A theoretical description of the contrast-imaging function is derived for tilted specimens that exhibit weak-phase object characteristics. We show that the tilted contrast-imaging function (TCIF) is a linear transformation, which can be approximated by the convolution operation for small tilt angles or for small specimens. This approximation is not valid for electron tomography, where specimen tilts are above 60 degrees and specimen dimensions amount to some 10mum. The approximation also breaks down for electron crystallography, where atomic resolution is to be achieved. Therefore, we do not make this approximation and propose a generalized algorithm for inverting the TCIF. The implications of our description are discussed in the context of electron tomography, single particle analysis, and electron crystallography, and the improved resolution is quantitatively demonstrated.