The rotating Pulfrich effect, and a new method of determining visual latency differences

A conic theorem generalised: directed angles and applications

“…This theorem crystallised from some experimental observations [4,5] in the area of vision physiology-a rich source of interesting mathematical problems. Hopefully, this article gives a flavour of the power of directed angles and brings to life a curious theorem, which can be used to establish tangent-focus properties of conics via an unusual perspective.…”

Visual Latency Difference Determined by Two ‘‘Rotating’’ Pulfrich Techniques

“…Nakamizo and Kondo (1985) also used a null method to estimate apparent depth due to the Pulfrich effect, in which the apparent depth was cancelled by adjusting the extent of the physical depth of the target moving in an elliptical path in the horizontal plane. Nickalls (1986) determined visual latency difference using the rotating Pulfrich illusion, by measuring the critical viewing distance at the ''transition'' null-point (when the rotating target appears to move only from side-to-side) for a given target angular velocity and filter density, using Equation ( 1),…”

“…where Ω is angular velocity (rev/min) of the target, a is the half of the interocular distance, and dΤ is the viewing distance (cm) at which the ''transition'' null-point is perceived (for derivation, see Nickalls, 1986Nickalls, , 1996. Equation (1) ought also to be equally valid if the ''transition'' null-point is identified using an alternative method, whereby the angular velocity is varied while keeping the viewing distance constant.…”

“…One manifestation of this stereoeffect is the ‘‘pendulum’’ illusion, in which a pendulum swinging horizontally in a fronto-parallel plane (i.e., at right-angles to the line of sight and at eye-level) and viewed binocularly with a neutral density filter in front of one eye, appears to move in an elliptical path (see Figure 1a). More recent investigations have been directed towards the ‘‘rotating’’ Pulfrich illusion (Nakamizo, Nawae, & Nickalls, 1998; Nickalls, 1986, 1996, 2000; Nickalls, Kazachkov, Vasylevska, & Kalinin, 2002) in which a vertical rod rotating in a horizontal circular path can, under certain circumstances, appear to move back-and-forth from side-to-side (see Figure 1b).…”

“…The method for determining visual latency difference used in the present study, is essentially one of the four ‘‘nulling’’ methods, which have been described (Nakamizo & Kondo, 1985; Nickalls, 1986; Pulfrich, 1922; Rogers & Anstis, 1972). Pulfrich (1922) appears to have been the first to observe that the apparent direction of rotation of a vertical rod mounted eccentrically on a horizontal turntable depends on the angular velocity of the turntable, reversing at some critical combination of angular velocity, filter, viewing distance and so on.…”