In a dynamic far-field diffraction experiment, we calculate the largest Lyapunov exponent of a time series obtained from the optical fluctuations in a dynamic diffraction pattern. The time series is used 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. The time series is derived from the intensity at one point in the diffraction pattern. 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 10 adult wildtype (N2) Caenorhabditis elegans is 1.27 ± 0.03 s − 1 .
Using coherent light, we analyze the temporal diffraction at a single point from real-time living C. elegans locomotion in three-dimensional space. We describe the frequency spectrum of single swimming nematodes in an optical cuvette at a single sampling point in the far-field diffraction pattern. An analytical expression of the double slit is used to model the frequency spectra of nematodes as oscillating segments. The frequency spectrum in the diffraction pattern expands discretely and linearly as a multiple of the fundamental frequency with increasing distance from the central maximum. The frequency spectrum of a worm at a single point in the frequency spectrum contains all the frequencies involved in the locomotion and is used to characterize and compare nematodes. The occurrence of resonant frequencies in the dynamic diffraction pattern increases with the distance from the central maximum. The regular spacing of the resonant frequencies is used to identify characteristic swimming frequencies.
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