1. A method for determining an image of a patterned object formed by a polychromatic lithographic projection system, the projection system having a radiation source of a finite spectral bandwidth for illuminating the patterned object and a lens for imaging the patterned object to a planar image space including an image plane within a resist layer, the method comprising: providing patterns for the object; providing a spectrum of the radiation source to be used in the lithographic projection system; providing an intensity and polarization distribution of the radiation source; providing a lens impulse response in a spatial domain or in a spatial frequency domain of the image; forming a polychromatic 4D bilinear vector kernel comprising a partially coherent polychromatic joint response between pairs of points in the spatial domain or in the spatial frequency domain, the polychromatic 4D bilinear vector kernel translating a scalar quantity of mask transmission into a scalar quantity of exposure dose; determining dominant polychromatic 2D kernels of the polychromatic 4D bilinear vector kernel; and determining the image of the patterned object by providing the intensity of the image to be projected at each desired point across the spectrum of the radiation source from convolutions of the object patterns with the dominant polychromatic 2D kernels.