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Chin. Phys. B, 2016, Vol. 25(1): 014211    DOI: 10.1088/1674-1056/25/1/014211

Data point selection for weighted least square fitting of cavity decay time constant

Xing He(何星)1,2,3, Hu Yan(晏虎)1,2,3, Li-Zhi Dong(董理治)1,2, Ping Yang(杨平)1,2, Bing Xu(许冰)1,2
1. Laboratory on Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China;
2. Key Laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu 610209, China;
3. University of the Chinese Academy of Sciences, Beijing 100039, China
Abstract  For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting (NLSF) method and the linear regression of the sum (LRS) method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.
Keywords:  cavity ring-down      decay time extraction      weighted least square method      data point selection  
Received:  05 May 2015      Revised:  17 August 2015      Published:  05 January 2016
PACS:  42.87.-d (Optical testing techniques)  
  07.05.Kf (Data analysis: algorithms and implementation; data management)  
  06.20.Dk (Measurement and error theory)  
Fund: Project supported by the Preeminent Youth Fund of Sichuan Province, China (Grant No. 2012JQ0012), the National Natural Science Foundation of China (Grant Nos. 11173008, 10974202, and 60978049), and the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2).
Corresponding Authors:  Bing Xu     E-mail:

Cite this article: 

Xing He(何星), Hu Yan(晏虎), Li-Zhi Dong(董理治), Ping Yang(杨平), Bing Xu(许冰) Data point selection for weighted least square fitting of cavity decay time constant 2016 Chin. Phys. B 25 014211

[1] O'Keefe A and Deacon D A G 1988 Rev. Sci. Instrum. 59 2544
[2] Anderson D Z, Frisch J C and Masser C S 1984 Appl. Opt. 23 1238
[3] Spence T G, Harb C C, Paldus B A, Zare R N, Willke B and Byer R L 2000 Rev. Sci. Instrum. 71 347
[4] Naus H, van Stokkum I H M, Hogervorst W and Ubachs W 2001 Appl. Opt. 40 4416
[5] von Lerber T and Sigrist M W 2002 Chem. Phys. Lett. 353 131
[6] Kallapur A G, Boyson T K, Petersen I R and Harb C C 2011 Opt. Exp. 19 6377
[7] Huang H F and Lehmann K K 2011 J. Phys. Chem. A 115 9411
[8] Romanini D and Lehmann K K 1993 J. Chem. Phys. 99 6287
[9] Boyson T K, Spence T G, Calzada M F and Harb C C 2011 Opt. Exp. 19 8092
[10] Mazurenka M, Wada R, Shillings A J L, Butler T J A, Beames J M and Orr-Ewing A J 2005 Appl. Phys. B 81 135
[11] Everest M A and Atkinson D B 2008 Rev. Sci. Instrum. 79 023108
[12] Processing_in_Cavity_Ring-Down_Spectroscopy
[13] Istratov A A and Vyvenko O F 1999 Rev. Sci. Instrum. 70 1233
[14] Fuhrmann N, Brühach J and Dreizler A 2014 Appl. Phys. B 116 359
[15] Wang D, Hu R Z, Xie P H, Qin M, Ling L Y and Duan J 2014 Spectroscopy and Spectral Analysis 34 2845 (in Chinese)
[16] Morville J and Romanini D 2002 Appl. Phys. B 74 495
[17] Gong Y, Li B C and Han Y L 2008 Appl. Phys. B 93 355
[18] Gong Y and Li B C 2007 Proc. SPIE 6720 67201E-1
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