Improvement of dynamic range of statistical interferometry and its application to monitor ultra-short term growth behaviour of plant

Abstract

In this study, a highly accurate optical interferometric technique called ‘statistical interferometry’[1–3] has been developed and improved to expand its dynamic range. 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 as a strain sensor to monitor growth behavior of plant in ultra-short term, aiming to investigate the influence of the environmental conditions. In the experiments, the plants were exposed to ozone that is the main substance of photochemical oxidants. It was demonstrated that growth behavior of the plant could be measured with the accuracy of sub-nanometer and a time scale of second achieving a dynamic range of several hundred microns.