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Compact polarimetry reduces hardware or acquisition demands by transmitting a selected polarisation state and coherently receiving two orthogonal components. That preserves more information than a single intensity channel but less than a fully polarimetric measurement. Derived Stokes parameters and reconstruction products can be useful, yet they do not turn unmeasured channels into observations.
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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. Separate full, dual and compact measurements
A fully polarimetric monostatic system measures the complex scattering responses needed to form the full reciprocal target vector under its stated convention. A linear dual-pol mode measures only selected channel pairs. A compact mode commonly transmits one fixed state and receives two coherent orthogonal components.
The word compact describes an acquisition architecture, not a universal data vector. State the transmitted state, receive basis, phase reference and product level before comparing algorithms or scenes.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Write the hybrid receive vector
Under one circular-transmit convention, the incident field is a complex combination of H and V. If the receiver records H and V coherently, the two measured components are linear combinations of entries in the target scattering matrix.
Changing circular handedness or propagation convention changes the signs of the imaginary terms. The convention must accompany every formula; otherwise two equivalent datasets can appear to disagree.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work an underdetermined matrix ledger
Assume reciprocity and a circular transmit state that gives xH=(SHH−iSHV)/√2 and xV=(SHV−iSVV)/√2. Two complex measurements constrain three complex reciprocal matrix entries, so one complex degree of freedom remains without extra assumptions.
| Reciprocal matrix choice | SHH | SHV | SVV | Measured pair (xH,xV) |
|---|---|---|---|---|
| A | √2 | 0 | 0 | (1,0) |
| B | √2−1 | i | 1 | (1,0) |
| Measured equality | Different matrix | Different cross term | Different VV | Same hybrid vector |
| Inference | Not unique | Assumption needed | Assumption needed | Data fixed |
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Build Stokes quantities from coherent channels
From two coherent receive components, one can form total power, power difference and real and imaginary cross-correlation terms. These Stokes-like quantities describe the received polarisation state and support compact-polarimetric decompositions.
Calibration errors in gain, relative phase, cross-talk or noise bias propagate directly into those quantities. A physically bounded or normalised index can still be biased when its numerator and denominator share errors.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Change the transmit state and move the blind direction
If a linear H transmit state is used instead of the circular state, the receiver samples the H column of the scattering matrix. The null space of unmeasured information changes even though two complex receive channels are still recorded.
| Mode | Transmit state | Coherent receive pair | What remains unmeasured |
|---|---|---|---|
| Hybrid circular | One circular state | H and V | One reciprocal complex degree |
| Linear H dual receive | H | HH and VH | Responses to V transmit |
| Linear V dual receive | V | HV and VV | Responses to H transmit |
| Full reciprocal quad-pol | H and V | HH,HV,VV | No reciprocal matrix entry |
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Treat reconstruction as a model-based estimate
Pseudo-quad-pol and covariance reconstruction methods introduce symmetry, scattering-model, reflection-symmetry, low-entropy or scene-statistical assumptions to fill missing degrees of freedom. The output may improve classification when those assumptions are approximately valid.
It should be labelled reconstructed, not measured. Validate against co-registered full polarimetry across relevant terrain types, incidence angles and signal-to-noise ranges, and report failure cases rather than one average agreement score.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Connect the established polarimetric routes
The bistatic-basis guide shows why transmit and receive coordinates must be explicit. The reciprocity guide explains when a three-component reduction is unavailable.
Use the Pauli guide and entropy–alpha guide to check whether a familiar full-pol interpretation survives the compact measurement and reconstruction chain.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Separate information efficiency from information equality
Compact modes can offer wider swath, simpler hardware or better power use, depending on the mission. Those engineering advantages do not mean the statistical information equals a full-pol acquisition for every target and task.
Evaluate the actual decision: crop discrimination, sea-ice type, soil condition, ship detection or another target. A compact mode can be sufficient for one task and inadequate for another because the missing degree aligns differently with the scattering mechanisms.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the limits and common misconceptions
A colourful compact decomposition is not a direct measurement of three full-pol scattering powers. Apparent entropy, alpha angle or surface-double-volume fractions may use definitions adapted to compact data and should not inherit full-pol thresholds automatically.
Circular transmit does not make the target circularly symmetric. Reciprocity, reflection symmetry and azimuthal symmetry are separate assumptions. Speckle filtering cannot restore a channel that was never acquired.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record transmit state, receive basis, handedness, propagation convention, complex calibration, noise floor, covariance estimator, multilooking, compact Stokes definition, reconstruction assumptions, positivity constraints, reference full-pol data, task metric, terrain strata, angle range and uncertainty.
ESA’s Compact Polarimetry workshop material compares hybrid and dual compact configurations. The ESA POLinSAR recommendations distinguish full, hybrid and compact polarimetric capabilities and their mission questions.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Is compact polarimetry the same as dual-pol?
No. Both use fewer measurements than full polarimetry, but the transmitted state, coherent receive pair and retained information can differ.
Can full polarimetry be reconstructed exactly?
Not in general from one compact state. Exact-looking products require assumptions, priors or restricted target classes.
Are Stokes parameters measured directly?
They are computed from calibrated coherent receive channels; their uncertainty inherits channel and covariance-estimation errors.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a null-space transfer check
Verify the two matrices in the worked ledger produce the same hybrid vector. Then change circular handedness and repeat. Identify the unmeasured degree in each convention and state one scene assumption that would select a reconstruction without turning it into observed data.
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