Abstract

Aberrations limit the resolution, signal intensity and achievable imaging depth in microscopy. Coherence-gated wavefront sensing (CGWS) allows the fast measurement of aberrations in scattering samples and therefore the implementation of adaptive corrections. However, CGWS has been demonstrated so far only in weakly scattering samples. We designed a new CGWS scheme based on a Linnik interferometer and a SLED light source, which is able to compensate dispersion automatically and can be implemented on any microscope. In the highly scattering rat brain tissue, where multiply scattered photons falling within the temporal gate of the CGWS can no longer be neglected, we have measured known defocus and spherical aberrations up to a depth of 400 µm.

© 2012 OSA

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2012

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A.109(1), 22–27 (2012).
[CrossRef] [PubMed]

J. Wang, J.-F. Leger, J. Binding, C. Boccara, S. Gigan, and L. Bourdieu, “Measuring aberrations in the rat brain by a new coherence-gated wavefront sensor using a Linnik interferometer,” Proc. SPIE8227, 822702, 822702-7 (2012).
[CrossRef]

T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
[CrossRef]

2011

C. Wang, L. Qiao, F. He, Y. Cheng, and Z. Xu, “Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source,” J. Microsc.243(2), 179–183 (2011).
[CrossRef] [PubMed]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

J. Binding, J. Ben Arous, J. F. Léger, S. Gigan, C. Boccara, and L. Bourdieu, “Brain refractive index measured in vivo with high-NA defocus-corrected full-field OCT and consequences for two-photon microscopy,” Opt. Express19(6), 4833–4847 (2011).
[CrossRef] [PubMed]

2010

S. Tuohy and A. G. Podoleanu, “Depth-resolved wavefront aberrations using a coherence-gated Shack-Hartmann wavefront sensor,” Opt. Express18(4), 3458–3476 (2010).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

2009

2008

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, “Adaptive optics for structured illumination microscopy,” Opt. Express16(13), 9290–9305 (2008).
[CrossRef] [PubMed]

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun.281(4), 880–887 (2008).
[CrossRef]

2007

2006

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

2005

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

2004

2003

P. Marsh, D. Burns, and J. Girkin, “Practical implementation of adaptive optics in multiphoton microscopy,” Opt. Express11(10), 1123–1130 (2003).
[CrossRef] [PubMed]

R. Gens, “Two-dimensional phase unwrapping for radar interferometry: developments and new challenges,” Int. J. Remote Sens.24(4), 703–710 (2003).
[CrossRef]

2002

2001

A. V. Larichev, P. V. Ivanov, I. G. Iroshnikov, and V. I. Shmal'gauzen, “Measurement of eye aberrations in a speckle field,” Quantum Electron.31(12), 1108–1112 (2001).
[CrossRef]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods111(1), 29–37 (2001).
[CrossRef] [PubMed]

2000

1998

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U.S.A.95(26), 15741–15746 (1998).
[CrossRef] [PubMed]

1995

1993

A. V. Koryabin, V. I. Polezhaev, and V. I. Shmal'gauzen, “Measurement of the thermooptic aberrations of active elements based on yttrium aluminate and garnet,” Quantum Electron.23(10), 899–901 (1993).
[CrossRef]

1987

1976

1969

R. Crane, “Interference phase measurement,” Appl. Opt.8, 538–542 (1969).

Agard, D. A.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

Albert, O.

Beaurepaire, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods111(1), 29–37 (2001).
[CrossRef] [PubMed]

Ben Arous, J.

Betzig, E.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A.109(1), 22–27 (2012).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Binding, J.

J. Wang, J.-F. Leger, J. Binding, C. Boccara, S. Gigan, and L. Bourdieu, “Measuring aberrations in the rat brain by a new coherence-gated wavefront sensor using a Linnik interferometer,” Proc. SPIE8227, 822702, 822702-7 (2012).
[CrossRef]

J. Binding, J. Ben Arous, J. F. Léger, S. Gigan, C. Boccara, and L. Bourdieu, “Brain refractive index measured in vivo with high-NA defocus-corrected full-field OCT and consequences for two-photon microscopy,” Opt. Express19(6), 4833–4847 (2011).
[CrossRef] [PubMed]

Boccara, C.

J. Wang, J.-F. Leger, J. Binding, C. Boccara, S. Gigan, and L. Bourdieu, “Measuring aberrations in the rat brain by a new coherence-gated wavefront sensor using a Linnik interferometer,” Proc. SPIE8227, 822702, 822702-7 (2012).
[CrossRef]

J. Binding, J. Ben Arous, J. F. Léger, S. Gigan, C. Boccara, and L. Bourdieu, “Brain refractive index measured in vivo with high-NA defocus-corrected full-field OCT and consequences for two-photon microscopy,” Opt. Express19(6), 4833–4847 (2011).
[CrossRef] [PubMed]

Booth, M. J.

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett.34(16), 2495–2497 (2009).
[CrossRef] [PubMed]

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun.281(4), 880–887 (2008).
[CrossRef]

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, “Adaptive optics for structured illumination microscopy,” Opt. Express16(13), 9290–9305 (2008).
[CrossRef] [PubMed]

M. J. Booth, M. A. Neil, and T. Wilson, “New modal wave-front sensor: application to adaptive confocal fluorescence microscopy and two-photon excitation fluorescence microscopy,” J. Opt. Soc. Am. A19(10), 2112–2120 (2002).
[CrossRef] [PubMed]

M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A.99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

Botcherby, E. J.

Bouma, B. E.

Bourdieu, L.

J. Wang, J.-F. Leger, J. Binding, C. Boccara, S. Gigan, and L. Bourdieu, “Measuring aberrations in the rat brain by a new coherence-gated wavefront sensor using a Linnik interferometer,” Proc. SPIE8227, 822702, 822702-7 (2012).
[CrossRef]

J. Binding, J. Ben Arous, J. F. Léger, S. Gigan, C. Boccara, and L. Bourdieu, “Brain refractive index measured in vivo with high-NA defocus-corrected full-field OCT and consequences for two-photon microscopy,” Opt. Express19(6), 4833–4847 (2011).
[CrossRef] [PubMed]

Brezinski, M. E.

Burns, D.

Cariou, J.

Chaigneau, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods111(1), 29–37 (2001).
[CrossRef] [PubMed]

Charpak, S.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods111(1), 29–37 (2001).
[CrossRef] [PubMed]

Cheng, Y.

C. Wang, L. Qiao, F. He, Y. Cheng, and Z. Xu, “Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source,” J. Microsc.243(2), 179–183 (2011).
[CrossRef] [PubMed]

Choi, W.

T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
[CrossRef]

Choi, Y.

T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
[CrossRef]

Crane, R.

R. Crane, “Interference phase measurement,” Appl. Opt.8, 538–542 (1969).

Dasari, R. R.

T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
[CrossRef]

Débarre, D.

Denk, W.

M. Rueckel and W. Denk, “Properties of coherence-gated wavefront sensing,” J. Opt. Soc. Am. A24(11), 3517–3529 (2007).
[CrossRef] [PubMed]

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

M. Feierabend, M. Rückel, and W. Denk, “Coherence-gated wave-front sensing in strongly scattering samples,” Opt. Lett.29(19), 2255–2257 (2004).
[CrossRef] [PubMed]

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U.S.A.95(26), 15741–15746 (1998).
[CrossRef] [PubMed]

Feierabend, M.

Fujimoto, J. G.

Gens, R.

R. Gens, “Two-dimensional phase unwrapping for radar interferometry: developments and new challenges,” Int. J. Remote Sens.24(4), 703–710 (2003).
[CrossRef]

Ghiglia, D. C.

Gigan, S.

J. Wang, J.-F. Leger, J. Binding, C. Boccara, S. Gigan, and L. Bourdieu, “Measuring aberrations in the rat brain by a new coherence-gated wavefront sensor using a Linnik interferometer,” Proc. SPIE8227, 822702, 822702-7 (2012).
[CrossRef]

J. Binding, J. Ben Arous, J. F. Léger, S. Gigan, C. Boccara, and L. Bourdieu, “Brain refractive index measured in vivo with high-NA defocus-corrected full-field OCT and consequences for two-photon microscopy,” Opt. Express19(6), 4833–4847 (2011).
[CrossRef] [PubMed]

Girkin, J.

Goodman, J. W.

Guern, Y.

Gustafsson, M. G.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

Hanser, B. M.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

He, F.

C. Wang, L. Qiao, F. He, Y. Cheng, and Z. Xu, “Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source,” J. Microsc.243(2), 179–183 (2011).
[CrossRef] [PubMed]

Hee, M. R.

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U.S.A.95(26), 15741–15746 (1998).
[CrossRef] [PubMed]

Hillman, T. R.

T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
[CrossRef]

Horton, N. G.

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

Iroshnikov, I. G.

A. V. Larichev, P. V. Ivanov, I. G. Iroshnikov, and V. I. Shmal'gauzen, “Measurement of eye aberrations in a speckle field,” Quantum Electron.31(12), 1108–1112 (2001).
[CrossRef]

Ivanov, P. V.

A. V. Larichev, P. V. Ivanov, I. G. Iroshnikov, and V. I. Shmal'gauzen, “Measurement of eye aberrations in a speckle field,” Quantum Electron.31(12), 1108–1112 (2001).
[CrossRef]

Ji, N.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A.109(1), 22–27 (2012).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Juskaitis, R.

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun.281(4), 880–887 (2008).
[CrossRef]

M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A.99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Kleinfeld, D.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U.S.A.95(26), 15741–15746 (1998).
[CrossRef] [PubMed]

Kobat, D.

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

Koryabin, A. V.

A. V. Koryabin, V. I. Polezhaev, and V. I. Shmal'gauzen, “Measurement of the thermooptic aberrations of active elements based on yttrium aluminate and garnet,” Quantum Electron.23(10), 899–901 (1993).
[CrossRef]

Larichev, A. V.

A. V. Larichev, P. V. Ivanov, I. G. Iroshnikov, and V. I. Shmal'gauzen, “Measurement of eye aberrations in a speckle field,” Quantum Electron.31(12), 1108–1112 (2001).
[CrossRef]

Le Brun, G.

Le Jeune, B.

Leger, J.-F.

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T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
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B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

C. Wang, L. Qiao, F. He, Y. Cheng, and Z. Xu, “Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source,” J. Microsc.243(2), 179–183 (2011).
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Opt. Lett.

Proc. Natl. Acad. Sci. U.S.A.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A.109(1), 22–27 (2012).
[CrossRef] [PubMed]

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A.99(9), 5788–5792 (2002).
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[CrossRef] [PubMed]

Proc. SPIE

T. R. Hillman, Y. Choi, N. Lue, Y. Sung, R. R. Dasari, W. Choi, and Z. Yaqoob, “A reflection-mode configuration for enhanced light delivery through turbidity,” Proc. SPIE8227, 82271T, 82271T-6 (2012).
[CrossRef]

J. Wang, J.-F. Leger, J. Binding, C. Boccara, S. Gigan, and L. Bourdieu, “Measuring aberrations in the rat brain by a new coherence-gated wavefront sensor using a Linnik interferometer,” Proc. SPIE8227, 822702, 822702-7 (2012).
[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic of the experiment. Illumination: SLED (Superluminescent Light Emitting diode), Pol (polarizer), QWP (quarter wave plate), BS1 (beam splitter). Sample arm: Obj. 1 (microscope objective), TS1 (motorized linear translation stage allowing axial movement of the sample), coverslip (to protect the sample), 2D lateral manual translation stage. Reference arm: coverslip (to compensate dispersion from the coverslip in the sample arm), Obj. 2 (microscope objective identical to Obj. 1), M (reference mirror), PZT (piezo actuator for phase-shifting), TS2 (motorized translation stage to adjust the reference arm length). Detection: L1 and L2 (lens doublets), CCD1 and CCD2 (CCD cameras), BS1 (beam splitter), FD (adjustable field diaphragm of the microscope). The piezo, camera, TS1 and TS2 are controlled by a PC running a modified version of the Light-CT software (LLTech).

Fig. 2
Fig. 2

Principle of the method used to create known aberration. (a) Initial state at the surface of the sample (no aberration). (b) When focusing into the sample, the index mismatch moves the CV and the AFP in opposite directions away from the NFP and introduces tractable aberrations. (c) By changing the reference arm length, the CV position can be further displaced to add or subtract aberrations.

Fig. 3
Fig. 3

Wavefront reconstruction procedure. (a) Raw image recorded on CCD1 (imaging the objective pupils), in a rat brain slice, for AFP located 160 µm deep below the coverslip and CG = −15 µm from AFP (20×/0.5 objective). (b) Corresponding amplitude of the electric field obtained by PSI. Bottom right corner, schematic of the virtual lens array. (c) Intensity distributions in the virtual image plane of the sublens in white of subfigure (b) obtained by discrete Fourier transform for 4 CGWS images obtained at 4 neighboring sample positions. (d) The wavefront reconstructed from the slopes of the centroids of the vSHS at a given position and then averaged over M = 5 neighboring positions (here corresponding to a Zernike defocus coefficient of 0.31 µm).

Fig. 4
Fig. 4

Measuring known aberrations at different depth for the 20×/0.5 and the 63×/0.9 objectives. (a) and (b): raw defocus measurement at different depths as a function of CG position for respectively the 20×/0.5 and 63×/0.9 objectives and theoretical curves. (c): raw 3rd order spherical aberration measurement for the 63×/0.9 objective at different depths as a function of CG position. In (a), (b) and (c), curves were vertically shifted for visibility. (d) and (e): from subfigures (a) and (b), defocus slope as a function of depth for respectively the 20×/0.5 and 63×/0.9 objectives. (f) and (g): slope of the 3rd order spherical aberration and comparison with theory for respectively the 20×/0.5 objective and 63×/0.9 objective.

Fig. 5
Fig. 5

Transition from single scattering to multiple scattering in CGWS measurement within rat brain slices (male Wistar, 45 days old.) and influence of the microscope FOV. (a) and (b) Speckle size as a function of depth when CG is centered on AFP. (c) and (d) dCV lateral extension estimated from the speckle size as a function of depth when CG is centered on AFP. (e) and (f) Defocus slope as a function of depth. (g) and (h) The magnitude of CGWS signal as a function of the depth. (a), (c), (e) and (g): 20×/0.5 objective; (b), (d), (f) and (h) 63×/0.9 objective. In each panel, the measurements are shown for four different diameters of the FD corresponding to four different FOV.

Fig. 6
Fig. 6

Influence of speckle sampling by the camera pixels on the CGWS measurement (wavefront obtained by averaging M = 40 positions). The slope of defocus is plotted at depths of 400 µm (a) and 200 µm (b) for respectively the 20×/0.5 and 63×/0.8 objectives as a function of the average number of pixels per grain of speckle, which was varied by binning the camera pixels before propagation through the vSHS (from left to right on the horizontal axis, the binning of the pixels is increased and therefore the speckle size in unit of pixels is decreased).

Fig. 7
Fig. 7

Point Spread Function as extracted from the wavefront measured by CGWS for the minimal defocus position using the first 28 coefficients. The PSF was scaled over the whole gray values (0-255). We observe that the PSF degrades notably over the range of reliability of the CGWS.

Fig. 8
Fig. 8

Geometry of schematic for ray tracing. Refractive index of water, glass slip, and sample are ni, ng, ns respectively. If the sample was a pure water solution and if there was no coverslip, the focus in this aberration free case would be located at the position N on the optical axis. The origin O is located at the cross point of the optical axis to the second surface of the glass coverslip, the Z axis is defined along the optical axis OA with the positive direction pointing towards the sample (away from objective). The distance ON is noted d, the thickness of the glass coverslip T, the actual point source is A and the distance AN is noted Δz.

Fig. 9
Fig. 9

CGWS calibration. Measured defocus slope with SHS and CGWS compared to the predicted curve (for eNA = 0.47 using the 20×/0.5 objective).

Fig. 10
Fig. 10

Speckle size as a function of the CG position relative to the AFP for different depths for the 20×/0.5 (a) and the 63×/0.9 (b) objectives.

Equations (3)

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OP(A)= n s AP+ n g PB= n s (d+Δz)/cos α s + n g T/cos α g .
OP(N)= n i NC= n i [ (d+T)/cos α i +BDsin α i ],
W(r)=(d+Δz) ( n s 2 N r 2 ) 1/2 +T ( n g 2 N r 2 ) 1/2 (d+T) ( n i 2 N r 2 ) 1/2 ,

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