Theoretical Study of Refraction Effects of Plano Ophthalmic Prisms

Abstract

Nominally plano prisms can have appreciable refractive errors that exceed the usual prescribing step of 0.25 D, particularly when an eye rotates to view off-axis objects. The purpose of this study was to determine theoretically the refractive power effects of nominally plano-refracting power prisms. Plano prisms with zero refraction were designed for the as-worn condition. A basic method was developed to determine refractive effects in the presence of pantoscopic tilt. A refined method was developed that considers the eye rotating behind the lens, and this and the basic method were compared with accurate raytracing. Plano prisms of 4 and 8 Δ were designed with astigmatic back surfaces to compensate for oblique incidence, and tangential and sagittal image vergence errors were investigated for base-up (BU) and base-down (BD) directions, 0 and -3.33 D object vergences, and pantoscopic tilts up to 10°. Basic and refined results did not differ from accurate results by more than 0.04 and 0.08 D, respectively. Errors for 8 Δ prisms were approximately twice those for 4 Δ prisms. Errors were approximately proportional to tilt. With 10° tilt, the errors ranged between -0.65 D/-0.23 D (8 Δ BD, -3.33 D object vergence) and +0.36 D/+0.15 D (8 Δ BU, 0 D object vergence). Sagittal errors were generally about one third of corresponding tangential errors. In the presence of tilt, BU prisms had positive errors, and BD prisms had similar, but negative, errors for distance objects. At -3.33 D object vergence with tilt, negative errors for BD were greater than positive errors for BU. When the eye rotates to look at objects at different positions, errors can increase beyond those occurring on-axis. When designed for nontilted conditions, but then subjected to tilt or to viewing off-axis objects, plano prisms can have errors exceeding the usual prescribing step of 0.25 D.