  This paper considers scattering screens that have arbitrary spatial
variations of scattering strength transverse to the line of sight, including
screens that are spatially well confined, such as disks and filaments. We
calculate the scattered image of a point source and the observed pulse shape of
a scattered impulse. The consequences of screen confinement include: (1) Source
image shapes that are determined by the physical extent of the screen rather
than by the shapes of much-smaller diffracting microirregularities. These
include image elongations and orientations that are frequency dependent. (2)
Variation with frequency of angular broadening that is much weaker than the
trademark \nu^{-2} scaling law (for a cold, unmagnetized plasma), including
frequency-independent cases; and (3) Similar departure of the pulse broadening
time from the usually expected \nu^{-4} scaling law. We briefly discuss
applications that include scattering of pulses from the Crab pulsar by
filaments in the Crab Nebula; image asymmetries from Galactic scattering of the
sources Cyg X-3, Sgr A*, and NGC 6334B; and scattering of background active
galactic nuclei by intervening galaxies. We also address the consequences for
inferences about the shape of the wavenumber spectrum of electron density
irregularities, which depend on scaling laws for the image size and the pulse
broadening. Future low-frequency (< 100 MHz) array observations will also be
strongly affected by the Galactic structure of scattering material. Our
formalism is derived in the context of radio scattering by plasma density
fluctuations. It is also applicable to optical, UV and X-ray scattering by
grains in the interstellar medium.
