  Compressive spectral imaging enables to reconstruct the entire
three-dimensional (3D) spectral cube from a few multiplexed images. Here, we
develop a novel compressive spectral imaging technique using diffractive
lenses. Our technique uses a coded aperture to spatially modulate the optical
field from the scene and a diffractive lens such as a photon-sieve for
dispersion. The coded field is passed through the diffractive lens and then
measured at a few planes using a monochrome detector. The 3D spectral cube is
then reconstructed from these highly compressed measurements through sparse
recovery. A fast sparse recovery method is developed to solve this large-scale
inverse problem. The imaging performance is illustrated at visible regime for
various scenarios with different compression ratios through numerical
simulations. The results demonstrate that promising reconstruction performance
can be achieved with as little as two measurements. This opens up new
possibilities for high resolution spectral imaging with low-cost and simple
designs.
