INVARIANCE OF OPHTHALMIC PROPERTIES UNDER SPHEROCYLINDRICAL TRANSPOSITION

Ophthalmic properties expressed as functions of dioptric power cannot depend on the particular spherocylindrical form (positive or negative cylinder) chosen to represent the power: they are necessarily invarian t under spherocylindrical transposition. This condition of invariance places restrictions on the mathematical form that valid ophthalmic fun ctions can assume. Tests are presented for checking the validity of pr oposed ophthalmic functions and properties. Examples from the literatu re are examined, including Keating's concept of torsional power and Pe ters' graphs of expected unaided visual acuity vs. ametropia. The form er satisfies the condition of invariance but the latter are shown to v iolate the condition for ametropias which are close to spherical. The analysis shows partly how the graphs need to be refined. Invariance un der spherocylindrical transposition can assist the researcher in devel oping new concepts and relationships that depend on power expressed in terms of sphere, cylinder, and axis.