There is much confusion about whether or not dioptric power exists in an off-axis meridian of a spherocylindrical lens. One source of this confusion is an overly simplified definition of dioptric power. This paper proposes the conditions that a good definition of dioptric power should meet. Under these conditions, dioptric power does exist in an off-axis meridian. However, that dioptric power has two components--a curvature component and a torsional component. A second source of confusion has been the neglect of the torsional component.
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Michael P. Keating (1986) studied this question.