In order to explore the physics essence of the imaging principle of the ultrasonic standing waves in Raman-Nath diffraction and clarify the confusion of the theory, a new method based on Fourier optics is proposed. The optical field of a laser beam vertically passing through the ultrasonic standing waves in Raman-Nath diffraction is analyzed via this method, which contains a series of incoherent light with different frequencies. The intensity distribution of this field is obtained by linear superposition of incoherent light of different frequencies after calculating the individual interference light intensity distribution. This expression proves the correctness of an existing acoustic velocity measuring method that has not been testified. The simplification of this expression according to actual conditions in the experiment is also accomplished and it is proved experimentally.