Time-optimality and the spectral overlap of saccadic eye movements.

Saccades exhibit remarkably stereotypical motor behavior, both in their bell-shaped velocity trajectories and in their peak velocity–amplitude and duration–amplitude relationships (the “main sequence”). It is sometimes assumed that this is the result of the system optimizing for movement duration, although no direct empirical evidence as such exists. However, formal time-optimal (“bang-bang”) models based on linear control theory1,2 do not produce realistic velocity profiles, as demonstrated recently in the Fourier domain.3 Here, we investigate high-frequency energy spectra for saccades of different amplitude and show that they overlap, indicating the existence of an absolute spectral limit. This provides the first clear empirical evidence that saccades are indeed optimal. The main sequence and trajectory shape reflect the minimum time with a spectral constraint.