A fully interferometric technique for obtaining hypermultispectral components of three-dimensional (3D) images has been tested for a polychromatic object that consists of spatially incoherent, planar light sources of different shapes. Each planar source has different continuous spectra, located at different 3D positions. The method is based on measurement of a five-dimensional (5D) interferogram. By applying synthetic aperture technique and spectral decomposition to that 5D interferogram, one obtains a set of complex holograms of different spectral components. From these holograms, 3D images of multiple spectral components have been retrieved. A decomposed continuous spectrum of each planar light source is also shown to demonstrate the potential applicability to identify materials of a particular part of an object under illumination by white light.