Reliability of measuring the roughness exponent in a small-length-scale regime

In this paper, the reliability of measuring the roughness exponent in a sma ll-length-scale regime is discussed. When the length scale is very small, t he measured size of one sampling is much smaller than that of the whole reg ion to be characterized, hence the reliability of the measured result shoul d be seriously considered. In a region with a given scaling property we sim ulate the actual experiment, in which the roughness exponent in a small-len gth-scale regime is measured by using scanning electron microscopy under hi gh resolution. We use the concept of the confidence coefficient to analyze the reliability of the measured result. It is shown that the reliability of the measured result can be influenced by two factors: one is the number of the samplings, the other is the size of the maximum band in the ''variable bandwidth method.'' [S0163-1829(99)13601-4].