Introduction 14 1 11 18 9 19 1 4 5 16 20 20 8 15 20 17 Methods Apparatus 1 Fig. 1 Herschel’s prisms mounted in front of the right eye. The observer, looking through shutter goggles, adjusts the prisms by means of a lever arm. A cogwheel belt transmits the prismatic power to a potentiometer  These prisms, equipped with a lever arm, allowed a variation of the prismatic power between 30 cm/m base in and 30 cm/m base out. A calibration performed with a laser beam showed that the readings on the scale of the prisms varied only about 2% around the true inflection. A cogwheel belt connected the prisms with a potentiometer that provided a signal linearly proportional to the prism power. The electric signal was directly transmitted to a computer. 2 Test figures Dissociated phoria 2 2 2 2 Fig. 2 a b 9 c  Associated phoria 2 9 Comfortable prism 2 Procedure and instructions 12 Associated phoria. 6 Dissociated phoria. Comfortable prism. To get used to the manoeuvring of Herschel’s prisms, the experiment was preceded by a few trials in which the observers practised bringing the white dot to the midline of the “O X O” (test for dissociated phoria) and aligning the Nonius lines to each other (test for associated phoria). To examine the reproducibility, we repeated the whole experiment for all observers in a second session after an interval of 24 to 130 days. Observers . decimal Snellen We explained to the observers that the study intended to optimise the comfort of seeing. Otherwise, the observers were kept naive as to the purpose of the study. Each observer provided informed written consent to participate in the experiments. The study followed the tenets of the Declaration of Helsinki and was approved by the institutional human review board. Data acquisition and analysis The prismatic power derived from the potentiometer attached to Herschel’s prisms was recorded by PowerLab with a sampling rate of 100 Hz. To enable analysis of the dynamic behaviour of the adjustments we recorded the full 30 seconds of each trial. Offline examination was accomplished with Igor Pro® (Wavemetrics, Inc., Lake Oswego, OR, USA) and Statview® (Abacus Concepts, Inc., Berkeley, California, USA). Statistical analysis was performed with Statview® and SPSS® (SPSS Inc., Chicago, Illinois, USA). We used multifactorial ANOVA (including condition, session and trial) and paired comparisons. For post-hoc tests, Bonferroni adjustment was performed. Results Inspection of curves 3 thin lines thicker lines p Fig. 3 upper panels lower panels solid lines dashed lines  For dissociated phoria, most observers saw an offset right at the beginning of each trial and promptly moved the lever arm accordingly. For associated phoria, some observers initially did not see an offset between the Nonius lines. In this case, the observers followed the instruction to “play” a little with the lever arm and find a position in which the lines appeared as stable as possible. 3 right panels Statistical analysis p 4 Fig. 4 DP AP CP  eso exo 13 p Comparison between dissociated phoria, associated phoria, and the comfortable prism n p 5 n p p Fig. 5 Mean of the two sessions ±SEM for associated phoria, dissociated phoria, and comfortable prism. The first column in each graph represents observer #1, followed by #2 etc  before p Discussion We compared three vergence parameters: dissociated phoria, associated phoria, and the comfortable prism. To avoid any (possibly prejudiced) influence of the experimenter, we recorded the prismatic power set by the observer with a potentiometer. The comfortable prism anticipates the real-life situation in which prismatic spectacles are worn. Therefore, the comfortable prism is very close to the endpoint of therapeutical considerations, i.e. prescribing prismatic spectacles. In contrast, dissociated and associated phoria, determined under artificial viewing conditions, are surrogate measures of the comfortable prism. We studied whether these surrogate measures predict the comfortable prism, assuming that dissociated phoria, associated phoria, and the comfortable prism might be similar, because all three parameters are determined by opening the feedback loop for fusional vergence. When measuring dissociated phoria, fusionable contours are absent; hence, there is no disparity error signal. When associated phoria is measured, any disparity of the (defective) fusional pattern, which initially constitutes an error signal, is promptly nullified by repeated prism adjustment. Concerning the comfortable prism, one has to realize that the fusional feedback loop, which uses disparity as its error signal, can stabilize the vergence angle only if the stimuli are presented to the two eyes in a fixed angle, e.g. through a certain unchanging prism. If, however, the observer is asked to adjust a variable prism according to his or her comfort, the fusional feedback loop is open and cannot stabilize the vergence angle. Instead, the fusional feedback loop is replaced by another feedback loop whose error signal is discomfort. Accordingly, the vergence position reached with the comfortable prism may also be described as the “vergence position of rest when both eyes are exposed to identical pictures”. 5 eso exo eso eso exo 7 8 What is the reason for the tendency towards eso deviation in the two phoria conditions? A different accommodative demand can be excluded, because we used a similar target in all three conditions. Rather, we suggest that the shift towards eso deviation is brought about by the dissimilarity between the images of the two eyes. This suggestion pertains even to the associated phoria condition, in which ample fusionable contours are available, and the dissimilarity is limited to the monocular Nonius lines. Nevertheless, this dissimilarity was conspicuous for the observers: most of them reported that one or both Nonius lines seemed to disappear every now and then. Correspondingly, the observers reported occasional disappearance of the white dot when they determined their dissociated phoria, although this was less pronounced than the disappearance of the Nonius lines in the associated phoria condition. These observations raise the possibility that the irritating perception of binocular rivalry drives the eso shift in the two phoria conditions. Compatible with this idea is that the eso shift was stronger in the associated than in the dissociated phoria condition, i.e. in the condition with the more pronounced fading. Considering the open feedback loop for fusional vergence in all three conditions, it is not surprising that the values obtained with all three methods (dissociated phoria, associated phoria, and comfortable prism) were rather variable. This was true in each of the two sessions. 10 12 What are the practical inferences of our study? 11 18 9 19 21 Although we did not use the relief from asthenopic complaints as a criterion, we think that our findings relate to the prescription of therapeutic prisms for such patients. The discrepancy between dissociated and associated phoria on the one hand and the comfortable prism on the other hand would probably also occur in patients with asthenopia, and it is plausible to assume that these patients would benefit more from the comfortable prism, chosen by themselves under natural viewing conditions, than from a prescription based on one of the phoria parameters, which carry artefacts due to the artificial test conditions. 13 What are the limitations of our study? p eso exo p The angles encountered in our 20 observers were relatively small: the dissociated phoria ranged from +9.3 cm/m eso to −5.9 cm/m exo deviation, the associated phoria from +11.2 cm/m eso to −3.3 cm/m exo deviation, and the comfortable prism from +4.8 cm/m eso to −4.1 cm/m exo deviation. An extrapolation of our conclusions to observers with larger angles may not be justified. 2 3 4