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By Yilong Han, A. M. Alsayed, M. Nobili, J. Zhang, Tom C. Lubensky and Arjun G. Yodh, credited as Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky and A. G. Yodh. Science 314(5799), 626–630, published 27 October 2006. The University of Pennsylvania author laboratory hosts the inspected PDF; its upload path does not date publication.

Inspected author copy: bpb-us-w2.wpmucdn.com/web.sas.upenn.edu/dist/b/502/files/2019/11/Science_2006.pdf

DOI: doi.org/10.1126/science.1130146

Inspected locators: pp. 626–628, apparatus and angular readout; Figure 1D–F; Figure 2A–B; p. 628, confinement and height fluctuations.

In 2006, Yilong Han and colleagues dispersed plastic ellipsoids in water inside a thin glass cell, using a very dilute suspension to limit particle interactions. A camera on an optical microscope recorded 30 frames per second. Image analysis extracted centre positions and long-axis angles, with reported angular resolution about $1^{\circ }$. Their shape supplied the observable axis. Reflected interference colours calibrated cell thickness; nearly constant particle interference colour checked vertical wandering. One tracked particle had dimensions $2.4\times 0.3\times 0.3\mu \mathrm{m}$ in an $846\mathrm{nm}$ gap. Angular displacement variance grew linearly with lag; displacement resolved along the particle's axes and in the laboratory showed how turning washes out translational anisotropy. These are observations of confined particles: walls alter drag, and slight out-of-plane tumbling affected positional resolution. They do not establish the bulk sphere formula. The paper's Figure 1A–B shows simulations; Figure 1F shows a measured trajectory.^[ref]

For interpreting such images, the director distinction is essential: identical ends give an angle modulo $\pi$. A continuously unwrapped trace can follow small successive turns, but it does not make the ends physically distinguishable. The invariant planar axis autocorrelation is $⟨\cos (2\Delta \varphi )⟩$, and its decay determines $D_r$ through $e^{-4D_{r}t}$. Separately measuring position and rigid body orientation is what makes the connection between translational anisotropy and loss of angular memory experimentally accessible.