Remote sensing and imaging of the surface is possible by using different parts of the electromagnetic spectrum. Using microwave in Synthetic Aperture Radar (SAR) has many benefits such as the ability to work in all weather conditions, take advantage of the day and night and to obtain high-resolution images even at high ranges. These advantages have led to many civilian and military applications for this radar. In synthetic aperture radar, the received signals, which are called raw data, can be considered as a two-dimensional function of the range and azimuth. In this data, the energy of a point target is distributed in both direction and so the information can not be extracted without a proper processing. Therefore, it needs to be processed by a focusing algorithm which is called image formation algorithm. Image formation algorithms can be divided into two categories: time domain and frequency domain algorithms. Frequency domain algorithms are efficient in terms of computational and are very useful. So, in this thesis we have investigated these kinds of image formation algorithms. It should be noted that if the radar is monostatic and the platform is an aircraft, atmospheric turbulence and aircraft maneuvers prevent to have direct movement. The distance from the plane to the earth’s surface(range) is changed due to the plane momentum deviation and so the image formation algorithms can not properly get the focused image. The compensation of these destructive effects is called motion compensation. The most common method of compensation is a two-stage method. The first stage is before range cell migration that is done at the beginning of the algorithm.The second stage will take place immediately after range cell migration. In this way, the obtained measurement error of the system is used for compensation, and the impact of the various parts of algorithms on the fault motion is not considered. In this thesis, a linear approximated model is considered for error and it is applied to range compression stage in RDA algorithm. It is shown that the added phase in the second stage of compensation algorithm is slightly changed. It is shown that the proposed method has better performance compared with the case of two-stage conventional method. Keywords: Synthetic Aperature Radar, Image forming, motion error, motion compensation
