the autocorrelation function in three different locations in the upper, in the lower and in the middle part of the sample leading to the same result due the uniform motion of the sample. Difference between theoretical and measured value was 6 % for vtheoretical ¼7 nm/s, 10 % for vtheoretical ¼14 nm/s and 7 % for vtheoretical ¼21 nm/s. 9.5 Conclusions In the present paper a set-up and a methodology to measure the velocity of an object moving at few nm per second was shown. The system is based on the evaluation of the phase oscillation of an interference speckle pattern due to the rigid motion of the sample. The methods essentially rely on the measurement of the frequency of the phase oscillation; this is done indirectly by measuring the frequency of the autocorrelation function of the intensity signal for a given pixel. Autocorrelation works like a filter and allows reducing noise disturbance. The system is able to correctly measure velocity with an error of 10 % in a time of 2 min and 16 s. An important aspect that should be highlighted is the rather quick velocity of this set up in giving the results. Improvement of the system could be done in the direction of optimizing the noise filtering process and to reduce the dimension of the system, this point could be afforded by using fiber optics to generate speckle pattern. Fig. 9.5 Plot of the measured velocity in correspondence of three different lines near the upper part, the middle part and the lower part of the sample. The measures reported refers to different pixel along the chosen line. The expected velocity was v ¼7 nm/s. The indicated average value has been calculated over 30 measurements Fig. 9.6 Plot of the measured velocity in correspondence of three different lines near the upper part, the middle part and the lower part of the sample. The measures reported refers to different pixel along the chosen line. The expected velocity was v ¼14 nm/s. The indicated average value has been calculated over 30 measurements 9 Design of a Double‐Illumination ESPI System for the Measurement of Very Slow Motions 101
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