Sub-diffraction-limit realization and micro-displacement measurements via complex Gaussian-correlated beam

•A special correlated partially coherent beam, the complex Gaussian-correlated (CGC) beam, is used to realize sub-diffraction-limit.•The minimum resolution distance of four symmetrical pinholes can achieve at least 0.05 times the classical Rayleigh limit by using the CGC beam.•Not only realize sub-diffraction-limit, this approach can also be used in sub-Rayleigh displacement measurements.