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Table I: Results of the ranking algorithm showing the top three frequencies ranked by mean error and standard deviation. Error
values are normalized.
in which T is the thickness of the coating, Cf1
is the capacitance measured at frequency f1, and K1, K2, and K3, respectively, are the quadratic, linear, and offset coefficients.
To determine these coefficients and the frequency to be used, a simple algorithm is performed. First, the measured capacitances
are averaged over the four samples for each of the coating levels. For each frequency, the minimum capacitance is subtracted
to remove offset errors. Then the values are divided by the maximum capacitance at each frequency to remove the linear errors.
The resulting capacitance ratios at each frequency are individually fitted to the quadratic equation above, and the resulting
error in estimation is computed. The mean of the estimation errors and the standard deviation is tabulated for each frequency.
The frequencies are ranked on the basis of least mean error and the least standard deviation. The product of these rankings
is used as a figure of merit for selection of the frequency f1. Table I shows the results obtained from the algorithm detailed above. It shows that the measurements at 100 kHz are the
most suitable for the estimation process. The coefficients K1, K2, and K3 were determined by least square methods. The resulting equation for estimation of coating thickness is
Figure 6 (ALL FIGURES ARE COURTESY OF THE AUTHORS.)
in which C100k is the mean compensated and normalized capacitance at 100 kHz. Figure 6 shows the comparison between the actual coating thickness
and estimated coating thickness. This process of estimation must be further validated by conducting experiments with many
more coating levels and samples. Therefore, for inline process measurements, a selected frequency of excitation can be ascertained
with some postprocessing of off-line data.
A. Mathur is a graduate student at the Sensors, Energy, and Automation Laboratory, Department of Electrical Engineering, University of Washington, Seattle.
Articles by A. Mathur
K. Sundara-Rajan is a PhD candidate at the Sensors, Energy, and Automation Laboratory, Department of Electrical Engineering, University of Washington, Seattle, tel. 206.351.8101.
Articles by K. Sundara-Rajan
G. Rowe
G. Rowe is a PhD candidate at the Sensors, Energy, and Automation Laboratory, Department of Electrical Engineering, University of Washington, Seattle
Articles by G. Rowe
A. V. Mamishev
A. V. Mamishev is an associate professor at the Sensors, Energy, and Automation Laboratory, Department of Electrical Engineering, University of Washington, Seattle.
Articles by A. V. Mamishev
Survey
How does your company apply quality-by-design (QbD) principles to manufacturing processes?
To all processes for both new and legacy products
20%
To all process for new products only
13%
To select process for new products only
24%
To select processes for both new and legacy products
