1. Apparatus for providing a multidimensional image of inanimate or animate objects comprising: a magnetization source for producing a magnetic field to magnetize a volume of an object to be imaged, the volume comprising a plurality of voxels; a radiation source for applying a radiation field to the object to be imaged when the object is disposed in the magnetic field to produce a secondary radiation field emanating from the object; an output signal detector for producing output signals in response to said secondary radiation at a plurality of spatial locations outside of the object as a function of time; a first processor for determining a plurality of Fourier components, each having the same frequency, an intensity and a phase angle; a second processor for associating the Fourier components due to each voxel of the object to be imaged by phase to form a set corresponding to a spatial variation of intensity of the secondary radiation due to each voxel at said plurality of spatial locations outside of the object; a third processor for converting each said set of components into a voxel location; and an image processor for producing an image based on the secondary radiation intensity from each voxel and the location of each voxel.