We used a spherical coordinate system (
Ψ,ϕ,r) to specify a simulated scene (
Figure 3A). This coordinate system (
Figure 3A) has its origin at the center of the test patch and is most easily specified if we first set up a Cartesian coordinate system (
x, y, z) with the same origin. The
z-axis lies along the observer’s line of sight to the center of the test patch. The
y-axis is vertical, in the fronto-parallel plane. The
x-axis is horizontal, also in the fronto-parallel plane. The positive half of the
x-axis,
y-axis, and
z-axis are to the observer’s right, upward, and toward the observer, respectively. If we represent a point as a vector (
x, y, z), the angle
Ψ is the angle between the positive
z-axis and the projection of the point into the
xz-plane, and it ranges from −180 to 180 degrees. The angle
ϕ is the angle between the point and the
xz-plane, and it ranges between −90 and +90 degrees. Any direction away from the origin can be specified by coordinates (
Ψ,ϕ). The positive
x-axis, for example, is (90°,0°), the positive
z-axis is (0°,0°), the direction toward the observer. The third coordinate
r is the radial distance from the origin to a point. We report radial distances and other measurements in centimeters, at the size that the simulated objects were presented to the observer.