BarajasCaldwell

Introduction

Our eyes are constantly moving, even when observing a stationary object. In fact, there are two distinct types of movements: larger, sporadic scanning, called saccades; and much smaller, high frequency movements called ocular drift. Past experiments have suggested that saccades are responsible for preventing image fading on our retina— that these movements "refresh" our visual system so that we have continual neural responses to static scenes. This result has largely satisfied inquiries of the purpose of eye movements for the visual system, and many in the scientific community assume both types of eye movements serve the single purpose of preventing fading. However, Michele Rucci and Jonothan D. Victor argue that this is an oversimplification and that in particular, ocular drift serves the more profound role of amplifying higher spatial frequencies on the retina to improve visual resolution. Our work throughout this project centers on assessing this hypothesis.

Background

Literature focuses on ocular drift, which generally occurs in the period between the larger saccade movements, and is thus also referred to as "fixational" eye movement. Rucci and Victor estimate ocular drift has a mean speed of 50 minutes of arc per second, with a distribution of gaze position that disperses as time passes. An important idea of theirs is that these small motions cause fluctuations in luminance on the retina that would not be possible with a motionless eye. Since temporal fluctuations result in higher spectral power at the frequencies of the fluctuations, and since higher spectral power is associated with amplification of an image by the visual system, it follows that fixational eye movements can lead to visual amplification.

The above figure show Rucci and Victor's qualitative argument. The left plot shows higher modulations in luminance for faster eye movements, and the right plot shows their conclusion that retinal amplification increases with spatial frequency. In our project we seek to support these plots with a more quantitative foundation. An interesting result of theirs is that amplification stops increasing after about 30 cycles per degree. They note that this is around the spatial frequency that coincides with the maximum resolution of the retina itself. They also note that "natural scenes" generally have lower contrast for higher spatial frequencies and higher contrast for lower spatial frequencies. Accounting for this, they argue that amplification of higher spatial frequencies by ocular drift equalizes the power across all spatial frequencies on the retina.

Results

Photocurrent tests

In this step we examined the spectra of the photocurrent generated by the cone mosaic from the stimulus. With some simple simulations, we already saw some unexpected results. With eye movements restricted to the horizontal axis and varying sinusoidally over time, we modified the sine parameters (amplitude and frequency) so that during the simulation, the eye completed an integer number of cycles over the grating. Interestingly, no matter the parameters, the average magnitude spectrum of the photocurrent over the cone mosaic was peaked at the second fft bin (7.8125 Hz). The below plot shows values of this temporal frequency at ten different spatial frequencies, from 0 to 36 cycles per degree (scaled by the number of time samples). Although there is some attenuation over spatial frequency, this peak value is always very high.