An optical image of a partially coherent planar source is studied with an imaging system in front of which an infinite linear edge is placed in an arbitrary position. The configuration can be regarded as a model for a partial eclipse in astronomy. The study includes cases of a primary source and a secondary source. The cross-spectral density in each stage of the system is derived in terms of the cross-spectral density of the source. In particular, the impulse-response functions for a coherent source and an incoherent source are derived in a closed form. Properties of the impulse-response function are investigated with respect to the position of the edge and the aperture size. It is shown that, if the imaging system is partially obstructed by an infinite linear edge, the system does not have shift invariance unless it is shift invariant itself. This fact may introduce heterogeneous red and blue spectral shifts and positional shifts of an obtained image. The spectral shift and the positional shift in each position of the image of a point source with a Gaussian spectrum are studied. The optical system studied is of importance for accurate measurement of spectra and positions in optical systems with partial obstructions, such as those in astronomy.