The power of a cylinder in an oblique meridian: revisiting an old controversy.
The sine-squared correlation states that the cylinder power in an oblique meridian forming an angle beta with the axis of the cylinder is reduced to sin(2)beta of the maximal power. The sine-squared relationship is fundamental in paraxial optics, but its validity has repeatedly been questioned during the last century. It appears that two powers are operative in an oblique meridian, curvital and torsional. Curvital power is responsible for refraction in the plane of the meridian, while the torsional component twists the light out of that plane. Curvital power is the traditional power concept, while torsional power has only recently been described. The long-standing criticism of the sine-squared correlation is based on the erroneous assumption that only curvital power is operational in paraxial imagery. Curvital and torsional power are both derived from the sine-squared correlation. The concept of these dual powers repudiates the criticism and is in complete accordance with paraxial optics.