README.md

Visual acuity charts

This repository contains a LaTeX file and a Python script for making random Snellen charts. A PDF with 10 charts, meant to be kept at a distance of 3 m, has been included with this repository. To generate new charts, first edit snellen.tex and change the distance \factor if required. To compile the file, run make or compile using XeLaTeX with the --shell-escape option. When compiling the file, the standard output of the snellen.py script, which produces LaTeX commands to make random charts, is automatically included. (This assumes that your version of XeLaTeX comes with an \input{|...} that allows capturing the standard outputs of commands.)

Background

The Snellen chart consists of a series of optotypes (usually the letters C, D, E, F, L, O, P, T, and Z) in different sizes. Using elementary trigonometry, the equation that relates the optotype width (or height) $w$, the subtended angle $φ$, and the distance to the chart $d$, is

$$w = 2d\tan(\varphi/2).$$

A person's vision is considered normal (i.e., 6/6 or 20/20 vision) if he or she can delineate 1-arcminute-wide features of an optotype that has an angular width of 5 arcminutes (= $π/2160~\text{rad}$). So if the Snellen chart is to be kept at a distance of 3m (as with the example PDF), the optotype width must be

$$w = (2×3~\text{m})\times\tan[(\pi/2160)/2] = 4.36~\text{mm}.$$

Further reading

R. J. Kolker, Subjective Refraction and Prescribing Glasses (American Academy of Opthalmology, San Francisco, CA, 2014).

A. R. Elkington, H. J. Frank, M. J. Greaney, Clinical Optics, 3rd ed. (Blackwell Science, Oxford, 1999).

Disclaimer and license

The contents of this repository are for informational purposes only and do not constitute medical advice. They are not intended to replace the advice of a licensed optometrist or a qualified health provider.

Optician Sans is licensed under the SIL Open Font License, Version 1.1. All other material is in the public domain. See the file UNLICENSE for more details.