We present a novel design of 3D spectrometer that can retrieve 3D spectral profile in a single measurement. The 3D spectrometer design is built upon the concept of compressed sensing to make it possible to retrieve 3D information from 2D data from a screen/camera... In contrast to common spectrometers, the 3D spectrometer uses a wide slit instead of a narrow slit and retrieve the 3D datacube that consists of 2D spatial and 1D spectral information. Numerical tests were performed to simulate the retrieval of spectral profiles. The results show that the retrieved profiles match well the original profiles. It is also shown that the retrieved signal from the 3D spectrometer is robust enough for a further post-processing analysis. (read more)