Hyperspectral microscopy recovers both 2D spatial and 1D spectral information, with applications in bioassays, cell biology, and tissue diagnostics. Traditional hyperspectral systems are bulky, expensive, and slow (require scanning). We designed a compact snapshot hyperspectral imager which uses a single acquisition and can achieve high spatial, spectral, and temporal resolution. The imager consists of a diffuser (random phase mask) placed in the Fourier plane followed by an image sensor with a 64-channel spectral filter array. The diffuser’s point spread function (PSF) enables each spatial point from the object to map onto all the spectral filter channels at once and generates a spatially varying caustic pattern, which encodes the position of the point. Hence, we can computationally reconstruct the object’s 2D spatial information and the full spectral information for each pixel by solving a sparsity-constrained inverse problem.