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Polarimetric radar transmits and receives selected field orientations. The resulting complex channels carry amplitude and relative-phase information about scattering geometry. Coherence measures how consistently two channels vary across an ensemble; it is not a label for a material. Before interpreting a change as surface, double-bounce or volume scattering, the analyst must separate sample variability, geometry and calibration drift.
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Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the decision
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE DECISION
1. Start with the measurement basis
A fully polarimetric monostatic measurement is commonly represented by a complex scattering matrix with HH, HV, VH and VV channels. Under reciprocity in suitable conditions, HV and VH are often treated as equal, but that assumption must be stated and checked.
The entries depend on wavelength, incidence angle, orientation, resolution and processing. A scattering matrix is an observation in a basis, not a permanent fingerprint of the target.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Distinguish covariance from coherence
For complex channels x and y, covariance preserves their joint scale, while normalized coherence γ=E[xy*]/sqrt(E|x|² E|y|²) removes channel power. Its magnitude lies between zero and one when the moments are well defined.
A high magnitude means stable linear association over the averaging ensemble. It does not prove that one physical mechanism is present or that two channels have equal power.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work a complex coherence example
Suppose four looks give x=(1,1,1,1) and y=(1,i,1,i). Using the uncentred polarimetric form, the cross-average is (1−i+1−i)/4=(1−i)/2. Both channel powers average to one, so |γ|=sqrt(1/2)≈0.707.
| Quantity | Calculation | Value |
|---|---|---|
| Mean cross-product | (1−i+1−i)/4 | (1−i)/2 |
| Mean x power | Σ|x|²/4 | 1 |
| Mean y power | Σ|y|²/4 | 1 |
| Coherence magnitude | |(1−i)/2| | about 0.707 |
If all y samples were one, the magnitude would be one. If phases were more dispersed, the cross-products would cancel more strongly.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. See why finite looks bias the estimate
Coherence is estimated by averaging. With only one look, the sample magnitude is trivially one for nonzero scalar samples, even when the underlying channels are not perfectly coherent. More independent looks reduce that upward small-sample bias.
| Averaging choice | Benefit | Risk |
|---|---|---|
| Too few looks | Preserves fine detail | Noisy and upward-biased magnitude |
| Large fixed window | Lower variance | Mixes distinct scatterers at boundaries |
| Adaptive homogeneous set | Balances variance and mixing | Selection rule must be documented |
A dark or bright boundary can therefore be a window-composition effect. Inspect support size and homogeneity before assigning a new scattering mechanism.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Interpret mechanisms through models, not colours alone
Surface scattering, dihedral or double-bounce scattering, and random-volume scattering are useful model components. Decompositions map covariance or coherency information into contributions that are easier to visualize.
The components are model-dependent and can be non-unique. Orientation, roughness, moisture and mixed resolution cells can move energy between categories without the scene acquiring a new object.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Transfer the analysis across viewing geometry
Rotate an urban block relative to the radar line of sight and its cross-polarized response can change even if the buildings are unchanged. Compare like incidence angles and orientations, or apply a justified orientation compensation.
The changed-context check is to predict the basis and geometry effect before interpreting temporal change. A class rule trained on one pass may not transfer to another orbit.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Model calibration drift as a channel transformation
Gain imbalance multiplies one channel differently from another, channel imbalance adds relative phase, and cross-talk leaks energy between channels. These effects transform the observed matrix before any physical decomposition is applied.
A stable reference target can reveal drift. If the reference changes with the scene, the evidence supports an instrument or processing explanation before a landscape explanation.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect to detection and motion routes
Use CFAR detection, guard cells and target masking when covariance estimates feed a detection threshold. Use weak echoes beside strong targets when leakage and sidelobes overwhelm a polarimetric component.
The guide to micro-Doppler signatures treats temporal modulation. Polarimetric coherence instead compares complex channels over a declared ensemble; the two axes of evidence should not be conflated.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the main limits and misconceptions
Coherence magnitude is not signal-to-noise ratio, target probability or material purity. A low value can result from noise, temporal change, geometric mixing or genuine mechanism diversity.
Calibration cannot recover information that was never measured, and a decomposition cannot make an under-resolved mixture unique. Report uncertainty and alternative explanations instead of treating a false-colour product as direct truth.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record transmit and receive basis, wavelength, incidence angle, look count, averaging support, noise correction, reciprocity assumption, calibration targets, cross-talk correction and software version. Retain a minimally processed reference product.
NASA Earthdata’s SAR Polarimetry training explains covariance matrices and polarimetric information. The official SAR Handbook develops scattering, calibration and applications, while ESA’s polarimetry tutorial demonstrates mechanism decompositions.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Does high coherence mean the channels are identical?
No. They may have different powers and a stable complex proportional relationship.
Why not average an entire image?
Because different terrain classes violate the common-population assumption and can hide local structure.
Can calibration drift create a false mechanism change?
Yes. Relative gain, phase and cross-talk errors can move energy among polarimetric components.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a calibration transfer check
Multiply every y sample in the four-look example by e^(iπ/4). Recalculate γ and show that its magnitude is unchanged while its phase rotates. Then explain why an uncorrected relative-phase drift still matters to phase-sensitive decompositions.
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