Fig 1.
Single zebra data set example.
The centre shows a typical zebra image, with eight regions of interest (ROI) denoted by the rectangles outlined in green. These areas were used consistently across individual subjects. For each ROI, the corresponding polarization data are indicated by the surrounding plots. In each, the luminance of the black and white stripes are shown by the closed and open circles, respectively; each is a single measurement from the ROI at that polarization angle. In each series, the -90° and +90° points are replicate, independent observations; they provide an estimate of the repeat reliability of the data. As expected, reliability is greater for the larger ROIs. Superimposed on each data set is the best-fit sinusoidal function (also see Fig 2). The zebra image in the centre corresponds to the individual data points at +30°. The colour scale in the zebra image has been adjusted here for illustration purposes only, because the 14-bit data appear very dark in standard rendering. Note the considerable change in luminance through filter angles in white stripes in most ROIs.
Fig 2.
Derivation of extracted quantities from fitted sinusoids.
This shows a single fit to the white stripes from a single ROI (foreleg in Fig 1). The phase angle corresponds to the offset of the fit from odd symmetry around the midpoint filter setting, which in this case was approximately 30 degrees. The d value is calculated from the contrast between the maximum and minimum values of the fit curve. It is important to note that the phase angle parameter is not the same as the angle in which more polarized light is present, but is linearly related to this physical parameter. See methods for details.
Fig 3.
Degree of polarization signals in black and white stripes.
The filled circles represent the subset of ROIs used in Fig 5, where there was a significant correlation between fit and data; these are the same cases illustrated in Fig 5.
Fig 4.
Box/whisker plot showing the distributions of d values in different ROIs for black and white stripes under different illumination conditions.
In each column, the dot surrounded by a circle depicts the mean, the box shows the quartiles, the whiskers the 95% confidence intervals, and the “o” symbols show outliers.
Fig 5.
Correlation between fit phases in black and white stripes.
Each data point represents a single ROI in a single zebra, and the phases of each were fit independently. Note the high degree of correlation evident in the data; outliers were present but rare. Because phase could only be accurately estimated in data where the d value was high, this analysis is restricted to the cases where there was a significant correlation between data and fit.
Fig 6.
Visibility of polarization and stripe contrast with respect to distance from the zebra, plotting each ROI separately, averaged across individuals.
The Y axis represents contrast units, which are d values for the polarization data (blue denotes black stripes, red denotes white stripes), and Michelson contrasts (black lines) for the luminance data. Both are equivalent, unitless measures of the corresponding optical quantity. Error bars depict S.E.M., and where they are not visible, they are smaller than the plotting symbol.