The contribution of interocular orientation differences to
depth perception, at either the neuronal or the psychophysical
level, is unclear. To understand the responses of binocular
neurons to orientation disparity, we extended the energy model
of Ohzawa et al. (1990) to incorporate binocular differences
in receptive-field orientation. The responses of the model to
grating stimuli with interocular orientation differences were
examined, along with the responses to random dot stereograms
(RDS) depicting slanted surfaces. The responses to combinations
of stimulus orientations in the two eyes were left–right
separable, which means there was no consistent response to the
binocular orientation difference. All existing neuronal data
concerning orientation disparity can be well described by this
type of model (even a version with no disparity selectivity).
The disparity sensitive model is nonetheless sensitive to changes
in RDS slant, although it requires narrow orientation bandwidth
to produce substantial modulation. The disparity-insensitive
model shows no selectivity to slant in this stimulus. Several
modifications to the model were attempted to improve its
selectivity for orientation disparity and/or slant. A model
built by summing several disparity-sensitive models showed
left–right inseparable responses, responding maximally
to a consistent orientation difference. Despite this property,
the selectivity for slant in RDS stimuli was no better than
the simple disparity-selective model. The range of models evaluated
here demonstrate that interocular orientation differences are
neither necessary nor sufficient for signaling slant. In contrast,
within the framework of the energy model, positional disparity
sensitivity appears to be both necessary and sufficient.