Background: the principle of SAR

PHARUS is a side-looking imaging radar on a moving platform (aircraft, satellite, etc.). The characteristic feature of Synthetic Aperture Radar (SAR) is the high resolution in the direction of motion, obtained by aperture synthesis. The result is an image, consisting of pixels, resembling an aerial photograph. SAR is in the category of coherent pulse radars, i.e., it transmits pulses (as opposed to a continuous wave), and measures both amplitude and phase of the received echo signal.
The radar illuminates with its antenna beam a patch on the ground, to the side of the platform. By the motion of the platform, an illuminated continuous strip is formed, called the swath, see Image. After processing, the strip is resolved into resolution cells, one of which is depicted in the image. 
After SAR processing, a SAR image consists of an array of pixels, where each pixel value is a measure of the radar reflectivity of the corresponding area, i.e., a resolution cell, on the ground. The image is therefore basically a reflectivity map. The measured value in each pixel is commonly referred to as the backscattering coefficient. For display purposes, it is common practice to display this map using a black and white intensity coding: dark for low backscatter, bright for high back-scatter. This greyscale map constitutes the ‘image’.

To achieve high resolution in the range direction, a short pulse is required. Instead of transmitting a very short pulse with very high peak power, a long time coded pulse with lower peak power, but equal energy is transmitted. The modulation allows compression of the received pulse, thus gathering the total pulse energy into a short pulse. This process is referred to as pulse compression or range compression. The most widely used form of coding is linear frequency modulation (chirp).
To achieve high resolution in the cross-range, or azimuth direction, a very narrow antenna beam would be needed, requiring a very large antenna aperture. The principle of SAR is to extend the small physical antenna aperture to a many times larger ‘synthetic aperture’ by coherent integration of echoes received over a certain distance travelled by the moving platform. In the case of PHARUS, for instance, the real antenna is 1 meter long, while the synthetic aperture may be several hundred metres long.

SAR principle schematic
SAR principle schematic

Coherent integration is mathematically analogous to pulse compression and is called azimuth compression. This equivalence can be understood by considering that the frequency modulation in the transmitted pulse is similar to the Doppler frequency modulation induced by the motion of the platform. Hence, the Doppler modulation that exists in a series of received pulses, due to motion, is used in a way similar to the frequency modulation within a pulse, which is intentionally generated by the radar.
A characteristic feature of SAR is that azimuth resolution is independent of range. In radars that do not employ the synthetic aperture principle (therefore sometimes called real aperture radars), cross-range resolution is determined by the antenna beam width and is, therefore, an angular resolution. The resulting geometric resolution gets worse as the distance increases. In SAR, the larger antenna footprint at longer range allows longer observation of an object (longer synthetic aperture), so that the resulting geometric resolution remains the same in the end. In practice, the range is limited by the amount of transmitting power available. Another basic property of coherent imaging radars, such as SAR, is the phenomenon of ‘speckle’. This is a type of noisiness that can be reduced by an averaging technique called multi-looking.

Principle of polarimetry

Early SAR systems used one single polarisation antenna for transmitting pulses and receiving their echoes. These were therefore called non-polarimetric systems. For instance, if the antenna was linearly horizontally polarised, the system was an HH polarised system, that is, it used horizontal polarisation for both transmission and reception. Analyses of the SAR images always left questions unanswered like, what would the image have been if another system had been used, for example, a VV, or an HV, or a differently polarised system? Is the polarisation used optimally for the application? These questions are answered completely by the use of polarimetric systems. The subject of polarimetry is the interpretation of polarimetric data.
The basic use of a polarimetric image is the synthesis of images with arbitrary transmit and receive polarisations. From the scattering matrix map, images can be created representing arbitrary transmit and receive polarisations, even arbitrary elliptical ones. The following advantages of polarimetry have been demonstrated:

  • contrasts between targets and backgrounds can be maximised by choosing the correct transmit and receive polarisations,
  • the accuracy of crop type and land-use classification results increases,
  • the estimation accuracy of soil and vegetation parameters (like forest biomass) increases.

In a non-polarimetric SAR image, the reflectivity of a single resolution cell is measured as a single number, the backscattering coefficient (usually HH or VV), which can be displayed using intensity coding (black and white). In a fully polarimetric SAR image, such as generated by PHARUS, four polarisation combinations of the backscatter coefficients are displayed, e.g. by using both intensity and colour coding. Furthermore, using these four polarisation channels, any other polarisation can be generated, e.g. for reasons of calibration or contrast optimisation.
The polarimetric generalisation of the backscattering coefficient is called the scattering matrix S. The matrix consists of four complex numbers, representing the complex backscattering coefficients for all four polarisation combinations, HH, HV, VH and VV.

Polarimetric scattering matrix
Polarimetric scattering matrix

PHARUS is capable of measuring the full scattering matrix rather than the backscatter coefficient for one polarisation setting only. It is measured as follows. The PHARUS polarimetric SAR in full polarisation mode uses a single phased array antenna which can be electronically switched between horizontal and vertical polarisation. In full polarimetric mode, it first transmits a horizontally polarised pulse and then records the horizontally and vertically received echoes (both amplitude and phase) simultaneously, using two receive channels. The generated complex numbers correspond to Shh and Svh, respectively. It then repeats this step for a vertically polarised transmitted pulse; both polarisations are interleaved on Transmit. This completes the 2 x 2 matrix.

Since the scattering matrix contains many independent variables, there are many ways in which a polarimetric image could be displayed. One way of doing this is to assign colours to the matrix elements, and thus create a colour image. However, it is not possible to convey all information contained in the scattering matrices in a single colour image.
The polarimetric analogue of multi-looking (for speckle reduction) is not performed by averaging scattering matrices, because the information would be lost by simply adding these complex matrices. An intermediate processing step is necessary: the conversion of the scattering matrices to 4´4 real symmetric Stokes matrices. These are subsequently averaged. The Stokes matrix consists of real numbers only, but still contains the information of the complex scattering matrix, even redundantly. When Stokes matrices are have been averaged, a transformation back to scattering matrices is generally not possible.