A system and method for performing four dimensional multicolor nanotomography with high harmonics and attosecond pulses to attain spectrally resolved absorption data about the three-dimensional volumetric structure of a sample are disclosed. Also disclosed are embodiments of the system and method that have been adapted to perform four dimensional multicolor nanotomography absorption and index of refraction data about the three- dimensional volumetric structure of a sample, to perform five dimensional multicolor nanotomography with high harmonics and attosecond pulses to obtain spectrally resolved absorption data about the three-dimensional volumetric structure and temporal dynamics of the sample, to perform five dimensional multicolor nanotomography to obtain spectrally resolved absorption and index of refraction data about the three-dimensional volumetric structure and temporal dynamics of the sample, and to perform Fourier-domain Optical Coherence Tomography.