Two-dimensional Hall probes are becoming increasingly popular as ''loc
al'' magnetometers for ferromagnetic and superconducting materials. In
many applications, the magnetic field at a sample surface varies on a
length scale much smaller than the Hall probe dimensions, and data in
terpretation requires a quantitative model of the Hall voltage in this
situation. We present here a classical numerical model of the Hall ef
fect in a strongly inhomogeneous magnetic field and show how a respons
e function can be defined to calculate the Hall voltage for an arbitra
ry magnetic-field distribution. The results are successfully applied t
o recent scanning Hall probe microscopy data on superconducting vortic
es. (C) 1997 American Institute of Physics.