Can we measure the three-dimensional orientation of \textit{Vorticella} from two-dimensional videos?

\textit{Vorticella} are aquatic suspension feeding microorganisms that live attached to surfaces and generate a feeding flow to draw in their food. They are crucial players in aquatic ecosystems, eating bacteria and debris as well as supporting larger aquatic organisms. To evaluate the impact of \textit{Vorticella} in their environments, as well as in practical applications like waste water treatment, it is important to understand \textit{Vorticella} feeding rates. Previous work has shown that the orientation of \textit{Vorticella} relative to the surface of attachment affects feeding flow and feeding rates. \textit{Vorticella} cell body orientation is defined by the polar angle, which is measured from the vertical axis, and the azimuthal angle. Previous experiments have observed \textit{Vorticella} using a horizontal microscope from which the polar angle was directly measured. The azimuthal angle was inferred as a function of the projected cell body length compared to a maximum measured cell body length. However, it is unknown how accurately this technique determines the azimuthal angle. We recorded time-lapse videos of \textit{Vorticella} simultaneously from the side and the top. We then compared the calculated azimuthal angle from the side view to a direct measurement from the top view. We report the error in the calculated azimuthal angle as a function of the organism orientation.