1. An imaging system for generating flexibly oriented electronic images, comprising: a mobile phone including: (a) an image sensor having a square pixel array; (b) imaging optics for forming an optical image on at least a portion of the square pixel array, the at least a portion being within an image circle of the imaging optics and the at least a portion including a plurality of rectangular sub-portions of mutually different orientations including at least one orientation that is not squarely aligned with the square pixel array; and (c) a processing module capable of generating an electronic image from any of the plurality of rectangular sub-portions, wherein the processing module is configured to, for each pixel of the electronic image and when a rectangular sub-portion is not squarely aligned with the square pixel array, populate the each pixel of the electronic image with values associated with signals from at least one pixel of the square pixel array located nearest a location corresponding to the each pixel of the electronic image.