1. New insights into analysis of polarimetric data from fundamental physics
Frank Ahern
TerreVista Earth Imaging
Brian Brisco
Canada Centre for Remote Sensing
Kevin Murnaghan
Don Atwood
MTRI (ret.)
__________________________________________________________________________________________________________University of Michigan
2017 – Oct – 27
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2. My background Astrophysics Remote Sensing Telescope turned upside down
University of Maryland (PhD, 1972)
University of Toronto (post-doc, )
Telescope turned upside down
Remote Sensing
Canada Centre for Remote Sensing, 1974 – 2001
TerreVista Earth Imaging, present
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3. Canada Centre for Remote Sensing 1974 - 2001
Optical radiometry and spectroradiometry
Forest applications
Optical (Landsat, primarily)
In Canada: Nova Scotia, New Brunswick, Ontario, Alberta, BC
Microwave (SAR-580, RADARSAT-1)
In Canada: Alberta
Latin America: Brazil, Venezuela, Peru, Bolivia, Costa Rica
No polarimetry except co-supervision of Maycira Costa PhD thesis
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4. TerreVista Earth Observation 2001 - present
Numerous projects on various topics
Of note for this presentation -- wetlands:
2002: ESA project investigating SAR for monitoring wetlands in conjunction with the Ramsar convention
Literature review included polarimetry, but actual evaluation was limited to single-band data
present: Interferometry and Polarimetry for the Lake Clear study site (many small wetlands in eastern Ontario)
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8. Imaging the earth with radar
Real aperture airborne radar
Synthetic aperture radar (SAR)
Polarimetric SAR
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9. Side looking radar: real and synthetic apertures
Azimuth resolution, real antenna beamwidth

10. Synthetic Aperture Radar (SAR)
Range resolution is proportional to pulse width (no change from real aperture technology)
Azimuth resolution is proportional to the Fourier Transform of the incoming wave EM field intercepted by the antenna
 The longer the antenna, the smaller the beam, and vice versa
So: make a long real aperture antenna, or
Make a small real antenna (to illuminate a wide area) and then make a synthetic aperture from a succession of measurements of the EM field. (Only option from space).
 learn Fourier analysis! (and complex analysis!)
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11. Polarimetric SAR HH VV HV VH Complex scattering coefficients
(amplitude and phase)
Tom Lukowski

12. TerreVista Earth Imaging putting you in the big picture
Current research
Supported by CCRS since (Dr. Brian Brisco)
Motivated to increase the use of spaceborne SAR for wetland mapping and monitoring
Responds to increasing national and global concerns about fresh water
Lake Clear studies, a part of much larger CCRS freshwater program
Interferometry: changes in water level
Polarimetry: what can polarimetry do for wetlands?
Brief summary of research leading to a mystery!
Problems with polarimetric decompositions
Hints
Physics
More observations
Mystery solved!
Guidelines for users
Next steps
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13. TerreVista Earth Imaging putting you in the big picture
Lake Clear study area
Courtesy AAAPOE tours
Our study area lies in the upper Ottawa Valley about 160 km west of Ottawa. There are many wetlands in this area (orange on lower map), mostly swamps and marshes.
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14. TerreVista Earth Imaging putting you in the big picture
Swamp: LCW 1
This is a typical dead black ash swamp. We are currently concentrating on black ash swamps because of their simplicity: mostly vertical trunks with few upper branches.
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15. TerreVista Earth Imaging putting you in the big picture
Swamp: Corrigan
This is a typical dead black ash swamp. We are currently concentrating on black ash swamps because of their simplicity: mostly vertical trunks with few upper branches.
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16. FQ and Spotlight mode data 2011 - 2013
Spotlight data: used for interferometry
SLA 23 beam mode
incidence angle of 46.6°
spatial resolution of 1.6 m in range and 0.8 m in azimuth
April through October, 2011 – 2013
FQ Data: used for polarimetry
FQ3 and FQ 14 beam modes in 2011 and 2013, respectively;
incidence angles of 21.9° and 33.8° respectively
spatial resolution of 5.2 m in range and 7.6 m in azimuth
Note that the interferometric data have much higher spatial resolution, and therefore many more pixels, to reduce speckle noise.

17. TerreVista Earth Imaging putting you in the big picture
marsh
open field
Forest (pine plantation)
pine plantation
swamp
Swamp
LCW-1
Phase difference between two dates
Coherence
open field
marsh
swamp
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Swamp LCW-1

18. A mystery story!
Our Freeman Durden results for wetlands with high interferometric coherence* (22° incidence)
DB = double bounce
VOL = volume scattering
RS = rough surface (single bounce)
TP = total power
*High interferometric coherence plus fringes related to water level change prove double-bounce dominates, yet FD disagrees.
The point of this slide is that the interferometric results only make sense with a double-bounce interaction of the microwaves with both the water and the vegetation, because we see a bright return and fringes that are clearly related to changes in water level. Yet the FD decomposition indicates only a very small double-bounce return.

19. Logic central to many popular decompositions
Freeman-Durden algorithm
All cross-pol comes from multiple scattering
CPD = co-pol phase difference = HH-VV phase
|CPD| < 90°  single bounce
|CPD| > 90°  double bounce
Other decompositions employing this algorithm
Yamaguchi
Pauli coherency matrix (when interpreted as a decomposition)
Hong-Wdowinski
The Van Zyl and Freeman-Durden decompositions, which led to many similar derivatives, all use the same logic. After subtracting the multiple scattering component which is given by the cross-pol power, the division into single (actually odd) bounce and double (actually even) bounce mechanisms is based on a threshold of 90-degrees. Any pixel with CPD<90 is assigned to single bounce, while any pixel with CPD>90 is assigned to double bounce. This logic is correct for a metalic dihedral, but we will show it has serious shortcomings for real-world dielectric targets.

20. New polarimetric observations as of 2015
FD threshold
Double Single
FD threshold
Single Double
21 deg
34 deg
These curves represent the histograms of the CPD for a large number of swamp pixels. There is an important change in the mean value: a small value for 21-degree incidence, and a larger (absolute) value for 34-degree incidence. The small absolute value at steep incidence provides an indication of the problem with the classical decomposition logic. Even though we know the double bounce mechanism dominates (through interferometry), the vast majority of pixels fail the “double-bounce test.”
These curves also show that the effects of speckle are very pronounced, and will create considerable noise in decomposition results. Mathematical purists will argue that the ensemble average should be larger, but in the real world the wetlands are too small.
We also see a pronounce shift towards larger absolute values of CPD when the incidence angle increases to 34 degrees. This provided early support for our hypothesis that Fresnel reflection was playing an important role.

21. Clues Takuma Watanabe, Hiroyoshi Yamada, Motofumi Arii, Ryoichi Sato,
Sang-Eun Park, and Yoshio Yamaguchi, Experimental study on effects of forest moisture on polarimetric radar backscatter, IGARSS 2014, Québec, Canada, July
This work, presented at IGARSS 2014 in Quebec, showed the important role of Fresnel physics and helped guide our thinking. We also found some earlier articles, particularly articles with Fawwaz Ulaby and Tony Freeman as lead authors, that supported our hypothesis that Fresnel physics was the primary reason for the anomalous results we were obtaining.

22. Hypothesis for follow-on work:
The CPD phase is strongly affected by the physics of reflection: Fresnel equations;
Fresnel reflection (Brewster angle effect) produces anomalous CPD for steep incidence angles that misleads popular decompositions.

23. Clues
Ulaby, F., D. Held, M. C. Dobson, K. C. McDonald, and T. B. A. Senior, Relating polarization phase difference of SAR signals to scene properties, IEEE Trans. On Geoscience and Remote Sensing, GE-25, No. 1, 1987.
(for dry corn stalks)

24. Clues
Freeman, Anthony, Relating polarization Fitting a two-component scattering model to polarimetric SAR data from forests, IEEE Trans. On Geoscience and Remote Sensing, GE-45, No. 8, 2007.
HH – VV phase
Acknowledgements to Craig Dobson, and to Bruce Chapman “…for his initial suggestion that it may be possible to find the pseudo-Brewster angle effect in double-bounce scattering.”

25. Fresnel Equations
describe reflection and refraction of electromagnetic radiation at a planar interface where there is a change in the index of refraction, n, where 𝑛= 𝜇𝜀
N = Sqrt(με)
Jackson, Figure (radiation incident from below)

26. Fresnel Equations for complex n (Wikipedia)
𝑟 𝑠 = 𝑛 0 𝑐𝑜𝑠 θ 𝑖 − 𝑛 1 𝑐𝑜𝑠 θ 𝑡 𝑛 0 𝑐𝑜𝑠 θ 𝑖 + 𝑛 1 𝑐𝑜𝑠 θ 𝑡
𝑟 𝑝 = 𝑛 1 𝑐𝑜𝑠 θ 𝑖 − 𝑛 0 𝑐𝑜𝑠 θ 𝑡 𝑛 0 𝑐𝑜𝑠 θ 𝑖 + 𝑛 1 𝑐𝑜𝑠 θ 𝑡
𝑠𝑖𝑛 θ 𝑡 = 𝑛 0 𝑛 1 𝑠𝑖𝑛 θ 𝑖
There are remarkably many different formulations of the Fresnel equations. Some of them become very messy when authors cast them in forms with real-numbers only. But when the index of refraction is allowed to be complex, they remain simple and calculations are simple using complex arithemetic.
(Snell’s law)

27. Reflection coefficients, glass, lossless case (n = 1.5 + 0.0i)
Brewster angle
Many of you will probably remember this set of curves from elementary optics texts. This is our starting point. The angle where the VV component disappears is called the Brewster angle.

28. Reflection coefficients, glass, lossy case (n = 1.5 + 0.5)
(pseudo) Brewster angle
When glass is allowed to become lossy, the VV component no longer disappears at the Brewster angle.

29. Phase angles for glass, lossless case (n = 1.5 + 0.0i)
The HH phase remains at 180-degrees for all angles of incidence (displaced to show the green and red lines), while the VV phase (red) and CPD (green) show an abrupt transition at the Brewster angle.

30. Phase angles for glass, lossy case (n = 1.5 + 0.5i)
As soon as the glass becomes lossy, the transitions of the phase angles become much smoother.

31. Phase angles for sample materials at C-band (glass at optical wavelengths)
n = i
n = i
n = i
n = i
Co-Pol phase difference, CPD (degrees)
Water has a high real index of refraction and a small imaginary (loss) component, so the Brewster angle is very large and the phase transition quite abrupt.

32. HH reflectance for sample materials at C-band (glass at optical wavelengths)
n = i
n = i
n = i
n = i
HH Reflectance
Water has a high real index of refraction and a small imaginary (loss) component, so the Brewster angle is very large and the phase transition quite abrupt.

33. VV reflectance for sample materials at C-band (glass at optical wavelengths)
n = i
n = i
n = i
n = i
VV Reflectance
Water has a high real index of refraction and a small imaginary (loss) component, so the Brewster angle is very large and the phase transition quite abrupt.

34. Fresnel incidence angles for dihedral geometry
ΘFv= 90-Θi
Watch carefully! Theta is the angle of incidence that is appropriate for Fresnel reflection calculations. For the water surface (blue line) 𝜃𝐹𝑅, for Fresnel reflection is the same as the radar incidence angle. But for the wood surface 𝜃𝐹𝑅 is the complement of the radar incidence angle.
ΘFh=Θi

35. Phase angles for dihedrals at C-band
Co-Pol phase difference, CPD (degrees)
Water has a high real index of refraction and a small imaginary (loss) component, so the Brewster angle is very large and the phase transition quite abrupt.

36. HH reflectance for dihedrals at C-band
Water has a high real index of refraction and a small imaginary (loss) component, so the Brewster angle is very large and the phase transition quite abrupt.

37. VV reflectance for dihedrals at C-band
Water has a high real index of refraction and a small imaginary (loss) component, so the Brewster angle is very large and the phase transition quite abrupt.

38. By 2015: shallow incidence and analysis
FD threshold
Double Single
FD threshold
Single Double
21 deg
34 deg
These curves represent the histograms of the CPD for a large number of swamp pixels. There is an important change in the mean value: a small value for 21-degree incidence, and a larger (absolute) value for 34-degree incidence. The small absolute value at steep incidence provides an indication of the problem with the classical decomposition logic. Even though we know the double bounce mechanism dominates (through interferometry), the vast majority of pixels fail the “double-bounce test.”
These curves also show that the effects of speckle are very pronounced, and will create considerable noise in decomposition results. We also see a pronounce shift towards larger absolute values of CPD when the incidence angle increases to 34 degrees. This provided early support for our hypothesis that Fresnel reflection was playing an important role.

39. Radarsat-2 data acquisitions 2016
We have an excellent data set with lots of acquisitions at many different incidence angles. The weather provided opportunities to study dry, wet, and damp wood.

40. Some 2016 CPD histograms showing phase unwrapping
No. of samples (SLC pixels
We have an excellent data set with lots of acquisitions at many different incidence angles. The weather provided opportunities to study dry, wet, and damp wood. PU
NPU
22°
Co-Pol phase difference (degrees)

41. Hot off the pre-press!

42. HH backscatter as a function of incidence angle
HH backscatter <|SHH|2>
HH backscatter lies between the dry wood model and the wet wood model. Note the wet points lie above the dry and damp points.

43. VV backscatter as a function of incidence angle
VV backscatter <|SVV|2>
VV backscatter does not lie between the dry wood model and the wet wood model. However, the dry and damp points have a curve similar to the dry wood model, with a suggestion of a Brewster angle. The wet points lie above the dry and damp points, in line with the general prediction of the wet wood model.

44. CPD as a function of incidence angle
Co-Pol phase difference (degrees)
Here we see that the dry wood dihedral model shows characteristics similar to the observation, but something else is going on also. A more realistic model is needed.
Note that the slower rise in CPD than the model predicts indicates that the anomalous results from decompositions will persist to higher incidence angles.

45. Cross-Pol backscatter as a function of incidence angle
Cross-Pol backscatter <|SHV|2>
The cross-pol backscatter is roughly 1/3 of the VV backscatter, and 1/10 of the HH backscatter. The dihedral model predicts zero cross-pol backscatter, but trees are not planes. A more realistic model is needed. The majority of the wet points lie above the dry and damp points, but two wet points do not.

46. Co-Pol phase difference (degrees)
Two 2016 CPD histograms showing pedestal effect This graph needs work: replace 43A PU with bars, and add counts to Y axis.
No. of samples (SLC pixels)
This graph needs work: replace 43A PU with bars, and add counts to Y axis.
Co-Pol phase difference (degrees)

47. Cross-pol fraction correlated with pedestal height
Cross-Pol /Total backscatter
We have an excellent data set with lots of acquisitions at many different incidence angles. The weather provided opportunities to study dry, wet, and damp wood.
Could data from a dual-pol HH and VV SAR provide cross-pol information?
Co-Pol phase difference (degrees)
Pedestal height (SLC pixels)

48. Conclusions
Steep incidence is often recommended for wetlands, yet decomposition results are misleading for wetlands when the incidence angle is small.
The Fresnel equations must be used, with realistic values for the dielectric constant, to understand the backscatter physics.
Strong HH backscatter, and a high HH/VV ratio at steep incidence are reliable indicators of water under a vegetation canopy;
Additional model development is needed to guide development of polarimetric applications.

49. Where do we go from here?
Adapt or develop a fully-polarimetric model for forest backscatter, starting with a water substrate with emergent cylinders.
MIMICS was not polarimetric
Lin-Sarabandi model (1997) ?
Other?
Use model to explore the possibility of wood moisture from space;
Start with simple model for swamps, and add branches later;
Explore the potential to retrieve information about vegetation structure.

50. Employment opportunities in Canada
Remote Sensing: mature technology after 45 years of work
Academia – all major universities have RS and GIS programs
Colleges (Community Colleges) – RS and GIS
Government: NRCan (geology, forestry, RS technology), Agriculture, Environment, Fisheries and Oceans
Industry:
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51. Employment opportunities in Canada
Medical Imaging
Canadian Institutes of Health Research
University of Toronto
University of Western Ontario
Other

52. Thank you!
The end.
Merci!