We propose to simulate holograms with the vectorial Rayleigh-Sommerfeld diffraction integral. This new approach is compared with a classical Fresnel diffraction integral, and that is done through the comparison of the kernels. We define the limit where the Fresnel approximation fails to simulate holograms. We show that the vectorial Rayleigh-Sommerfeld diffraction integral is well adapted to simulate holograms in extremely near field conditions. This is particularly interesting when dealing with very small particles.