The two-frame movies were visual stimuli presented to the subjects. Each frame contained a bandpass filtered vertical one-dimensional pink noise pattern (512 × 512 pixels). Creating a sample of such pattern involved a series of stimulus transformations, starting with a one-dimensional vertical binary white noise sample—Random Line Stimulus (RLS;
Figure 1A)—constructed by randomly assigning a “black” or “white” value to each successive column of pixels. The actual luminance of black and white pixels was set to 0.25 and 0.75 of maximal luminance, respectively, resulting in 50% root mean square (RMS) contrast. RMS contrast was calculated using the following formula:
\begin{eqnarray*}
RMS = \frac{{\sqrt {\frac{{\sum\nolimits_{i = 1}^N {{{\left( {Lu{m_i} - Lu{m_{mean}}} \right)}^2}} }}{N}} }}{{Lu{m_{mean}}}},
\end{eqnarray*}
using actual pixel luminance values (
Lum). One-dimensional Fast Fourier Transformation (FFT) of such a sample along the horizontal axis—axis of motion—is shown in
Figure 1B in black color. If one averages many random samples (shown in black in
Figure 1D), the mean amplitudes of different Fourier components will be quite similar (shown in red in
Figure 1D), hence a
white noise stimulus. For a single sample, however, there is quite a lot of variability in the amplitudes of different Fourier components (black color, see
Figure 1B), and those might be very different for another same-contrast random one-dimensional vertical RLS sample (
Figure 1C). Such “undesirable” trial-to-trial variability in the amplitudes of Fourier components would necessarily result in the trial-to-trial variability in the magnitude of ocular responses to horizontal motion of these stimuli. We, therefore, calculated the mean of the amplitudes of all Fourier components (in a sample) and set this mean value as the amplitude of each Fourier component of this and all other randomly generated one-dimensional vertical RLS samples (shown in red in
Figures 1B,
1C)
2. Fourier components’ phases, on the other hand, were never altered and remained random. A white noise sample was then transformed into a pink noise one, by dividing the amplitude of each Fourier component by the square root of its SF. Consequently, as illustrated in
Figure 1E, in pink noise samples (dashed blue line) Fourier components with SF <1 cpd had greater amplitudes, whereas those with SF >1 cpd had smaller amplitudes than the corresponding Fourier components in white noise samples (red solid line). The last step of stimulus transformation was applying an SF bandpass filter whose attenuation function was Gaussian on a log scale. Such a filter has central SF (cSF) and bandwidth, expressed as full width at half maximum (FWHM). In
Figure 1E, three examples of 1-octave FWHM filters with 0.25, 0.5, and 1 cpd cSFs are shown by orange, black, and green traces, respectively. In different experiments, FWHM was set to either 1 or 2 octaves. Applying the filter of certain FWHM and cSF (cSF
1) to a given pink noise sample would create the first frame of a two-frame movie. To create the second frame of the movie, the phases of
all Fourier components in this same pink noise sample were shifted by 90 degrees in one direction (
Figure 1F): leftward (−90 degrees; backward) or rightward (+90 degrees; forward). The filter was then applied, whose cSF (cSF
2) was either lower or the same, or higher than cSF
1, whereas the FWHM was the same. We used bandpass filtered vertical one-dimensional
pink noise patterns, because, for a given FWHM of the filter, such patterns had very similar RMS contrast, regardless of the filter cSF: approximately 9.3% for 1-octave FWHM and approximately 13.3% for two-octave FWHM.