ANSI-C program: m-delta.c
NAME
m-delta - Calculate m-delta polarimetric decomposition
using information derived from the Stokes parameters.
delta is the relative
H-V phase: atan(s3/s2)
SYNOPSIS
m-delta <s0> <m> <delta> <S_par>
<c1> <c2 <c3>
| <s0> | Stokes parameter for the total power in the H and V polarizations <|E_h|**2 + |E_v|**2> |
| <m> | degree of polarization: sqrt(s1**2 +
s2**2 + s3**2)/s0
(float) |
| <delta> | (input) relative H-V phase:
atan(s3/s2) |
| <S_par> | (input) MLI image parameter file associated with the Stokes parameter data files |
| <c1> | (output) s0*m*(1 + sin(delta))/2 (float) |
| <c2> | (output) s0*(1 - m) depolarized component (float) |
| <c3> | (output) s0*m*(1 - cos(delta))/2 (float) |
EXAMPLE
m-delta 20080409_RCP.m 20080409_RCP.delta
20080409_RCP.mli.par 20080409_RCP.c1 20080409_RCP.c2
20080409_RCP.c3
calculates the three components of the m-delta decomposition that are proportional to the single-bounce, random, and double-bounce components of the backscatter
DESCRIPTION
The m-delta decomposition displays the degree of polarization derived from the Stokes parameters and the H/V phase difference as 3 parameters. In the case of circular polarization illumination, the H-V phase difference contains information if the number of bounces is odd or even for the scattered field under the condition that the backscatter is strongly polarized. Strongly polarized fields are indicative of a single dominant scattering mechanism for the set of pixels in the sampling window.
The Stokes parameters (see the documentation on stokes) are derived from local second-order statistics of the SLC images of the two receive channels. The s0 Stokes parameter is the total energy of the scattered field and is the sum of the polarized and unpolarized field components. The Stokes parameters s1, s2, and s3 represent a vector in 3 dimensions on the Poincaré sphere, see http://en.wikipedia.org/wiki/Polarization_(waves) and http://spie.org/x32375.xml. Each point on the sphere characterizes a particular polarization state. The Stokes parameter s3 describes the circularity of the scattered field and is assigned to the z-axis coordinate, while the s1 and s2 parameters represent components of the field that are linear (H,V) or linear (45, 135) degrees. The north pole of the sphere represents a Left Circularly Polarized (LCP) wave, while the south pole represents Right Circularly Polarized (RCP) wave.
The degree of polarization m is the ratio of the polarized component of the field to the total scattered power and can be derived from the Stokes parameters:
m = (s12 + s22 + s32)1/2 / s0
The phase difference between the H and V channels can be derived from the Stokes parameters:
delta = atan(s3/s2)
Raney [1] [2] has proposed the use of hybrid compact polarization (CP) radars. In a SAR instrument using CP, a single polarization is transmitted and 2 orthogonal channels are received. Selection of circular polarization for the transmitted signal has the advantage of rotational invariance. In this case polarization signatures are robust with respect to Faraday rotation caused by the ionosphere and the rotational orientation of the target. The Indian RISAT-1 satellite as well as the planned Radarsat constellation use circular polarized transmit and horizontal (H) and vertical (V) polarized receive channels. It is also possible to synthesize compact polarization data (circular transmit, H,V linear receive) from quad-polarized (HH, HV, VH, VV) data with the Gamma software, see quad2cp.
Specifically, when circular polarization is used to illuminate the scene, then the phase value delta combined with the degree of polarization m and the total power s0 can be used to differentiate if the backscatter is predominantly single or double-bounce. m*s0 is the coherent scattered field component power.
The m-delta decomposition considers 3 component
c1 = s0*m*cos (1 + sin(delta))/2
c2 = s0 *(1 - m) depolarized component
c3 = s0*m*(1 - sin(delta))/2
The quantities m, and delta are calculated from the Stokes parameters using the program stokes_qm [3] .
For display purposes using an RGB or HSI composite image the usual color assignments are that double-bounce is the red channel, single-bounce is the blue channel, and random scattering to the green channel. Generating the 3-channel composite image can either be done using the program ras3pwr or generating 3 dB gray-scale images using ras_dB from the 3 components c1, c2, and c3 and combining them using the programs ras_to_hsi or ras_to_rgb.
[1] Raney, R. K. et al., "The m-chi decomposition of hybrid dual-polarimetric radar data with application to lunar craters," Journal of Geophysical Research, vol 117, Maym 2012 doi: 10.1029/2011JE003986.
[2] Raney, R. K. et al. (2011), "The lunar Mini-RF Radars: Hybrid polarimetric architecture and initial results," Proc. IEEE, 99(5), 808-823, 2011, doi: 10.1109/JPROC.2010.2084970.
[3] Cloude, S.R., "Compact Decomposition Theory," IEEE Geoscience and Remote Sensing Letters, vol. 9, no. 1, Jan 2012, pp. 28-32, doi: 10.1109/LGRS.2011.2158983.
SEE ALSO
typedef_ISP.h, m-chi, m-alpha, ras_to_hsi,
ras_to_rgb,
ras_dB,
stokes_qm