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In monostatic radar, transmitter and receiver are co-located and a familiar backscatter basis can be reused on both paths. In bistatic radar they occupy different directions, so the scattering matrix maps a transmit basis into a separately defined receive basis. A sign, handedness or cross-polar difference can therefore come from geometry and coordinates before it says anything about the target.
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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. Draw two propagation paths before writing a matrix
Let k_i describe propagation from the transmitter to the target and k_s propagation from the target to the receiver. The bistatic angle is the angle between the relevant incident and scattered directions under the stated convention. Monostatic backscatter is a special limiting geometry, not the default for all formulae.
Record transmitter, target and receiver positions or equivalent incidence, scattering and azimuth angles. A diagram should also show whether arrows represent wave propagation or look direction, because reversing one without changing the basis can reverse signs.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Treat the scattering matrix as a basis-to-basis map
Write E_s = S E_i after choosing two transverse components for the incident field and two for the scattered field. The rows belong to the receive basis and the columns to the transmit basis. In bistatic geometry those bases generally live in different transverse planes.
A four-entry matrix can therefore be physically correct without being symmetric. Transposing it, comparing cross channels or applying a monostatic reciprocal reduction requires a matched definition of propagation directions, polarisation vectors and calibration.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work an original geometry-and-basis ledger
Suppose the transmitter views a surface at 30 degrees incidence and the receiver at 50 degrees on the opposite side of the local normal. Under one common convention the bistatic separation is 80 degrees. A local horizontal-vertical basis must be constructed separately for each path.
| Item | Transmit side | Receive side | Why it matters |
|---|---|---|---|
| Direction | 30° from normal | 50° from normal | Different transverse planes |
| Horizontal vector | Perpendicular to incident plane | Perpendicular to scattering plane | Not automatically parallel |
| Vertical vector | Completes transverse pair | Completes transverse pair | Sign depends on handedness |
| Matrix role | Columns | Rows | Do not interchange silently |
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Locate specular geometry before interpreting brightness
For a smooth surface, specular geometry satisfies the reflection relation between incident direction, surface normal and scattered direction. Energy can concentrate near that direction, while roughness spreads energy over a wider angular region.
A bright bistatic return near the specular direction is not by itself evidence of a new material response. Compare angular position, footprint, roughness scale, wavelength and polarisation before separating coherent reflection from diffuse scattering.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Change one basis sign and watch cross terms move
Take a matrix S with entries SHH=1, SHV=0.2, SVH=0.1 and SVV=0.6. If the receive vertical unit vector is reversed while the transmit basis is unchanged, the receive-V row changes sign: SVH becomes −0.1 and SVV becomes −0.6.
| Convention change | SHH | SHV | SVH | SVV |
|---|---|---|---|---|
| Original basis | 1.0 | 0.2 | 0.1 | 0.6 |
| Reverse receive V | 1.0 | 0.2 | −0.1 | −0.6 |
| Reverse transmit V | 1.0 | −0.2 | 0.1 | −0.6 |
| Reverse both V axes | 1.0 | −0.2 | −0.1 | 0.6 |
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Transform bases explicitly
If U_i changes the incident basis and U_s changes the scattered basis, the matrix transforms with both operators, with transpose or conjugate-transpose details set by the field convention. Write the exact formula used by the data product.
Linear, circular and local spherical bases are not interchangeable labels. Circular handedness is especially sensitive to propagation direction: a convention defined looking into the oncoming wave can swap names when copied into a viewpoint looking along propagation.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Connect the established polarimetric routes
The reciprocity and helicity guide explains when non-symmetric scattering must be retained. The Pauli guide shows how familiar colours depend on basis and reduction assumptions.
Use polarimetric deorientation for roll-angle effects and the Kennaugh and Huynen guide for real representations and invariants. Those monostatic tools need their hypotheses rechecked in bistatic data.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Separate geometry, target and instrument
A bistatic observation mixes target response with two antenna patterns, two path losses, two propagation media, timing and synchronisation, footprint overlap and independent channel calibrations. Geometry-dependent normalisation should be documented before cross-angle comparisons.
Use calibration targets whose bistatic response is understood, and keep complex phase reference information. A magnitude-only product cannot support every basis transformation or reciprocity diagnostic.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the limits and common misconceptions
The label HH does not guarantee the same physical polarisation vector at transmitter and receiver. A symmetric-looking matrix is not proof of reciprocity, and a non-symmetric matrix is not proof of exotic target physics.
The specular point is set by geometry and the local normal, not merely the midpoint between platforms. Terrain slope, Earth curvature, motion and finite footprints can all shift the effective configuration.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record platform positions, time, propagation-direction convention, incident and scattered planes, basis vectors, handedness, bistatic and aspect angles, surface normal, wavelength, complex calibration, antenna patterns, path-loss correction, synchronisation, footprint overlap and uncertainty.
ESA’s SAR Polarimetry Basic Concepts develops scattering matrices, bases and reciprocal monostatic reductions. The ESA POLinSAR session report identifies bistatic polarimetry as a distinct theory and application question.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Is monostatic radar just a zero-angle bistatic case?
It is a limiting geometry, but conventions and reciprocal reductions must also converge consistently; simply setting an angle to zero may not repair mismatched bases.
Can I compare HH power across bistatic angles?
Only after accounting for geometry, antenna response, path loss, footprint, calibration and the precise basis vectors.
Does a strong specular return imply a smooth surface?
It is evidence consistent with coherent reflection, but roughness, wavelength, slope distribution and volume contributions still require checks.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a changed-basis transfer check
Choose orthonormal transmit and receive bases for two non-coplanar paths. Transform a four-entry complex scattering matrix after reversing one receive vector, then after rotating the transmit basis by 30 degrees. Identify which powers, phases and invariants should remain comparable.
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