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Recent work suggests that changing Convolutional Neural Network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively comparing trained networks. The fields of electrophysiology and psychophysics have developed a wealth of methods for characterising visual systems which permit such comparisons. Inspired by these methods, we propose an approach to obtaining spatial and colour tuning curves for convolutional neurons, which can be used to classify cells in terms of their spatial and colour opponency. We perform these classifications for a range of CNNs with different depths and bottleneck widths. Our key finding is that networks with a bottleneck show a strong functional organisation: almost all cells in the bottleneck layer become both spatially and colour opponent, cells in the layer following the bottleneck become non-opponent. The colour tuning data can further be used to form a rich understanding of how colour is encoded by a network. As a concrete demonstration, we show that shallower networks without a bottleneck learn a complex non-linear colour system, whereas deeper networks with tight bottlenecks learn a simple channel opponent code in the bottleneck layer. We further develop a method of obtaining a hue sensitivity curve for a trained CNN which enables high level insights that complement the low level findings from the colour tuning data. We go on to train a series of networks under different conditions to ascertain the robustness of the discussed results. Ultimately, our methods and findings coalesce with prior art, strengthening our ability to interpret trained CNNs and furthering our understanding of the connection between architecture and learned representation. Code for all experiments is available at https://github.com/ecs-vlc/opponency.