The traditional clinical designation of spherocylindrical power unambi
guously specifies the refractive properties of a thin lens or refracti
ve surface. This representation of dioptric power is not, however, opt
imum in mathematical terms, as is apparent when, for example, two sphe
rocylindrical lens powers are added. Alternative systems have been des
cribed which are not subject to this same type of difficulty, and the
essential feature of these other systems is that spherocylindrical pow
er is defined in terms of a three-dimensional dioptric space in which
the axes are usually orthogonal. The advantages of this orthogonality
can be exploited in the practice of clinical refraction, provided lens
powers in these three dimensions can be physically implemented. Syste
ms using these characteristics have been introduced in the past, but t
he clinical community has not adopted them on a widespread basis. Howe
ver, systems which take advantages of these features do have unique ad
vantages relative to traditional clinical refraction procedures. These
characteristics, and refractive procedures which exploit their advant
ages, are described.