Polarimetric microscope comprising a hollow-cone and point-focusing illumination optical device comprising illumination means comprising: - a point light source, said illumination means being able to generate a collimated incident light beam, - an optical objective having an optical axis (8, 8') and an image focal plane, the optical objective being arranged so as to receive a cylindrical incident light beam and to form an image of the source at one point in the image focal point, - an optical system comprising a first conical lens and a second conical lens, said optical system being arranged on the optical path of the incident light beam between the illumination means and the optical objective, - the first conical lens being arranged so as to receive said collimated incident light beam and to form a hollow-cone light beam having, in a plane transverse to the beam axis, a light distribution comprising a dark central part and a bright ring part, - the second conical lens being arranged so as to receive said first hollow-cone light beam (20, 40) from the first conical lens and to form a black-background cylindrical light beam having, in a plane transverse to the beam axis, a light distribution comprising a dark central part and a bright ring part, and - the optical objective being arranged so as to receive said black-background cylindrical light beam from the second conical lens, to form a hollow-cone light beam and to focus said hollow-cone light beam at one point of micrometric size in the image focal plane, and further comprising a polarisation state generator (13, 14) and a Cartesian-Cylindrical polarisation converter arranged on the path of the illumination beam between the second conical lens and the objective, so that the hollow-cone incident light beam is polarized with a cylindrical polarisation distribution around the optical axis and means (7, 7') for collecting a beam scattered, reflected or transmitted by a sample. - a point light source, said illumination means being able to generate a collimated incident light beam, - an optical objective having an optical axis (8, 8') and an image focal plane, the optical objective being arranged so as to receive a cylindrical incident light beam and to form an image of the source at one point in the image focal point, - an optical system comprising a first conical lens and a second conical lens, said optical system being arranged on the optical path of the incident light beam between the illumination means and the optical objective, - the first conical lens being arranged so as to receive said collimated incident light beam and to form a hollow-cone light beam having, in a plane transverse to the beam axis, a light distribution comprising a dark central part and a bright ring part, - the second conical lens being arranged so as to receive said first hollow-cone light beam (20, 40) from the first conical lens and to form a black-background cylindrical light beam having, in a plane transverse to the beam axis, a light distribution comprising a dark central part and a bright ring part, and - the optical objective being arranged so as to receive said black-background cylindrical light beam from the second conical lens, to form a hollow-cone light beam and to focus said hollow-cone light beam at one point of micrometric size in the image focal plane, and further comprising a polarisation state generator (13, 14) and a Cartesian-Cylindrical polarisation converter arranged on the path of the illumination beam between the second conical lens and the objective, so that the hollow-cone incident light beam is polarized with a cylindrical polarisation distribution around the optical axis and