The beam quality and far-field beam profile of broad-area diode laser (BAL) are investigated. In accord with the theory of self-consistency, the wave propagation of the output laser of external cavity BAL is calculated. In Fourier optic methods, the external cavity can be interpreted as a spatial filter in the Fourier plane of the laser diode. The transverse mode can be selected by changing the position of the filter. The relative external cavity BAL experiment is completed, and a single-lobed output beam of the external cavity BAL is achieved. The output laser with divergence angle of 0.074° (full-width of half-maximum (FWHM)) and corresponding M2 factor of 1.16 is obtained when external cavity feedback at I=1.18Ith, which agrees well with the theoretical result.