Recent advances in compressive spectral imagers have demonstrated the potential of spatio-spectral modulation (SSM) for improved reconstruction performance. Existing SSM techniques, however, use either a color filter array or a complex optical arrangement, both of which can only provide limited modulation bandwidth in the spectral dimension. This paper proposes a practical SSM method to help address the "missing cone" problem of chromo-tomography. A high-resolution binary coded aperture is used to modulate the dispersed images, which in the Fourier domain fulfills a 3D convolution of the probed spectrum with the aperture’s wide spectrum. This spectrum spreading process facilitates the compressed sensing strategy determined by the Fourier Slice Theorem and we demonstrate the advantages of the proposed approach with numerical experiments.