Optimal tuning curves for neurons spiking as a Poisson process

We calculate the information capacity of a neuron emitting as a Poisson process in response to a static stimulus, and the stimulus distribution required to reach the capacity, in the case of a constraint on the average frequency. These optimal stimulus distributions (i.e. the ones reaching the information capacity) are then reexpressed in terms of`tuning curves' for neurons with a continuous response to a scalar stimulus.