( n ) = + { H ( 0 , z ) FT 1 [ F ( m , z ) H ( m , z ) ] + e i 2 H ( g , z ) FT 1 [ F ( m g , z ) H ( m , z ) ]
+ e i 2 H ( g , z ) FT 1 [ F ( m + g , z ) H ( m , z ) ] } d z ,
I sect ( n ) = 3 2 + H ( g , z ) FT 1 [ F ( m , z ) H ( g + m , z ) ] d z .
M = + I sect 2 ( n ) d n S F ( m ) 2 + H ( g , z ) H ( g + m , z ) d z 2 d m .
M F 0 + H ( g , z ) 2 d z 2 .
H ( g , z ) = 1 π D ( g ) ζ ( g , r , z ) d r + j π D ( g ) Δ Φ ( g , r ) ζ ( g , r , z ) d r 1 2 π D ( g ) Δ Φ ( g , r ) 2 ζ ( g , r , z ) d r
ζ ( g , r , z ) = exp [ j Δ Φ d ( g , r , z ) ]
M F 0 + H 0 2 d z 2 F 0 { 2 π 2 + H 0 2 d z + [ D ( g ) Δ Φ ζ d r ] 2 d z
+ 2 π + H 0 2 d z + H 0 D ( g ) Δ Φ 2 ζ d r d z 4 π 2 [ + H 0 2 D ( g ) Δ Φ ζ d r d z ] 2 } ,
X i , X j grid z = F 0 { 2 π 2 + H 0 2 d z + [ D ( g ) Δ X i ζ d r ] [ D ( g ) Δ X j ζ d r ] d z
+ 2 π + H 0 2 d z + H 0 D ( g ) Δ X i Δ X j ζ d r d z
4 π 2 [ + H 0 2 D ( g ) Δ X i ζ d r d z ] [ + H 0 2 D ( g ) Δ X j ζ d r d z ]
M = S F ( m ) 2 H ( g ) H ( g + m ) 2 d m ,
M = S F ( m ) 2 H ( g ) 2 ( H ( g ) 2 + ( m . ) H ( g ) 2 + 1 2 [ ( m . ) 2 H ( g ) 2 ] ) d m
S F ( m ) 2 m d m = 0
S F ( m ) 2 m x m y d m = 0
M = F 0 H ( g ) 4 + F 1 H ( g ) 2 2 ( H ( g ) 2 ) ,
F 1 = 1 2 S F ( m ) 2 m 2 d m .
H ( g + m ) 2 H 0 ( g + m ) 2 H 0 ( g + m ) π D ( g + m ) Δ Φ ( g + m , r ) 2 d r + [ 1 π D ( g + m ) Δ Φ ( g + m , r ) d r ] 2
Δ Φ ( g + m , r ) = Δ Φ ( g , r ) + Φ ( r g ) Φ ( r g m )
Δ Φ ( g , r ) + ( m . ) Φ ( r g ) .
Δ Φ ( g + m , r ) ( m . ) Φ ( r g ) .
H ( g + m ) 2 H 0 ( g + m ) 2 H 0 ( g ) π D ( g ) [ ( m . ) Φ ( r g ) ] 2 d r + [ 1 π D ( g ) ( m . ) Φ ( r g ) d r ] 2
M = M 0 2 F 1 { H 0 ( g ) π D ( g ) [ Φ ( r g ) ] 2 d r [ 1 π D ( g ) Φ ( r g ) d r ] 2 } ,
M 0 = F 0 H 0 ( g ) 4 + F 1 H 0 ( g ) 2 2 H 0 ( g ) 2
X i , X j non grid = 2 F 1 { H 0 ( g ) π D ( g ) X i ( r g ) X j ( r g ) d r
1 π 2 D ( g ) X i ( r g ) d r D ( g ) X j ( r g ) d r }

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