Based on the transmission characteristics of electromagnetic waves in periodic nanomaterial and the optical Abbe sine condition, the optical system that can measure photonic isofrequency curves and band structures is proposed. By using a grating spectrometer equipped with a two-dimensional CCD and an infinite tube length microscope objective that can directly transform the wave vector space into real space, the information of photonic isofrequency curves and band structures are obtained with a snapshot, leading to a simple, rapid and nondestructive detection method. This experimental scheme is applied to measure a two-dimensional periodic nanomaterial which is prepared by using self-assembly technology. By comparing experimental results and theoretical calculation, feasibility and reliability of this system are verified. It indicates an unique advantage in studying the optical property of the periodic nonmaterial.