Compact PolInSAR for vegetation characterisation

Sébastien Angelliaume(1), Pascale Dubois-Fernandez(1), Jean-Claude Souyris(2)

(1) Office National d’Etude et de Recherches Aérospatiales

Département Electromagnétisme et Radar BA701 13661 Salon Air cedex, France

Sebastien.Angelliaume@onera.fr

(2) Centre National d’Etudes Spatiales

DCT/SI/AR 18 Avenue Edouard Belin, 31401 Toulouse cedex 9, France

Abstract—In this paper, we analyse the potential associated with a compact polarimetry (CP) P band spaceborne SAR system. Indeed, this architecture allows polarimetric acquisition without the usual reduction in swath. The CP data is shown to be almost equivalent to the full polarimetric data over extended targets, and the PolInSAR analysis can be performed without a significant loss of performance.

Keywords- compact polarimetry, PolInSAR, RVoG model, ionospheric effect, vegetation characterisation

I. INTRODUCTION The state, the dynamics and the evolution of the terrestrial

biosphere, at every scale, are the least known elements of the global carbon cycle. Among these uncertainties, the vegetation biomass is identified as key information. The proposed Biomass mission, consisting in a P band SAR instrument onboard a satellite is aiming at filling this gap. The low frequency allows a sufficient penetration of the electromagnetic waves in the vegetation to provide a consistent and precise measure of the vegetation dynamics. In the case of a spaceborne instrument at low frequency, several aspects have to be taken into account: the ionospheric effect and the associated Faraday rotation, the relatively smaller antenna size compared to the wavelength and the system overall performance. The system design will rely on compromise and one attractive alternative to the full polarimetry configuration is the compact polarimetry [1][2][3][4] for which only one polarisation is transmitted while two are received.

In this paper, we first briefly review the basics of compact polarimetry and the ionospheric effect, we then present results about the full polarimetric reconstruction and finally a PolInSAR analysis with compact polarimetric data is presented.

II. COMPACT POLARIMETRY SPACEBORNE SAR DESIGN

A. Compact polarimetry The usual polarimetric SAR design architectures are built around the standard linear basis, H and V. On transmission, the radar interleaves pulses with a horizontal (H) and vertical (V) polarisation. Both polarisations are received simultaneously. Full polarimetry has proved its increased potential compared to single channel acquisition in a wide range of applications, and especially for forest parameters

estimation [5]. Thus several spaceborne SAR systems in the near future will have this capability but will operate in the polarimetric mode only punctually. To maintain performance, the imaged swath is usually halved, resulting in a reduced coverage. A very attractive alternative was proposed by JC Souyris in [1] where the system transmits only one polarisation either H+V or circular (right or left circular, RC, LC). He called this mode compact polarimetry (CP). He showed that the polarimetric information is well preserved for natural targets for which some symmetrical properties can be assumed. For these targets, he reconstructed an equivalent to the coherence matrix very similar to the one issued from full polarimetric data (FP). The main advantage to the CP mode is then to access the polarimetric information without reducing coverage and consequently with the same revisit time then a single-polarimetric system. Other papers have also explored the same concepts [2-9].

B. The ionospheric effect Another aspect that must by taken into account in the case

of a P band spaceborne instrument is the ionospheric effect. When an electromagnetic wave travels through the ionosphere, it undergoes a transformation depending on the polarisation state of the electromagnetic wave. It is a simple phase shift when the wave is circularly polarised and this shift has opposite sign for clockwise and counter clockwise circular polarisations. The effect on a linearly polarised wave is a rotation of the polarisation plane. The angle associated with the phase shift or the rotation is called the Faraday angle and depends on the total electron density (TEC) and the electromagnetic wave frequency.

The effect of this Faraday angle on the measured scattering matrix can then be modelled as [10][11]

ΩΩ−ΩΩ

ΩΩ−ΩΩ

=cossinsincos

cossinsincos

VVHVHVHH

M (1)

where Ω is the one-way Faraday rotation. The two matrices associated with the Faraday angle are simply rotation matrices with an Ω angle.

If the transmit wave is linearly polarised, the surface will be illuminated by a linearly polarised wave with an Ω orientation angle. At P band, where the Faraday rotation is easily larger than 90°, the impinging wave associated with a linearly polarised transmitted wave can therefore have any orientation.

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Over the same area, the scattering at two different times characterized by two ionospheric states will therefore access different scattering mechanisms, depending on the Faraday rotation.

On the other hand, if a circularly polarized wave is transmitted, the EM wave impinging on the scattering element will have the same polarisation independently of the Faraday rotation. The scattering mechanisms will be identical.

In order to be invariant with ionosphere in the case of a CP spaceborne SAR system at low frequency, it is necessary to transmit a circular polarization. On the way back through the ionosphere, the scattered wave will also be affected by the Faraday rotation. However, the reception is performed on two orthogonal polarizations, allowing the polarisation synthesis on receive. One can therefore correct the return path rotation readily if the Faraday rotation is known.

III. FP RECONSTRUCTION WITH CP As explain above, the best compromise to implement

polarimetry on space segment is to transmit a circularly polarised wave (e.g. left circular polarization), and on receive two orthogonal linearly polarizations (H and V).

The covariance matrix attached to this configuration is given by

[ ]

==

2212

1211*.JJJJ

kkJ t (2)

[ ]VvHvHvHht SiSSiSk ⋅+⋅+= ;

21 (3)

Using the procedure describe in [5], we can now reconstruct iteratively the full polarimetric scattering matrix:

)8(**2.

)7(2

)6(2

)5(3

1)(

)4(22

**2

122*

222

2

211

2

)(

)(

2211

)(2

)1(222

)1(211

12

)1(2

)(

JiSSS

SJS

SJS

JJS

SJSJ

JiS

HvVvHh

HvVv

HvHh

ivh

ivhi

Hv

i

Hv

i

Hv

i

Hvivh

+=

−=

−=

−

−+=

−

−

+=

−

−

−−

−

−

ρ

ρ

ρ

This full polarimetric reconstruction has been applied on an ONERA/RAMSES P band dataset over the Landes Forest. In Fig 1 we can see the result of this reconstruction compute with only 5 iterations and a 7x7 window. We are able to reconstruct the covariance matrix with a very good accuracy.

(a)

(b)

(c)

Figure 1. CP reconstruction versus FP (dBm2/m2) for the three terms

2HhS (a),

2VvS (b) and

2HvS (c)

IV. COMPACT POLINSAR ANALYSIS This technique cannot be applied to perform the PolInSAR

analysis as we need to reconstruct the actual interferometric phases. The idea behind the PolInSAR analysis is to compute a sub-space of the interferometric coherence, that is the location of the coherence as the orientation and ellipticity of the receive antennas are varied [6].

In the Random Volume Over Ground (RVoG) model [12], the signal backscattered from the forest is modelled as the combination of a ground contribution and a volume only contribution. But, in the Landes forest at P band, the volume only coherence was in general not observed [6]. The inversion then consists in fitting a line through the coherences and computing the intersection of this line with the volume only coherence associated with a given attenuation. This point provides the vegetation height. The key step is therefore to produce this line. In the standard inversion with full polarimetric data, the loci of all interferometric coherences associated with the different polarisation states of the receiving and transmitting antennas is used to obtain this line. This is a four parameter space as the polarisation of the both antennas can be parameterised with the ellipticity and the orientation. In this compact polarimetry mode, the transmit polarisation is fixed resulting in a two parameter space corresponding to the polarisation state of the receiving antenna. Notice that because the reception occurs on two orthogonal polarisation (H and V), any receiving antenna can be synthesized from the data. In the compact PolInSAR inversion, we compute the loci associated

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with all the polarisation state of the receiving antenna. The previous inversion technique is then applied directly

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Measured Height [m]

Estim

ated

Hei

ght [

m]

CPFP

Figure 2. Compact PolInSAR inversion results compared to the full polar

case

Fig 2 presents the inversion results for the CP and the FP case over the Landes forest at P band - where a very accurate ground truth is available. On our dataset and in case of perfectly calibrated data, compact PolInSAR performs as well as full polarimetric interferometry.

The results obtained on compact polarimetry are very encouraging but need to be taken one step further. As explain below, propagation through the ionosphere at P band introduces atmospheric effects and up-to-now, most of the papers dealing with Faraday rotation correction stress the fact that correction cannot be performed on dual-pol data (e.g. H on transmission, H and V on receive).

Assuming a different ionosphere on the two acquisitions to be used in the interferometric processing (one measurement vector not disturbed while the other is perturbed by a given Faraday rotation), we compute the measurement vectors associated with the Compact Polarimetric mode disturbed by the ionosphere and perform the inversion on these vectors.

0,8

0,9

1

1,1

1,2

1,3

1,4

0 5 10 15 20

Variation of ionopheric angle [°]

RM

S he

ight

err

or [m

]

CP

Figure 3. Influence of the one-way Faraday angle on the inversion from compact Polarimetry with different ionosphere on both measurements.

In Fig 3, the inversion results are showing little sensitivity to the ionosphere for a Faraday rotation difference of less than 15°. After 15°, the inversion results are degrading significantly.

The inversion proves to be performing very well at P band with a measured rms height error of 1.2m. Moreover, the ionospheric effect can be neglected when the differential Faraday rotation is less than 15° or when the uncorrected Faraday rotation is less than 15°

V. CONCLUSION We have presented a PolInSAR inversion on P band data

relying on the compact polarimetric reconstruction.

The principle of the compact polarimetry has been explained with the advantages of this architecture: larger swath than a full polarimetric SAR system with the polarimetric information. To produce meaningfull time series with a P band spaceborne system with ionospheric effects, we have shown that the best implementation is to transmit a circularly polarised wave and on receive two orthogonal linearly polarizations.

Finally, inversion results from compact PolInSAR were shown to be comparable to those associated with full polarimetry. The effect of the ionosphere was taken into account and the preliminary assessment is very encouraging with a 15° range of ionosphere or differential ionosphere causing little to no degradation on the inversion. This needs to be tested on other types of forest (including denser forest and forest on sloping terrain), but it could have important impact on the design of a spaceborne mission.

ACKNOWLEDGMENT We want to thank the CNES and ESA for providing part of

the fundings for this work. Our gratitude also goes to the RAMSES team for acquiring and processing the data and to I Champion, INRA for the in situ knowledge

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[3] K. Raney, “Dual-Polarized SAR and Stokes Parameters,” IEEE Geoscience and Remote Sensing Letters, vol. 3, pp. 317-319, 2006.

[4] N. Stacy, M. Preiss, “Compact polarimetric analysis of X band SAR data”, in. Proc. EUSAR'06, Dresden, Germany, May 2006

[5] T. Le Toan, A. Beaudoin, J. Riom and D. Guyon, “Relating forest biomass to SAR data”, IEEE Trans. Geosci. Remote Sens., vol. 30, no. 2, Mar. 1992.

[6] P. Dubois-Fernandez., S. Angelliaume, JC Souyris, F. Garestier, I. Champion“, The specificity of P band PolInSAR data over vegetation”, POLINSAR07, http:/earth.esa.int/workshops/polinsar2007

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[8] T. Ainsworth et al., “Analysis of Compact polarimetry Imaging Modes” Proc. of POLINSAR07, http:/earth.esa.int/workshops/polinsar2007.

[9] K Raney, “Decomposition of Hybrid-Polarity SAR data”, Proceedings of POLINSAR07, http:/earth.esa.int/workshops/polinsar2007

[10] A. Freeman and S. Saatchi, “On the detection of Faraday Rotation in linearly polarized L-Band SAR backscatter signatures”, IEEE Trans. Geosci. Remote Sens, vol 42, n°8, August 2004 DOI10.1109/TGRS.2004.830163

[11] P. Wright, S. Quegan, N. Wheadon and C. David Hall, “Faraday rotation effects on L-Band spaceborne SAR data” , IEEE Trans. Geosci. Remote Sens., vol 41, n°12 Dec. 2003 DOI10.1109/TGRS.2003.815399

[12] S.R. Cloude and K.P. Papathanassiou, “A three stage inversion process for polarimetric SAR interferometry”, IEE proceedings, Radar, sonar and Navigation, Vol. 150, Issue 03, June 2003, pp 125-134.

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