Polarimetric Holo-SAR

Spaceborne SAR and airborne SAR move along a straight pass to obtain a 2D SAR image. There are various flight configurations for SAR as shown in Figure 10.34. If the flight path and trajectory become circular, it is called a circular-SAR (C-SAR). C-SAR observes a target from 360° view angles. Therefore, the target structure can be reconstructed using the angular data. If this C-SAR observation is repeated at different heights along the vertical direction, it is called Holo-SAR. Then the Holo-SAR can provide a 3D image viewed from 360° angles.

If polarimetric measurement is applied to Holo-SAR, the system becomes polarimetric Holo- SAR. In order to check the 3D polarimetric imaging capability, we conducted the following experiments in an anechoic chamber.

Experimental setup for polarimetric Holo-SAR

FIGURE 10.35 Experimental setup for polarimetric Holo-SAR.

The first one is a mixture of concrete blocks as shown in Figure 10.35. The blocks are modeled as a normal building, collapsed building by an earthquake, and inclined buildings at 0, 10, 20, and 30° from the vertical direction. These blocks are imaged by a network analyzer-based polarimetric radar system on a turntable in the anechoic chamber. A C-SAR measurement was repeated 50 times to scan a total length of 1 m along the vertical direction in 2-cm increments.

After the Holo-SAR signal processing, polarimetric scattering decomposition is applied to the 3D data sets. The final images are shown in Figure 10.36. RGB color-coding is used to display the scattering mechanisms. Red (double-bounce scattering) is strong around z = 0 where the metallic ground plane and vertical concrete wall form right-angle structures. On the top of the normal building, the color exhibits green (volume scattering), which comes from concrete surface. This situation is the same as the scattering of an oblique flat surface, which induces the cross-polarized component, yielding the volume-scattering power. On the other hand, blue (surface scattering) is significant if the oblique angle of the surface is more than 20°. This situation happens in the collapsed building scenario. These angular characteristics are well detected on the rooftop of inclined buildings in Figure 10.36b. For small oblique angles less than 10°, the main scattering power is Pv (green). As the oblique angle becomes larger than 10°, the scattering tends to exhibit Ps (blue). The difference in the scattering mechanism in the vertical direction is well detected in the side-view image as shown in Figure 10.36c.

The second example is conifer and broad-leaf trees. Two trees were measured in the same way. Not only a concrete-metal object but also vegetation can be reconstructed as shown in Figure 10.37. It is seen that conifer tree produces the cross-polarized HV component more compared to the broad-leaf tree. This causes the volume scattering (green) to be dominant for the conifer tree. On the other hand, the surface scattering (blue) is rather significant in the broad-leaf tree. The decomposition powers are retrieved from rectangular boxes in the side-view image of Figure 10.37, and the power ratio is listed in Table 10.3. These values are typical for these tree species at Ku- and X-band [19,20].

Polarimetric decomposition image of Holo-SAR (concrete)

FIGURE 10.36 Polarimetric decomposition image of Holo-SAR (concrete): (a) 3D view of decomposition image, (b) top view, and (c) side view.

TABLE 10.3

Decomposition Power Ratio (%) of Conifer and Broad-Leaf Tree

Ps

Pd

P>

Pc

Conifer

22.5

5.4

71.8

0.3

Broad leaf

48.3

4.9

44.7

2.1

Therefore, we can confirm polarimetric Holo-SAR is capable of retrieving a 3D scattering mechanism of an object from all circumference directions.

Summary

In this chapter, synthetic aperture processing is explained with illustrations. The range resolution is determined by the bandwidth of the transmitting signal. This point holds to pulse, step frequency, and FMCW radar systems. Since the frequency allocation to spaceborne radar is decided (Table 10.1), high resolution less than 1 m on the ground can be achieved only above S-band.

In SAR processing, Fourier transform is frequently used to generate high-resolution 2D images, not only in the range compression but also in the azimuth direction as well as for range migration processing. Since PolSAR is considered a multiple of single-polarization SAR, it requires computation four times more, in addition to polarimetric calibration. After obtaining a scattering matrix, some application examples are shown: decomposition, target angle estimation, equivalent STC for FMCW radar and its GPR application, 3D imaging of buried objects in snowpack with polarization state filtering, real-time polarimetric FMCW radar, and polarimetric Holo-SAR imaging viewed from 360°. All of the polarimetric results are satisfactory and promising.

Appendix

A 10.1: WINDOW FUNCTIONS

A window function is defined as a mathematical function that is nonzero-valued inside of a chosen interval, normally symmetric around the middle of the interval, and usually tapering away from the middle. Mathematically, when another function is multiplied by a window function, the product is also nonzero inside the interval. The simplest form of a window function is a gate function, which has a unit magnitude inside the interval (-T/2/2) and zero-valued outside. Figure AlO.l shows the gate function in the time domain and its Fourier transform in the frequency domain. If the time interval is taken small, the frequency response spreads, and the frequency characteristics of the system become important to preserve the signal.

When the Fourier transform is performed, we use a window function. In the actual signal processing, we only have signals of finite length. In order to suppress unwanted frequency responses, an appropriate window function for finite time interval should be selected.

There are several kinds of window functions. Each window' has special characteristics. For example, a rectangular window (gate function) yields a Sine function after the Fourier transform. The width of the main lobe is the smallest among other functions. This sharp beam is suitable for making a fine resolution images. The width of the main lobe is also called half-power width. The first side-lobe peak is -13 dB, which is a rather big value. If this value is larger than the echo of other targets, this side lobe masks the main beam of other desired targets. For example, the echo from the land area is big compared to those from the sea surface in radar sensing, and the side-lobe image of land sometimes appears on the sea surface. In order to overcome this undesired situation, various window' functions are devised to suppress the side-lobe level. Representative window functions are listed in Table A10.1. The side-lobe levels are suppressed by these functions; however, the main lobe w'idth increases instead.

If we would like to reduce side-lobe levels, then the main beam increases, and vice versa. This trade-off is caused by the property of the Fourier transform. Since the ultimate main lobe width is c/2B in radar, the window function provides us the choice of side-lobe level reduction at the sacrifice of the resolution. The window function modifies the amplitude of the data but does not affect phase information of the data in signal processing.

The main lobe width corresponds to the resolution. A rectangular window or gate function has the sharpest resolution. We take it as the basis and compare other window resolutions w'ith respect to the basis. According to Table A 10.1, the width becomes two times for Hanning and Hamming window's and more for Kaiser windows. The Hamming window is preferred because the Hamming w'indow has a lower side-lobe level compared to the Hanning window, although they have the same main lobe width. By adjusting the parameter p, the Kaiser window [12] can be adjusted to any resolution.

• Kaiser window

where I0 (•) is the modified Bessel function and x is a normalized variable.

It is easy to adjust the trade-off relation by changing parameter p in the Kaiser window. Figure A 10.2 show's the Kaiser window' as a function of p. p = 0 makes the Kaiser window' to the gate function, p = 2.5 has the side-lobe level as -20 dB, although resolution w'idth increases 20%. This is

TABLE A10.1

Representative Window Function

Window Function

Equation

First Side-Lobe Level

Main Lobe Width

Rectangular

-13

1

Hanning

-32

2

Hamming

-41

2

Kaiser

A10.2 Kaiser window

FIGURE A10.2 Kaiser window.

frequently used in SAR processing, [i = 5 has side-lobe level as low as 37 dB, but the main lobe width increases 50%. [i = 2n derives -46 dB side-lobe level.

A 10.2: RANGE MIGRATION PROCESSING

Suppose we measure a point target by radar as shown in Figure 10.15. The antenna scans over a target. The range-compressed trajectory becomes curved one as shown in the upper left side of Figure A10.3. The image axes consist of the azimuth direction and the range direction. This curve is caused by the distance between the antenna and the point target.

If we apply the Fourier transform to this curved trajectory image without range migration, then the right-hand side image comes out. Since the Fourier transform is carried out horizontally line by line, the transformed image does not show focusing at all but rather blurring the surroundings of the target. This degradation comes from the data arrangement in the compressed image. In order to arrange data in a straight line, range migration processing is needed.

The range migration arranges data from a curved one to a straight one as shown in Figure A 10.3. After the range migration, the Fourier transform yields the focused image of the point target (PSF) as shown in the figure.

There are several methods proposed in range migration. Here, a simple method of using the Fourier transform is explained. Fourier transform has the following phase-shift property:

Equation (A10.2.2) shows that if the position t moves by a, the phase shift in the frequency domain becomes eia“. If we can know the position shift a, then the corresponding phase shift will serve to rearrange the data location.

In the range-compressed image, we have a Sine function. We would like to arrange the data location change as

Moving the space variable ——— is equivalent to the phase shift of exp J jin ————i.

AR I AR M I

We first execute the Fourier transform of the data in the range direction. Then after multiplying the phase shift to the frequency domain data, the frequency data is again inversely Fourier transformed. This procedure is repeated along the azimuth direction. Then the compressed peak aligns in the horizontal line at z = Zo- In this way, the phase-shift property can be used for range migration.

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