OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 14 — May. 10, 2014
  • pp: 2988–2997

Optimization of fixture layouts of glass laser optics using multiple kernel regression

Jianhua Su, Enhua Cao, and Hong Qiao  »View Author Affiliations

Applied Optics, Vol. 53, Issue 14, pp. 2988-2997 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (724 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We aim to build an integrated fixturing model to describe the structural properties and thermal properties of the support frame of glass laser optics. Therefore, (a) a near global optimal set of clamps can be computed to minimize the surface shape error of the glass laser optic based on the proposed model, and (b) a desired surface shape error can be obtained by adjusting the clamping forces under various environmental temperatures based on the model. To construct the model, we develop a new multiple kernel learning method and call it multiple kernel support vector functional regression. The proposed method uses two layer regressions to group and order the data sources by the weights of the kernels and the factors of the layers. Because of that, the influences of the clamps and the temperature can be evaluated by grouping them into different layers.

© 2014 Optical Society of America

OCIS Codes
(220.4880) Optical design and fabrication : Optomechanics
(220.1080) Optical design and fabrication : Active or adaptive optics

ToC Category:
Optical Design and Fabrication

Original Manuscript: January 28, 2014
Revised Manuscript: March 27, 2014
Manuscript Accepted: March 28, 2014
Published: May 5, 2014

Jianhua Su, Enhua Cao, and Hong Qiao, "Optimization of fixture layouts of glass laser optics using multiple kernel regression," Appl. Opt. 53, 2988-2997 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. P. Zhou and D. W. Tang, “A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method,” Opt. Laser Technol. 39, 980–986 (2007). [CrossRef]
  2. G. L. Herrit and H. E. Reedy, “Advanced figure of merit evaluation for CO2 laser optics using finite element analysis,” Proc. SPIE 1047, 33–42 (1989). [CrossRef]
  3. Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006). [CrossRef]
  4. Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).
  5. K. B. Doyle, V. L. Genberg, and G. J. Michels, “Integrated optomechanical analysis of adaptive optical systems,” Proc. SPIE 5178, 20–28 (2004). [CrossRef]
  6. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11, pp. 38–39.
  7. G. M. Dai, “Modal wave-front reconstruction with Zernike polynomials and Karhunen-Loève functions,” J. Opt. Soc. Am. A 13, 1218–1225 (1996). [CrossRef]
  8. T. Ruppel, O. Sawodny, and W. Osten, “Actuator placement for minimum force modal control of continuous faceplate deformable mirrors,” in IEEE International Conference on Control Applications (2010), pp. 867–872.
  9. V. L. Genberg, G. J. Michels, and K. B. Doyle, “Design optimization of actuator layouts of adaptive optics using a genetic algorithm,” Proc. SPIE 5877, 58770L (2005).
  10. G. J. Michels and V. L. Genberg, “Optomechanical analysis and design tool for adaptive x-ray optics,” Proc. SPIE 7803, 780308 (2010). [CrossRef]
  11. M. K. Cho, “Performance prediction of the TMT tertiary mirror support system,” Proc. SPIE 7018, 70184F (2008). [CrossRef]
  12. H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998). [CrossRef]
  13. J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).
  14. L. Daudeville and H. Carre, “Thermal tempering simulation of glass plates: Inner and edge residual stresses,” J. Therm. Stress. 21, 667–689 (1998). [CrossRef]
  15. H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).
  16. J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).
  17. Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
  18. G. J. Michels and V. L. Genberg, “Advances in the analysis and design of adaptive optics,” in Imaging and Applied Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMC2.
  19. M. K. Cho, R. S. Price, and I. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006). [CrossRef]
  20. A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput 14, 199–222 (2004). [CrossRef]
  21. M. Gönen and E. Alpaydim, “Multiple kernel learning algorithms,” J. Mach. Learn. Res. 12, 2211–2268 (2011).
  22. D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004). [CrossRef]
  23. P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012). [CrossRef]
  24. Y. H. Liu, H. P. Huang, and C. H. Weng, “Recognition of electromyographic signals using cascaded kernel learning machine,” IEEE/ASME Trans. Mechatron. 12, 253–264 (2007). [CrossRef]
  25. G. Wang, Y. Li, and D. Bi, “Support vector machine networks for friction modeling,” IEEE/ASME Trans. Mechatron. 9, 601–606 (2004). [CrossRef]
  26. Y. Li and D. Bi, “A method for dynamics identification for haptic display of the operating feel in virtual environments,” IEEE/ASME Trans. Mechatron. 8, 476–482 (2003). [CrossRef]
  27. R. Pelossof, A. Miller, P. Allen, and T. Jebara, “A SVM learning approach to robotic grasping,” in IEEE International Conference on Robotics and Automation (2004), Vol. 4, pp. 3512–3518.
  28. H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010). [CrossRef]
  29. M. Gönen and E. Alpaydin, “Localized multiple kernel regression,” in Proceedings 20th IAPR International Conference on Pattern Recognition (2010), pp. 1425–1428.
  30. M. Gönen and E. Alpaydin, “Localized multiple kernel learning,” in Proceedings 25th International Conference on Machine Learning (2008), pp. 352–359.
  31. F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012). [CrossRef]
  32. J. M. Moguerza, A. Muñoz, and I. M. de Diego, “Improving support vector classification via the combination of multiple sources of information,” in Proceedings of the Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshops (2004).
  33. O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002). [CrossRef]
  34. G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).
  35. S. B. Qiu and T. Lane, “A framework for multiple kernel support vector regression and its applications to siRNA efficacy prediction,” IEEE/ACM Trans. Comput. Biol. Bioinform. 6, 90–199 (2009).
  36. N. Kingsbury, D. B. H. Tay, and M. Palaniswami, “Multi-scale kernel methods for classification,” in Proceedings of the IEEE Workshop on Machine Learning for Signal Processing (2005), pp. 43–48.
  37. J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.
  38. H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010). [CrossRef]
  39. R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005). [CrossRef]
  40. J. Clausen, “Branch and bound algorithms-principles and examples,” in Parallel Computing in Optimization (Applied Optimization) (Springer, 1997), pp. 239–267.

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