How do ants use menotaxis to return to a nest?

In the context of stereotyped response, menotaxis is a form of transverse orientation where an organism maintains a constant angle relative to a directional stimulus, such as the Sun.1

For foraging insects like ants, menotaxis serves as a light-compass reaction that allows them to navigate back to a fixed nest. By maintaining a specific angle to the Sun, an ant can plot a consistent course. This behavior is highly reliable; for instance, if an ant is temporarily hidden from the light while returning to its nest, it will resume its journey at the exact same angle to the Sun that it held before being covered, rather than immediately heading toward the nest.1

While menotaxis provides the directional compass, ants often augment this with other mechanisms. For example, Sahara desert ants use polarized light as a compass and employ proprioception to count their steps, allowing them to measure the distance traveled. Upon nearing the nest, they further refine their search using visual and olfactory cues.2