We present a new method to map the surface brightness of the accretion stre
ams in AM Herculis systems from observed light curves. Extensive tests of t
he algorithm show that it reliably reproduces the intensity distribution of
the stream for data with a signal-to-noise ratio greater than or similar t
o 5. As a first application, we map the accretion stream emission of C IV l
ambda 1550 in the polar UZ Fornacis using HST FOS high state spectra. We fi
nd three main emission regions along the accretion stream: (1) On the balli
stic part of the accretion stream, (2) on the magnetically funneled stream
near the primary accretion spot, and (3) on the magnetically funneled strea
m at a position above the stagnation region.