TY - JOUR

T1 - An accurate and precise polynomial model of angular interrogation surface plasmon resonance data

AU - Wang, Zhiyou

AU - Diamond, J. J.

AU - Hou, Rui

AU - Wang, Kun

AU - Song, Lusheng

AU - Su, Yalin

AU - Zheng, Zheng

AU - Zhu, Jinsong

N1 - Funding Information:
This research was supported under 973 Program (2009CB930702). One of us (JJD) would like to thank the Chinese Academy of Sciences and the National Center for Nanoscience and Technology for their hospitality and support, Professors Zheng Zheng and Zhu Jingsong for their support and friendship, and Linfield College for its sabbatical support as well.

PY - 2011/1/28

Y1 - 2011/1/28

N2 - We present a simple, statistically based method of fitting waveguide-coupled surface plasmon resonance (WCSPR) angular interrogation experiment data in the vicinity of the resonance angle using an appropriate polynomial model. This method allows one to determine the resonance angle to within precision of as little as 2% of the sampling step size, with mean results averaging about 8% of the step size, better than an order of magnitude improvement over no regression, achieved with little effort. In testing this method, we use theoretical and experimental WCSPR data. We have compared the statistical significance of using additional terms in a given polynomial representation. F-Ratio tests based on the "extra sum of squares" principle indicate that, in the vicinity of the resonance, approximately 20 millidegrees about the minimum, the addition of quintic or higher order terms to the quartic polynomial representation is not statistically significant. We have found that both cubic and quartic models produce estimates of the position of the minimum in which the confidence interval is both accurate and precise with an error of less than one tenth of a millidegree. In addition, a similar analysis of theoretical calculations suggests that this polynomial method, which is generally applicable to the determination of extrema in any spectrum, is capable of very high accuracy and precision.

AB - We present a simple, statistically based method of fitting waveguide-coupled surface plasmon resonance (WCSPR) angular interrogation experiment data in the vicinity of the resonance angle using an appropriate polynomial model. This method allows one to determine the resonance angle to within precision of as little as 2% of the sampling step size, with mean results averaging about 8% of the step size, better than an order of magnitude improvement over no regression, achieved with little effort. In testing this method, we use theoretical and experimental WCSPR data. We have compared the statistical significance of using additional terms in a given polynomial representation. F-Ratio tests based on the "extra sum of squares" principle indicate that, in the vicinity of the resonance, approximately 20 millidegrees about the minimum, the addition of quintic or higher order terms to the quartic polynomial representation is not statistically significant. We have found that both cubic and quartic models produce estimates of the position of the minimum in which the confidence interval is both accurate and precise with an error of less than one tenth of a millidegree. In addition, a similar analysis of theoretical calculations suggests that this polynomial method, which is generally applicable to the determination of extrema in any spectrum, is capable of very high accuracy and precision.

KW - Angular interrogation

KW - Confidence interval

KW - Polynomial fitting

KW - Regression model

KW - SPR

KW - Spectroscopy

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UR - http://www.scopus.com/inward/citedby.url?scp=78751570935&partnerID=8YFLogxK

U2 - 10.1016/j.snb.2010.02.055

DO - 10.1016/j.snb.2010.02.055

M3 - Article

AN - SCOPUS:78751570935

SN - 0925-4005

VL - 151

SP - 309

EP - 319

JO - Sensors and Actuators, B: Chemical

JF - Sensors and Actuators, B: Chemical

IS - 2

ER -