In a dynamic far-field diffraction experiment, we use the optical fluctuations in the diffraction pattern to calculate the largest Lyapunov exponent to characterize the locomotory predictability of an oversampled microscopic species. We use a live nematode, Caenorhabditis elegans, as a model organism to demonstrate our method. One point in the visible diffraction pattern allows for the monitoring of the relative phase of all points on the nematode in time. This single time-series displays chaotic markers in the locomotion of the Caenorhabditis elegans by reconstructing the multidimensional phase space. The average largest Lyapunov exponent (base e) associated with the dynamic diffraction of ten adult wildtype (N2) Caenorhabditis elegans is 1.443 +- 0.040 1/s.
Traditionally, the locomotion of microscopic species is studied through visual inspection under a microscope which is often combined with video analysis . There are several benefits in diffraction studies that provide information complementary to classical microscopy. Diffraction allows the species to be probed in more natural environments than conventional microscopy because diffraction is tied to an image plane. Another feature of diffraction microscopy is rooted in subtle changes in the plasticity of the object that can be detected to less than a wavelength without a microscope. Diffraction microscopy complements traditional microscopy by using light to process information embedded in the structure of the species hence saving computing power. Fraunhofer diffraction lends itself to optically process data through diffraction as the pattern evolves in time which can produce a single time series by probing a point in the diffraction pattern. Consequently, the time series contains information about the time evolution of every single point outlining the object. In this work, we demonstrate that condensing locomotion optically into a single time-series allows for the use of readily available complex systems tools.