We propose a novel method to obtain non-lens holographic images of micro-objects in white light with diffraction limit quality, based on fourier-spectroscopy principles. We developed a simple method for numerical acquisition of digital holograms of micro-objects at any spectral component from the set of two-dimensional interferograms, registered by fourier-spectrometer. In our experiments we used spectrally-spatial holographic fourier-spectrometer (SSHFS), equipped with supercontinuum light source and CCD camera for registration. Holographic images of several test objects acquired experimentally at different spectral components are presented. Visualization of local spatially-spectral inhomogeneities of micro-objects is discussed through the example of silver berry scaly hair sample.