Signs of surface torsion and torsional dioptric power.
Although there is agreement in the literature over the magnitude of torsion and torsional dioptric power, there is ambiguity over the signs of those quantities. The purpose of this paper is to define terms in such a way that the ambiguity is removed. Explicit equations are presented for torsion and torsional power along a meridian of a surface. In keeping with common practice in other disciplines, right-handed torsion is chosen to be positive. The components of the dioptric power matrix of thin systems and of the reduced vergence matrix are reinterpreted in terms of curvital and torsional power. In this reinterpretation the off-diagonal components of the matrices remain the torsional power and the reduced torsion along the meridian orthogonal to the reference meridian. However, they become the negatives of those quantities along the reference meridian. In particular, the top-right component can be interpreted as the reduced torsion or the torsional power along the meridian orthogonal to the reference meridian and the bottom-left as the negative of those quantities along the reference meridian. Torsion and torsional power along a meridian, as well as curvature and curvital power, are invariant under change of reference meridian and under spherocylindrical transposition.
Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa. wfh@na.rau.ac.za
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Harris
D005139:Eyeglasses; D008433:Mathematics; D055095:Optics and Photonics