Accommodation and the third spatial harmonic.

Abstract

Mathews and Kruger recently reported that accommodative tracking of sine wave grating targets is best between 1 and 7 cpd. Their study suggests that the spatial third harmonic might not enhance the accommodative response if the fundamental is higher than roughly 2 cpd. This study tested the effect of adding the third harmonic with targets that included 1, 3, and 5 cpd fundamental sine wave gratings, compound gratings with the third harmonic of each of these fundamentals added in either peaks-add or peaks-subtract phase, as well as each third harmonic presented alone at one-third of the contrast of the fundamental gratings. Accommodation was monitored continuously with a dynamic infrared optometer while the subject viewed the gratings in a Badal stimulus system. Dioptric vergence changed sinusoidally over a 2.00 or 0.50 D range at 0.2 Hz. A Fast Fourier Transform extracted the amplitude and phase of each response at the temporal frequency of the stimulus. The third harmonic enhanced the accommodative response only when the fundamental was 1 cpd. This was true at both amplitudes of target motion. This contradicts models that suggest that high spatial frequencies are used to refine the accommodative response. Second, the responses to the peaks-add and peaks-subtract phase conditions were essentially the same for each fundamental. This suggests that the effect of harmonics cannot be described by any simple linear relationship between the increased luminance gradient of the grating target and the accommodative response. Third, the accommodative response to gratings with a 5 cpd fundamental were smaller than the responses to gratings with the 3 cpd fundamental. This contradicts the gradient hypothesis of accommodative control inasmuch as the luminance gradient is steeper in the gratings with the 5 cpd fundamental. Alternatively, it seems that harmonics will enhance an accommodative response regardless of phase if they are effective accommodative stimuli on their own.