  The point-spread function (PSF) of an imaging system describes the response
of the system to a point source. Accurately determining the PSF enables one to
correct for the combined effects of focussing and scattering within the imaging
system, and thereby enhance the spatial resolution and dynamic contrast of the
resulting images. We present a semi-empirical semi-blind methodology to derive
a PSF from partially occulted images. We partition the two-dimensional PSF into
multiple segments, set up a multi-linear system of equations, and directly fit
the system of equations to determine the PSF weight in each segment. The
algorithm is guaranteed to converge towards the correct instrumental PSF for a
large class of occultations, does not require a predefined functional form of
the PSF, and can be applied to a large variety of partially occulted images,
such as within laboratory settings, regular calibrations within a production
line or in the field, astronomical images of distant clusters of stars, or
partial solar eclipse images. We show that the central weight of the PSF, which
gives the percentage of photons that are not scattered by the instrument, is
accurate to bettern than 1.2%. The mean absolute percentage error between the
reconstructed and true PSF is usually between 0.5% and 5% for the entire PSF,
between 0.5% and 5% for the PSF core, and between 0.5% and 3% for the PSF tail.
