Microwave Remote Sensing (MRS) Essential

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1. Why Microwaves in Remote Sensing? Unique Interaction Properties: Microwaves interact differently with matter compared to optical/IR. They are sensitive to size, shape, and water content rather than chlorophyll. Penetration Capabilities: Clouds and precipitation: Many microwave wavelengths can penetrate clouds, fog, and light rain, enabling all-weather observation. Dry soils/sand: Longer microwave wavelengths (e.g., L-band, P-band) can penetrate several meters into dry soil or sand, revealing subsurface features. Vegetation: Longer wavelengths can penetrate vegetation canopies to interact with underlying ground or tree trunks. All-Day/Night Operation: Active microwave instruments provide their own illumination, allowing data acquisition regardless of solar illumination. Passive imagers detect thermal emission, also independent of sunlight. Atmospheric Transparency: Certain microwave windows exist where atmospheric attenuation is minimal, crucial for surface observation. Conversely, atmospheric "walls" are exploited for atmospheric sounding. Quantitative Measurements: Microwave instruments can make precise quantitative measurements (e.g., centimeter-scale ground deformation, atmospheric concentrations to parts per billion). Limitations and Challenges Large Antennas: Due to longer wavelengths, achieving high spatial resolution often requires very large antennas (meters or more), posing challenges for satellite deployment (weight, size, power). Complexity: Microwave remote sensing is mathematically and physically challenging, involving concepts like coherence, polarimetry, and interference. Data Interpretation: Interpretation of microwave data (especially radar images) is complex, often requiring specialized knowledge due to speckle, geometric distortions, and unique interaction mechanisms. Power Consumption: Active systems (e.g., SAR) are typically heavy, large, and power-intensive. 2. A Brief History of Microwaves 2.1 Early Foundations (19th Century) Electricity and Magnetism: Luigi Galvani & "animal electricity": Early experiments with electric currents on biological tissues. Franz Anton Mesmer & "animal magnetism": Popularized magnetic healing, later debunked as hypnotic suggestion. Hans Christian Ørsted & Michael Faraday: Demonstrated the interconnectedness of electricity and magnetism (induction). Faraday's concept of "fields" was crucial. Light as a Wave: Thomas Young & Augustin Jean Fresnel: Re-established the wave theory of light, demonstrating interference (Young's double-slit experiment) and proposing transverse waves (explaining polarization). Armand Fizeau & Jean Foucault: Measured the speed of light, showing it was slower in water than air, supporting wave theory. 2.2 Maxwell and Hertz: Unification and Confirmation James Clerk Maxwell: Unified electricity, magnetism, and light into a single theory with his four "Maxwell's Equations." Postulated the existence of electromagnetic waves propagating through space at the speed of light: $c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$. His theory established the electromagnetic spectrum, from radio waves to gamma rays. Heinrich Hertz: Experimentally confirmed Maxwell's theory in 1886, generating and detecting radio waves. Demonstrated wave properties like reflection, refraction, interference, and polarization for these "invisible" waves. Microwave Definition: EM radiation with wavelengths from 1mm to 30cm (1 GHz to 300 GHz), though modern radar extends this. 2.3 Radios, Death Rays and Radar Early Radio: Guglielmo Marconi's transatlantic radio transmission (1901) ushered in global communication. Echolocation Concept: Nikola Tesla (1900) conceived of using radio waves for object detection and movement tracking. Christian Hülsmeyer (1904) patented an obstacle detector. Radar Development: Robert Watson-Watt: Pioneered operational pulsed radar systems in the UK, leading to the "Chain Home" network. WWII Impact: Radar became crucial for air defense (Battle of Britain) and anti-submarine warfare (Battle of the Atlantic). Cavity Magnetron: A key breakthrough allowing generation of powerful 10cm waves, making airborne radar feasible (e.g., H2S system for ground mapping). Radar Nomenclature: Wartime secrecy led to arbitrary letter designations for frequency bands (P, L, S, C, X, Ku, Ka, V, W, mm bands), which persist today. 2.4 Post-War Diversification Radio and Radar Astronomy: Jodrell Bank: Sir Bernard Lovell's facility became a leading radio observatory. Discoveries: Quasars, pulsars (LGM-1), and the cosmic microwave background radiation (Penzias and Wilson, 1965) revolutionized astronomy. Planetary Radar: Used to map Venus and other solar system bodies, improving distance measurements (e.g., Astronomical Unit). 2.5 Imaging Radar Side-Looking Airborne Radar (SLAR): Developed for military reconnaissance in the 1950s, providing images through darkness and clouds. Doppler Beam Sharpening (Carl Wiley, 1952): Concept that led to Synthetic Aperture Radar (SAR), improving spatial resolution by using Doppler shifts. Civilian Applications: Large-scale mapping projects in Panama (1967) and the Amazon (Project Radam, 1971) demonstrated SAR's utility for resource management and inaccessible regions. 2.6 Microwave Remote Sensing from Space Early Atmospheric Sounding: Soviet Cosmos 243 (1968) and US Nimbus-5 (1972) carried microwave radiometers for atmospheric measurements. Spaceborne Radar: Altimeters and Scatterometers: Used for Apollo moon landings (1969-70) and Skylab missions (1973-74). Seasat (1978): Carried the first civilian spaceborne imaging SAR, revolutionizing oceanography. Modern SAR Missions: ERS-1/2, JERS-1, Radarsat, Envisat, ALOS, TerraSAR-X, SRTM, Marsis, Cassini Radar. 3. Physical Fundamentals of EM Waves 3.1 Physical Properties of EM Waves Wave-Particle Duality: EM radiation can be described as waves (frequency, wavelength, refraction, diffraction, interference, polarization, scattering) or particles (photons). Wave theory is dominant for microwaves. Harmonic Waves: Simplest mathematical description, based on sine/cosine functions. Wave function: $\psi(z, t) = A \sin \kappa (z - \upsilon t)$ $A$: Amplitude (maximum disturbance). $\kappa$: Wavenumber (spatial frequency) $[\text{rad/m}]$. $z$: Position along propagation direction. $\upsilon$: Wave speed. $t$: Time. Wavelength ($\lambda$): Spatial period. $\kappa = \frac{2\pi}{\lambda}$. Measured in meters $[\text{m}]$. Period ($T$): Temporal period. $T = \frac{\lambda}{\upsilon}$. Measured in seconds $[\text{s}]$. Frequency ($\nu$): Number of cycles per unit time. $\nu = \frac{1}{T}$. Measured in Hertz $[\text{Hz}]$. Relationship: $c = \lambda \nu$ (where $c$ is the speed of EM radiation). Angular Frequency ($\omega$): $\omega = \frac{2\pi}{T} = \kappa \upsilon$. Measured in radians per second $[\text{rad/s}]$. Wave function: $\psi(z, t) = A \sin (\kappa z - \omega t)$ Phase ($\phi_0$): Initial angle of the wave at $t=0, z=0$. Complete wave function: $\psi(z, t) = A \sin (\kappa z - \omega t + \phi_0)$ Wave Vector ($\mathbf{k}$): Characterizes direction and wavenumber. $\mathbf{k} = \kappa \hat{\mathbf{k}}$, where $\hat{\mathbf{k}}$ is a unit vector. 3.2 Complex Wave Description Uses Euler's formula: $e^{i\theta} = \cos \theta + i \sin \theta$. Complex wave function: $\psi(z, t) = A e^{i(\omega t - \kappa z + \phi_0)} = A e^{i\phi}$ The real part (cosine) is typically taken for the actual wave profile. Simplifies mathematical operations for wave combinations. Visualized as a rotating vector in the complex plane (amplitude $A$, phase $\phi$). 3.3 Energy and Power of Waves Power ($P$): Energy per unit time. Proportional to the square of the amplitude of the electric field ($E_0$). $P = \frac{|E(z, t)|^2}{2\eta}$ (for EM waves, where $\eta$ is impedance). Power scales differently from amplitude. Power Density: Power per unit area $[\text{W/m}^2]$. Irradiance ($E$): Total radiant power incident on a unit area. Radiant Exitance ($M$): Total outgoing radiated power from a unit area. Radiance ($L$): Power per unit solid angle per unit area $[\text{W/m}^2\text{sr}^{-1}]$. Spectral Radiance: Radiance per unit frequency $[\text{W/m}^2\text{sr}^{-1}\text{Hz}^{-1}]$ or per unit wavelength $[\text{W/m}^2\text{sr}^{-1}\text{m}^{-1}]$. Brightness/Intensity: Conveniently refers to spectral radiance incident on a detector. 3.4 Polarization Property of transverse waves describing the direction of electric field oscillation. Linear Polarization: Oscillation along a straight line (e.g., horizontal or vertical). Can be represented as superposition of two orthogonal components (e.g., $E_x, E_y$). $E_x(z, t) = E_{0x} e^{i\phi}$ $E_y(z, t) = E_{0y} e^{i(\phi + \epsilon)}$ (where $\epsilon$ is phase difference between components). 3.5 Combination of Waves (Interference) Interference: Superposition of waves. Resulting wave amplitude depends on the phase difference between individual waves. Constructive Interference: Waves are in-phase ($\delta\phi = 0, 2\pi, \dots$), amplitudes add. Destructive Interference: Waves are out-of-phase ($\delta\phi = \pi, 3\pi, \dots$), amplitudes cancel. Vector Representation: Waves can be represented as vectors (length = amplitude, angle = phase). Summing vectors gives the resultant wave. 3.6 Coherence Definition: Two waves with a phase difference that remains constant over time are coherent. Implies identical frequencies. Complex Coherence ($\Gamma_{12}$): Quantifies predictability/similarity between waves. $\Gamma_{12} = \langle E_1 E_2^* \rangle$ (ensemble average of product of wave $E_1$ and conjugate of $E_2$). Normalized Coherence ($\gamma_{12}$): Independent of absolute amplitudes. $\gamma_{12} = \frac{\langle E_1 E_2^* \rangle}{\sqrt{\langle |E_1|^2 \rangle \langle |E_2|^2 \rangle}}$. Ranges from 0 (incoherent) to 1 (fully coherent). A complex number with amplitude and phase. Practical Considerations: Real-world waves are often partially coherent. Ensemble averaging can be approximated by spatial or temporal averaging for remote sensing. 3.7 Phase as a (Relative) Distance Measure Phase changes with distance. Measuring phase difference between two detectors can reveal path length differences. Phase Ambiguity: Phase is cyclic ($0 \text{ to } 2\pi$). A phase difference tells about the fractional wavelength difference, but not the absolute number of whole wavelengths ($\pm 2\pi n$). This principle is fundamental to antenna beamforming, directivity, and interferometry. Analogy to human binaural hearing (interaural phase difference). 3.8 Multiple Source Interference Pattern Combining multiple coherent sources (e.g., array antenna) can direct wave energy into a single, narrow beam. Far Field vs. Near Field: Near Field: Complex patterns close to sources. Far Field: Regular patterns of radiating beams (simplification: parallel rays). Remote sensing typically operates in the far field. Beamwidth and Angular Resolution: Narrower beam for larger aperture ($D$) or shorter wavelength ($\lambda$). Angular width of beam: $\theta \approx \frac{\lambda}{D}$. Angular resolution (Rayleigh criterion): $\theta_r \approx \frac{\lambda}{D}$. For circular aperture: $\theta_{\text{cd}} \approx \frac{1.22\lambda}{D}$. Huygens' Wavelets: Any wavefront can be considered a collection of secondary, isotropic sources, explaining diffraction and antenna patterns. 4. Propagation of Microwaves Electromagnetic Properties of Materials: Electric Permittivity ($\epsilon$): Influences electric field. Related to relative permittivity ($\epsilon_r = \epsilon_r' - i\epsilon_r''$). $\epsilon_r'$ (real part) is the dielectric constant. Magnetic Permeability ($\mu$): Influences magnetic field. For most Earth materials, $\mu \approx \mu_0$ (permeability of free space). Electric Conductivity ($g$): Ability to conduct current. High for metals (good reflectors, opaque to EM waves). Wave Speed in Media: $\upsilon = \frac{c}{\sqrt{\epsilon_r}}$. Wavelength is also reduced: $\lambda_{\text{medium}} = \frac{\lambda_{\text{vacuum}}}{\sqrt{\epsilon_r}}$. $\sqrt{\epsilon_r}$ is the refractive index ($n$). Lossy Media: Energy loss (attenuation) as wave propagates. Penetration Depth ($\delta_p$): Distance where power is reduced by factor $e$. $\delta_p \approx \frac{\lambda \sqrt{\epsilon_r'}}{2\pi \epsilon_r''}$ (for $\epsilon_r''/\epsilon_r' Longer wavelengths penetrate deeper into dry, low-loss media. Doppler Effect: Frequency shift when source and detector move relative to each other. $f_D = \frac{V}{\lambda}$ (where $V$ is relative velocity). 4.1 Sources of Microwaves Natural Production (Thermal Emission): Blackbody Radiation: Any object with physical temperature $T$ emits EM radiation. Planck Function: $B_\nu(T) = \frac{2h\nu^3}{c^2} \frac{1}{e^{h\nu/\kappa T} - 1}$ (intensity per unit frequency, per steradian). Peak emission shifts to higher frequencies with increasing $T$ (Wien's Law). Rayleigh-Jeans Law (low frequency approximation): $B_\nu(T) \approx \frac{2\nu^2\kappa}{c^2} T$. Linear relationship between intensity and $T$. Brightness Temperature ($T_B$): Convenient way to express microwave intensity in units of temperature. $T_B = \epsilon T$ (where $\epsilon$ is emissivity, $T$ is physical temperature). Emissivity ($\epsilon$): Ratio of object's emission to blackbody emission at same $T$. Reflectivity ($\rho$), Transmissivity ($\Upsilon$), Absorptivity ($\kappa$): $\rho + \Upsilon + \kappa = 1$. Kirchoff's Law: Good absorbers are good emitters ($\epsilon = \kappa$). For opaque objects: $\rho + \epsilon = 1$. Spectral Lines: Molecular transitions (rotational/vibrational states) cause discrete absorption/emission lines (e.g., O2, H2O). Line broadening occurs due to temperature and pressure. Artificial Production: Accelerating charges: Fundamental principle. Dipole Antenna: Simple conducting rod with oscillating current. Maser: Microwave amplification by stimulated emission of radiation (coherent source). Electron Tubes (e.g., Magnetron): Use high-speed electrons in magnetic fields to generate microwaves. Radio Waves: Generated by periodic currents in wires (lower frequencies). Polarization: Artificial sources can be linearly polarized. Natural sources are often unpolarized but can be polarized by reflection/transmission. 5. Polarimetry 5.1 Describing Polarized Waves Polarization Basis: Orthogonal states used to describe any polarization (e.g., linear horizontal/vertical, circular left/right). Coordinate Systems: Forward Scattering Alignment (FSA): Z-axis along wave propagation, common in optics. Back-Scatter Alignment (BSA): Z-axis parallel to propagation, but antenna-centric, common in radar. 5.2 Superposition of Polarized Waves Combining orthogonal polarized waves creates new polarization states. Linear Polarization: Created by in-phase H and V waves. Orientation angle ($\psi$) depends on relative amplitudes. Elliptical Polarization: Created by H and V waves with phase difference ($\delta$). Ellipticity angle ($\chi$) depends on phase difference and relative amplitudes. Circular Polarization: Special case of elliptical polarization when H and V amplitudes are equal and phase difference is $\pm \pi/2$. Polarization Synthesis: Fully polarimetric systems can synthesize any transmit/receive polarization from measured H and V components. 5.3 Representing Polarization Poincaré Sphere: Geometric representation where polarization states are points on a sphere (latitude = $2\chi$, longitude = $2\psi$). Orthogonal polarizations are antipodal points. Radius can represent intensity. Stokes Vector ($\mathbf{g}$): Four parameters ($I_0, Q, U, V$) describing total intensity and polarization state. Measurable with polarizing filters. $\mathbf{g} = \begin{pmatrix} I_0 \\ Q \\ U \\ V \end{pmatrix} = \begin{pmatrix} \langle E_y^2 \rangle + \langle E_x^2 \rangle \\ \langle E_y^2 \rangle - \langle E_x^2 \rangle \\ 2 \operatorname{Re}\langle E_y E_x^* \rangle \\ 2 \operatorname{Im}\langle E_y E_x^* \rangle \end{pmatrix} = I_0 \begin{pmatrix} 1 \\ \cos 2\psi \cos 2\chi \\ \sin 2\psi \cos 2\chi \\ \sin 2\chi \end{pmatrix}$ $I_0$: Total intensity (unpolarized power). $Q$: Tendency towards vertical/horizontal linear polarization. $U$: Tendency towards $\pm 45^\circ$ linear polarization. $V$: Tendency towards left/right circular polarization. Partially Polarized Waves: Stokes vector can describe. $I_0^2 \ge Q^2 + U^2 + V^2$. Degree of Polarization ($m$): $m = \frac{\sqrt{Q^2 + U^2 + V^2}}{I_0}$. (0 for unpolarized, 1 for fully polarized). Brightness Stokes Vector: Expresses Stokes parameters in terms of brightness temperature. 5.4 Stokes Scattering Matrix ($\mathbf{M}$) / Mueller Matrix Describes how a target transforms an incident Stokes vector ($\mathbf{g}_i$) into a scattered Stokes vector ($\mathbf{g}_s$). $\mathbf{g}_s = \mathbf{M} \mathbf{g}_i$ A $4 \times 4$ real matrix, contains full polarimetric response of the target. 5.5 The Scattering Matrix ($\mathbf{S}$) For radar polarimetry, relates incident electric field vector to scattered electric field vector. $\mathbf{S} = \begin{pmatrix} S_{VV} & S_{VH} \\ S_{HV} & S_{HH} \end{pmatrix}$ $S_{pq}$: Complex number representing phase and amplitude for $q$-transmit, $p$-receive. Co-polarized ($S_{HH}, S_{VV}$), Cross-polarized ($S_{HV}, S_{VH}$). Reciprocity: $S_{HV} = S_{VH}$ for most Earth observation. Target Vector ($\mathbf{k}$): Compact representation. $\mathbf{k} = [S_{VV} \quad S_{HV} \quad S_{HH}]^T$. Pauli Basis Target Vector ($\mathbf{k}_P$): $\mathbf{k}_P = \frac{1}{\sqrt{2}} [S_{HH} + S_{VV} \quad S_{HH} - S_{VV} \quad 2S_{HV}]^T$. Emphasizes different scattering mechanisms. Covariance Matrix ($\mathbf{C}$): Statistical inter-relationship between polarimetric channels. $\mathbf{C} = \mathbf{k} \mathbf{k}^{*T}$. Coherency Matrix ($\mathbf{T}$): Similar to covariance, but using Pauli target vector. $\mathbf{T} = \mathbf{k}_P \mathbf{k}_P^{*T}$. 5.6 Passive Polarimetry Polarimetric measurements are important for discriminating between targets and understanding microwave sources, especially for off-nadir viewing. Increased surface roughness and volume scattering (vegetation, rain) tend to depolarize signals. 5.7 Polarimetry in Radar Radar polarimeters transmit two orthogonal polarizations and receive both, capturing full phase and amplitude information. Polarization Synthesis: Simulate response for any transmit/receive polarization post-data collection. Polarization Response Curves (Signatures): Visualizes backscatter power as a function of transmit/receive polarization states (e.g., on a Poincaré sphere projection). 5.8 Important Polarimetric Properties Unpolarized Power (Span): Total power scattered back to antenna, regardless of polarization. $T_u = \frac{1}{4} (|S_{HH}|^2 + 2|S_{HV}|^2 + |S_{VV}|^2)$. Basis invariant. Degree of Polarization ($m$): For Stokes vector. Coefficient of Variation ($\upsilon_u$): Radar equivalent, ratio of minimum to maximum power in polarization synthesis. $\upsilon_u = P_{\min} / P_{\max}$. Polarimetric Ratios: (e.g., $T_V/T_H$, $|S_{VV}|^2/|S_{HH}|^2$, $|S_{HV}|^2/|S_{HH}|^2$). Indicate geometric/shape properties. Coherent Parameters: Polarimetric Coherence ($\gamma_{pq, p'q'}$): Complex cross-correlation between different polarization channels. Magnitude indicates degree of coherence, phase indicates phase difference. Polarimetric Phase Difference (PPD): Phase of $\gamma_{HH,VV}$. Indicates scattering mechanisms (single/double bounce). Polarimetric Entropy ($H$): Basis-invariant measure of "total" polarimetric coherence. High entropy implies depolarization (randomness). Polarimetric Decomposition: Expresses target response as a combination of idealized scatterers (e.g., diplane, sphere, helix; or surface, double-bounce, volume scattering). 6. Microwave Interaction with Earth Materials 6.1 Continuous Media and the Atmosphere Radiative Transfer Theory: Describes intensity changes in a medium that absorbs, emits, and scatters radiation. $I_\nu(s) = I_\nu(0) e^{-\tau_\nu(0,s)} + \int_0^s \kappa_\nu(s') B_\nu(T(s')) e^{-\tau_\nu(s',s)} ds'$ $I_\nu(s)$: Intensity at position $s$. $I_\nu(0)$: Initial intensity. $\kappa_\nu(s')$: Volume absorption coefficient. $B_\nu(T(s'))$: Planck function. $\tau_\nu(s',s)$: Optical depth (opacity). Microwave Brightness Temperature ($T_B$): Replaces intensity using Rayleigh-Jeans approximation. $T_B(s) = T_B(0) e^{-\tau_\nu(0,s)} + \int_0^s \kappa_\nu(s') T(s') e^{-\tau_\nu(s',s)} ds'$ For homogeneous medium: $T_B = T_B(0)\Upsilon + T(1-\Upsilon)$. Spectral Lines: Discrete absorption/emission frequencies due to molecular transitions (e.g., H2O, O2, O3). Line Broadening: Spreading of spectral lines due to temperature (Doppler broadening) and pressure (collisional broadening). Faraday Rotation: Rotation of polarization plane by ionosphere, significant at lower frequencies ($ \propto 1/\nu^2 $). 6.2 Interaction with Discrete Objects Diffraction: Interaction of waves with objects or apertures. Diffraction Limit: Fundamental limit to angular resolution of an aperture. Fraunhofer Diffraction: Occurs in the far field (plane waves). Scattering: Redirection of incident EM energy by an object. Scattering Cross-Section ($\sigma$): Quantifies effectiveness of a scatterer. Effective area that intercepts power and scatters it. $\sigma(\theta) = \frac{\text{Scattered power per unit solid angle into direction } \theta}{\text{Incident intensity } / 4\pi}$ Radar Cross-Section (RCS): Power scattered back to the radar. $\sigma = P_r \frac{(4\pi)^3 R^4}{P_t G^2 \lambda^2}$ Normalized Radar Cross-Section ($\sigma^0$): For distributed targets, $\sigma^0 = \sigma / A$. (Unitless). Scattering Regimes: Optical Region (geometric optics): Object size $\gg \lambda$. $\sigma \propto \text{physical area}$. Rayleigh Scattering: Object size $\ll \lambda$. $\sigma \propto 1/\lambda^4$. Mie Scattering: Object size $\approx \lambda$. Resonant effects, complex $\sigma$. 6.3 Scattering and Emission from Volumes Volume Scatterers (Inhomogeneous Media): Composed of randomly distributed discrete elements. (e.g., vegetation, snow, clouds). Volume-Scattering Coefficient ($\kappa_s$), Volume-Absorption Coefficient ($\kappa_a$): Describe energy loss from path. Total Extinction Coefficient: $\kappa_e = \kappa_a + \kappa_s$. Single Scattering Albedo ($a$): $a = \kappa_s / \kappa_e$. Emission from Homogeneous Volume: $T_V(\theta) = T(1-a)(1 - \Upsilon_V(\theta))$ (where $\Upsilon_V(\theta) = e^{-\kappa_e h / \cos\theta}$ is volume transmissivity). Backscatter from Homogeneous Volume: $\sigma^0_{\text{vol}}(\theta) = \frac{3a}{4} (1 - \Upsilon_V^2(\theta)) \cos\theta$ (Water Cloud Model). 6.4 Reflection and Emission from Smooth Surfaces Reflection: Coherent scattering at boundaries much larger than $\lambda$. Specular reflection: angle of incidence = angle of reflection. Refraction (Snell's Law): Bending of wave as it enters a new medium. $\frac{\sin\theta_i}{\sin\theta_t} = \frac{n_2}{n_1}$. Reflection Coefficients (Fresnel): Describe proportion of EM wave reflected, dependent on polarization and incidence angle. $R_{VV} = \frac{\epsilon \cos\theta_1 - \sqrt{\epsilon - \sin^2\theta_1}}{\epsilon \cos\theta_1 + \sqrt{\epsilon - \sin^2\theta_1}}$ $R_{HH} = \frac{\cos\theta_1 - \sqrt{\epsilon - \sin^2\theta_1}}{\cos\theta_1 + \sqrt{\epsilon - \sin^2\theta_1}}$ Power Reflection Coefficient (Reflectivity): $\rho_{HH} = |R_{HH}|^2$, $\rho_{VV} = |R_{VV}|^2$. Brewster Angle: Angle where $R_{VV}$ is zero (only HH reflected). Emission from Smooth Surfaces: $T_B = \epsilon_p(\theta_i) T$ (where $\epsilon_p = 1 - \rho_p$). 6.5 Scattering and Emission from Rough Surfaces Definition of "Rough": Relative to wavelength ($\lambda$). Rayleigh Criterion: Surface is smooth if $h_{\text{rms}} Fraunhoffer Criterion: Stricter, $h_{\text{rms}} Effects of Roughness: Increases diffuse scattering, reduces specular reflection, tends to depolarize signal, reduces H-V contrast. 6.6 Non-Random (Periodic) Surfaces Bragg Scattering: Coherent scattering from periodic surfaces (e.g., wind ripples on water). Strong sensitivity to observation angle. 6.7 Scattering and Emission from Natural Surfaces Oceans and Lakes: Calm: High $\epsilon$, $\rho$ depends on $T$ and salinity. Rough: Wind-induced capillary and gravity waves increase roughness, affecting $\epsilon$ and $\sigma^0$. Used to estimate wind speed. Asymmetry: Wave patterns aligned with wind cause azimuthal asymmetry in backscatter. Hydrometeors: Cloud droplets: Absorb effectively, scatter little. Rain droplets, ice/snow particles: Significant scattering, especially at higher frequencies. Basis for rain radar. Ice and Snow: Liquid water content is key. Ice has low $\epsilon_r'$, transparent. Water has high $\epsilon_r'$, opaque. Dry Snow: Volume scatterer for high frequencies, penetrable for low. $\epsilon$ and $\sigma^0$ depend on thickness, grain size. Wet Snow: High absorption, reduced scattering. Freshwater Ice: Very low $\epsilon_r'$, highly penetrable. Interaction at ice-water or ice-soil boundaries. Glacial Ice: Layered structure, can be highly penetrable (L/P-band). Sea Ice: Salinity significantly affects $\epsilon_r'$. Brine pockets/air bubbles act as scatterers. Different types (young, first-year, multi-year) have distinct microwave signatures. Bare Rock and Deserts: Surface roughness is dominant. Dry Sand: Very low $\epsilon_r'$, highly penetrable. Allows mapping subsurface features with long wavelengths. Wind ripples on sand: Bragg scattering. Soils: Composition of soil, air, water. Liquid water content is primary driver of $\epsilon_r'$. Dry soils: Volume scatterers. Wet soils: Rough surface. Soil moisture profile: Deeper penetration for longer wavelengths. Frozen vs. Thawed: Dramatic change in $\epsilon_r'$. Vegetation: Heterogeneous volume of scatterers (leaves, branches). Longer wavelengths penetrate deeper. L/P-band sensitive to woody biomass. Water Cloud Model: Canopy as a cloud of randomly oriented scatterers above a surface. $\sigma^0_{\text{canopy}}(\theta) = \sigma^0_s(\theta)\Upsilon_V^2(\theta) + \sigma^0_V(\theta)$ (where $\Upsilon_V$ is canopy transmissivity, $\sigma^0_s$ surface backscatter, $\sigma^0_V$ volume backscatter). Depolarization: Vegetation tends to depolarize signals. Special Scatterers: Corner Reflectors: (Dihedral, Trihedral) Return incident waves directly back to source over a wide range of angles. Very high RCS. Used for calibration. Phase changes depend on number of reflections. Moving Targets: Introduce Doppler shift. Mixed Targets: Horizontal Mixing: Incoherent addition of signals from different surface types. $T_B = \sum C_i \epsilon_i T_i$, $\sigma^0 = \sum C_i \sigma^0_i$. Vertical Mixing (Layered Media): E.g., vegetation over soil, snow over ice. Double-bounce effects at interfaces. 7. Detecting Microwaves 7.1 General Approach Components: Antenna (collects radiation), Receiver (amplifies, detects, filters), Data Handling System. Active systems also have a Pulse Generator and Transmitter. Antenna: Collects EM radiation, provides directivity. Size constraints due to $\lambda$. Receiver: Converts EM energy to electrical signal (voltage). Square-law detectors output power. Audio Analogy: Microwave systems share many functional similarities with the human ear (collecting, filtering, detecting, processing sound). 7.2 The Antenna Parabolic Antennas: Focus incident energy to a point. Used for short wavelengths or when size is not constrained. Dipole Antenna: Basic transmitting/receiving element. Low directivity, sensitive to polarization along its axis. Array Antennas: Multiple dipoles combined. Phased Array: Electronically steered beams by controlling phase of individual elements. Slotted Waveguide Array: Uses waveguides to channel microwaves to array elements. Antenna Properties: Gain ($G$): Combination of directivity ($D$) and efficiency ($\rho$). $G = \rho D = \rho \frac{4\pi A}{\lambda^2}$. Effective area $A_e = \rho A$. Half-Power Beamwidth (HPBW or $3\text{dB beamwidth}$): Angular width where gain is half of peak. $\theta_{3\text{dB}} \approx \frac{1.5\lambda}{D}$. Sidelobes: Off-axis peaks in gain pattern. Can cause spurious signals. 7.3 The Receiver Heterodyne Receiver: Converts high-frequency microwave signal (RF) to lower intermediate frequency (IF) for easier processing. Combines RF with a Local Oscillator (LO) signal. Detector: Converts IF signal to measurable electrical output (e.g., voltage). Square-law detector output is proportional to power. 7.4 Coherent Systems Measure both amplitude and phase. I/Q (In-phase/Quadrature) Channels: Signal split and mixed with two reference signals ($\pi/2$ out of phase) to extract real (I) and imaginary (Q) components, forming a complex number representation. 7.5 Active Systems (Radar) Monostatic: Transmitter and receiver share same antenna. Components: Stable Local Oscillator (SLO), Pulse Modulator, Transmitter (high power amplifier), Duplexer (switch between transmit/receive), Antenna. 7.6 System Performance Signal-to-Noise Ratio (SNR): Crucial for instrument performance. $\text{SNR} = \frac{\text{Signal of interest}}{\text{Unwanted signal}}$. Noise and Sensitivity: Antenna Temperature ($T_a$): Equivalent temperature of received power. System Temperature ($T_s$): Sum of antenna temperature and receiver temperature ($T_r$). Radiometric Sensitivity ($\Delta T$): Precision of $T_a$ estimation. $\Delta T = \frac{k_r T_s}{\sqrt{B_n t}}$. Noise-Equivalent $\sigma^0$: For radar systems, $\sigma^0$ value that gives $\text{SNR}=1$. 7.7 Calibration Definition: Quantitative characterization of instrument performance, relating raw output (voltage) to physical property. Absolute Calibration: Direct relationship known. Relative Calibration: Scaling/trend known. Internal Calibration: Uses known signal sources within instrument (e.g., hot/cold loads). Monitors detector system. External Calibration: Uses known external sources (e.g., moon, corner reflectors, distributed targets like rainforests). Includes antenna response. Calibration and Validation (Cal-Val): Campaigns to ensure reliable calibration. Types of Calibration: Radiometric, Phase, Polarimetric Channel Imbalance, Cross-Talk. 8. Atmospheric Sounding 8.1 Need for Measurements Microwaves suitable for sensing atmospheric constituents (O2, O3, H2O, ClO) via spectral lines. All-weather, day/night operation. High accuracy, long operational lifetimes. Crucial for climate change, ozone depletion, hydrological cycle, weather prediction. 8.2 Earth's Atmosphere Layers: Troposphere (0-15km), Stratosphere (15-50km), Mesosphere (50-85km), Thermosphere (>85km). Defined by temperature profile. Key Constituents: Water Vapour (H2O): Strong lines at 22, 183 GHz. Dynamic, major greenhouse gas. Molecular Oxygen (O2): Lines 50-70 GHz, 118 GHz. Well-mixed, used for temperature/pressure. Ozone (O3): Important UV absorber, greenhouse gas. Chlorine Monoxide (ClO): Key in ozone destruction. 8.3 Principles of Measurement Measure brightness temperature at emission lines. $T_B$ depends on physical $T$ and concentration. Temperature Sounding: Uses well-mixed gases (O2). Concentration Sounding: Requires $T$ measurement (e.g., from O2 line) and measurement at target gas line. Microwave sounders often have poor spatial resolution (tens of km), but good vertical resolution for limb sounding. 8.4 Theoretical Basis of Sounding Forward Model (Direct Model): Predicts measurements ($y$) from atmospheric state ($x$). $y = F(x, b_M, b_I) + \epsilon_y$ For TOA brightness: $T_{TOA} = \Upsilon T_{BG} + T_{UP}$. Inverse Model (Retrieval/Inversion): Determines atmospheric state from measurements. Ill-posed problem (many solutions). Requires additional information/constraints (e.g., prior knowledge, smoothness). Empirical Approach: Statistical regression from in-situ data. Physical Modelling: Based on physical laws and instrument characteristics. Influence Functions (Weighting Functions): Describe sensitivity of observation to different atmospheric layers. Peak indicates dominant layer. 8.5 Viewing Geometries Nadir Sounding: Looks straight down. Good horizontal resolution, poor vertical resolution. Surface signal is strong background. Limb Sounding: Looks across atmosphere's edge. Poor horizontal, excellent vertical resolution. Cold space background allows detection of weak signals from upper atmosphere. (e.g., UARS MLS). 8.6 Passive Rainfall Mapping Microwaves measure precipitation directly (unlike visible/IR). Emission Method: Below 50 GHz, over oceans. Rain increases emission, $T_B$ increases. Scattering Method: Above 50 GHz. Ice particles scatter upwelling radiation, $T_B$ decreases. Applicable over land/ocean. (e.g., SSM/I). 9. Passive Imaging of Earth's Surface 9.1 Principles of Measurement Microwave window regions (typically Sensitivity to $T$, roughness, salinity, moisture content. Poor spatial resolution (tens of km) due to long wavelengths and antenna size constraints. All-weather, day/night. Relatively lightweight, low power. Practical Radiometers: Require high sensitivity (long integration time or large beamwidth). (e.g., SSM/I). Viewing Geometries: Conical scanning for constant incidence angle, useful for polarimetry. Generic Forward Model ($T_{TOA}$): $T_{TOA} = \Upsilon (T_{\text{SURF}} + T_{\text{SC}}) + T_{UP}$ (where $T_{\text{SC}}$ is scattered downwelling radiation, $T_{\text{UP}}$ is upwelling atmospheric emission). For low frequencies ( 9.2 Oceans Need: Oceans store thermal energy, drive global circulation (thermohaline). SST and salinity are crucial for climate. SST Measurement: $T_B$ related to $T$ and salinity. Surface roughness from wind complicates. Thermal IR often preferred for accuracy despite cloud issues. Ocean Salinity Measurement: Only possible with microwaves (L-band). (e.g., SMOS). Challenging as both $T$ and salinity affect $\epsilon$. Ocean Winds Measurement: Surface roughness (capillary waves) caused by wind affects $\epsilon$ and $\sigma^0$. Higher frequencies (> 5 GHz) used. (e.g., SSM/I). 9.3 Sea Ice Need: Mapping ice coverage, type, thickness for navigation, climate studies. All-weather, day/night crucial. Sea Ice Concentration: Ice has different $\epsilon$ than open water. $T_B = c_i \epsilon_i T_i + (1-c_i) \epsilon_w T_w$ Different ice types (first-year, multi-year) have distinct $\epsilon$. Multiple frequencies/polarizations (e.g., SSM/I Polarization Ratio and Gradient Ratio) used to discriminate. 9.4 Land Need: Soil moisture, snow properties (SWE) for hydrology, weather prediction, climate models. Forward Problem Over Land (Volume over Surface Model): $T_B = T_s \epsilon_s \Upsilon_V + T_V (1-a)(1 - \Upsilon_V) (1 + \Gamma \Upsilon_V)$ (where $\Upsilon_V$ is volume transmissivity, $T_V$ volume emission, $\epsilon_s$ surface emissivity, $T_s$ surface temperature). Empirical Approaches (Snow Depth): Use difference indices between frequencies (e.g., 18 GHz H and 37 GHz H for snow depth). 10. Active Microwaves (Radar) 10.1 Principles of Measurement Echolocation: Transmit signal, measure echoes. Time delay gives distance. Advantages: Active illumination, precise time delay measurements. All-weather. Spatial Resolution: Typically poor for altimeters/scatterometers (tens of km). Applications: Oceanography, ice sheets. Radar Definition: RAdio Detection And Ranging. Basic Operation: Transmit pulse of duration $\tau_p$. Range $R = c\tau/2$. 10.2 Generic Equations of Radar Performance Radar Equation: Relates received power ($P_r$) to transmitted power ($P_t$), system parameters, and target RCS ($\sigma$). $P_r = \frac{P_t G^2 \lambda^2 \sigma}{(4\pi)^3 R^4}$ (for point target) Range dependence: $1/R^4$. SNR: $\frac{P_r}{N_0} = \frac{P_t G^2 \lambda^2 \sigma}{(4\pi)^3 R^4 N_0}$. Normalized Radar Cross-Section ($\sigma^0$): For distributed targets. $\sigma^0 = P_r \frac{(4\pi)^3 R^4}{A P_t G^2 \lambda^2}$ Range Resolution ($\rho_r$): Ability to distinguish targets in range. For simple pulse: $\rho_r = c\tau_p/2$. For chirped pulse: $\rho_r = c/(2B_p)$ (where $B_p$ is pulse bandwidth). Range compression (matched filtering) with chirped pulses improves range resolution without sacrificing power. 10.3 Radar Altimeters Function: Measure range with high accuracy (cm-level precision). Applications: Ocean topography, ice sheet height changes, planetary mapping. Footprint Size: Pulse-limited: $F_p = 2\sqrt{2c\tau_p H}$. Dominant for satellite altimeters. Beam-limited: $F_b \approx \lambda H / D$. Echo Shape Analysis: Returned echo is stretched due to surface roughness and topography. Used to infer significant wave height, surface slope. Range Ambiguity: Overlapping echoes from successive pulses if PRF is too high. Accuracy of Height Retrievals: Affected by instrument, platform location, wave speed (atmosphere, ionosphere), surface topography. Scanning Altimeters: Narrow beam scanned across-track for increased coverage. 10.4 Improving Directionality (Sub-Beamwidth Resolution) Planetary Radar: Uses range-Doppler processing to resolve features on a planetary disk (e.g., Mars, Venus). Doppler shift due to planetary rotation resolves East-West ambiguity. Synthetic Aperture Altimeters: Uses Doppler shift from platform motion to improve along-track resolution (aperture synthesis). 10.5 Scatterometers Function: Accurate measurements of RCS, sacrificing range/spatial resolution. Applications: Sea surface roughness (wind speed/direction), soil moisture, vegetation cover, rain radar. Operation: Transmit pulses, measure echoes. Can be nadir-pointing or oblique. Conical scanning for constant incidence angle. Rain Radar: Exploits scattering from hydrometeors (>10 GHz). (e.g., TRMM PR) Windscatterometers: Measures azimuthal asymmetry of ocean backscatter to infer wind speed and direction. (e.g., ERS WSC, QuickSCAT). Polarimetric Scatterometers: Provide additional information on wind direction, potentially reducing need for multiple look angles. 11. Imaging Radar 11.1 Need for Imaging Radar Coverage: All-weather, day/night operation crucial for regions with persistent cloud cover (e.g., Darien Province, Arctic sea ice). Unique Information: Detailed ocean surface properties (waves, currents), soil moisture, forest biomass. Key Missions: Seasat (first civilian SAR), Radarsat (ice mapping). Emerging Drivers: High-precision topographic data (InSAR), forest biomass mapping (L/P-band). 11.2 Radar Image Construction Side-Looking Geometry: Antenna points sideways, perpendicular to flight path. Range Direction: Determined by time delay of echo. Range resolution $\rho_r = c/(2B_p)$. Ground Range Resolution: $\rho_g = \rho_r / \sin\theta_i$. Varies across swath. Azimuth Direction: Scanned by platform motion. Azimuth Resolution (RAR): Determined by physical antenna beamwidth. $\rho_a \approx \lambda R / D$. Requires very long antennas for high resolution. 11.3 Synthetic Aperture Radar (SAR) Principle: Synthesizes a large "virtual" antenna from a small physical antenna moving along a flight path. Doppler Interpretation: Targets in front have positive Doppler shift, targets behind have negative. Doppler bandwidth ($B_D$) is proportional to antenna beamwidth and platform velocity. Azimuth compression: Correlates echoes based on their Doppler history. Azimuth Resolution: $\rho_a = D/2$ (where $D$ is physical antenna length). Independent of range and wavelength. (Theoretical optimum). Geometric Interpretation (Phase History): Phase of echoes changes as target moves through beam (parabolic phase history). Azimuth compression: Correlates echoes based on this phase history. Requires coherent pulses. SAR Focussing: Accounts for phase shifts due to changing range, achieving the theoretical azimuth resolution. Radar Equation for SAR: Accounts for coherent addition of multiple echoes. SNR increases with number of echoes (PRF, antenna length, inverse velocity). 11.4 Geometric Distortions in Radar Images Due to side-looking geometry and projection onto a reference surface. Layover: Top of object is closer to radar than base, appears "leaning over." Occurs on steep slopes oriented towards radar. Extreme foreshortening. Foreshortening: Slopes facing radar appear compressed. Worse at smaller incidence angles. Radar Shadow: Areas behind objects from which no echo is received. Appear black. Worse at larger incidence angles. 11.5 Operational Limits Motion Errors: Platform motion (pitch, yaw, roll) affects phase history, degrading azimuth resolution. Moving Targets: Introduce extra Doppler shift, causing displacement in azimuth direction. Ambiguities: Range Ambiguities: Echoes from outside intended swath or from previous pulses. Azimuth Ambiguities: Occur if phase shift exceeds $2\pi$ within beamwidth. Coverage vs. PRF: PRF choice is critical to avoid ambiguities (especially nadir return) and ensure continuous coverage. Trade-offs between swath width, resolution, incidence angle. 11.6 Other SAR Modes ScanSAR: Achieves wide swath by sequentially imaging multiple narrow sub-swaths with different PRFs. (e.g., ASAR, Radarsat). Spotlight Mode: Steers antenna beam to "dwell" on a specific ground area longer, increasing synthetic aperture length and azimuth resolution for that area. Sacrifices along-track coverage. 11.7 Working with SAR Images Data Representation: Pixels can be complex numbers (amplitude + phase) or real numbers (power). Calibrated values usually $\sigma^0$ or $\beta^0$. Speckle: Granular, "salt and pepper" noise unique to coherent imaging. Caused by interference of multiple scatterers within a resolution cell. Not true noise, but deterministic. Speckle Statistics: Follows negative exponential distribution for intensity. Mean = standard deviation. Multi-looking: Averages multiple independent "looks" (from sub-apertures) to reduce speckle at expense of azimuth resolution. Speckle Filtering: Post-processing to reduce speckle while preserving features (e.g., Lee filter). Relies on ergodicity and "cartoon model." Geometric Correction: Geocoded/Orthorectified: Corrects for topographic distortions using a DEM. Ground Control Points (GCPs): Used for co-registration and referencing. Limitations: Layover and shadow regions remain problematic. Resampling can alter image statistics. SAR Data Formats: Single Look Complex (SLC): Rawest processed data, complex numbers, highest resolution, maximum speckle. Essential for interferometry. Multi-Look Detected (MLD): Speckle reduced by incoherent averaging, real numbers. Precision Image (PRI): MLD resampled to square pixels, georeferenced but still with topographic distortion. 11.8 Extracting Topography from SAR Images Stereo SAR Radargrammetry: Uses two SAR images from different look angles to create parallax, inferring height. SAR Clinometry: Infers local slope from variations in backscatter, assuming constant surface properties. 12. Interferometry 12.1 Need for Interferometric Measurements Improve spatial resolution of passive microwave sensors. Correct topographic distortion in imaging radar. Generate high-resolution Digital Elevation Models (DEMs) and Differential DEMs (DifDEMs) for precise surface change detection (cm-level). (e.g., SRTM for global DEMs; earthquake monitoring). 12.2 Principles of Interferometry Phase Measurements: Phase is a sensitive measure of path length difference. Phase ambiguity means only relative phase difference is typically known (within $2\pi$). Application of Dual Systems: Two or more measurements combined. Interferometric Baseline ($B$): Distance between antennas. Used to resolve N-S ambiguity in Venus radar imaging. Resolving Direction: Interferometry uses phase differences to infer signal direction. (Analogy to human binaural hearing for sound direction). 12.3 Passive Imaging Interferometry Challenge: Natural thermal emission is largely incoherent. Solution: Use narrow bandwidth, and correlate signals from two antennas. A signal is coherent with itself. Complex Correlation: $\Gamma = \langle E(t_1) E^*(t_2) \rangle$. Allows synthesizing a large aperture from smaller antennas (e.g., SMOS for L-band soil moisture/salinity). 12.4 Radar Interferometry (InSAR) Interferometric Altimetry: Uses two antennas in cross-track direction to improve angular resolution and elevation estimates over complex topography (e.g., Cryosat SIRAL). Combines with aperture synthesis for along-track resolution. Interferometric SAR (InSAR): Purpose: Resolve directional ambiguity in SAR images to determine topography. Viewing Geometries: Across-Track Interferometry (XTI): Antennas displaced perpendicular to flight path. Single-Pass InSAR: Two antennas on one platform (fast, avoids temporal decorrelation). Repeat-Pass InSAR: Two acquisitions from different passes (sensitive to surface changes). Phase Difference ($\delta\phi$): Related to path length difference ($\Delta R$) and look angle ($\theta_l$). $\delta\phi = \kappa \Delta R \approx \kappa B \sin(\alpha - \theta_l)$ Interferogram: Image showing phase differences. Fringes (lines of equal phase) resemble contour lines after flat-Earth correction. Flat-Earth Correction: Subtracts expected phase for a reference surface. Phase Unwrapping: Converts wrapped phase (0 to $2\pi$) to absolute phase, assuming continuous terrain. Height ambiguity is the height associated with $2\pi$ phase change. Limitations: Layover and shadow regions are problematic. Requires high coherence. 12.5 Interferometric Coherence Magnitude Definition: Magnitude of complex correlation between two SLC images. $\gamma = \frac{\langle p_1 p_2^* \rangle}{\sqrt{\langle |p_1|^2 \rangle \langle |p_2|^2 \rangle}}$ Phase of $\gamma$ gives interferometric phase difference. Magnitude ($|\gamma|$): Degree of coherence (0 to 1). Indicates "meaningfulness" of phase. Decorrelation: Factors reducing coherence. Noise Decorrelation: Random noise in measurements. Baseline Decorrelation: Due to spatial separation of antennas. Volume Decorrelation: Due to vertical spread of scatterers (e.g., vegetation). Temporal Decorrelation: Due to changes in scatterers between repeat passes. Total Coherence: $|\gamma| = |\gamma_{\text{noise}}| \cdot |\gamma_h| \cdot |\gamma_t|$. Applications of Coherence: Landcover classification, change detection (e.g., tracks in deserts). 12.6 Practical DEM Generation InSAR is a well-established technique for high-resolution DEMs. (e.g., SRTM). InSAR Processing Chain: Pre-processing (SLC data, baseline estimation), Co-registration, Interferogram generation (flat-Earth correction), Phase unwrapping. 12.7 Vegetation Height Estimation Scattering Phase Centre: Effective height from which radar signal appears to originate within a volume. Single-Frequency InSAR: (e.g., X-band). Provides top-of-canopy DEM. Ground DEM derived by interpolation or external source. Dual-Frequency InSAR: Combines short wavelength (canopy top) and long wavelength (ground) DEMs. Polarimetric Interferometry (PolInSAR): Uses polarimetric information to distinguish canopy and ground contributions, estimating height and vertical structure. Multi-Baseline Interferometry: Uses data from many passes/baselines to retrieve vertical structure. SAR Tomography: Advanced technique using multiple polarimetric acquisitions to reconstruct 3D volumetric scattering. 12.8 Differential SAR Interferometry (DInSAR) Principle: Measures small ground/ice movements (cm-level) between repeat passes. Requires zero (or known) baseline. Phase Change: $\phi_D = 2\pi \frac{\Delta R}{\lambda}$ (where $\Delta R$ is motion component in range direction). Applications: Earthquake monitoring, subsidence, volcanic deformation, glaciology (ice flow). Limitations: Requires high coherence, susceptible to atmospheric water vapour changes. 12.9 Permanent Scatterer Interferometry (PSI) Extension of DInSAR. Uses long time series of images to identify stable "permanent scatterers" (e.g., buildings, bare rock). Measures millimetre-level displacements over years, even in urban areas. 12.10 Along-Track Interferometry (ATI) Antennas separated in along-track direction. Used for measuring water surface currents and identifying moving targets. Effectively a repeat-pass configuration with very short temporal baseline (milliseconds).