In this study, a novel optical interferometric technique called 'statistical interferometry'1-3 has been developed. In contrast to the conventional interferometry where the phase is determined in a completely deterministic way, we consider the interference of completely random wave fronts, i.e., speckle fields, and it has been proved that the complete randomness of the speckle field can play the role of a standard phase in a statistical sense. The advantage of the method is that since the phase of the object under testing can be derived in a statistical way, the accuracy of the measurement depends only on the number of data taken to calculate a probability density distribution of speckle phase. This feature permits a simple optical system to achieve measurements with an extremely high accuracy. According to a computer simulation, the accuracy of λ/1000 can be achieved using 40,000 data of the speckle intensity.
Statistical interferometry was applied to monitor biological activity or growth rate of plant, aiming to investigate the influence of the environmental pollutions. In the experiments, the plants were exposed to Ozone that is the main substance of photochemical smog, and the growth rates were measured before and after the exposure. It was clearly observed that the fluctuation of growth rate as well as its mean rate was dramatically affected by the exposure of ozone. By the observation of growth rate of plant with the accuracy of sub-nanometer scale and a time scale of second, it was newly revealed that the fluctuation of the growth rate reflects the biological activity of the plant.