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To check and measure the converse piezoelectric effect in bone samples, we had to detect displacements in the range of 1–100 pm with three kinds of restrictions: (1) the biological nature of the samples imposes severe limits in selecting a suitable device and method; (2) such a method has to take into account some clinical applications to which the experiment is devoted; (3) the piezoelectric behavior of bone samples is particularly interesting at low frequencies, around 1 Hz. For such reasons we modified an existing dilatometer based on a microwave differential spectrometer. A 14 GHz klystron, linearly modulated in frequency by a triangular 50 Hz voltage applied to the repeller, is connected, via magic T, to two identical cavities tunable around 14 GHz and whose resonance curves are recorded by crystal detectors. When one of the two cavities changes its height according to the length variations of the sample, its resonance frequency varies resulting in a shift of the resonant curve with respect to the resonance curve of the other cavity acting as reference. The comparison between the cavities’ responses is performed by a pulse technique transforming the frequency shifts into time intervals, that are then converted into dc voltages. The differential character of this measurement avoids the need for the microwave source stabilization. The relative shift in frequency is measured with an accuracy better than 500 Hz. This accuracy allows us to measure displacements smaller than 7 nm in the cavity’s height. After 2 h of warmup, thanks to the differential arrangement of the system, thermal or other drifts are not detectable within a lapse of time of 12 h. This feature allows coherent signal averaging over long periods. With a piezoelectric ceramic stack moving 100 pm in square wave fashion at 50 mHz we found that the signal to noise ratio was 20 dB after 1000 cycles of signal averaging, when our bandpass filter was tuned at 1 Hz. In conclusion, this system can detect periodic displacements as small as 1 pm in a short time and reliably. Due to the operational simplicity and stability, at room temperature and humidity, the device is suitable for dilatometric measurements on biological samples.

A HeNe laser driven optical dilatometer with differential properties, which can measure displacements with a resolution of m over the flat frequency range from 0 to 1 kHz, is described. Its principal feature is a parallel arrangement of two, mirror symmetrical, optical paths of which one has an actively operated measurement sample to be studied and the other a similar, passive sample. The arrangement ensures good short- and long-term stability, thus allowing coherent averaging of sample responses over extended periods of time. Resolution thereby increases to m when averaging over 10 000 responses. Since both channels are about equally affected by environmental mechanical disturbances, an algorithm compares the outputs from the parallel channels and rejects correlated vibration and noise components. This increases resolution by an additional factor of five under a reduction in the frequency response. It brings the total obtainable resolution of the dilatometer to m. The instrument is low cost and operates at normal room temperature, pressure and humidity. Since the spring constant of the lever sensing dilatation is , thus exerting negligible force on the sample, the instrument is particularly suitable for the study of small (piezoelectric) strains of soft biological tissues, but is not limited to such applications.