A new method for exact measurements of visual acuity

Abstract

The paper presents a new test method for investigations of threshold curves for the resolving power of the eye and for exact measurements of visual acuity. This method measures static visual acuity within confidence limits of 9% compared to the acuity steps in Snellen notation of 33% to 50%. Furthermore, the method introduces the slope of the threshold curve as a parameter of suggested importance in the judgement of visual capability. The test mathematic is based on a method described by Finney (1952) for calculations on dose-response curves. To calculate the results and the test statistics an iterative curve fitting programme was designed to be run on a micro-computer. By connecting the presentation system and the response panel to the same computer the test could be performed almost automatically. The new test method was used to study visual acuity measured by projected ortotypes compared to acuity when measured by printed ortotypes. Tests using projected ortotypes were found to equal traditional acuity measurements, but the test results stressed the need for perfect and adjusted optics when projecting systems are used in visual acuity test.

Simulation of visual acuity by personalizable neuro-physiological model of the human eye

“…In our former paper 52 we concluded that thresholding the visual psychometric function of a given subject provides the most precise acuity result without any bias 52,54 . If we express the letter size s , in logMAR units:where α denotes the visual angle of the stroke width of letters, then the relation represents the psychometric function of vision 55–57 . We describe its profile by the sigmoid-shape logistic function L ( s ), which is the most common two-parameter curve used to approximate any psychometric function 55,56,58 .…”

“…We describe its profile by the sigmoid-shape logistic function L ( s ), which is the most common two-parameter curve used to approximate any psychometric function 55,56,58 . We linearly transform the logistic function to ensure its limits correspond to the theoretically expected RR values, according to the total number of possible responses 57 (i.e. all 26 letters of the English alphabet).…”

Application of Correlation-Based Scoring Scheme for Visual Acuity Measurements in the Clinical Practice

“…}\end{equation}\end{document}The x mp parameter sets the midpoint position of the sigmoid, while k /4 determines the steepness of the curve at this point. To make sure that the limits of the psychometric function correspond to the theoretically expected RR values, it has to be further transformed linearly as22,27: \begin{document}\newcommand{\bialpha}{\boldsymbol{\alpha}}\newcommand{\bibeta}{\boldsymbol{\beta}}\newcommand{\bigamma}{\boldsymbol{\gamma}}\newcommand{\bidelta}{\boldsymbol{\delta}}\newcommand{\bivarepsilon}{\boldsymbol{\varepsilon}}\newcommand{\bizeta}{\boldsymbol{\zeta}}\newcommand{\bieta}{\boldsymbol{\eta}}\newcommand{\bitheta}{\boldsymbol{\theta}}\newcommand{\biiota}{\boldsymbol{\iota}}\newcommand{\bikappa}{\boldsymbol{\kappa}}\newcommand{\bilambda}{\boldsymbol{\lambda}}\newcommand{\bimu}{\boldsymbol{\mu}}\newcommand{\binu}{\boldsymbol{\nu}}\newcommand{\bixi}{\boldsymbol{\xi}}\newcommand{\biomicron}{\boldsymbol{\micron}}\newcommand{\bipi}{\boldsymbol{\pi}}\newcommand{\birho}{\boldsymbol{\rho}}\newcommand{\bisigma}{\boldsymbol{\sigma}}\newcommand{\bitau}{\boldsymbol{\tau}}\newcommand{\biupsilon}{\boldsymbol{\upsilon}}\newcommand{\biphi}{\boldsymbol{\phi}}\newcommand{\bichi}{\boldsymbol{\chi}}\newcommand{\bipsi}{\boldsymbol{\psi}}\newcommand{\biomega}{\boldsymbol{\omega}}\begin{equation}\tag{6}L^{\prime} (x) = {{25} \over {26}} \cdot L(x) + {1 \over {26}}{\rm ,}\end{equation}\end{document}so that \begin{document}\newcommand{\bialpha}{\boldsymbol{\alpha}}\newcommand{\bibeta}{\boldsymbol{\beta}}\newcommand{\bigamma}{\boldsymbol{\gamma}}\newcommand{\bidelta}{\boldsymbol{\delta}}\newcommand{\bivarepsilon}{\boldsymbol{\varepsilon}}\newcommand{\bizeta}{\boldsymbol{\zeta}}\newcommand{\bieta}{\boldsymbol{\eta}}\newcommand{\bitheta}{\boldsymbol{\theta}}\newcommand{\biiota}{\boldsymbol{\iota}}\newcommand{\bikappa}{\boldsymbol{\kappa}}\newcommand{\bilambda}{\boldsymbol{\lambda}}\newcommand{\bimu}{\boldsymbol{\mu}}\newcommand{\binu}{\boldsymbol{\nu}}\newcommand{\bixi}{\boldsymbol{\xi}}\newcommand{\biomicron}{\boldsymbol{\micron}}\newcommand{\bipi}{\boldsymbol{\pi}}\newcommand{\birho}{\boldsymbol{\rho}}\newcommand{\bisigma}{\boldsymbol{\sigma}}\newcommand{\bitau}{\boldsymbol{\tau}}\newcommand{\biupsilon}{\boldsymbol{\upsilon}}\newcommand{\biphi}{\boldsymbol{\phi}}\newcommand{\bichi}{\boldsymbol{\chi}}\newcommand{\bipsi}{\boldsymbol{\psi}}\newcommand{\biomega}{\boldsymbol{\omega}}{\lim _{x \to \infty }}L^{\prime} (x) = 1\end{document}, and \begin{document}\newcommand{\bialpha}{\boldsymbol{\alpha}}\newcommand{\bibeta}{\boldsymbol{\beta}}\newcommand{\bigamma}{\boldsymbol{\gamma}}\newcommand{\bidelta}{\boldsymbol{\delta}}\newcommand{\bivarepsilon}{\boldsymbol{\varepsilon}}\newcommand{\bizeta}{\boldsymbol{\zeta}}\newcommand{\bieta}{\boldsymbol{\eta}}\newcommand{\bitheta}{\boldsymbol{\theta}}\newcommand{\biiota}{\boldsymbol{\iota}}\newcommand{\bikappa}{\boldsymbol{\kappa}}\newcommand{\bilambda}{\boldsymbol{\lambda}}\newcommand{\bimu}{\boldsymbol{\mu}}\newcommand{\binu}{\boldsymbol{\nu}}\newcommand{\bixi}{\boldsymbol{\xi}}\newcommand{\biomicron}{\boldsymbol{\micron}}\newcommand{\bipi}{\boldsymbol{\pi}}\newcommand{\birho}{\boldsymbol{\rho}}\newcommand{\bisigma}{\boldsymbol{\sigma}}\newcommand{\bitau}{\boldsymbol{\tau}}\newcommand{\biupsilon}{\boldsymbol{\upsilon}}\newcommand{\biphi}{\boldsymbol{\phi}}\newcommand{\bichi}{\boldsymbol{\chi}}\newcommand{\bipsi}{\boldsymbol{\psi}}\newcommand{\biomega}{\boldsymbol{\omega}}{\lim _{x \to - \infty }}L^{\prime} (x) = 1/26\end{document} according to the total number of potential answers.…”

“…In this case, the measured P recognition probability values at the x = log 10 ( α ) letter sizes are fitted by a monotonic differentiable S-shaped curve, the so-called psychometric function of vision 16,24–26. Visual acuity is determined by the x 0 letter size at which the L(x) psychometric function intersects the theoretical P 0 = 0.5 probability threshold,22,27,28 that is: \begin{document}\newcommand{\bialpha}{\boldsymbol{\alpha}}\newcommand{\bibeta}{\boldsymbol{\beta}}\newcommand{\bigamma}{\boldsymbol{\gamma}}\newcommand{\bidelta}{\boldsymbol{\delta}}\newcommand{\bivarepsilon}{\boldsymbol{\varepsilon}}\newcommand{\bizeta}{\boldsymbol{\zeta}}\newcommand{\bieta}{\boldsymbol{\eta}}\newcommand{\bitheta}{\boldsymbol{\theta}}\newcommand{\biiota}{\boldsymbol{\iota}}\newcommand{\bikappa}{\boldsymbol{\kappa}}\newcommand{\bilambda}{\boldsymbol{\lambda}}\newcommand{\bimu}{\boldsymbol{\mu}}\newcommand{\binu}{\boldsymbol{\nu}}\newcommand{\bixi}{\boldsymbol{\xi}}\newcommand{\biomicron}{\boldsymbol{\micron}}\newcommand{\bipi}{\boldsymbol{\pi}}\newcommand{\birho}{\boldsymbol{\rho}}\newcommand{\bisigma}{\boldsymbol{\sigma}}\newcommand{\bitau}{\boldsymbol{\tau}}\newcommand{\biupsilon}{\boldsymbol{\upsilon}}\newcommand{\biphi}{\boldsymbol{\phi}}\newcommand{\bichi}{\boldsymbol{\chi}}\newcommand{\bipsi}{\boldsymbol{\psi}}\newcommand{\biomega}{\boldsymbol{\omega}}\begin{equation}\tag{3}L(x)\left| {_{x = {x_0}} = {P_0} \Rightarrow {\cal V} \equiv {x_0}} \right. {\rm .…”