At the present days, the key and critical part of industrial IC manufacture is the optical lithography technology which can duplicate the design patterns at the mask onto wafer by light exposure.The most direct and accurate simulation is the imaging of patterns on wafer. Accurate imaging simulation can show exposed and unexposed regions after photolithography by computer. We propose an analytical solution for Hopkins formula that we don't need to transfer the mask patterns into frequency domain or convolve them with the kernels. Actually, we can directly compute the image intensity of each single pixel by using integration of power series or polynomials of the kernals.