# Key Technique in Airborne SAR Mechanic Scanning Mode

## Mechanic Scanning Mode and the Principle of DBS

In the mechanic scanning mode, in the existence of the antenna scanning, a target in the observation area has a shorter observation time compared with the stripmap SAR mode. Therefore, the resolution of the mechanic scanning mode is lower than that of the stripmap SAR mode, and the imaging geometry is different [2].

The geometry of mechanic scanning system is illustrated in Fig. 4.1. The aircraft flies at velocity V_{a} along axis x. The angle between beam center and axis y is в. The 3-dB azimuth beam-width is denoted as Дв. The antenna is scanning along azimuth direction at constant speed в. The nearest slant range from O to the ground is R_{0}, and the instantaneous slant range from O to B is denoted as *R(t _{a}).*

The Doppler centroid along the LOS can be expressed as

**Fig. 4.1 ****Geometry of a mechanic scanning system**

The Doppler bandwidth *Dfd* (h) can be expressed as

According to Eq. 4.2.2, the Doppler bandwidth is linearly correlated to the beam-width. The principle of DBS technique is: since targets from different azimuth cells have different Doppler frequency, the division of azimuth spectrum can be regarded as the division of azimuth beam. Therefore, the azimuth angle resolution can be improved by operating narrowband filtering of azimuth frequency band. In practice, narrowband filter can be achieved by Fourier transform.

An important parameter in DBS imaging is Sharpening ratio. Sharpening ratio N represents the ratio of bandwidth to sub-bandwidth, which determines the azimuth resolution. Sharpening ratio N can be defined as

where *Sf _{d}* and

*SO*denote Doppler resolution and beam resolution, respectively.

*Sf*can be defined as

_{d }

where *T _{a}* is azimuth synthetic time, M is the number of coherent pulses [3]. Substituting Eq. 4.2.2 and Eq. 4.2.4 into Eq. 4.2.3, it yields

In practice, the narrowband filter of a traditional DBS algorithm can be achieved by Fourier transform. Therefore, the DBS algorithm is highly simple and suited for real-time processing. The processing steps of the traditional DBS algorithm are illustrated in Fig. 4.2. After imaging each frame by DBS, operations such as non-coherent integration, coordinate transformation, and image stitching are also required [4]. However, these steps are not relevant to the imaging quality of each frame, so these are not discussed in this chapter.

In Fig. 4.1, *R(t _{a})* can be expressed as

After Taylor expansion, R(t_{a}) can be approximated as

where Ф(t^) is the quadratic azimuth phase and can be neglected in mechanic scanning system.

The echo of a point target in mechanic scanning system can be expressed as

where *P _{0}* represents backscattering coefficient, X denotes wavelength, K

_{r}stands for frequency modulation rate, c is light speed, t

_{a}and t

_{r}denote azimuth and range time, respectively.

Substitute Eq. 4.2.7 into Eq. 4.2.8, and transform Eq. 4.2.8 into range-frequency domain, then it can be rewritten as

The last term of Eq. 4.2.9 is the RCM, and must be corrected during DBS imaging.

**Fig. 4.2 ****Flowchart of the traditional DBS algorithm**