The spectral main sequence of human saccades

Despite the many models of saccadic eye movements, little attention has been paid to the shape of saccade trajectories. Some investigators have argued that saccades are driven by a rectangular "bang-bang" neural control signal, whereas others have emphasized the similarity to fast arm movement trajectories, such as the "minimum jerk" profile. However, models have not been tested rigorously against empirical trajectories. We examined the Fourier transforms of saccades and compared them with theoretical models. Horizontal saccades were recorded from 10 healthy subjects. The Fourier transform of each saccade was accurately computed using a padded fast Fourier transform (FFT), and the frequencies of the first three minima (M1, M2, M3) in each energy spectrum were measured to a precision of 0.12 Hz. Each subject showed near-linear trends in the relationships among M1, M2, and M3 and the reciprocal of duration (1/T), which we call the "spectral main sequence." Extrapolation of plots did not pass through the origin, indicating a subtle departure from self-similarity. Bivariate confidence regions were established to allow for slope-intercept variability. The nonharmonic relationships seen cannot arise from a rectangular saccadic pulse driving a linear ocular plant. The relationships are also incompatible with minimum acceleration, minimum jerk, or higher-order minimum square derivative trajectories. The best fits were made by trajectories that minimize postmovement variance with signal-dependent noise (). It is concluded that the spectral main sequence is exquisitely sensitive to the saccade trajectory and should be used to test objectively all present and future models of saccades.