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Sensors 2015, 15(3), 5865-5883; doi:10.3390/s150305865

Accurate Calibration and Uncertainty Estimation of the Normal Spring Constant of Various AFM Cantilevers

State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
Author to whom correspondence should be addressed.
Academic Editor: Wilmar Hernandez
Received: 26 November 2014 / Revised: 8 January 2015 / Accepted: 10 February 2015 / Published: 10 March 2015
(This article belongs to the Section Physical Sensors)
View Full-Text   |   Download PDF [1174 KB, uploaded 10 March 2015]   |  


Measurement of force on a micro- or nano-Newton scale is important when exploring the mechanical properties of materials in the biophysics and nanomechanical fields. The atomic force microscope (AFM) is widely used in microforce measurement. The cantilever probe works as an AFM force sensor, and the spring constant of the cantilever is of great significance to the accuracy of the measurement results. This paper presents a normal spring constant calibration method with the combined use of an electromagnetic balance and a homemade AFM head. When the cantilever presses the balance, its deflection is detected through an optical lever integrated in the AFM head. Meanwhile, the corresponding bending force is recorded by the balance. Then the spring constant can be simply calculated using Hooke’s law. During the calibration, a feedback loop is applied to control the deflection of the cantilever. Errors that may affect the stability of the cantilever could be compensated rapidly. Five types of commercial cantilevers with different shapes, stiffness, and operating modes were chosen to evaluate the performance of our system. Based on the uncertainty analysis, the expanded relative standard uncertainties of the normal spring constant of most measured cantilevers are believed to be better than 2%. View Full-Text
Keywords: AFM cantilever; normal spring constant; calibration; balance; uncertainty estimation AFM cantilever; normal spring constant; calibration; balance; uncertainty estimation

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Song, Y.; Wu, S.; Xu, L.; Fu, X. Accurate Calibration and Uncertainty Estimation of the Normal Spring Constant of Various AFM Cantilevers. Sensors 2015, 15, 5865-5883.

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