SAR interferometry has been successfully used to make a topographic map of the surface of the Earth. However, there is uncertainty as to whether the radar returns come from the actual ground surface, or from a higher point such as the canopy of a forest. By investigating the interferometric properties of the polarimetric data, some information can be gained on where the scattering is coming from, as the polarization signatures of the vegetated canopy and the ground are quite different and can be separated using polarimetric data analysis. In the ideal case, information can be obtained on both the height of the surface and on the height of the trees, as well as parameters of the scattering volumes in between .

When two polarimetric images are obtained that satisfy the usual interferometric conditions of baseline and time lapse, the complete polarimetric/interferometric information is stored in three 3x3 complex matrices, the coherency matrix of each image, and the analogous matrix formed from the scattering vector of Image 1 times the scattering vector Image 2 . Cloude and Papathanassiou develop a phase-preserving polarimetric basis transformation that allows them to form interferograms between all possible elliptical polarization states. Then they develop an optimization procedure based on singular value decomposition, which is used to find the polarization of Image 1 and the polarization of Image 2 that maximizes the interferometric coherence between the images. Most likely, the maximum coherence is obtained when the polarization of the two images is the same. The optimization finds polarizations that reduce the effect of baseline and temporal decorrelation, although if the temporal decorrelation is high, the procedure does not help significantly, as the coherence will remain low independent of polarization.

Furthermore, they develop a modified coherent target decomposition method, so that when combined with the coherence optimization procedure, the optimum scattering mechanisms can be found that lead to the best differential phase measurements (i.e. the highest coherence). The interferometric phase difference leads to the height difference between the physical scatterers possessing these mechanisms. The decomposition helps to understand the structure of the canopy of forests, by separating the return that comes from the upper and lower parts of the trees, or from the ground.

Looking at some quantitative aspects of the technology, Papathanassiou and Cloude use a forest model involving a random volume of scatterers situated over a ground scattering model. Their model involves 6 parameters: the vegetation height, the topographic phase at the ground level, the mean volume extinction coefficient (attenuation in dB/m that is related to canopy density) and three ground to volume scattering ratios (at 3 analyzed polarizations). When six measurements of coherence magnitude and angle (at the three polarizations) are obtained, the model can be "inverted", i.e. solved for the model coefficients given the radar observations. This is done using a non-linear optimization procedure, which finds the model parameters that fit the data best in the mean squared sense. The quality of the results and their physical interpretation are monitored by viewing the complex coherence of the interferogram as a function of polarization (which affects mainly the ground to volume scattering ratio). Ideally, the complex coherence forms a straight line in the complex plane as polarization is varied, and the intercept with the unit circle gives the topographic phase angle (i.e. bald-Earth terrain height - see Figure 6 of ). They analyze data from an L-band airborne radar, and find that the rms difference between measured and radar-estimated tree heights to be 2.5 m. They show that longer radar wavelengths give a longer, more accurate coherence line in the complex plane (see Figure 2 in ), and that the use of multi-baselines adds additional information to solve for the model coefficients . In this way, a more accurate estimate of the forest height, canopy density (biomass), stem biomass and ground height may be obtained.

Although the analysis techniques are still being developed, there is some promise that the technology can be used to improve quantitative remote sensing applications such as

- crop monitoring,
- mapping of clear-cut areas, deforestation and burn zones,
- land surface structure for geological analysis, damage assessment and land use,
- hydrology (soil moisture, flood assessment),
- land mine detection , and
- ocean and coastal monitoring (sea ice, oil spills).

A recent snapshot of progress in the field can be found in the five papers on the topic presented at IGARSS in 2002:

- T. Mette, K. P. Papathanassiou, I. Hajnsek and R. Zimmermann,
**Forest Biomass Estimation using Polarimetric SAR Interferometry**, pp. 817-819. - D. Kasilingam, M. Nomula and S. Cloude,
**A Technique for Removing Vegetation Bias from Polarimetric SAR Interferometry**, pp. 1017-1019. - H. Woodhouse, S. Cloude, K. Papathanassiou, J. Hope, J. Suarez, P. Osborne and G. Wright,
**Polarimetric Interferometry in the Glen Affric Project: Results and Conclusions**, pp. 820-822. - S. R. Cloude,
**Robust Parameter Estimation Using Dual Baseline Polarimetric SAR Interferometry**, pp. 838-840. - M. Tabb, T. Flynn and R. Carande,
**An Extended Model for Characterizing Vegetation Canopies Using Polarimetric SAR Interferometry**, pp. 1020-1022.

as well as the January 2003 Frascati Workshop on Applications of SAR Polarimetry and Polarimetric Interferometry .

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