  The H-scan approach is a matched filter methodology that aims to add
information to the traditional ultrasound B-scan. The theory is based on the
differences in the echoes produced by different classes of reflectors or
scatterers. Matched filters can be created for different types of scatterers,
whereby the maximum output indicates a match and color schemes can be used to
indicate the class of scatterer responsible for echoes, providing a visual
interpretation of the results. However, within the theory of weak scattering
from a variety of shapes, small changes in the size of the inhomogeneous
objects will create shifts in the scattering transfer function. In this paper,
we determine the shift in center frequency, along with time and frequency
domain characteristics of echoes and argue for a general power law transfer
function to capture the major characteristics of scattering types. With this
general approach, the H-scan matched filters can be set to elicit more fine
grain shifts in scattering types, commensurate with more subtle changes in
tissue morphology. Compensation for frequency dependent attenuation is helpful
for avoiding beam softening effects with increasing depths. Examples from
phantoms and normal and pathological tissues are provided to demonstrate that
the H-scan analysis and displays are sensitive to scatterer size and
morphology, and can be adapted to conventional imaging systems.
