*Communication* **Calibration and Validation of Polarimetric ALOS2-PALSAR2**

**Ridha Touzi 1,\*, Masanobu Shimada 2,3 and Takeshi Motohka <sup>3</sup>**


**Abstract:** PALSAR2 polarimetric distortion matrix is measured using corner reflectors deployed in the Amazonian forest. The Amazonian forest near the geomagnetic equator provides ideal sites for the assessment of L-band PALSAR2 antenna parameters, at free Faraday rotation. Corner reflectors (CRs) deployed at free Faraday rotation provide accurate estimation of antenna cross-talks in contrast to the biased measurements obtained with CRs deployed at significant Faraday rotation. The extended Freeman–Van Zyl calibration method introduced and validated for ALOS-PALSAR calibration is used for the assessment of PALSAR-2 calibration parameters. Six datasets collected over the Amazonian rainforests (with CRs) are used to assess PALSAR-2 distortion matrix for five beams (FP6-3 to FP6-7) with incidence angle varying from 25◦ to 40◦ . It is shown that the PALSAR2 antenna is highly isolated with very low cross-talks (lower than −40 dB). Finally, the impact of a significant Faraday rotation on antenna cross-talk measurements using CR is discussed.

**Keywords:** radar polarimetry; synthetic aperture radar; calibration; Faraday rotation

#### **1. Introduction**

ALOS2, which was launched on the 24th of May 2014, is equipped with a fully polarimetric L-band SAR, PALSAR2 [1–3]. Unlike ALOS-PALSAR, which used to collect polarimetric data at only one off-nadir angle (21.5◦ ) [4], PALSAR-2 offers the possibility of providing polarimetric measurements at various beams (seven beams, with incidence angle varying from 25◦ to 40◦ ) [1,2]. The active antenna uses 180 transmit-receive (T/R) modules; each T/R excites a single subarray [1]. The requirement on the overall antenna array crosstalk is low (better than −30 dB [1,2]), and this should permit the measurement of pure HV (at low Faraday conditions) [5,6]. However, different distortion matrices might be required for the extraction of pure HH, HV, VH, and VV from the PALSAR2 PLR measurements at the various beams. Calibration residual errors should be minimized since PALSAR-2 is expected to have a signal-to-noise ratio (S/N) 3-dB better than PALSAR. The latter was already operating at low noise floor (NESZ better than −34 dB [5]).

Like L-band JERS-1 SAR and ALOS PALSAR, PALSAR-2 measurements might be affected by Faraday rotation. In the past, the use of corner reflector (CR) measurements in the presence of Faraday rotation led to mixed conclusions regarding the actual isolation of the ALOS-PALSAR antenna [7–9]. PALSAR antenna measurements using CR deployed in Germany and Australia led to the conclusion that the PALSAR antenna is not highly isolated (−23 dB isolation) [7,8]. However, the use of the CR measurements collected in the Amazonian rainforests, at low Faraday rotation conditions, led to the conclusion that PALSAR antenna is highly isolated, with a cross-talk lower than −37 dB [3,5,6,9,10].

In Section 2, the lessons learned from PALSAR calibration are first presented. The sites of calibration in the Amazonian rainforests and the polarimetric PALSAR2 images used for the assessment of PALSAR2 calibration, are described in Section 3. The extended Freeman–VanZyl calibration method [6] is briefly presented in Section 4 and used for the assessment of polarimetric PALSAR2 transmit-receive distortion matrices. In Section 5, an

**Citation:** Touzi, R.; Shimada, M.; Motohka, T. Calibration and Validation of Polarimetric ALOS2-PALSAR2. *Remote Sens.* **2022**, *14*, 2452. https://doi.org/10.3390/ rs14102452

Academic Editors: Takeo Tadono and Masato Ohki

Received: 22 February 2022 Accepted: 16 April 2022 Published: 20 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

estimation of PALSAR-2 distortion matrix is provided for five beams (FP6-3 to FP6-7) with incidence angle varying between 25◦ and 40◦ . Measurement of the Faraday rotation during PALSAR2 acquisition is conducted to confirm the legitimacy of the estimation of antenna cross-talks under negligible Faraday rotation. Finally, the impact of a significant Faraday rotation on CR-based measurements of antenna cross-talks is discussed using PALSAR2 images collected over the CCRS calibration site in Ottawa (Canada).

#### **2. Lessons Learned from ALOS-PALSAR Calibration**

ALOS-PALSAR, launched in 2006, was the first polarimetric L-band SAR satellite mission. The use of various calibration sites led to confusion that arose at the 2006 ALOS Calibration/Validation meeting regarding the actual PALSAR antenna isolation. The presence of Faraday rotation in addition to the uncertainty regarding the actual isolation of the PALSAR antenna, led to mixed conclusions regarding the actual isolation of the H-V PALSAR antenna [8,9,11].

The use of the CR measurements obtained at the DLR calibration site led to the following misleading conclusion regarding PALSAR antenna isolation; PALSAR antenna is not well isolated with significant antenna cross-talks varying between −18 dB and −23 dB [7,11]. Such significant cross-talk would have made the use of PALSAR HV in dual-pol (HH-HV) useless since the contamination of HV by the like polarization (HH and VV) cannot be corrected for, as discussed in [12]. In fact, PALSAR antenna is higly isolated and this permits an excellent exploitation of PALSAR dual-pol (HH-HV) systematic coverage for global forest mapping and monitoring [3,13,14].

Using CR deployed in the Amazonian rainforests, Touzi and Shimada [6] showed that the PALSAR antenna is highly isolated (−37 dB isolation) [9,10]. The thorough investigation they conducted in [6] using PALSAR data collected over various calibration sites (with CRs), in Japan (JAXA, Sweden (Chalmers University), Germany (DLR), and Canada (CCRS), in addition to the ones collected over the Amazonian rainforests, led to the following conclusions:


These lessons learned with the calibration of ALOS-PALSAR has encouraged JAXA to deploy CRs in the Amazonian rainforests. The latter should permit accurate assessment of ALOS2-PALSAR2 calibration parameters, as discussed in Section 3.

However, the impact of a significant Faraday rotation on CR response in addition to the antenna cross-talks related contamination was not thoroughly investigated in [6]. This is conducted in the following Section 4. The analytical response of CR is derived as a function of the Faraday rotation and antenna cross-talks, and the cross-pol (HV and VH) contamination with the like-pol (HH and VV) due to the Faraday rotation is demonstrated using PALSAR2 data collected over the CCRS calibration site in Ottawa.

#### **3. The Extended Freeman-Van Zyl Calibration Method for Accurate Assessment of Antenna Cross-Talks**

The van Zyl calibration, which offers a more convenient solution than the conventional method that requires the deployment of many reference point targets across the swath, has become the standard method for estimation and calibration of antenna distortion matrix variations with incidence angle [17–19]. However, the van Zyl algorithm is limited to symmetric SAR systems. This problem has been circumvented by Freeman [17] who introduced

a symmetrization method to adapt the van Zyl calibration to non-symmetric SAR systems. The Freeman–van Zyl calibration technique [17], which symmetrizes the system prior to the estimation of the distortion matrix elements, uses the van Zyl iterative method [16] for antenna cross-talk estimation. Recently, the accuracy of the van Zyl method [16] has been questioned [6,18] for azimuthally symmetric targets of low HV return in comparison with HH, VV, and the HH-VV cross-correlation. The van Zyl algorithm [16] was reconsidered [6] and an extension of van Zyl algorithm was introduced to solve this problem. An entity *RR* was introduced to quantify the importance of the HV return in comparison with HH, VV, and the HH-VV cross-correlation. The van Zyl equations of [16] were expressed in terms of *RR*, and this led to the development of an iterative method for accurate estimation of antenna X-talk, at low and significant *RR* conditions, using azimuthally symmetric targets. The method was validated using PALSAR data collected over the Amazonian forest [6]. Errors higher than 10 dB can occur when *RR* is ignored. The iterative method corrects for these errors, and permits the demonstration of ALOS-PALSAR high isolation (better than −37 dB) [6].

The extended Freeman–van Zyl calibration method [6] includes two steps:


#### *3.1. The FREEMAN Symmetrization Method*

The "Uncalibrated" PALSAR2 data provided by JAXA were in fact calibrated for the transmit-receive antenna gain variations with incidence angle, as well as for slant range variations [2,20]. At free Faraday rotations, the following model can be used to express the voltage measurements, as a function of the illuminated target scattering matrix [*S*] [17,21]:

$$[V] = \begin{bmatrix} 1 & \delta\_1 \\ \delta\_2 & F\_1 \end{bmatrix}^T [S] \begin{bmatrix} 1 & \delta\_3 \\ \delta\_4 & F\_2 \end{bmatrix} \tag{1}$$

where the measured voltage matrix [*V*] is given by:

$$\begin{bmatrix} V \end{bmatrix} = \begin{bmatrix} V\_{hh} & V\_{hv} \\ V\_{vh} & V\_{vv} \end{bmatrix} \tag{2}$$

and the actual target scattering matrix [*S*] is given by:

$$\begin{bmatrix} \mathbf{S} \end{bmatrix} = \begin{bmatrix} \mathbf{S}\_{hh} & \mathbf{S}\_{hv} \\ \mathbf{S}\_{vh} & \mathbf{S}\_{vv} \end{bmatrix} \tag{3}$$

In Equation (1), [.] *<sup>T</sup>* denotes the matrix transpose; *F*<sup>1</sup> and *F*<sup>2</sup> are the channel imbalances between the H and V channels on receive and transmit, respectively. *δ*<sup>3</sup> and *δ*<sup>1</sup> are the cross-talks when a vertically polarized wave is transmitted and received, respectively. *δ*<sup>4</sup> and *δ*<sup>2</sup> are the cross-talks when a horizontally polarized wave is transmitted and received, respectively. The van Zyl calibration method assumes that the SAR system is symmetric; the transmitting and receiving distortion matrices are identical with *F*<sup>1</sup> = *F*2, *δ*<sup>1</sup> = *δ*3, and *δ*<sup>2</sup> = *δ*4. Such assumptions may not be satisfied in general, and as result, the van Zyl calibration method might be of limited use in certain applications. Freeman introduced the symmetrization method to extend the use of the van Zyl algorithm to non-symmetric systems. After application of the Freeman symmetrization [17], the symmetrized measured

voltage matrix [*V*]*sym* is related to the actual scattering matrix [*S*] by the following equation (with *Shv* = *Svh* under target reciprocity assumption):

$$[V]\_{sym} = \begin{bmatrix} 1 & \Delta\_1 \\ \Delta\_2 & F \end{bmatrix}^T [\mathbb{S}] \begin{bmatrix} 1 & \Delta\_1 \\ \Delta\_2 & F \end{bmatrix} \tag{4}$$

where *F* = |*F*2|; and ∆<sup>1</sup> and ∆<sup>2</sup> are expressed in [17] as functions of *δ<sup>i</sup>* (*i* = 1, 4) and *F<sup>j</sup>* (*j* = 1, 2) [6]. The van Zyl algorithm can then be applied to the symmetrized system of Equation (4), as follows [16]:


#### *3.2. Reconsideration of Van Zyl Algorithm*

The accuracy of van Zyl's algorithm [16] has been questioned for azimuthally symmetric reference targets of low HV return in comparison with HH, VV, and their crosscorrelation [6,18]. This issue was taken into account during the development of the calibration method specific for the Convair-580 SAR [19]. The Convair-580 SAR system, which uses different receiving configurations depending on the transmitted (horizontal or vertical) polarization, required a more complex calibration method than the ones developed for systems with one receiving configuration (such as the JPL AIRSAR system, for example). To quantify the residual relative error that would result if the entities < |*HH*| <sup>2</sup> <sup>&</sup>gt;, <sup>&</sup>lt; <sup>|</sup>*VV*<sup>|</sup> <sup>2</sup> >, and < *HHVV*∗ > were ignored during the cross-talk estimation process, the following entity *RR* (of Equation (23) in [19]) was introduced [6,19]:

$$RR = \begin{array}{c} |\Delta\_1|^2 \cdot \frac{<|V\_{hh}|^2>}{<|V\_{hv}'|^2>} + |\Delta\_2'|^2 \cdot \frac{<|V\_{vv}|^2>}{<|V\_{hv}'|^2>} + \\ 2Real(\Delta\_1 \Delta\_2'^\* \cdot \frac{<|V\_{hh} \cdot V\_{vv}^\*|^2>}{<|V\_{hv}'|^2>}) \end{array} \tag{5}$$

where *V* 0 *hv* = *Vhv* + *C* · *Vvh* and *C* is a calibration constant [19]. The actual cross-polarized intensity mean < |*Shv*| <sup>2</sup> > is expressed as a function of the measured voltage and *RR* as:

$$<|S\_{hv}|^2 > \quad \simeq \quad (1/F^2) \cdot < |V\_{hv}'|^2 > \cdot (1 - RR) \tag{6}$$

For an azimuthally symmetric target of < |*Shv*| <sup>2</sup> > that is significant in comparison with < |*Shh*| <sup>2</sup> <sup>&</sup>gt;, <sup>&</sup>lt; <sup>|</sup>*Svv*<sup>|</sup> <sup>2</sup> <sup>&</sup>gt;, <sup>|</sup> <sup>&</sup>lt; *<sup>S</sup>hh<sup>S</sup>* ∗ *hv* > |, and | < *SvvS* ∗ *hv* > |, *RR* is close to zero, and the measured and actual cross-polarized intensity means are identical (modulo a multiplicative coefficient). Since the calibration of the Convair-580 X-band polarimetric SAR becomes too complex if *RR* is not negligible [19], only azimuthally symmetric targets with *RR* close to zero are used [19]. PALSAR2, like PALSAR and most of the conventional polarimetric SARs, requires the use of a calibration model much simpler than the Convair-580 SAR (whose receiver is adapted to the transmitted polarization [19]). The van Zyl model can then be retained for PALSAR2 calibration, and the van Zyl equations [16] are expressed as a function of *RR*, which takes into account all the required terms for unbiased estimation of antenna X-talks [6].
