  Despite recent advances, high performance single-shot 3D microscopy remains
an elusive task. By introducing designed diffractive optical elements (DOEs),
one is capable of converting a microscope into a 3D "kaleidoscope", in which
case the snapshot image consists of an array of tiles and each tile focuses on
different depths. However, the acquired multifocal microscopic (MFM) image
suffers from multiple sources of degradation, which prevents MFM from further
applications. We propose a unifying computational framework which simplifies
the imaging system and achieves 3D reconstruction via computation. Our optical
configuration omits chromatic correction grating and redesigns the multifocal
grating to enlarge the tracking area. Our proposed setup features only one
single grating in addition to a regular microscope. The aberration correction,
along with Poisson and background denoising, are incorporated in our
deconvolution-based fully-automated algorithm, which requires no empirical
parameter-tuning. In experiments, we achieve the spatial resolutions of
$0.35$um (lateral) and $0.5$um (axial), which are comparable to the resolution
that can be achieved with confocal deconvolution microscopy. We demonstrate a
3D video of moving bacteria recorded at $25$ frames per second using our
proposed computational multifocal microscopy technique.
