Consider layering an inhibitory input on top of the input from relay cells, an input with a receptive field identical to that of the excitatory input, but with opposite response polarity (ON instead of OFF, and OFF instead of ON). Each ON region would then receive ON excitation and OFF inhibition, and each OFF region would receive OFF excitation and ON inhibition. With these inhibitory inputs in place, the peak response to a bar or grating of the preferred orientation would be unaffected because the excitation and inhibition would occur out of phase with one another: Whenever the excitation was peaking, the inhibition would be at its minimum, and vice versa. The response to orthogonally oriented bars, on the other hand, would be strongly affected. If the inhibition had the same contrast sensitivity and strength as the excitation, and if ON and OFF regions had equal strength, an orthogonally oriented bar would activate ON inhibition from the OFF region that exactly cancelled the ON excitation from the ON region, no matter what the contrast of the stimulus.
With excitation and inhibition of exactly equal strength, the baseline in the tuning curve of the synaptic input to a simple cell would be invariant with contrast: At non-preferred orientations, the excitation and inhibition would exactly cancel one another at all contrasts. But even if ON and OFF regions had equal strengths, this antiphase inhibition would not entirely solve the problem of contrast-invariant tuning (Troyer et al., 1998). The height of the curves would still grow in amplitude with contrast so the portion of the peak that reaches above threshold would still widen with contrast. The orientation tuning of the spike responses would then still not be completely contrast invariant.
A full solution can be found by assuming that the antiphase inhibition is sufficiently stronger than the relay-cell excitation (Troyer et al., 1998). This has the effect of actually pulling the baseline in Figure 4D down as contrast is increased and the peak grows, so that the width of the peak at the point that it crosses threshold remains constant (Figure 4E). In this way, the feedforward model with added inhibition can achieve contrast invariant orientation tuning. Furthermore, this mechanism is surprisingly insensitive to the strength of the inhibition: once the inhibition is sufficiently strong, increasing it further simply sharpens the orientation tuning, while maintaining the contrast invariance of the tuning (Troyer et al., 1998).