  We discuss the Meissner response to a known field source of superconductors
having inhomogeneities in their penetration depth. We simplify the general
problem by assuming that the perturbations of the fields by the penetration
depth inhomogeneities are small. We present expressions for inhomogeneities in
several geometries, but concentrate for comparison with experiment on planar
defects, perpendicular to the sample surfaces, with superfluid densities
different from the rest of the samples. These calculations are relevant for
magnetic microscopies, such as Scanning Superconducting Quantum Interference
Device (SQUID) and Magnetic Force Microscope, which image the local diamagnetic
susceptibility of a sample.
