Abstract

We present a direct slope-based correction algorithm to simultaneously control two deformable mirrors (DMs) in a woofer-tweeter adaptive optics system. A global response matrix was derived from the response matrices of each deformable mirror and the voltages for both deformable mirrors were calculated simultaneously. This control algorithm was tested and compared with a 2-step sequential control method in five normal human eyes using an adaptive optics scanning laser ophthalmoscope. The mean residual total root-mean-square (RMS) wavefront errors across subjects after adaptive optics (AO) correction were 0.128 ± 0.025 μm and 0.107 ± 0.033 μm for simultaneous and 2-step control, respectively (7.75-mm pupil). The mean intensity of reflectance images acquired after AO convergence was slightly higher for 2-step control. Radially-averaged power spectra calculated from registered reflectance images were nearly identical for all subjects using simultaneous or 2-step control. The correction performance of our new simultaneous dual DM control algorithm is comparable to 2-step control, but is more efficient. This method can be applied to any woofer-tweeter AO system.

© 2010 OSA

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References

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    [CrossRef] [PubMed]

2010 (1)

2009 (7)

R. J. Zawadzki, S. S. Choi, A. R. Fuller, J. W. Evans, B. Hamann, and J. S. Werner, “Cellular resolution volumetric in vivo retinal imaging with adaptive optics-optical coherence tomography,” Opt. Express 17(5), 4084–4094 (2009).
[CrossRef] [PubMed]

B. Cense, E. Koperda, J. M. Brown, O. P. Kocaoglu, W. Gao, R. S. Jonnal, and D. T. Miller, “Volumetric retinal imaging with ultrahigh-resolution spectral-domain optical coherence tomography and adaptive optics using two broadband light sources,” Opt. Express 17(5), 4095–4111 (2009).
[CrossRef] [PubMed]

J. W. Evans, R. J. Zawadzki, S. M. Jones, S. S. Olivier, and J. S. Werner, “Error budget analysis for an adaptive optics optical coherence tomography system,” Opt. Express 17(16), 13768–13784 (2009).
[CrossRef] [PubMed]

E. J. Fernández, P. M. Prieto, and P. Artal, “Binocular adaptive optics visual simulator,” Opt. Lett. 34(17), 2628–2630 (2009).
[CrossRef] [PubMed]

C. Torti, B. Povazay, B. Hofer, A. Unterhuber, J. Carroll, P. K. Ahnelt, and W. Drexler, “Adaptive optics optical coherence tomography at 120,000 depth scans/s for non-invasive cellular phenotyping of the living human retina,” Opt. Express 17(22), 19382–19400 (2009).
[CrossRef] [PubMed]

W. Zou and S. A. Burns, “High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics,” Opt. Express 17(22), 20167–20177 (2009).
[CrossRef] [PubMed]

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis. 9(6), 4 (2009).
[CrossRef] [PubMed]

2008 (4)

2007 (6)

2006 (2)

2002 (2)

2001 (1)

1999 (1)

X. Li, C. Wang, H. Xian, X. Wu, and W. Jiang, “Zernike modal compensation analysis for an adaptive optics system using direct-gradient wavefront reconstruction algorithm,” Proc. SPIE 3762, 116–124 (1999).
[CrossRef]

1998 (1)

1997 (1)

1993 (1)

R. A. Applegate and H. C. Howland, “Magnification and visual acuity in refractive surgery,” Arch. Ophthalmol. 111(10), 1335–1342 (1993).
[PubMed]

Ahamd, K.

Ahnelt, P. K.

Applegate, R. A.

R. A. Applegate and H. C. Howland, “Magnification and visual acuity in refractive surgery,” Arch. Ophthalmol. 111(10), 1335–1342 (1993).
[PubMed]

Artal, P.

Besecker, J. R.

Blain, C.

Bradley, C.

Brown, J. M.

Burns, S. A.

Campbell, M. C. W.

Carroll, J.

Cense, B.

Chen, D. C.

Chen, L.

Choi, S. S.

Chui, T. Y.

T. Y. Chui, H. Song, and S. A. Burns, “Individual variations in human cone photoreceptor packing density: variations with refractive error,” Invest. Ophthalmol. Vis. Sci. 49(10), 4679–4687 (2008).
[CrossRef] [PubMed]

Conan, R.

Delori, F. C.

Derby, J. C.

Donnelly Iii, W.

Dorronsoro, C.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis. 9(6), 4 (2009).
[CrossRef] [PubMed]

Drexler, W.

Dubra, A.

Evans, J. W.

Fernández, E. J.

Fuller, A. R.

Gambra, E.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis. 9(6), 4 (2009).
[CrossRef] [PubMed]

Gao, W.

Gee, B. P.

Gray, D. C.

Hamann, B.

Hampton, P.

Hebert, T. J.

Hilton, A.

Hofer, B.

Hofer, H.

Hou, J.

Howland, H. C.

R. A. Applegate and H. C. Howland, “Magnification and visual acuity in refractive surgery,” Arch. Ophthalmol. 111(10), 1335–1342 (1993).
[PubMed]

Hu, S.

Jiang, W.

Jones, S. M.

Jonnal, R. S.

Keskin, O.

Kocaoglu, O. P.

Koperda, E.

Lee, D. J.

Li, X.

X. Li, C. Wang, H. Xian, X. Wu, and W. Jiang, “Zernike modal compensation analysis for an adaptive optics system using direct-gradient wavefront reconstruction algorithm,” Proc. SPIE 3762, 116–124 (1999).
[CrossRef]

Liang, J.

Liu, G.

Marcos, S.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis. 9(6), 4 (2009).
[CrossRef] [PubMed]

Merigan, W.

Miller, D. T.

Oliver, S. S.

Olivier, S. S.

Petrig, B. L.

Porter, J.

Povazay, B.

Prieto, P. M.

Qi, X.

Queener, H.

Rao, C.

Reinholz, F.

Roggemann, M. C.

Romero-Borja, F.

Roorda, A.

E. A. Rossi, P. Weiser, J. Tarrant, and A. Roorda, “Visual performance in emmetropia and low myopia after correction of high-order aberrations,” J. Vis. 7(8), 14 (2007).
[CrossRef] [PubMed]

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Rossi, E. A.

E. A. Rossi, P. Weiser, J. Tarrant, and A. Roorda, “Visual performance in emmetropia and low myopia after correction of high-order aberrations,” J. Vis. 7(8), 14 (2007).
[CrossRef] [PubMed]

Sawides, L.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis. 9(6), 4 (2009).
[CrossRef] [PubMed]

Silva, D. A.

Singer, B.

Sliney, D. H.

Song, H.

T. Y. Chui, H. Song, and S. A. Burns, “Individual variations in human cone photoreceptor packing density: variations with refractive error,” Invest. Ophthalmol. Vis. Sci. 49(10), 4679–4687 (2008).
[CrossRef] [PubMed]

Tarrant, J.

E. A. Rossi, P. Weiser, J. Tarrant, and A. Roorda, “Visual performance in emmetropia and low myopia after correction of high-order aberrations,” J. Vis. 7(8), 14 (2007).
[CrossRef] [PubMed]

Torti, C.

Tumbar, R.

Twietmeyer, T. H.

Unterhuber, A.

Wang, C.

X. Li, C. Wang, H. Xian, X. Wu, and W. Jiang, “Zernike modal compensation analysis for an adaptive optics system using direct-gradient wavefront reconstruction algorithm,” Proc. SPIE 3762, 116–124 (1999).
[CrossRef]

Wang, Q.

Webb, R. H.

Weiser, P.

E. A. Rossi, P. Weiser, J. Tarrant, and A. Roorda, “Visual performance in emmetropia and low myopia after correction of high-order aberrations,” J. Vis. 7(8), 14 (2007).
[CrossRef] [PubMed]

Werner, J. S.

Williams, D. R.

Wolfing, J. I.

Wu, J.

Wu, X.

X. Li, C. Wang, H. Xian, X. Wu, and W. Jiang, “Zernike modal compensation analysis for an adaptive optics system using direct-gradient wavefront reconstruction algorithm,” Proc. SPIE 3762, 116–124 (1999).
[CrossRef]

Xian, H.

X. Li, C. Wang, H. Xian, X. Wu, and W. Jiang, “Zernike modal compensation analysis for an adaptive optics system using direct-gradient wavefront reconstruction algorithm,” Proc. SPIE 3762, 116–124 (1999).
[CrossRef]

Xu, B.

Yamauchi, Y.

Yang, H.

Yoon, G. Y.

Zawadzki, R. J.

Zhang, X.

Zhang, Y.

Zhong, Z.

Zou, W.

Appl. Opt. (3)

Arch. Ophthalmol. (1)

R. A. Applegate and H. C. Howland, “Magnification and visual acuity in refractive surgery,” Arch. Ophthalmol. 111(10), 1335–1342 (1993).
[PubMed]

Chin. Opt. Lett. (1)

Invest. Ophthalmol. Vis. Sci. (1)

T. Y. Chui, H. Song, and S. A. Burns, “Individual variations in human cone photoreceptor packing density: variations with refractive error,” Invest. Ophthalmol. Vis. Sci. 49(10), 4679–4687 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (5)

J. Vis. (2)

E. A. Rossi, P. Weiser, J. Tarrant, and A. Roorda, “Visual performance in emmetropia and low myopia after correction of high-order aberrations,” J. Vis. 7(8), 14 (2007).
[CrossRef] [PubMed]

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis. 9(6), 4 (2009).
[CrossRef] [PubMed]

Opt. Express (11)

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

H. Hofer, L. Chen, G. Y. Yoon, B. Singer, Y. Yamauchi, and D. R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberrations,” Opt. Express 8(11), 631–643 (2001).
[CrossRef] [PubMed]

D. C. Gray, W. Merigan, J. I. Wolfing, B. P. Gee, J. Porter, A. Dubra, T. H. Twietmeyer, K. Ahamd, R. Tumbar, F. Reinholz, and D. R. Williams, “In vivo fluorescence imaging of primate retinal ganglion cells and retinal pigment epithelial cells,” Opt. Express 14(16), 7144–7158 (2006).
[CrossRef] [PubMed]

C. Torti, B. Povazay, B. Hofer, A. Unterhuber, J. Carroll, P. K. Ahnelt, and W. Drexler, “Adaptive optics optical coherence tomography at 120,000 depth scans/s for non-invasive cellular phenotyping of the living human retina,” Opt. Express 17(22), 19382–19400 (2009).
[CrossRef] [PubMed]

W. Zou and S. A. Burns, “High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics,” Opt. Express 17(22), 20167–20177 (2009).
[CrossRef] [PubMed]

R. S. Jonnal, J. R. Besecker, J. C. Derby, O. P. Kocaoglu, B. Cense, W. Gao, Q. Wang, and D. T. Miller, “Imaging outer segment renewal in living human cone photoreceptors,” Opt. Express 18(5), 5257–5270 (2010).
[CrossRef] [PubMed]

R. J. Zawadzki, B. Cense, Y. Zhang, S. S. Choi, D. T. Miller, and J. S. Werner, “Ultrahigh-resolution optical coherence tomography with monochromatic and chromatic aberration correction,” Opt. Express 16(11), 8126–8143 (2008).
[CrossRef] [PubMed]

Z. Zhong, B. L. Petrig, X. Qi, and S. A. Burns, “In vivo measurement of erythrocyte velocity and retinal blood flow using adaptive optics scanning laser ophthalmoscopy,” Opt. Express 16(17), 12746–12756 (2008).
[PubMed]

R. J. Zawadzki, S. S. Choi, A. R. Fuller, J. W. Evans, B. Hamann, and J. S. Werner, “Cellular resolution volumetric in vivo retinal imaging with adaptive optics-optical coherence tomography,” Opt. Express 17(5), 4084–4094 (2009).
[CrossRef] [PubMed]

B. Cense, E. Koperda, J. M. Brown, O. P. Kocaoglu, W. Gao, R. S. Jonnal, and D. T. Miller, “Volumetric retinal imaging with ultrahigh-resolution spectral-domain optical coherence tomography and adaptive optics using two broadband light sources,” Opt. Express 17(5), 4095–4111 (2009).
[CrossRef] [PubMed]

J. W. Evans, R. J. Zawadzki, S. M. Jones, S. S. Olivier, and J. S. Werner, “Error budget analysis for an adaptive optics optical coherence tomography system,” Opt. Express 17(16), 13768–13784 (2009).
[CrossRef] [PubMed]

Opt. Lett. (2)

Proc. SPIE (1)

X. Li, C. Wang, H. Xian, X. Wu, and W. Jiang, “Zernike modal compensation analysis for an adaptive optics system using direct-gradient wavefront reconstruction algorithm,” Proc. SPIE 3762, 116–124 (1999).
[CrossRef]

Other (5)

W. Jiang, Y. Zhang, H. Xian, C. Guan, and N. Ling, “A wavefront correction system for inertial confinement fusion,” Proc. of the Second International Workshop on Adaptive Optics for Industry and Medicine pages 8–15, (2000).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C: The art of scientific computing (Cambridge University Press, Cambridge, United Kingdom, 2nd edition, 1992).

ANSI, American National Standard for safe use of lasers (ANSI 136.1–2000) (The Laser Institute of America, 2000).

ANSI, American National Standard for ophthalmics-Methods for reporting optical aberrations of eyes (ANSI Z80.28–2004) (American National Standards Institute, Inc., 2004).

W. Jiang, and H. Li, “Hartmann-Shack wavefront sensing and wavefront control” Proc. SPIE 1271, 82:93 (1990).

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Figures (6)

Fig. 1
Fig. 1

(a) The woofer-tweeter adaptive optics scanning laser ophthalmoscope (AOSLO). 840nm: SLD with center wavelength of 840 nm, Tweeter: BMC MEMS deformable mirror, HS: horizontal scanner (14.62 kHz), VS: vertical scanner (25 Hz), Woofer: Mirao-52e deformable mirror, SHWS: Shack-Hartmann wavefront sensor, PMT: photomultiplier tube for near-infrared reflectance imaging. (b) Spatial geometry of the Shack-Hartmann lenslets (green squares), tweeter actuators (blue circles), and woofer actuators (red squares) in the pupil plane.

Fig. 2
Fig. 2

Changes in mean spot displacement (solid lines) and normalized pupil radius (dashed lines) of the Shack-Hartmann wavefront sensor spots as a function of time in 5 subjects for 3 different control methods: woofer only (black), 2-step sequential, and simultaneous (red). The 2-step sequential control method includes two components: woofer only correction (black), followed by the 2-step (post-woofer) correction (green), or tweeter only correction, initiated after the woofer converged. Each curve represents the mean of 5 trials. The mean standard deviation of the mean spot displacement (MSD) is shown in Table 2 and represents the variability inherent in each mean curve. AO correction was initiated at time = 0 seconds. In general, the time to convergence increased in eyes with increasing amounts of aberration. However, the convergence time and the MSD values after convergence were nearly identical for 2-step and simultaneous control within a subject.

Fig. 3
Fig. 3

Average intensity of the retinal reflectance images acquired using different control methods in 5 subjects. Plotted are the mean intensity values averaged over 500 frames acquired for each of 5 trials after AO convergence using the woofer only (black bars), simultaneous dual DM (orange bars) and 2-step sequential (green bars) control methods. Error bars represent ± 1 standard deviation about the mean intensity. The 2-step control method yielded average intensity values that tended to be slightly greater than those obtained from simultaneous control.

Fig. 4
Fig. 4

Registered reflectance images and associated radially-averaged power spectra for two AO control methods in 2 subjects. Registered images of the cone photoreceptor mosaic were constructed from 20 frames acquired after AO convergence using (a,d) simultaneous dual DM and (b,e) 2-step sequential control algorithms. Images were taken at an eccentricity of 1 degree. Scale bar represents 30 microns. Qualitatively, retinal images were very similar across control methods within individual subjects. (c,f) Radially-averaged power spectra (computed from the registered images) for simultaneous control (red line) and 2-step control (blue line) as a function of spatial frequency. The radial power spectra obtained using both control methods are quantitatively similar.

Fig. 5
Fig. 5

Ratio of the radial power spectrum density (PSD) obtained from retinal images acquired using simultaneous control to the radial power spectrum density from retinal images acquired using 2-step sequential control in 5 subjects. A ratio of 1 (dashed black line) indicates that the radial power spectrum was identical for each control method. A ratio greater/less than 1 implies that the radial power spectrum was greater for the simultaneous/2-step control method, respectively. Across the majority of spatial frequencies, the ratio hovered around 1, indicating that the radial power spectrum was approximately the same between the two control methods.

Fig. 6
Fig. 6

(a) Shack-Hartmann spot array pattern and (b) registered reflectance image for a subject whose eyelid partially covered their dilated pupil. The top two rows of Shack-Hartmann spots were fully blocked in (a). Nevertheless, it was still possible to achieve a high quality retinal image of the cone mosaic. Registered image was taken at an eccentricity of ~1 degree and constructed from 20 frames. Scale bar represents 30 microns.

Tables (1)

Tables Icon

Table 1 Sphere, cylinder, total RMS and higher order RMS wavefront errors before and after AO correction using simultaneous and 2-step dual DM control methods for 5 subjects (7.75-mm pupil)

Equations (12)

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S = D V
D t ' = D t D t w
D t w = D w C t w
S = D t V t S = D w V w
V w = D w S = D w D t V t = C t w V t
D t ' = D t D w C t w = D t D w ( D w D t )
i = 1 n w V w , i = i = 1 n t V t , i = 0
i = 1 n w X i V w , i = i = 1 n w Y i V w , i = 0 i = 1 n t X i V t , i = i = 1 n t Y i V t , i = 0
[ 1 ... 1 X 1 ... X n w Y 1 ... Y n w ] [ V w , 1 ... V w , n w ] = C w V w = 0 and [ 1 ... 1 X 1 ... X n t Y 1 ... Y n t ] [ V t , 1 ... V t , n t ] = C t V t = 0
D w t = [ D w D t ' C w 0 0 C t ]
S = D w t V w t = [ D w D t ' C w 0 0 C t ] [ V w V t ] = D w V w + D t ' V t
[ V w ; V t ] = D w t [ 1 : ( n w + n t ) , 1 : n s ] S

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