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

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]

Acta Astron. Sin.

• 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.

• 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]
• E. Glatzel and R. Wilson, “Adaptive automatic correction in optical design,” Appl. Opt. 7, 265–276 (1968). [CrossRef]
• D. R. Buchele, “Damping factor for the least-squares method of optical design,” Appl. Opt. 7, 2433–2435 (1968). [CrossRef]
• 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]
• 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]
• 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]
• 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]

Biomed. Opt. Express

• 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]
• 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]

J. Biomed. Opt.

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

J. Opt. Soc. Am.

• V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. 73, 860–861 (1983). [CrossRef]
• J. Meiron, “Damped least-squares method for automatic lens design,” J. Opt. Soc. Am. 55, 1105–1107 (1965). [CrossRef]

J. Opt. Soc. Am. A

• 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.

• 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.

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

Opt. Eng.

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

Opt. Express

• 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]
• X. Wei and L. Thibos, “Modeling the eye’s optical system by ocular wavefront tomography,” Opt. Express 16, 20490–20502(2008). [CrossRef]
• 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]
• 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]
• 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]

Opt. Instrum. Technol.

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

Opt. Lett.

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

Proc. SPIE

• 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.

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

Vis. Res.

• 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.

• 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

• 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).

Click here to see a list of articles that cite this paper

Related Journal Articles

• MEMS-based adaptive optics scanning laser ophthalmoscopy (OL)
• Wavefront-aberration sorting and correction for a dual-deformable-mirror adaptive-optics system (OL)
• High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics (OE)
• Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm (BOE)
• Improving wavefront boundary condition for in vivo high resolution adaptive optics ophthalmic imaging (BOE)

Related Conference Papers

• Progress in Developing the 2nd Generation Adaptive Optics Scanning Laser Ophthalmoscope (AOSLO)
• Hartmann Fourier Analysis for Sensing and Correction
• MEMS-Based Adaptive-Optics Scanning Laser Ophthalmoscope
• Dual-Wavelength Focusing and Simultaneous Image Registration for <i>In Vivo</i> High-Resolution Retinal Imaging
• Pushing the limits of high-resolution retinal imaging