OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 9 — Mar. 20, 2012
  • pp: 1198–1208

Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics

Weiyao Zou and Stephen A. Burns  »View Author Affiliations

Applied Optics, Vol. 51, Issue 9, pp. 1198-1208 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1993 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(170.1790) Medical optics and biotechnology : Confocal microscopy
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(220.1080) Optical design and fabrication : Active or adaptive optics

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: November 8, 2011
Revised Manuscript: December 12, 2011
Manuscript Accepted: December 13, 2011
Published: March 12, 2012

Virtual Issues
Vol. 7, Iss. 5 Virtual Journal for Biomedical Optics

Weiyao Zou and Stephen A. Burns, "Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics," Appl. Opt. 51, 1198-1208 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited