Method for producing a polarizing optical element by applying a multilayer structure onto a pseudospherical surface of a base optical element, the structure comprising an orienting first layer and a polarizing second layer itself comprising liquid crystal polymers and at least one dichroic dye, said dichroic dye having an angular orientation determined by the first layer, the method comprising the following steps: (a) producing the multilayer structure on a temporary support, said step (a) comprising the following substeps: forming, on said temporary support, a first layer based on photoorientable polymers having photoreactive groups; curing said first layer under a first linearly polarized ultraviolet radiation, so as to produce a polymer network that is photooriented along a direction imposed by the polarization direction of said first ultraviolet radiation; forming, on said first layer, a second layer comprising a mixture of dichroic dyes with at least one crosslinkable liquid crystal monomer, these being angularly oriented by the first layer; and at least partly curing the liquid crystal monomers of the second layer, so as to fix the dichroic dyes in the angular orientation determined by the first layer, while using a dose of a second ultraviolet radiation adjusted so that said second layer is undercured and has a glass transition temperature less than or equal to a room temperature which may vary by plus or minus 5°C; (b) removing the multilayer structure from the temporary support, so as to obtain the structure in the form of a self-supported membrane; and (c) applying the multilayer structure onto the pseudospherical surface of the base optical element. (a) producing the multilayer structure on a temporary support, said step (a) comprising the following substeps: forming, on said temporary support, a first layer based on photoorientable polymers having photoreactive groups; curing said first layer under a first linearly polarized ultraviolet radiation, so as to produce a polymer network that is photooriented along a direction imposed by the polarization direction of said first ultraviolet radiation; forming, on said first layer, a second layer comprising a mixture of dichroic dyes with at least one crosslinkable liquid crystal monomer, these being angularly oriented by the first layer; and at least partly curing the liquid crystal monomers of the second layer, so as to fix the dichroic dyes in the angular orientation determined by the first layer, while using a dose of a second ultraviolet radiation adjusted so that said second layer is undercured and has a glass transition temperature less than or equal to a room temperature which may vary by plus or minus 5°C; forming, on said temporary support, a first layer based on photoorientable polymers having photoreactive groups; curing said first layer under a first linearly polarized ultraviolet radiation, so as to produce a polymer network that is photooriented along a direction imposed by the polarization direction of said first ultraviolet radiation; forming, on said first layer, a second layer comprising a mixture of dichroic dyes with at least one crosslinkable liquid crystal monomer, these being angularly oriented by the first layer; and at least partly curing the liquid crystal monomers of the second layer, so as to fix the dichroic dyes in the angular orientation determined by the first layer, while using a dose of a second ultraviolet radiation adjusted so that said second layer is undercured and has a glass transition temperature less than or equal to a room temperature which may vary by plus or minus 5°C; (b) removing the multilayer structure from the temporary support, so as to obtain the structure in the form of a self-supported membrane; and (c) applying the multilayer structure onto the pseudospherical surface of the base optical element.