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In this paper, the ultrasonic frequency coordination relation has been re-designed in the high-dimensional space by the principle of Kernel function nonlinear mapping. The relative deviation of ultrasonic frequency coordination relation from the original formula has been obtained by analyzing I.C.Chang theoretical model and P.A.Gass revised theoretical model concretely, theraby indicating the inadequacy of the two theoretical models; Using the principle of the nonlinear mapping to map the original data samples into a high dimensional kernel space, in other words, translating the nonlinear problem into a linear problem can clarify the relationships not only between ultrasonic frequency and incident angle but also between ultrasonic frequency and optical wavelength, leading to an appropriate kernel function and the improved coordination of the ultrasonic frequency relation.
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Keywords:
- kernel function /
- nonlinear mapping /
- ultrasonic frequency coordination relation /
- acousto-optic tunable filter
[1] Dixon R W 1967 IEEE.J. Quantum Electron. QE-3 85
[2] Huang Y, Zhang W, Wang Y, Huang Y D, Peng J D 2008 Acta Phys. Sin. 57 1737(in Chinese)[黄 俨、张 巍、王 胤、黄翊东、彭江得 2008 57 1737]
[3] Liu H, Yao J Q, Zheng F H, Lu Y, Wang P 2007 Acta Phys. Sin. 56 237(in Chinese)[刘 欢、姚建铨、郑芳华、路 洋、王 鹏 2007 56 237]
[4] Xu J P 1982 The principle of acousto-optic devices, design and application (Beijing:Science Press) p4—12(in Chinese)[徐介平 1982 声光器件的原理、设计和应用(北京:科技出版社)第4—12页]
[5] Yang W, Liu Y, Xiao L F, Gao S L 2009 Acta Phys. Sin. 58 1035(in Chinese)[杨 薇、刘 迎、肖立峰、高树理 2009 58 1035]
[6] Zeng S, Bi K, Xue S, C, Sun J, Lü X H, Li D R, Luo Q M 2006 Rev. Sci。 Instrum。 78 015103(in Chinese)[曾绍群、毕 昆、薛松超、孙 健、吕晓华、李德荣、骆清铭 2006 分析仪器评论 78 015103]
[7] He Z H,Lian W L, Wu M J 2006 Journal of Near Infrared Spectroscopy 14 45
[8] Dixon R W 1967 IEEE Journal of Quantum Electronics 3 85
[9] Takabayashi K,Takada K, Hashimoto N 2004 Electronics Letters 40 1187
[10] Harris S E, Wallace R W 1969 Journal of the Optical Society of America 59 744
[11] Gass P A, Sambler J R 1991 Opt. Lett. 16 429
[12] Hwang W S, Weng J 1999 IEEE Trans. on Pattern Analysis and Machine Intelligence 21 386
[13] Mika S, Ratsch G, Weston J, Schölkopf B, Müller K R 1999 Proc of the 1999 IEEE Signal Processing Society Workshop Madison, 41248
[14] Scholkopf B, Mika S, Burges C J C 1990 IEEE Trans on Neural Networks 10 100021017
[15] Rosipal R, Trejo L J 2001 J. of Machine L earning Research 2 972123
[16] Vapnik V N 1999 The nature of statistical learning theory Second Edition (New York: Springer2 Verlag)
[17] Vapnik V N 1998 Statistical Learning Theory (New York: John Wiley & Sons)
[18] Scholkopf B, Smola A J 2001 Advances in Neural Information Processing Systems (Cambridge MA: M IT Press)
[19] Zein A, Raetsch G, Mika S, Lengauer T, Müller K R 2000 Bioin-formatics 16 7992807
[20] J aakkola T, Diekhaus M, Haussler D 2000 J. of Computational Biology 7 952114
[21] Tsuda K, Akaho S, Kawanabe M, Müller K P 2004 Neural Computation 16 1152137
[22] Tsuda K, Kawanabe M, Ratsch G, Sonnenburg S, Muller K R 2002 Neural Computation 14 239722414
-
[1] Dixon R W 1967 IEEE.J. Quantum Electron. QE-3 85
[2] Huang Y, Zhang W, Wang Y, Huang Y D, Peng J D 2008 Acta Phys. Sin. 57 1737(in Chinese)[黄 俨、张 巍、王 胤、黄翊东、彭江得 2008 57 1737]
[3] Liu H, Yao J Q, Zheng F H, Lu Y, Wang P 2007 Acta Phys. Sin. 56 237(in Chinese)[刘 欢、姚建铨、郑芳华、路 洋、王 鹏 2007 56 237]
[4] Xu J P 1982 The principle of acousto-optic devices, design and application (Beijing:Science Press) p4—12(in Chinese)[徐介平 1982 声光器件的原理、设计和应用(北京:科技出版社)第4—12页]
[5] Yang W, Liu Y, Xiao L F, Gao S L 2009 Acta Phys. Sin. 58 1035(in Chinese)[杨 薇、刘 迎、肖立峰、高树理 2009 58 1035]
[6] Zeng S, Bi K, Xue S, C, Sun J, Lü X H, Li D R, Luo Q M 2006 Rev. Sci。 Instrum。 78 015103(in Chinese)[曾绍群、毕 昆、薛松超、孙 健、吕晓华、李德荣、骆清铭 2006 分析仪器评论 78 015103]
[7] He Z H,Lian W L, Wu M J 2006 Journal of Near Infrared Spectroscopy 14 45
[8] Dixon R W 1967 IEEE Journal of Quantum Electronics 3 85
[9] Takabayashi K,Takada K, Hashimoto N 2004 Electronics Letters 40 1187
[10] Harris S E, Wallace R W 1969 Journal of the Optical Society of America 59 744
[11] Gass P A, Sambler J R 1991 Opt. Lett. 16 429
[12] Hwang W S, Weng J 1999 IEEE Trans. on Pattern Analysis and Machine Intelligence 21 386
[13] Mika S, Ratsch G, Weston J, Schölkopf B, Müller K R 1999 Proc of the 1999 IEEE Signal Processing Society Workshop Madison, 41248
[14] Scholkopf B, Mika S, Burges C J C 1990 IEEE Trans on Neural Networks 10 100021017
[15] Rosipal R, Trejo L J 2001 J. of Machine L earning Research 2 972123
[16] Vapnik V N 1999 The nature of statistical learning theory Second Edition (New York: Springer2 Verlag)
[17] Vapnik V N 1998 Statistical Learning Theory (New York: John Wiley & Sons)
[18] Scholkopf B, Smola A J 2001 Advances in Neural Information Processing Systems (Cambridge MA: M IT Press)
[19] Zein A, Raetsch G, Mika S, Lengauer T, Müller K R 2000 Bioin-formatics 16 7992807
[20] J aakkola T, Diekhaus M, Haussler D 2000 J. of Computational Biology 7 952114
[21] Tsuda K, Akaho S, Kawanabe M, Müller K P 2004 Neural Computation 16 1152137
[22] Tsuda K, Kawanabe M, Ratsch G, Sonnenburg S, Muller K R 2002 Neural Computation 14 239722414
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