Calculation of the probability of detecting deviations when measuring in the nanometer range
Keywords:
nano measurement, scanning probe microscope, Poisson distribution, destabilizing factors, probability of deviations, random processAbstract
The article proves that when measuring in the nanometer range, there is always the possibility of certain deviations in the images obtained with a probe scanning microscope from the actual shape and flatness of the nano-object, as well as the appearance of artifacts. Methods for calculating the probability of deviations and artifacts in images have been studied and it has been proved that the flow of introduced deviations is due to the random nature of external destabilizing factors. It is proved that the greater the influence of external destabilizing factors on the measuring nano-object, the greater the probability of these deviations and artifacts. It is proposed to mathematically describe the probability of deviations from the actual shape and flatness of the nano-object by the Poisson distribution. A mathematical model for estimating the number of deviations in the image from the actual parameters of the measuring nano-object is presented, which allows the use of computer programming to predict the possible manifestation of distortions and artifacts.
References
Measuring system automatically recognizes geometric features // Mod. Mashing Shop.-1996.-Vol. 69‚ №3.-Р. 484.
Muller Ernst. 3D - Koordinen - Messtechnik der Zukunst / Muller Ernst // masehinenbau.- 1994.-23, №12.-р 21.
Tukey, J.W. The future of data analysis / J.W. Tukey. – Annals of mathematical statistics, 1962. – 167 p.
Bliss, C.J. Biometrika / C.J. Bliss, W.G. Cochen, J.W. Tukey. - Boston, 1956. – 340 p.
Thompson, W.R. The problem of negative estimates of variance components / W.R. Thompson. – Annals of mathematical statistics, 1962. – 214- 265.p.
Agterberg F. P. Trend surface analysis. / F. P. Agterberg, G. L. Gaile, C. J Willmott, D. Reidel, A Cliff. // Spatial Statistics and Models. – Spatial Autocorrelation. London: Pion. – 1984. – P 147-171.
National Instruments, SCXI Universal Strain Grade Input: SCXI-1540. – Available at: http://www.ni.com/pdf/products/us/4scxisc293_ETC_196.pdf
Voltage Output Programmable Sensor Conditioner – Available at: http://elcodis.com/parts/5884374/PGA309.html#datasheet
