These results can be improved by using the averaged nature of Peters’s data. To do so, for each $(S,C)$ pair, we generated a set of $N$ random values of the four fitting parameters ${Vbc,D,q,Am}$, using a Gaussian random number generator. In this way, we have an $N\xd74$ matrix with rows representing a random state of the fitting parameters ${Vbcj,Dj,qj,Amaxj}j=1,2,\u2026,N$, and we computed the visual acuity corresponding to each of those states, $Vj=fV(S,C,Vbcj,Dj,qj,Amaxj)$, where $fV$ stands for the function described in Eq. (10). Finally, we computed the average value of the visual acuity $\u27e8Vj\u27e9$ which depends on the spherical and cylindrical errors and also, on the mean and standard deviation of each fit parameter used in the Gaussian random number generator. To simplify the fitting problem, we used fixed values for the standard deviations of the randomly generated parameters, so the average value of the visual acuity obtained for each $(S,C)$ pair only depends on the set of mean values ${\u27e8Vbc\u27e9,\u27e8D\u27e9,\u27e8q\u27e9,\u27e8Amax\u27e9}$, which are the fitting parameters of our problem.