a) Forward calculation in the A-stacking framework, subdivided into the algorithmic steps described by (18). b) Forward calculation using A-projection. The A-projection convolution kernel size is N_gA × N_gA, as determined by the spatial frequency content of the direction-dependent effects on the sky, and can result in a relatively expensive gridding cost. A-stacking aims to reduce this cost by decreasing the size of the gridding convolution kernel to N_g × N_g, as determined by the required image dynamic range; the penalty is that multiple FFTs and gridding operations are required.