In this paper we propose a new method of the measurement of the Doppler frequency shift due to the moving grating inside a BaTiO3 crystal when a self- pumped phase conjugate mirror is coupled to a ring dye laser. The experimental results show that the Doppler frequency shift is less than 0.2 Hz. Furtheremore, the analysis indicates that the Doppler frequency shift cannot be Used to explain the wavelength self-scanning initially towards the longer wavelength.