Frequency identification is the prerequisite for eliminating or reducing ripple wave error in ultra precision diamond fly cutting on KDP crystals. To address this problem, a method for the identification of the ripple waves error of diamond fly cutting trajectory based on spatial frequency transformation was proposed. The method calculated the spatial frequencies of ripple wave error according to the fly cutting profile of the arc-shaped trajectories. Then, the accurate separation of the characteristic frequencies was realized when the frequencies were transformed in time . The contrast between the characteristic frequencies of wave error with the cutting vibration frequencies and the natural frequencies of air spindle showed that the self-excited vibration at the natural frequencies of air spindle under intermittent cutting forces and the forced vibration from the motor was the primary reasons for ripple wave erro. Base on the above conclusion, by optimizing the structure and drive of the air spindle, the RMS value at PSD1 band (2.5~33 mm) of KDP crystal fly cutting surface reduced from 53nm to 12nm.