The working process of aperture Scanning Near-Field Optical Microscopy (a-SNOM) under the illumination mode is simulated by using the finite element method of electromagnetic field. With changing the length and nanogap size of the optical resonant dipole antenna, the scanning curves of the radiative emission rate as a function of the central coordinate of the a-SNOM probe end surface are calculated. A superresolving measurement of the metallic nano-gap of the antenna beyond the aperture size of the a-SNOM probe is realized. For the a-SNOM probe with an aperture size of 100 nm, the smallest size of the antenna nanogap that can be resolved is 10 nm (0.016 times of the wavelength). By comparing the calculated results of the measured radiative emission rate of the a-SNOM probe for the metal and the dielectric dipole antennas, it is shown that the realization of the superresolving measurement of the metallic nanogap is due to the excitation of the gap surface plasmon polariton.