Pincushion distortion from spherical detectors

[senan]

I'm wondering how the use of spherical shaped detectors causes pincushion distortion. I can understand the shape of the detector affecting the final image but I thought the lines would bend out as when a hemisphere is laid out flat, a point appearing near the center from the front on angle would appear further away when the detector is flat. However every image of pincushion distortion has the lines bending in.

 

[Andy Resnick]

Can you provide some context? I'm more familiar with field curvature in this regard.