  The optical counterpart of the transient, millisecond X-ray pulsar SAX
J1808.4-3658 was observed in four colours (BVRI) for five weeks during the 2005
June-July outburst. The optical fluxes declined by ~2 magnitudes during the
first 16 days and then commenced quasi-periodic secondary outbursts, with
time-scales of several days, similar to those seen in 2000 and 2002. The
broadband spectra derived from these measurements were generally consistent
with emission from an X-ray heated accretion disc. During the first 16 days
decline in intensity the spectrum became redder. We suggest that the primary
outburst was initiated by a viscosity change driven instability in the inner
disc and note the contrast with another accreting millisecond pulsar, XTE
J0929--314, for which the spectrum becomes bluer during the decline. On the
night of 2005 June 5 (HJD 2453527) the I band flux was ~0.45 magnitudes
brighter than on the preceding or following nights whereas the BVR bands showed
no obvious enhancement. A Type I X-ray burst was detected by the RXTE
spacecraft during this I band integration. It seems unlikely that reprocessed
radiation from the burst was sufficient to explain the observed increase. We
suggest that a major part of the I band excess was due to synchrotron emission
triggered by the X-ray burst. Several other significant short duration changes
in V-I were detected. One occurred at about HJD 2453546 in the early phase of
the first secondary outburst and may be due to a mass transfer instability or
to another synchrotron emission event.
