Abstract

In traditional zonal wavefront sensing for adaptive optics, after local wavefront gradients are obtained, the entire wavefront can be calculated by assuming that the wavefront is a continuous surface. Such an approach will lead to sub-optimal performance in reconstructing wavefronts which are either discontinuous or undersampled by the zonal wavefront sensor. Here, we report a new method to reconstruct the wavefront by directly measuring local wavefront phases in parallel using multidither coherent optical adaptive technique. This method determines the relative phases of each pupil segment independently, and thus produces an accurate wavefront for even discontinuous wavefronts. We implemented this method in an adaptive optical two-photon fluorescence microscopy and demonstrated its superior performance in correcting large or discontinuous aberrations.

© 2014 Optical Society of America

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2011 (2)

2010 (1)

N. Ji, D. E. Milkie, E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[CrossRef] [PubMed]

2007 (1)

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

2006 (1)

2002 (1)

D. M. Topa, “Wavefront reconstruction for the Shack-Hartmann wavefront sensor,” Proc. SPIE 4769, 101–115 (2002).
[CrossRef]

2000 (3)

G. Chanan, M. Troy, C. Ohara, “Phasing the primary mirror segments of the Keck telescopes: a comparison of different techniques,” Proc. SPIE 4003, 188–202 (2000).
[CrossRef]

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

G. Chanan, C. Ohara, M. Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39(25), 4706–4714 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

1980 (1)

1977 (3)

1976 (1)

1974 (1)

1971 (1)

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–658 (1971).

Baker, J. T.

Benham, V.

Bernstein, M.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Betzig, E.

D. E. Milkie, E. Betzig, N. Ji, “Pupil-segmentation-based adaptive optical microscopy with full-pupil illumination,” Opt. Lett. 36(21), 4206–4208 (2011).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[CrossRef] [PubMed]

Bridges, W. B.

Brown, W. P.

Brunner, P. T.

Cauwenberghs, G.

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

Chanan, G.

Cui, M.

Culpepper, M. A.

Dekens, F.

Feng, G. P.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Hansen, S.

Ji, N.

D. E. Milkie, E. Betzig, N. Ji, “Pupil-segmentation-based adaptive optical microscopy with full-pupil illumination,” Opt. Lett. 36(21), 4206–4208 (2011).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[CrossRef] [PubMed]

Keller-Peck, C.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Kirkman, D.

Lazzara, S. P.

Lichtman, J. W.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Liu, L.

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

Loizos, D. N.

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

Lu, C. A.

Mast, T.

Mellor, R. H.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Michaels, S.

Milkie, D. E.

D. E. Milkie, E. Betzig, N. Ji, “Pupil-segmentation-based adaptive optical microscopy with full-pupil illumination,” Opt. Lett. 36(21), 4206–4208 (2011).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[CrossRef] [PubMed]

Nelson, D. J.

Nelson, J.

Nerbonne, J. M.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Nguyen, Q. T.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Nussmeier, T. A.

O’Meara, T. R.

Ohara, C.

G. Chanan, C. Ohara, M. Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39(25), 4706–4714 (2000).
[CrossRef] [PubMed]

G. Chanan, M. Troy, C. Ohara, “Phasing the primary mirror segments of the Keck telescopes: a comparison of different techniques,” Proc. SPIE 4003, 188–202 (2000).
[CrossRef]

O'Meara, T. R.

Pearson, J. E.

Pilkington, D.

Platt, B. C.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–658 (1971).

Sanchez, A. D.

Sanes, J. R.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Sanguinet, J. A.

Shack, R. V.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–658 (1971).

Shay, T. M.

Sirko, E.

Sotiriadis, P. P.

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

Southwell, W. H.

Spring, J.

Topa, D. M.

D. M. Topa, “Wavefront reconstruction for the Shack-Hartmann wavefront sensor,” Proc. SPIE 4769, 101–115 (2002).
[CrossRef]

Troy, M.

Vorontsov, M. A.

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

Wallace, M.

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Ward, B.

Appl. Opt. (5)

J. Opt. Soc. Am. (5)

Nat. Methods (1)

N. Ji, D. E. Milkie, E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[CrossRef] [PubMed]

Neuron (1)

G. P. Feng, R. H. Mellor, M. Bernstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, J. R. Sanes, “Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (3)

L. Liu, D. N. Loizos, M. A. Vorontsov, P. P. Sotiriadis, G. Cauwenberghs, “Coherent combining of multiple beams with multi-dithering technique: 100 KHz closed-loop compensation demonstration,” Proc. SPIE 6708, 67080D (2007).
[CrossRef]

D. M. Topa, “Wavefront reconstruction for the Shack-Hartmann wavefront sensor,” Proc. SPIE 4769, 101–115 (2002).
[CrossRef]

G. Chanan, M. Troy, C. Ohara, “Phasing the primary mirror segments of the Keck telescopes: a comparison of different techniques,” Proc. SPIE 4003, 188–202 (2000).
[CrossRef]

Other (3)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes. (Oxford University, 1998)

J. A. Kubby, Adaptive Optics for Biological Imaging. (CRC, 2013).

J. Porter, Adaptive Optics for Vision Science: Principles, Practices, Design, and Applications. (Wiley-Interscience, 2006).

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Figures (4)

Fig. 1
Fig. 1

Schematics of multidither COAT used to directly measure the phases of pupil segments for an AO two-photon fluorescence microscope. (a) We first modulate the phases of half of the segments (e.g., grey segments) at distinct frequencies ωi’s and keep the phases of the other half (e.g., white segments), which serves as the reference, constant. (b) The modulated rays and the reference ray interfere and modulate the focal intensity, resulting in two-photon fluorescence signal variation. (c-d) The phase for each modulated segment Δθi is directly read out from the Fourier transform of the signal trace at its modulation frequency. (a-d) is repeated to obtain the phases for the other half segments (e.g., modulate white segments with the grey segments as reference). (e) Schematics for the AO two-photon fluorescence microscope. Output from a Ti:Sapphire oscillator reflects off a mirror (M) or a segmented mirror (SM), a spatial light modulator (SLM), a X galvanometer (X galvo), a Y galvanometer (Y galvo), another mirror (M), and is focused by a microscope objective (Obj) into a sample (S). The resulting fluorescence is separated by a dichroic beamsplitter (Dichr), collected by a lens, and detected by a photomultiplier tube (PMT). Achromatic lens pairs are used throughout the beam path for conjugation. A field stop (FS) is used to block the higher diffraction order from the SM when needed.

Fig. 2
Fig. 2

Application of direct phase measurement method to two moderate aberrations. For the first aberration, (a) Wavefront gradients for 36 pupil segments are determined from the centroid shifts. (b) Axial fluorescence images of a 2 µm diameter bead (b1) before AO correction (“No AO”), (b2) after applying corrective wavefront that only corrected the tilt (“Tilt Only”), (b3) after applying the corrective wavefront calculated by phase reconstruction (“PR”), after applying the corrective wavefronts obtained with (b4) the 1st (“PM 1st”) and (b5) 2nd (“PM 2nd”) iteration of phase measurements, and (b6) under ideal, aberration-free condition (“Ideal”), respectively. (c) Line intensity profiles along the dotted yellow line of the images in (b). (d) Final corrective wavefront patterns in units of waves (λ = 900nm) obtained by phase reconstruction and direct phase measurement, respectively. (e-h) same as (a-d), except for the second aberration. Scale bars: (a) 6 μm, (b, f) 2 μm, and (e) 10 μm.

Fig. 3
Fig. 3

Application of direct phase measurement method to undersampled aberrations. (a) Wavefront gradients for 36 pupil segments are determined from the centroid shifts. (b) Axial fluorescence images of a 2 µm diameter bead (b1) before AO correction (obtained at a laser power increased by 13 × , thus 170 × increase in signal), (b2) after applying the corrective wavefront calculated by phase reconstruction, after (b3) the 1st and (b4) 2nd iteration of the direct phase measurement, and (b5) under ideal aberration-free condition, respectively. (c) Final corrective wavefront patterns in units of waves (λ = 900 nm) obtained by phase reconstruction and direct phase measurement, respectively. (d) Line intensity profiles along the dotted yellow lines of the images in (b). (e) Lateral (XY) and axial (XZ) fluorescence images of YFP-labeled dendrites at 270 µm depth in mouse brain in vivo. The axial images were taken along the green solid line. (f) Line intensity profiles along the dotted yellow line of the images in (e). (g) Final corrective wavefront patterns in units of waves (λ = 900 nm) obtained by phase reconstruction and direct wavefront phase measurement, respectively. Scale bars: (a) 16 μm, (b) 2 μm, and (e) 5 μm.

Fig. 4
Fig. 4

Application of direct phase measurement method to a discontinuous aberration introduced by a segmented mirror. (a) Wavefront gradients for 37 mirror segments were determined from the centroid shifts. (b) Final corrective wavefronts in units of waves (λ = 900 nm) obtained using phase reconstruction, direct phase measurement method implemented on the SM, and direct phase measurement method implemented on the liquid crystal SLM, respectively. (c) Axial fluorescence images of a 2 µm diameter bead (c1) without AO correction, (c2) after applying the wavefront that only corrected the tilt, (c3) after applying the corrective wavefront calculated by phase reconstruction, after (c4) the 1st and (c5) 2nd iteration of the direct phase measurement method implemented on the segmented mirror (SM), after (c6) the 1st and (c7) 2nd iteration of direct phase measurement implemented on a liquid crystal SLM conjugated to the SM, respectively. (d) Line intensity profiles along the dotted yellow line of the images in (c). (e) The discontinuous aberration of the segmented mirror was temporally stable: a previously measured corrective wavefront, when applied 8 hours later, improved the signal by the same amount as a contemporaneously obtained wavefront. Scale bars: (a) 26 μm and (c) 2 μm.

Equations (3)

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E(t)= E r e i( θ r +ωt) + i=1 N E i e i( θ i i t+ωt)
I(t)= | E(t) | 2 = E r 2 + i=1 N E i 2 + i=1 N 2 E r E i cos( ω i t+ θ i r )+M(t)
S(t)=I (t) 2 = i=1 N C i cos( ω i t+θ i r )+C(t)

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