Abstract

A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DM correcting the low-stroke, high-order aberrations. The optimal damping factor for a DM is found to be the median of the eigenvalue spectrum of the influence matrix of that DM. Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy.

© 2012 Optical Society of America

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  1. A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vis. Res. 39, 207–217 (1999).
    [CrossRef]
  2. D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 34026 (2006).
    [CrossRef]
  3. D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46, 1450–1458 (2006).
    [CrossRef]
  4. A. Mathur, D. A. Atchison, and D. H. Scott, “Ocular aberrations in the peripheral visual field,” Opt. Lett. 33, 863–865 (2008).
    [CrossRef]
  5. X. Wei and L. Thibos, “Modeling the eye’s optical system by ocular wavefront tomography,” Opt. Express 16, 20490–20502(2008).
    [CrossRef]
  6. L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vis. 9 (6), 17 (2009).
    [CrossRef]
  7. W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalm. Physiol. Opt. 8, 153–163 (1988).
    [CrossRef]
  8. D. C. Chen, S. M. Jones, D. A. Silva, and S. S. Olivier, “High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors,” J. Opt. Soc. Am. A 24, 1305–1312 (2007).
    [CrossRef]
  9. R. J. Zawadzki, S. S. Choi, S. M. Jones, S. S. Oliver, and J. S. Werner, “Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions,” J. Opt. Soc. Am. A 24, 1373–1383 (2007).
    [CrossRef]
  10. 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, 4095–4111 (2009).
    [CrossRef]
  11. M. C. Roggemann and D. J. Lee, “Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere,” Appl. Opt. 37, 4577–4585 (1998).
    [CrossRef]
  12. J. D. Barchers, “Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation,” J. Opt. Soc. Am. A 19, 54–63 (2002).
    [CrossRef]
  13. J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. A 19, 926–945 (2002).
    [CrossRef]
  14. L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
    [CrossRef]
  15. J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
    [CrossRef]
  16. T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth, high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
    [CrossRef]
  17. O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.
  18. R. Conan, “Mean-square residual error of a wavefront after propagation through atmospheric turbulence and after correction with Zernike polynomials,” J. Opt. Soc. Am. A 25, 526–536 (2008).
    [CrossRef]
  19. K. Morzinski, B. Macintosh, D. Gavel, and D. Dillon, “Stroke saturation on a MEMS deformable mirror for woofer-tweeter adaptive optics,” Opt. Express 17, 5829–5844(2009).
    [CrossRef]
  20. 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, 2638–2642 (2006).
    [CrossRef]
  21. J.-F. Lavigne and J.-P. Véran, “Woofer-tweeter control in an adaptive optics system using a Fourier reconstructor,” J. Opt. Soc. Am. A 25, 2271–2279 (2008).
    [CrossRef]
  22. R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007).
    [CrossRef]
  23. C. Li, N. Sredar, K. M. Ivers, H. Queener, and J. Porter, “A correction algorithm to simultaneously control dual deformable mirrors in a woofer-tweeter adaptive optics system,” Opt. Express 18, 16671–16684 (2010).
    [CrossRef]
  24. W. Zou, X. Qi, and S. A. Burns, “Wavefront-aberration sorting and correction for a dual-deformable-mirror adaptive-optics system,” Opt. Lett. 33, 2602–2604 (2008).
    [CrossRef]
  25. W. Zou and S. A. Burns, “High-accuracy wavefront control for retinal imaging with adaptive-influence-matrix adaptive optics,” Opt. Express 17, 20167–20177 (2009).
    [CrossRef]
  26. W. Zou, X. Qi, and S. A. Burns, “Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm,” Biomed. Opt. Express 2, 1986–2004 (2011).
    [CrossRef]
  27. http://www.imagine-eyes.com/content/view/45/103/ .
  28. Specifications of product Model no. μDM140-450-E-AgMgF, SN: 09w200#108-450D16-9, Boston MicroMachines Corporation (2007).
  29. Device no. SLD-261-HP1-DIL-SM-PD, http://www.superlumdiodes.com/ .
  30. Product no. 0300-7.6-S, http://www.st.northropgrumman.com/aoa/beamcontrol/microoptics/catalog_arrays.html .
  31. Product no. UP-1830CL-12B, http://www.uniqvision.com/html/manuals .
  32. W. Zou, “New phasing algorithm for large segmented telescope mirrors,” Opt. Eng. 41, 2338–2344 (2002).
    [CrossRef]
  33. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168(1944).
  34. J. Meiron, “Damped least-squares method for automatic lens design,” J. Opt. Soc. Am. 55, 1105–1107 (1965).
    [CrossRef]
  35. E. Glatzel and R. Wilson, “Adaptive automatic correction in optical design,” Appl. Opt. 7, 265–276 (1968).
    [CrossRef]
  36. D. R. Buchele, “Damping factor for the least-squares method of optical design,” Appl. Opt. 7, 2433–2435 (1968).
    [CrossRef]
  37. D. Q. Su and Y. N. Wang, “Automatic correction of aberration in astro-optical system,” Acta Astron. Sin. 15(1), 51–60(1974).
  38. D. Q. Su, “Spot-diagram merit function and damped least-squares method,” Opt. Instrum. Technol. 31, 1–12 (1980).
  39. H. Matsui and K. Tanaka, “Determination method of an initial damping factor in the damped-least-squares problem,” Appl. Opt. 33, 2411–2418 (1994).
    [CrossRef]
  40. V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. 73, 860–861 (1983).
    [CrossRef]
  41. http://en.wikipedia.org/wiki/Tikhonov_regularization .
  42. N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
    [CrossRef]
  43. N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
    [CrossRef]
  44. T. Farrell, “Woofer-tweeter adaptive optics for astronomy,” Ph.D. dissertation (National University of Ireland Galway, 2010).
  45. W. Zou, X. Qi, G. Huang, and S. A. Burns, “Improving wavefront boundary condition for in vivo high resolution adaptive optics ophthalmic imaging,” Biomed. Opt. Express 2, 3309–3320 (2011).
    [CrossRef]

2011 (2)

2010 (1)

2009 (4)

2008 (7)

2007 (3)

2006 (4)

D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 34026 (2006).
[CrossRef]

D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46, 1450–1458 (2006).
[CrossRef]

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth, high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (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, 2638–2642 (2006).
[CrossRef]

2002 (4)

2001 (1)

1999 (1)

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vis. Res. 39, 207–217 (1999).
[CrossRef]

1998 (1)

1994 (1)

1988 (1)

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalm. Physiol. Opt. 8, 153–163 (1988).
[CrossRef]

1983 (1)

1980 (1)

D. Q. Su, “Spot-diagram merit function and damped least-squares method,” Opt. Instrum. Technol. 31, 1–12 (1980).

1974 (1)

D. Q. Su and Y. N. Wang, “Automatic correction of aberration in astro-optical system,” Acta Astron. Sin. 15(1), 51–60(1974).

1968 (2)

1965 (1)

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168(1944).

Artal, P.

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vis. 9 (6), 17 (2009).
[CrossRef]

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vis. Res. 39, 207–217 (1999).
[CrossRef]

Atchison, D. A.

A. Mathur, D. A. Atchison, and D. H. Scott, “Ocular aberrations in the peripheral visual field,” Opt. Lett. 33, 863–865 (2008).
[CrossRef]

D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 34026 (2006).
[CrossRef]

D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46, 1450–1458 (2006).
[CrossRef]

Barchers, J. D.

Blain, C.

R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007).
[CrossRef]

O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.

Bradley, A.

Bradley, C.

R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007).
[CrossRef]

O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.

Brennan, T. J.

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth, high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[CrossRef]

Brown, J. M.

Buchele, D. R.

Burns, S. A.

Cense, B.

Charman, W. N.

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalm. Physiol. Opt. 8, 153–163 (1988).
[CrossRef]

Chen, D. C.

Cheng, X.

Choi, S. S.

Coburn, D.

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

Coleman, C.

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

Conan, R.

Cox, I. G.

Dainty, C.

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

Dalimier, E.

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

Daly, E.

Devaney, N.

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

Dillon, D.

Farrell, T.

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

T. Farrell, “Woofer-tweeter adaptive optics for astronomy,” Ph.D. dissertation (National University of Ireland Galway, 2010).

Gao, W.

Gavel, D.

Glatzel, E.

Guirao, A.

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
[CrossRef]

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vis. Res. 39, 207–217 (1999).
[CrossRef]

Hampton, P.

R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007).
[CrossRef]

O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.

Heron, G.

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalm. Physiol. Opt. 8, 153–163 (1988).
[CrossRef]

Hilton, A.

R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007).
[CrossRef]

O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.

Hong, X.

Hou, J.

Hu, S.

Huang, G.

Ivers, K. M.

Jiang, W.

Jones, S. M.

Jonnal, R. S.

Keskin, O.

R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007).
[CrossRef]

O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.

Kocaoglu, O. P.

Koperda, E.

Laurent, F.

Lavigne, J.-F.

Lee, D. J.

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168(1944).

Li, C.

Lundström, L.

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vis. 9 (6), 17 (2009).
[CrossRef]

Macintosh, B.

Mackey, D.

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

Mackey, R.

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

N. Devaney, E. Dalimier, T. Farrell, D. Coburn, R. Mackey, D. Mackey, F. Laurent, E. Daly, and C. Dainty, “Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors,” Appl. Opt. 47, 6550–6562 (2008).
[CrossRef]

Mahajan, V. N.

Mathur, A.

Matsui, H.

Meiron, J.

Miller, D. T.

Mira-Agudelo, A.

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vis. 9 (6), 17 (2009).
[CrossRef]

Morzinski, K.

Oliver, S. S.

Olivier, S. S.

Porter, J.

Pritchard, N.

D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46, 1450–1458 (2006).
[CrossRef]

Qi, X.

Queener, H.

Rhoadarmer, T. A.

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth, high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[CrossRef]

Roggemann, M. C.

Schmid, K. L.

D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46, 1450–1458 (2006).
[CrossRef]

Scott, D. H.

Silva, D. A.

Sredar, N.

Su, D. Q.

D. Q. Su, “Spot-diagram merit function and damped least-squares method,” Opt. Instrum. Technol. 31, 1–12 (1980).

D. Q. Su and Y. N. Wang, “Automatic correction of aberration in astro-optical system,” Acta Astron. Sin. 15(1), 51–60(1974).

Tanaka, K.

Thibos, L.

Thibos, L. N.

Véran, J.-P.

Wang, Y. N.

D. Q. Su and Y. N. Wang, “Automatic correction of aberration in astro-optical system,” Acta Astron. Sin. 15(1), 51–60(1974).

Wei, X.

Werner, J. S.

Williams, D. R.

Wilson, R.

Wu, J.

Xu, B.

Zawadzki, R. J.

Zhang, X.

Zou, W.

Acta Astron. Sin. (1)

D. Q. Su and Y. N. Wang, “Automatic correction of aberration in astro-optical system,” Acta Astron. Sin. 15(1), 51–60(1974).

Appl. Opt. (7)

Biomed. Opt. Express (2)

J. Biomed. Opt. (1)

D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 34026 (2006).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

D. C. Chen, S. M. Jones, D. A. Silva, and S. S. Olivier, “High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors,” J. Opt. Soc. Am. A 24, 1305–1312 (2007).
[CrossRef]

R. J. Zawadzki, S. S. Choi, S. M. Jones, S. S. Oliver, and J. S. Werner, “Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions,” J. Opt. Soc. Am. A 24, 1373–1383 (2007).
[CrossRef]

J.-F. Lavigne and J.-P. Véran, “Woofer-tweeter control in an adaptive optics system using a Fourier reconstructor,” J. Opt. Soc. Am. A 25, 2271–2279 (2008).
[CrossRef]

R. Conan, “Mean-square residual error of a wavefront after propagation through atmospheric turbulence and after correction with Zernike polynomials,” J. Opt. Soc. Am. A 25, 526–536 (2008).
[CrossRef]

J. D. Barchers, “Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation,” J. Opt. Soc. Am. A 19, 54–63 (2002).
[CrossRef]

J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. A 19, 926–945 (2002).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
[CrossRef]

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
[CrossRef]

J. Vis. (1)

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vis. 9 (6), 17 (2009).
[CrossRef]

Ophthalm. Physiol. Opt. (1)

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalm. Physiol. Opt. 8, 153–163 (1988).
[CrossRef]

Opt. Eng. (1)

W. Zou, “New phasing algorithm for large segmented telescope mirrors,” Opt. Eng. 41, 2338–2344 (2002).
[CrossRef]

Opt. Express (5)

Opt. Instrum. Technol. (1)

D. Q. Su, “Spot-diagram merit function and damped least-squares method,” Opt. Instrum. Technol. 31, 1–12 (1980).

Opt. Lett. (2)

Proc. SPIE (2)

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth, high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[CrossRef]

N. Devaney, D. Coburn, C. Coleman, C. Dainty, E. Dalimier, T. Farrell, D. Mackey, and R. Mackey, “Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction,” Proc. SPIE 6888, 688802(2008).
[CrossRef]

Q. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168(1944).

Vis. Res. (1)

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vis. Res. 39, 207–217 (1999).
[CrossRef]

Vision Res. (1)

D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46, 1450–1458 (2006).
[CrossRef]

Other (8)

O. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton, and C. Blain, “Woofer-tweeter adaptive optics test bench,” in First NASA/ESA Conference on Adaptive Hardware and Systems (IEEE, 2006), pp. 74–80.

http://en.wikipedia.org/wiki/Tikhonov_regularization .

http://www.imagine-eyes.com/content/view/45/103/ .

Specifications of product Model no. μDM140-450-E-AgMgF, SN: 09w200#108-450D16-9, Boston MicroMachines Corporation (2007).

Device no. SLD-261-HP1-DIL-SM-PD, http://www.superlumdiodes.com/ .

Product no. 0300-7.6-S, http://www.st.northropgrumman.com/aoa/beamcontrol/microoptics/catalog_arrays.html .

Product no. UP-1830CL-12B, http://www.uniqvision.com/html/manuals .

T. Farrell, “Woofer-tweeter adaptive optics for astronomy,” Ph.D. dissertation (National University of Ireland Galway, 2010).

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Figures (17)

Fig. 1.
Fig. 1.

Optical layout of the WT AO breadboard system.

Fig. 2.
Fig. 2.

Actuator distributions of (a) BMC DM and (b) Mirao DM.

Fig. 3.
Fig. 3.

Problem description of W-T dual-DM AO correction.

Fig. 4.
Fig. 4.

Actuator-interlaced dual-DM AO. It is equivalent to a single-DM AO with double actuator density.

Fig. 5.
Fig. 5.

Eigenvalue spectrum of normal matrices ATA (blue curve), BTB (green curve), and CTC (red curve) with LM λ=1. Mirao actuators were numbered as 051, and the BMC actuators were numbered as 52191. Due to the different voltage units adopted, the eigenvalues of the Mirao DM are much larger than those of the BMC DM.

Fig. 6.
Fig. 6.

Wavefront error reduction across four iterations of dual-DM AO correction with the damping factors β1=100 and β1=0.05, LM λ=1.0, and control gain of 0.75.

Fig. 7.
Fig. 7.

PSF of the breadboard system across dual-DM AO iterations. (a) PSF before AO correction. (b)–(f) PSFs during AO correction at first, second, third, fourth, and fifth iterations. The Strehl ratio for each PSF was estimated from the real-time wavefront RMS error.

Fig. 8.
Fig. 8.

Wavefront RMS error reduction of dual-DM AO (generic AO) for small wavefront aberrations (Curve 1) and comparison of the generic AO and DIM AO for large amplitude wavefront aberrations (Curves 2 and 3). Curve 1 and Fig. 6 use the same data.

Fig. 9.
Fig. 9.

Wavefront RMS error reduction of single BMC DM AO (generic AO) for small wavefront aberrations and comparison of the generic AO and DIM AO with single Mirao DM for large-amplitude wavefront aberrations.

Fig. 10.
Fig. 10.

Damping factor optimization for W-T dual-DM AO correction. This figure shows the contour plot of the final wavefront residual RMS error as the function of the damping factors. We can see that the optimum values of the two damping factors are at 1000 for the woofer DM and 0.004 for the tweeter DM, respectively.

Fig. 11.
Fig. 11.

Optimization of LM for the LM DLS algorithm.

Fig. 12.
Fig. 12.

(a) Optimization of control gain. (b) Final averaged wavefront RMS error (16–60 iterations) as a function of control gain.

Fig. 13.
Fig. 13.

Bayesian estimation of the damping factors. The damping factor is square of the Tikhonov factor, where the damping factor 1 (β1) is for the Mirao DM, and damping factor 2 (β2) is for the BMC DM.

Fig. 14.
Fig. 14.

Simulation of LM DLS dual-DM AO correction (1-Step) for the given wavefront shown in Fig. 6(a) (control gain set to 1), where (a), (b) are the expected wavefront corrections by the Mirao DM and the BMC DM, respectively, and (c) is the expected wavefront fitting error of the dual-DM AO.

Fig. 15.
Fig. 15.

Simulations of single DM AO correction, where (a), (c) are the expected wavefront corrections by single Mirao DM and single BMC DM, respectively, and (b), (d) are their corresponding wavefront fitting errors.

Fig. 16.
Fig. 16.

Simulation of LM DLS AO correction with the 2-Step computation for the given wavefront shown in Fig. 6(a) (control gain set to 1), where (a) is the expected wavefront correction by single Mirao DM (β1=100), (b) is the corresponding wavefront fitting error of Mirao DM, (c) is the expected wavefront correction by the BMC DM (β2=0.05) for the wavefront fitting error of (b), and (d) is the final wavefront fitting error of the 2-Step computation.

Fig. 17.
Fig. 17.

Comparison of wavefront fitting errors of single Mirao DM (Curve 2), single BMC DM (Curve 3), LM DLS dual-DM AO (1-Step) (Curve 4), and (2-Step) (Curve 5). Wavefront RMS error reduction of the dual-DM AO (Curve 1), which used the same data as in Fig. 8, provided a reference for the wavefront fitting errors.

Equations (2)

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ψ(X,Y)=ρ2[AX+λBY,S]=AX+λBYS22,
[XY]=[ATA+β1I1λATBλBTAλ2BTB+β2I2]1[ATλBT]S,

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