Abstract
A correlation coefficient is often used as a measure of the strength of a linear relationship (i.e., the degree of similarity) between two sets of data in a variety of fields. However, in the field of scanning electron microscopy (SEM), it is frequently difficult to properly use the correlation coefficient because SEM images generally include severe noise, which affects the measurement of this coefficient. The current study describes a method of obtaining a correlation coefficient that is unaffected by SEM noise in principle. This correlation coefficient is obtained from a total of four SEM images, comprising two sets of two images with identical views, by calculating several covariance values. Numerical experiments confirm that the measured correlation coefficients obtained using the proposed method for noisy images are equal to those for noise-free images. Furthermore, the present method can be combined with a highly accurate and noise-robust position alignment as needed. As one application, we show that it is possible to immediately examine the degree of specimen damage due to electron beam irradiation during a certain SEM observation, which has been difficult until now.
Highlights
The general-purpose scanning electron microscope is used to observe a variety of surface structures in individual specimens under various operating conditions
We propose a correlation coefficient that is unaffected by the scanning electron microscopy (SEM) noise component (CCunaffected N ) to address the above problem in a fundamental manner
A method of calculating a correlation coefficient that is unaffected by SEM noise in principle, which is understandable and easy to use, was proposed
Summary
The general-purpose scanning electron microscope is used to observe a variety of surface structures in individual specimens under various operating conditions (i.e., operational parameters, such as the accelerating voltage, incident current, pressure, scanning mode, working distance, magnification, and detector). Compared with the true value of the CC obtained from a noise-free image, the measurement disturbed by noise will be considerably smaller than the amplitude of the noise This problem has to be solved because it adversely affects various studies in the field of microscopy. Severe noise in an SEM image interferes with the measurements of the CC, and it remains difficult to numerically examine the degree of specimen damage due to electron beam irradiation during a certain SEM observation To settle this problem, an intuitive and understandable method of evaluating sample degradation should be as unaffected by SEM noise as possible, even under extremely noisy conditions. We study a useful technique that further improves the robustness of the CC against noise and fully satisfies this requirement
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