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On March 31 and April 1, 1997, simultaneous photometry and polarimetry of comet Hale–Bopp's dust was conducted with the two-channel focal reducer of the Max-Planck-Institute for Aeronomy attached to the 2 m telescope of Pik Terskol Observatory (Northern Caucasus)). Interference filters at 642 nm and 443 nm selected red and blue narrow-band continuum windows. The observations have been averaged over the one hour of time the comet could be observed. The polarization maps cover an area of about 1 arcmin2around the nucleus. The values of polarization degree measured close to the nucleus agree very well with observations obtained with aperture polarimetry. They are lower than in the surrounding coma by about 1%. In our field of view the polarization increases along the sun-comet line from the solar to the antisolar side by about 3%. The dust shells are visible in the polarization images. The polarization in the shells is higher by 1 to 2% and this increase is higher in the red than in the blue range. Therefore the ratio of red to blue polarization (≈ 1.2)) increases in the shells by ≈ 0.03. In principle, the polarization excess in the shells, the ratio of red/blue polarization and the higher integrated polarization as compared to other comets can be explained by an excess of particles of radius of about 0.1 μm. Such particles, however, are subject to strong radiation pressure and will be pushed back into the tail before they reach the observed location of the shells. Real Rayleigh particles cannot explain the observed increase in the ratio of red/blue polarization. One therefore cannot exclude the possibility that the excess polarization in the shells is caused by fluffy aggregates via effects which are presently not well understood. The colour map shows features not well related to intensity and polarization, perhaps another dust shell of a different particle size.