Abstract

In adaptive optical microscopy of thick biological tissue, strong scattering and aberrations can change the effective pupil shape by rendering some Shack-Hartmann spots unusable. The change of pupil shape leads to a change of wavefront reconstruction or control matrix that should be updated accordingly. Modified slope and modal wavefront control methods based on measurements of a Shack-Hartmann wavefront sensor are proposed to accommodate an arbitrarily shaped pupil. Furthermore, we present partial wavefront control methods that remove specific aberration modes like tip, tilt and defocus from the control loop. The proposed control methods were investigated and compared by simulation using experimentally obtained aberration data. The performance was then tested experimentally through closed-loop aberration corrections using an obscured pupil.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

I. Mochi and K. A. Goldberg, “Modal wavefront reconstruction from its gradient,” Appl. Opt. 54(12), 3780–3785 (2015).
[Crossref]

J. Ye, W. Wang, Z. Gao, Z. Liu, S. Wang, P. Benítez, J. C. Miñano, and Q. Yuan, “Modal wavefront estimation from its slopes by numerical orthogonal transformation method over general shaped aperture,” Opt. Express 23(20), 26208–26220 (2015).
[Crossref] [PubMed]

2014 (1)

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

2013 (1)

2011 (1)

2010 (1)

2008 (1)

2007 (2)

2006 (2)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, “Double-deformable-mirror adaptive optics system for phase compensation,” Appl. Opt. 45(12), 2638–2642 (2006).
[Crossref] [PubMed]

2005 (2)

M. J. Booth, M. Schwertner, and T. Wilson, “Specimen-induced aberrations and adaptive optics for microscopy,” Proc. SPIE 5894, 589403 (2005).
[Crossref]

W. Zou and J. P. Rolland, “Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils,” J. Opt. Soc. Am. A 22(5), 938–951 (2005).
[Crossref] [PubMed]

2004 (1)

2000 (1)

1996 (1)

1990 (1)

W. Jiang and H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[Crossref]

Azucena, O.

Benítez, P.

Betzig, E.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Booth, M.

Booth, M. J.

S. A. Rahman and M. J. Booth, “Direct wavefront sensing in adaptive optical microscopy using backscattered light,” Appl. Opt. 52(22), 5523–5532 (2013).
[Crossref] [PubMed]

M. J. Booth, M. Schwertner, and T. Wilson, “Specimen-induced aberrations and adaptive optics for microscopy,” Proc. SPIE 5894, 589403 (2005).
[Crossref]

Bronner, M. E.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Cao, Z.

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Chen, D. C.

Dai, G. M.

Dubra, A.

Engerer, P.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Fernandez, B.

Fu, M.

Fusco, T.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Gao, Z.

Garcia, D.

Ghiglia, D. C.

Goldberg, K. A.

Harvey, B. K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

Hou, J.

Hu, S.

Ivers, K. M.

Ji, N.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

Jiang, W.

Kubby, J.

Li, C.

Li, H.

W. Jiang and H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[Crossref]

Li, X.

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Liu, Z.

Loktev, M.

Mahajan, V. N.

Michau, V.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Milkie, D. E.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Miñano, J. C.

Misgeld, T.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Mochi, I.

Mumm, J.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Porter, J.

Qu, Q.

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Queener, H.

Rahman, S. A.

Richie, C. T.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

Rolland, J. P.

Romero, L. A.

Rousset, G.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Samokhin, A.

Saxena, A.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Schwertner, M.

M. J. Booth, M. Schwertner, and T. Wilson, “Specimen-induced aberrations and adaptive optics for microscopy,” Proc. SPIE 5894, 589403 (2005).
[Crossref]

M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004).
[Crossref] [PubMed]

Soloviev, O.

Sredar, N.

Sun, W.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

Tao, X.

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Vdovin, G.

Wang, K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Wang, S.

Wang, W.

Wang, Y.

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Wilson, T.

M. J. Booth, M. Schwertner, and T. Wilson, “Specimen-induced aberrations and adaptive optics for microscopy,” Proc. SPIE 5894, 589403 (2005).
[Crossref]

M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004).
[Crossref] [PubMed]

Wu, J.

Xu, B.

Xu, H.

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Yang, C.

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Ye, J.

Yuan, Q.

Zhang, X.

Zhang, Z.

Zou, W.

Zuo, Y.

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

Mon. Not. R. Astron. Soc. (1)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack- Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Nat. Commun. (1)

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6, 7276 (2015).
[Crossref] [PubMed]

Nat. Methods (1)

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref] [PubMed]

Opt. Commun. (1)

Z. Cao, Q. Qu, Y. Wang, H. Xu, S. Wang, C. Yang, and X. Li, “Shape based zonal wave-front reconstruction for arbitrary shape pupils,” Opt. Commun. 336, 160–165 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Proc. SPIE (2)

M. J. Booth, M. Schwertner, and T. Wilson, “Specimen-induced aberrations and adaptive optics for microscopy,” Proc. SPIE 5894, 589403 (2005).
[Crossref]

W. Jiang and H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[Crossref]

Other (1)

R. K. Tyson, Principles of Adaptive Optics (CRC, 2011).

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Figures (16)

Fig. 1
Fig. 1 Flowchart of (a) slope control and (b) modal control for arbitrarily shaped pupils.
Fig. 2
Fig. 2 Mapping of SHS and DM. A 25 × 25 square lenslet array was mapped on a 12 × 12 actuator (4 inactive corner actuators) DM. The shaded area denotes fully illuminated circular pupil including 349 valid subapertures.
Fig. 3
Fig. 3 (a) An example wavefront aberration map from a C. elegans specimen. Color bar unit: μm; the root mean square (RMS) value is 0.172μm; (b) Corresponding first 65 Zernike coefficients. First 3 coefficients: C1 (tip) = 0.0623, C2 (tilt) = 0.0152, C3 (defocus) = −0.0555.
Fig. 4
Fig. 4 Wavefront correction simulation results using modal control. (a) DM induced wavefront, RMS = 0.162μm. (b) Residual wavefront, RMS = 0.0488μm.
Fig. 5
Fig. 5 RMS value of residual wavefront aberration varies with maximum Zernike number in modal wavefront control. Sample 1: rat brain tissue; Sample 2: mouse liver tissue; Sample 3: rat vas deferens; Sample 4: C. elegans;
Fig. 6
Fig. 6 Wavefront correction result using slope control. (a) DM induced wavefront, RMS = 0.159μm. (b) Residual wavefront, RMS = 0.0467μm.
Fig. 7
Fig. 7 Wavefront aberration directly fitted by DM. (a) DM fitted wavefront, RMS = 0.167μm. (b) Residual wavefront, RMS = 0.0430μm.
Fig. 8
Fig. 8 Partial wavefront correction using modal control without correction of tip, tilt and defocus. (a) Residual wavefront, RMS = 0.108μm (b) Residual wavefront fitted by Zernike modes, first 3 coefficients: C1 (tip) = 0.0632, C2 (tilt) = 0.0143, C3 (defocus) = −0.0546; Rc = 0.0029.
Fig. 9
Fig. 9 Partial wavefront correction using slope control without correction of tip, tilt and defocus. (a) Residual wavefront, RMS = 0.107μm. (b) Residual wavefront fitted by Zernike modes, first 3 coefficients: C1 (tip) = 0.0620, C2 (tilt) = 0.0166, C3 (defocus) = −0.0550; Rc = 0.017.
Fig. 10
Fig. 10 (a) Wavefront aberration of thick brain tissue measured by the interferometer. (b) Spot pattern on SHS sensor, the image sharpness in red squares is lower than 0.03. (c) Wavefront aberration with pupil mask. (d) Orthogonal mode coefficients of the masked wavefront. First three coefficients: C1 = 0.471, C2 = −0.0525, C3 = 0.333.
Fig. 11
Fig. 11 Wavefront correction results for all aberration modes. (a) Residual wavefront using modal control, reconstructing 85 modes, RMS = 0.0957μm. (b) Residual wavefront using slope control, RMS = 0.0950μm. (c) Residual wavefront using DM fitting, RMS = 0.0717μm. (d) Residual wavefront using zero to replace invalid slopes, RMS = 0.204μm.
Fig. 12
Fig. 12 Wavefront correction results using modal control without correction of first 3 orthogonal modes. (a) Residual wavefront, RMS = 0.667μm, (b) Residual wavefront fitted by new orthogonal modes, first 3 coefficients: C1 = 0.473, C2 = −0.0514, C3 = 0.342. Rc = 0.0052.
Fig. 13
Fig. 13 Wavefront correction results using slope control without correction of first 3 orthogonal modes. (a) Residual wavefront, RMS = 0.668μm, (b) Residual wavefront fitted by new orthogonal modes, first 3 coefficients: C1 = 0.437, C2 = −0.0773, C3 = 0.346. Rc = 0.157.
Fig. 14
Fig. 14 Experimental system schematic layout. DM: deformable mirror. BS: Beam Splitter, L1 etc., lenses.
Fig. 15
Fig. 15 Wavefront correction results with fully illuminated circular pupil. (a) Initial wavefront, RMS = 0.145μm, (b) Residual wavefront using modal control, RMS = 0.00917μm (c) Residual wavefront using slope control, RMS = 0.00814μm (d) Residual wavefront using modal control and partial correction, RMS = 0.0906μm (e) Residual wavefront using slope control and partial correction, RMS = 0.0870μm (f) Zernike coefficients of wavefront before and after correction.
Fig. 16
Fig. 16 Wavefront correction results with obstructed pupil. (a) Initial wavefront, RMS = 0.163μm (b) Residual wavefront using modal control, RMS = 0.0065μm (c) Residual wavefront using slope control, RMS = 0.0057μm (d) Residual wavefront using modal control and partial correction, RMS = 0.100μm, (e) Residual wavefront using slope control and partial correction, RMS = 0.102μm. (f) Zernike coefficients of wavefront before and after correction.

Equations (31)

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

S= R s A
S= [ S x S y ] 2M×1 A= [ a 1 a n ] N×1 R s = [ S 1,1 x S 1,2 x S 1,N x S M,1 x S M,2 x S M,N x S 1,1 y S 1,2 y S 1,N y S M,1 y S M,2 y S M,N y ] 2M×N
A= ( R s T R s ) 1 R s T S
R s =UΣ V T
R s + =V Σ + U T
A= R s + S
A= R ˜ s + S ˜
W Err ( x,y )= i=1 I c i Q i ( x,y )
W Err =QC
S= W Err =( Q )C
C= ( Q ) + S
C= R c A
R c = ( Q ) + R s
A= R s + ( Q )C
Q n = k=1 K D nk Z k
Q=Z D T
Q T Q=D Z T Q=MI
D Z T Z D T =MI
P T P= Z T Z/M
C=P ( Z ˜ ) + S ˜
R c =P ( Z ˜ ) + R ˜ s
A= R ˜ s + ( Z ˜ ) P 1 C
A= R ˜ s + ( Z ˜ ) P 1 C r
W DM , Q j =0
W DM = n=1 N a n F n = n=1 N a n ( i=1 I b ni Q i )
n=1 N a n ( i=1 I b ni Q i ), Q j =0
n=1 N a n b nj =0
[ S 0 ]=[ R s γ R d ]A
F n (x,y)=exp[ lnc (x x n ) 2 + (y y n ) 2 d 2 ]
R c = i=4 N C i 2
IS= I 2 ( x,y ) [ I ( x,y ) ] 2

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