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##### Session: Poster session A

### A free online tool for conversion between rectangular and polar representation of prism prescription

Introduction

Prismatic specifications of spectacles is paramount in evaluating the strabismus patient with built-in prisms, as the total strabismic deviation is the sum of any built-in prism effect in the two spectacle lenses and any residual deviation measured at the orthoptic evaluation. However, these components are typically reported in polar and rectangular representation, respectively, yielding summation complicated. The reverse calculation is needed when attaching Fresnel prisms to spectacles in patients requiring horizontal and vertical correction. Online calculators exist for converting prescription between polar and rectangular representation only for one lens, but to our knowledge, no tool exists evaluating two lenses in a spectacle specification, allowing unnecessary room for human error.

Methods

Converting a prism from polar (with a given prism power and angle [v]) to rectangular (vertical and horizontal prism diopters) representation requires resolving the vertical and horizontal part using sin(v) and cos(v) of the angle respectively, factoring the power of the prism on each intermediate result. Converting from rectangular to polar representation uses the reverse calculation, respecting signs based on laterality. Intermediate results from the two lenses are added.

Results

We propose a free online web-based calculator which allows conversion from an entire two-lens spectacle prescription to vertical and horizontal prism diopter values or conversion from vertical and horizontal prism diopters to polar representation in one lens or distributed over two lenses.

Conclusions

A free online calculator will allow polar-to-rectangular conversion when evaluating spectacles with built-in prisms and the reverse conversion when attaching Fresnel prisms will minimize possible errors due to user calculations.