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An interferogram may display colourful phase fringes even where the two radar acquisitions no longer preserve a reliable phase relationship. Coherence helps judge that relationship, but it is an estimate with several possible causes.
Open the chapter contents · Remote Sensing root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the question, or read from Chapter 1 for the complete argument. The chapters remain open on the page; these grouped routes are an index.
Route 1 · Build the complex comparison
Route 2 · Work a coherence estimate
Route 3 · Separate decorrelation causes
Route 4 · Interpret without overclaiming
Route 5 · Check and continue
CHAPTER 1 OF 12 · BUILD THE COMPLEX COMPARISON
1. InSAR compares complex signals, not two coloured pictures
Synthetic aperture radar records a complex signal with amplitude and phase. Interferometric SAR combines two co-registered acquisitions of the same ground area. Their phase difference can contain information about path-length change, topography, atmosphere, orbit and processing.
The comparison is useful only where the phase relationship remains sufficiently stable. Interferometric coherence estimates the normalised complex correlation between the two acquisitions in a local window. Its magnitude usually lies between zero and one: values near one indicate a consistent relationship, while values near zero indicate strong decorrelation.
Coherence is not a physical displacement and it is not a universal confidence probability. It is an estimated property of an image pair, processing chain, neighbourhood and acquisition geometry.
CHAPTER 2 OF 12 · BUILD THE COMPLEX COMPARISON
2. The normalisation separates agreement from raw power
For complex samples s₁,k and s₂,k in a window, a common sample coherence magnitude is the absolute value of Σs₁,ks₂,k* divided by the square root of (Σ|s₁,k|²)(Σ|s₂,k|²). The conjugate aligns the phase comparison, while the denominator normalises for power.
If one image is simply multiplied by a positive gain, numerator and denominator scale together, so coherence need not change. A backscatter increase is therefore not automatically a coherence decrease. Conversely, similar average amplitudes can coexist with randomised phase and low coherence.
The estimated interferometric phase is the argument of the complex cross-sum. Coherence describes how consistently the samples support that phase inside the chosen window.
CHAPTER 3 OF 12 · WORK A COHERENCE ESTIMATE
3. Work a small complex-correlation example
Suppose a four-look window has unit amplitudes. Let the phase differences between corresponding samples be 0°, 10°, −10° and 0°. The complex contributions are eⁱ⁰, eⁱ¹⁰°, e⁻ⁱ¹⁰° and eⁱ⁰. Their imaginary parts cancel, and the real sum is 2+2cos10°≈3.970.
With four unit-power samples in each image, the denominator is four. The estimated coherence magnitude is about 3.970/4=0.992. The estimated phase is approximately 0°.
| Phase differences | Cross-sum magnitude | Estimated coherence | Interpretation |
|---|---|---|---|
| 0°, 10°, −10°, 0° | 3.970 | 0.992 | Strongly consistent local phase |
| 0°, 90°, 180°, 270° | 0 | 0 | Contributions cancel completely |
CHAPTER 4 OF 12 · WORK A COHERENCE ESTIMATE
4. Changed context: the same mean phase can have weak support
Now use phase differences 0°, 60°, −60° and 0°. The cross-sum is 2+2cos60°=3, so coherence is 0.75 even though the estimated mean phase remains 0°.
This changed context separates estimate from reliability. Both windows point to the same average phase, but the second has more phase scatter. A displayed fringe can therefore look similar while its evidential support differs.
Transfer check: double every amplitude in the second acquisition but keep the phase differences unchanged. The normalisation cancels the gain, leaving the same idealised coherence. Then randomise the phase differences while keeping amplitudes fixed; coherence falls. These tests clarify what the statistic is measuring.
CHAPTER 5 OF 12 · WORK A COHERENCE ESTIMATE
5. Window size trades spatial detail for estimator stability
A very small window preserves local boundaries but supplies few samples, so the coherence estimate is noisy. A larger window reduces sampling variability but can mix roads, vegetation, water and buildings or smear a narrow deformation gradient.
Neighbouring SAR samples may also be correlated, so the number of stored pixels exceeds the number of independent looks. The effective information depends on processing bandwidth, multilooking and spatial correlation.
| Choice | Benefit | Cost | Evidence check |
|---|---|---|---|
| Small window | Preserves boundaries | Noisy coherence estimate | Compare repeated pairs or confidence intervals |
| Large window | More stable estimate | Mixes surfaces and phases | Inspect land-cover and phase gradients |
| More multilooking | Reduces speckle variance | Coarser resolution | Report effective resolution and looks |
CHAPTER 6 OF 12 · SEPARATE DECORRELATION CAUSES
6. Temporal decorrelation is one cause, not the definition
Scatterers can change between acquisitions because of vegetation motion, moisture, snow, flooding, construction or surface disturbance. Their complex contributions then differ, reducing coherence. This is temporal decorrelation.
The time interval matters, but “longer always means lower coherence” is not a law for every surface. Stable urban structures can remain coherent over long intervals, while vegetation can decorrelate quickly. Seasonal similarity can sometimes matter more than elapsed days alone.
Low coherence may therefore contain useful change information, yet it does not identify which change occurred. Interpretation needs land cover, weather, acquisition timing and alternative observations.
CHAPTER 7 OF 12 · SEPARATE DECORRELATION CAUSES
7. Geometry and processing can also reduce coherence
Perpendicular baseline changes the viewing geometry and the spatial-frequency content sampled by the two acquisitions. Large separation can cause geometric decorrelation. Thermal noise, inaccurate co-registration, Doppler differences and processing choices contribute further losses.
An apparent low-coherence patch should not be labelled physical change until these alternatives are checked. Pair metadata, baseline, orbit quality, co-registration residuals and neighbouring stable targets provide important controls.
Different decorrelation contributions are often discussed multiplicatively in idealised models. That framework is useful, but real causes may not be perfectly separable or independently identifiable from one image pair.
CHAPTER 8 OF 12 · SEPARATE DECORRELATION CAUSES
8. Coherence and phase unwrapping influence each other operationally
Wrapped interferometric phase is observed modulo 2π. Phase unwrapping attempts to reconstruct continuous phase differences by choosing integer cycles across the image. Low-coherence regions provide weak constraints, so errors can propagate or force masks and disconnected components.
A fixed threshold is a processing decision, not a universal law. Official products use documented thresholds for particular workflows, while another sensor, look count, terrain or purpose may require different treatment.
Preserve the coherence layer, mask logic and connected-component information alongside unwrapped displacement. A smooth map after masking does not mean the omitted region had zero movement.
CHAPTER 9 OF 12 · INTERPRET WITHOUT OVERCLAIMING
9. High coherence is not proof of deformation
Stable phase can include topography, orbital ramps, atmospheric delay and systematic processing residuals. Coherence says the complex relationship is consistent, not that its cause is ground motion.
Likewise, low coherence does not prove no deformation. It means the phase-derived measurement is difficult or unreliable under that pair and method. Complementary longer-wavelength data, shorter temporal baselines, persistent-scatterer methods or ground observations may recover evidence.
The defensible statement names both the measurement and its support: “relative line-of-sight phase change in coherent pixels after stated corrections,” not “the ground moved everywhere shown.”
CHAPTER 10 OF 12 · INTERPRET WITHOUT OVERCLAIMING
10. Report coherence as part of an evidence chain
Record sensor and product level, acquisition dates, orbit direction, polarisation, wavelength, temporal and perpendicular baselines, DEM, co-registration method, multilooking, coherence window, filters, mask thresholds and unwrapping method.
Check known stable and unstable surfaces. Compare adjacent pairs and, when possible, independent tracks or ground measurements. Inspect whether a deformation signal persists under reasonable processing choices.
Avoid treating a coherence image as a generic land-cover map without validation. Its values are pair-specific and sensitive to both surface behaviour and imaging conditions.
CHAPTER 11 OF 12 · CHECK AND CONTINUE
11. Questions readers should ask
Is coherence the same as amplitude correlation?
No. Interferometric coherence uses complex samples and therefore includes phase consistency. Similar intensity alone does not guarantee reliable phase.
Does coherence equal one for unchanged ground?
Not necessarily. Thermal noise, baseline, vegetation motion, moisture and processing can reduce it even without the target deformation of interest.
Can low coherence itself map change?
Sometimes it is a useful indicator, but causes are ambiguous. Validate against acquisition conditions, land cover and independent evidence.
What threshold should I use?
There is no context-free threshold. Use product guidance, effective looks, error tolerance and the needs of the unwrapping or change task.
CHAPTER 12 OF 12 · CHECK AND CONTINUE
12. Continue through the verified remote-sensing ecosystem
Begin with the Remote Sensing root, the Gold Standard of Education and the How X Works hub. For supporting SAR measurement habits, read Speckle Averaging, Equivalent Looks and Uncertainty in a SAR Mean, Incidence Angle, SAR Backscatter and False Change Across Orbits and Co-Registration Offsets and False Change at a Boundary.
For numerical-domain checks, continue to SAR Backscatter Decibels and False Change Claims. For sampling over time, use Revisit Gaps, Cloud Cover and Missed Short Events.
Authoritative technical reading: the NISAR Data User Guide on phase and coherence defines the 0-to-1 interpretation and reliability role. NASA Earthdata’s unwrapped-interferogram recipe connects decorrelation with deformation mapping, while ESA’s InSAR principles and processing guidelines details geometric, temporal and processing effects.
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