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(11.4.16)
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The reference signal Eo is chosen to be a constant. As shown in (11.4.3)~ (11.4.4), (11.4.16) has well defined peaks when f o approaches the location of the scatterers. To have a fair comparison with ACF imaging which is proportional to the square of the signal, we also take the absolute valued square of (11.4.16). That is C2P(f o )
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(11.4.17)
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The result of (11.4.16)~(11.4.17) is known as field imaging. Next we calculate ACF imaging. The ACF imaging is to correlate two signals received at different angles and to sum over frequency and angles. From (11.4.12),
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Note that the integrand in (11.4.10) is the angular correlation function. The memory effect of random scattering is avoided by n2 oF nl. In practical simulations, we let Inl-n21 > No instead of just n2 oF nl in (11.4.18) so that the angular difference d = I nl - n21 is larger than the correlation angle of the angular correlation function. The choice of No depends on the correlation angle of random scattering. The correlation angle of random scattering is usually small, which is in the order of AIL where L is the size of the medium. By having In2 - nIl> No, only a small portion of information is removed for the target. Therefore, target information is essentially preserved in (11.4.18) while the clutter due to random scattering is significantly suppressed.
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4.3 Simulations of SAR Data and ACF Processing
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In the numerical simulations, 80,000 small particles with radius of a = 0.04>'0 are used to model clutter. They are randomly distributed in a layer region of 40>'0 x 40>'0 x 0.5>'0. Four target spheres with radius of a = 0.3>'0 are placed at positions of (10,14,0)>'0' (10,28,0)>'0' (30,10,0)>'0' and (30,32,0)>'0. The dielectric constant of both the targets and the small particles are (3.23+iO.36). All distances are in terms of the wavelength >'0 of the center frequency. The circular path of the receiver has a radius of R o = 1732>'0 at height of H = 1000>'0. The backscattering amplitudes for targets and particles are calculated based on Mie scattering. The received signal is calculated by Eq. (11.4.14). The frequency band is from 0.5fo to 1.5fo with an increment of O.Olfo. Thus Nk = 100, k l = 0.5fo, k 2 = 0.51fo, ... , etc. The azimuth angle is from 0 to 360 at an interval of 3.6 degrees. Thus N = 100, (PI = 0 , rP2 = 3.6 , rP3 = 7.2 , etc. The simulated data is processed by field imaging and ACF imaging. The results are normalized by the maximum of the target. The normalized results are shown in Fig. 11.4.2 and 11.4.3. Figure 11.4.2 shows the results of the square of (11.4.16), i.e., the results of (11.4.17) of field imaging. The 4 targets are spread out to a two wavelength size and are obscured by the background clutter. Figure 11.4.3 shows the results of ACF imaging. We see that the spot size of targets is smaller, which is a result of finer resolution. The background clutter is significantly suppressed. We use the condition of Inl - n21 > 5, i.e., No = 5, to ensure that the angular pairs rPnl and rPn2 are away from the memory dot. The better performance of ACF imaging is due to (1) the clutter effect is minimized by avoiding the memory effect of random scattering and (2) the spreading due to the frequency dependence of scattering is compensated by the cross-range resolution in ACF imaging. The angular correlation function with focusing (ACF focusing) is also shown in Fig. 11.4.4. The ACF focusing Cdfo, rPd) is obtained by using Eq. (11.4.18) with the summation over I::~ =l replaced by n2 = nl + nd, as given by
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