  Spectral imaging is a fundamental diagnostic technique with widespread
application. Conventional spectral imaging approaches have intrinsic
limitations on spatial and spectral resolutions due to the physical components
they rely on. To overcome these physical limitations, in this paper, we develop
a novel multi-spectral imaging modality that enables higher spatial and
spectral resolutions. In the developed computational imaging modality, we
exploit a diffractive lens, such as a photon sieve, for both dispersing and
focusing the optical field, and achieve measurement diversity by changing the
focusing behavior of this lens. Because the focal length of a diffractive lens
is wavelength-dependent, each measurement is a superposition of differently
blurred spectral components. To reconstruct the individual spectral images from
these superimposed and blurred measurements, model-based fast reconstruction
algorithms are developed with deep and analytical priors using alternating
minimization and unrolling. Finally, the effectiveness and performance of the
developed technique is illustrated for an application in astrophysical imaging
under various observation scenarios in the extreme ultraviolet (EUV) regime.
The results demonstrate that the technique provides not only
diffraction-limited high spatial resolution, as enabled by diffractive lenses,
but also the capability of resolving close-by spectral sources that would not
otherwise be possible with the existing techniques. This work enables high
resolution multi-spectral imaging with low cost designs for a variety of
applications and spectral regimes.
