  Unresolved spatially-random microstructure, in an illuminated sample, can
lead to position-dependent blur when an image of that sample is formed. For a
small propagation distance, between the exit surface of the sample and the
entrance surface of a position-sensitive detector, the paraxial approximation
implies that the blurring influence of the sample may be modeled using an
anomalous-diffusion field. This diffusion field may have a scalar or tensor
character, depending on whether the random microstructure has an
autocorrelation function that is rotationally isotropic or anisotropic,
respectively. Partial differential equations are written down and then solved,
in a closed-form manner, for several variants of the inverse problem of
diffusion-field retrieval given suitable intensity images. Both
uniform-illumination and structured-illumination schemes are considered. Links
are made, between the recovered diffusion field and certain statistical
properties of the unresolved microstructure. The developed theory -- which may
be viewed as a crudely parallel form of small-angle scattering under the
Guinier approximation -- is applicable to a range of paraxial radiation and
matter fields, such as visible light, x rays, neutrons, and electrons.
