Radial frequency (RF) patterns, circles which have had their radius modulated as a function of their polar angle, have been used in the examination of the integration of contour information around closed contour patterns. Typically, these patterns have been presented in a random orientation from trial-to-trial in order to maintain spatial uncertainty as to the location of the deformation on the pattern, as it may affect observer strategy and performance. However, the effect of fixed and random orientation (phase) on observer gaze strategies used to discriminate RF patterns has not been directly tested. This study compared fixation patterns across four conditions: fixed phase single cycle; random phase single cycle; fixed phase three cycle; and random phase three cycle RF3 patterns. The results showed that observers fixated on the known location of deformation for the fixed phase single cycle condition but used a more central fixation for the other three conditions. This strategy had a significant effect on observer thresholds for the fixed phase single cycle condition, with greater adherence to the strategy resulting in lower thresholds. It was also found that for the single cycle patterns observers tended to fixate on different locations on the pattern: on the maximum orientation difference from circular for the fixed phase pattern; and on the point of maximum curvature for the random phase pattern. These differences in gaze patterns are likely driven by the underlying local or global processing of the fixed or random phase single cycle patterns, respectively.

*R*) defined as a function of polar angle (θ):

*R*

_{0}is the radius of the unmodulated circle (2 degrees of visual angle),

*A*is the amplitude of the sine wave (as a proportion of

*R*

_{0}), ω is the RF number (3), which defines the radial frequency by setting the number of complete sine waves that can fit within 2π radians, and ϕ is the phase (orientation) of the pattern. Two patterns were used: an RF3 with all three cycles of modulation present (RF3); and an RF3 with one cycle of modulation present (RF3(1)). As established by Loffler et al. (2003), for patterns with one cycle of modulation (i.e. RF3(1)), the modulated portion of the contour conforms solely to a first derivative of a Gaussian (D1) with a slope and amplitude identical to that of the sine waves used for completely modulated patterns (i.e. RF3). Using a sine wave may result in unintended local cues which the observer may use to differentiate the RF pattern and circle. In other words, at one cycle of modulation a D1, not a sine wave, is used to modulate the pattern's radius, which provides a smooth transition the modulated and unmodulated portions of the pattern. The cross-sectional luminance profile of the contour was defined by the fourth derivative of a Gaussian (D4) with a peak spatial frequency of 8 c/deg. The center of the pattern was jittered randomly within a 20′ box in the center of the screen.

*A*= 0 in Equation 1) and the other an RF pattern, with the order of presentation randomized between trials. Each trial consisted sequentially of a 500 ms fixation cross, 500 ms blank screen, 1000 ms presentation of interval one, 500 ms blank screen, 1000 ms presentation of interval two, and ending with response collection (see Figure 1). The observer indicated which interval contained the pattern most deformed from circular by clicking either the left (first interval) or right (second interval) mouse button. At the beginning of each testing block observers were instructed to “always look at the fixation cross when it is on-screen; when it is gone you may look anywhere you like.”

*n*) from 1 to 20 was used in the equation \(\varphi = \frac{{2\pi n}}{{20}}\) for RF3(1) and \(\varphi = \frac{{2\pi n}}{{60}}\) for RF3 so that observers would not be able to anticipate the location of deformation on the circle. The equations differ because unique orientations of an RF3 are only possible from 0 to \(\frac{{2\pi }}{3}\) radians.

*k*) of each observer's testing block. Higher values of

*k*indicate observers are fixating more in one area than any other.

*F*(2,156) = 1.48,

*p*= 0.23.

*t*(54.81) = 7.42,

*p*< 0.001, BF = 3.34*10

^{4}(see Figure 4). Therefore, we investigated the effect of an observer's peakedness and polar angle of fixation on their threshold for detection. There was a significant negative effect of peakedness

*t*(31.44) = −1.80,

*p*= 0.04, BF = 1.71 (one tailed) and a significant positive effect of polar angle

*t*(30.29) = 2.59,

*p*= 0.01, BF = 3.15 on thresholds for the fixed phase condition. For the random phase condition, there was a significant positive effect of peakedness on thresholds,

*t*(21.19) = 2.98,

*p*< 0.001, BF = 12.68 (one tailed) but no significant effect of polar angle

*t*(26.53) = −0.60,

*p*= 0.55, BF = 0.27 on thresholds.

*t*(52.65) = 7.12,

*p*< 0.001, BF = 1.96*10

^{4}. Figure 5 shows the mean polar angle of all observers’ mean fixation position for both conditions. Note that for the random phase condition (left) observers seem to favor the peak of the lobe (i.e. the point of maximum radius), whereas for the fixed phase condition (right) observers favor the maximum deviation from circular (i.e. the zero crossing of the sine wave).

*t*(70.00) = 1.46,

*p*= 0.15, BF = 0.58. Observer thresholds were not affected by peakedness,

*t*(32.90) = 0.34,

*p*= 0.73, BF = 0.24, or polar angle

*t*(32.22) = 0.33,

*p*= 0.75, BF = 0.24, for the fixed phase condition. Similarly, for the random phase condition, peakedness

*t*(24.73) = 0.71,

*p*= 0.49, BF = 0.29, and polar angle

*t*(20.70) = 0.68,

*p*= 0.51, BF = 0.28, had no effect on thresholds. Following the analysis of the single cycle patterns, the standard deviation of the polar angle of the fixation vectors were calculated for the first 15 trials. There was a significantly higher amount of variation in fixation vectors for the random phase condition than the fixed phase condition

*t*(68.00) = 5.92,

*p*< 0.001, BF = 2.08*10

^{3}.

*t*(297.00) = −1.32,

*p*= 0.19, BF = 0.49, or interval,

*t*(297.00) = 0.39,

*p*= 0.70, BF = 0.24. For peakedness, there was a significant effect of both condition,

*t*(297.00) = −5.40,

*p*< 0.001, BF = 7.54*10

^{2}, and interval,

*t*(297.00) = 5.55,

*p*< 0.001, BF = 1.01*10

^{3}. Bonferroni adjusted pairwise comparisons showed the fixed phase, one cycle of modulation condition had a significantly more peaked distribution of fixational eye-movements than all other three conditions (

*p*< 0.05). There were no other differences in peakedness between conditions (

*p*> 0.05). For fixed phase at one cycle of modulation and random phase at three cycles of modulation, there was no significant difference in peakedness when the reference stimulus appeared in either the first or second interval (

*p*> 0.05). For random phase at one cycle of modulation and fixed phase at three cycles of modulation the reference stimulus appearing in the second interval had a significantly higher peakedness compared to when it was shown in the first interval (

*p*< 0.05).

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