Quantitative analysis of associated and disassociated phorias: linear and nonlinear static models

Ogle proposed two measures of oculomotor balance, called associated and disassociated phorias, which he assumed were equivalent. However, experimentally determined values of these phorias do not show a close correspondence. To analyze the rationale behind Ogle's assumption of equality, a linear static model was evaluated. It was found that indeed the linear model predicts an exact correspondence between associated and disassociated phorias. Thus, his assumption depended on the presence of a linear model. To account for the discrepancy between these two measures, a nonlinear static model, containing the dead space operators depth of field and Panum's fusional area, was evaluated. Four equations for fixation disparity were derived corresponding to the four combinations of deadspace operator outputs. It was found that only one of these four equally possible solutions for associated phoria corresponded to the disassociated phoria. This suggests that the variability in the four solutions may account for the scatter in the experimental data. The nonlinear model was analyzed further to determine its sensitivity to parameter changes and to show how such a model could generate the classical shape of the fixation disparity curve.