1 Introduction

Compositions of the silicate grains in the coma of comet Hale-Bopp have been derived from the spectral emission signatures in the 10 $\mu$m region by Crovisier et al. (1997), Hayward & Hanner (1997) and Wooden et al. (1999). Hayward et al. (2000) from their thermal infrared imaging and spectroscopy of Comet Hale-Bopp found that the silicate features were up to $15\%$ stronger in the jets and halos compared to regions between the halos. Further, the leading edge of the shells were found by these authors to have higher color temperature and silicate/continuum flux ratio. Variation of the silicate features from central coma to the first two shells has been reported by Galdemard et al. (1997).

In the optical and near IR regions, extensive polarization observations at a range of solar phase angles have been reported by Ganesh et al. (1998), Hadamcik et al. (1997), Hasegawa et al. (1999), Jockers et al. (1997), Jones & Gehrz (2000), Manset & Bastien (1998) and Tanga et al. (1997). Use of the technique of imaging polarimetry by most of these groups yielded valuable information on the spatial variation of polarization. Polarization was found to be high in the anti-sunward direction and in the new shells but rapidly declined in the older shells in the sunward direction. Information on the colour of the grains has been reported by Kiselev & Velichko (1997), Kolokolova et al. (2001) and Bellucci (1998). The full potential of these spatially resolved infrared, colour and polarimetric observational data can be harvested to investigate the porosity p, silicate to organic mass ratio $r_{\rm m}=m_{\rm sil}/m_{\rm org}$ of the grains and their size distributions separately in the coma and the shells. The present work describes a photometric model to map the trajectory of the grains and to compute the theoretical brightness distribution, colour and polarization in the coma and the shells for comparison with these reported observations.