Based on the impulse response model of a point target of a side - looking SAR and by using the Tree-step method with directly processing the original echoes in their corresponding time - domain and frequency - domain, detail analysis and induction of the Fourier transform of azimuth in chirp - scaling algorithm are described with the finding of error source of the algorithm and with the providing of the expansion technique of the Tailor series. The paper has a significant effect on the steps analyzed next.