Book summary “Introduction to microwave remote sensing”: summary

Introduction

You need to observe the Earth and atmosphere using methods that transcend the limitations of optical photography and cloud cover. You face the challenge of interpreting complex electromagnetic signals that interact with physical targets through scattering, absorption, and emission.

Microwave remote sensing uses active and passive electromagnetic techniques governed by physical parameters like scattering, dielectric properties, and polarization to observe the Earth and atmosphere.

Iain H. Woodhouse guides you through the foundations of wave propagation, instrument design, and data interpretation. You will explore how physical principles translate into actionable measurements across passive radiometers and active radar systems.

• How do electromagnetic waves propagate through the atmosphere and interact with different surface materials?
• What mechanisms govern radar polarimetry and scattering from rough surfaces?
• How do active and passive microwave instruments acquire and calibrate data for environmental monitoring?

1. Why Microwaves and Historical Foundations

Microwave remote sensing relies on electromagnetic principles established in the 19th century rather than optical photography, offering unique capabilities to penetrate clouds and measure physical properties.

Why Microwaves?

Microwave remote sensing provides unique capabilities that complement optical methods because microwave interactions are governed by different physical parameters. The amount of microwave energy scattered from an object like a green leaf depends on its size, shape, and water content rather than its chlorophyll or greenness. Additionally, certain microwaves can penetrate clouds and dry soils or sand by up to several metres, and measurements can be made at any time without relying on solar illumination.

Microwave remote sensing instruments are broadly categorized into passive sensors that measure natural radiation and active sensors that supply their own illumination. Passive sensors or radiometers measure microwave energy radiated through thermal emission or reflected from natural sources like the sun, while microwave sounders specifically measure atmospheric emission. Active sensors, such as radar systems, generate their own illumination by transmitting pulses of microwave radiation and measuring the scattered signal. Active sensors primarily use wavelengths greater than 3 cm, where the atmosphere becomes virtually transparent, corresponding to frequencies less than 10 GHz.

History and Foundations

Microwave remote sensing shares little history with optical remote sensing and photography, deriving instead from 19th-century investigations into electricity and magnetism. While optical remote sensing relies on the heritage of photography and the pinhole camera, microwave remote sensing developed independently. Mistakenly viewing microwaves as a direct progression from optical systems leads students to misunderstand imaging radar.

Nadar's balloon-borne photograph of Paris in the 19th century is often cited as the root of optical remote sensing, whereas microwave remote sensing is rooted in electromagnetic theory.

James Clerk Maxwell unified electricity, magnetism, and light into four concise equations, proving theoretically that electromagnetic fields propagate as waves at the speed of light. Maxwell combined experimental evidence from researchers like Faraday and Oersted into four equations. Between 1831 and 79, James Clerk Maxwell lived, and in 1868 he published his theory of electromagnetic waves. By evaluating these equations in a vacuum with zero charges and currents, he deduced that self-perpetuating oscillating electric and magnetic fields propagate at the speed of visible light.

Heinrich Hertz experimentally confirmed Maxwell's theory by demonstrating that electric force propagates through space as electromagnetic waves at light speed. Hertz spent 8 years working on Maxwell's theory before he experimentally confirmed it in 1886. He used a transmitter involving an oscillatory electric discharge across a spark gap and a receiving antenna consisting of an open loop of wire. He performed optical-like experiments on these invisible waves, reflecting, refracting, polarizing, and measuring their wavelengths.

Hertz measured wavelengths a little less than a metre, closely resembling the wavelengths used by low-frequency microwave radars today.

World War II drove the rapid evolution of operational pulsed radar systems and airborne microwave technology, serving as a critical turning point for remote sensing. The urgent military need to track enemy aircraft day or night spurred massive investments in radar. In 1940, developers produced the cavity magnetron, which enabled the generation of powerful short-wave radio signals and allowed compact antennas to be mounted on aircraft for navigation and submarine hunting. Prior to technological upgrades requiring shorter wavelengths, the maximum antenna size that could be carried by an aircraft was 1.5m.

The Chain Home system of tall towers along Britain's eastern coastline provided crucial early warning and location data during the Battle of Britain, utilizing aerials with a height of 12m.

2. Physical Properties and Wave Propagation

Electromagnetic waves can be modeled using harmonic wave functions based on sine or cosine curves defined by amplitude, wavelength, and wavenumber. You can combine these elements into complex exponential notation using Euler's relation for easier mathematical manipulation.

Electromagnetic waves are governed by harmonic functions, polarization, interference, and dielectric media properties that dictate how signals interact with targets.

Physical Properties of EM Waves

The wave profile is characterized by an amplitude A, wavelength lambda, wavenumber kappa linked as kappa = 2pi / lambda, and angular frequency omega = kappa * c. Euler's constant e equals 2.718281828. Power P is given by the squared electric field amplitude E_0 squared divided by 2 * eta where eta is impedance.

Spectral radiance per unit solid angle defines brightness or intensity, which remains constant with distance because expanding area and shrinking solid angle balance out. Power density uses the unit Wm^-2, while radiance uses Wm^-2 sr^-1.

A white A4 page of paper does not look less bright when moved further away because the decreasing total energy is condensed into a smaller solid angle.

Polarisation

Transverse waves like microwaves have oscillations that can be split into independent orthogonal x and y components. These are termed horizontal and vertical polarization respectively, with a phase difference epsilon between them.

Polaroid sunglasses selectively extinguish glare from horizontal surfaces by only allowing vertically polarized light to pass through. Interference occurs when waves overlap, producing amplitudes ranging from zero to 2A. Coherence requires waves to maintain a constant phase difference over time and space, allowing their predictability and vector addition. Phase angles cycle through a range from 0 to 2pi.

Two coherent wave sources generate an interference pattern in the far field whose angular peaks depend on path length differences and wavelength. The path length difference delta_l = d * sin(theta) creates a phase difference delta_phi. Measuring this phase difference allows the detection of source direction.

Humans achieve a horizontal sound resolution of about 5-10 degrees and echolocating bats achieve 1.5 degrees using Interaural Phase Difference (IPD), supported by research from Masters et al. in 1985. Increasing the number of in-phase point sources across an aperture focuses most radiated energy into a single narrow beam with minimal sidelobes.

As more sources are added with spacing less than a wavelength, sidelobe amplitudes decrease and energy concentrates in the central boresight direction. The angular resolution of a circular disk aperture is defined by the Airy disk using the multiplier 1.22 for the circular disk Airy disk resolution formula theta_cd approx 1.22 * lambda / d.

Propagation of Microwaves

Propagation of microwaves through media is governed by electric permittivity, magnetic permeability, and electrical conductivity. Dielectric media are non-conducting materials characterized by relative permittivity epsilon_r.

The real part of relative permittivity determines the lossless dielectric constant, while the imaginary part accounts for energy losses and attenuation. The permeability of free space mu_0 is 4pi * 10^-7 Ns^2 C^-2. The permittivity of free space epsilon_0 is 8.8542 * 10^-12 C^2 N^-1 m^-2. The real part of relative permittivity for Earth materials ranges from 1 to 80.

3. Polarimetry and Scattering Mechanisms

Radar polarimetry and scattering models characterize target structures using Stokes vectors, scattering matrices, and surface roughness criteria.

Polarisation describes the path of the electric field vector in a transverse plane. Its mathematical description relies on an orthogonal coordinate basis and a consistent frame of reference.

The linear basis uses two orthogonal horizontal and vertical states. Because travel direction matters for spatial descriptions, systems use either Forward Scattering Alignment or Back-Scatter Alignment.

Combining orthogonally polarised waves with varying amplitudes and relative phases generates linear, circular, or generalized elliptical polarisation states.

• A half-cycle pi phase shift corresponds to sin(theta + pi) = -sin(theta).
• A pi/4 angle works for in-phase combination of equal amplitudes.
• Delta equals 90 degrees or pi/2 for circular polarisation.

George Gabriel Stokes introduced parameters in 1852 to describe completely and partially polarised waves. The Stokes vector consists of four elements representing total intensity, linear preference, and phase covariances. It handles partially polarised waves where total power satisfies an inequality rather than an exact square equality.

• I0^2 >= Q^2 + U^2 + V^2 applies for general partially polarised waves.

Interaction With Discrete Objects

Radar polarimetry characterizes target scattering properties by relating incident and scattered wave fields using scattering matrices, target vectors, and covariance matrices. Fully polarimetric radar measures complex scattering matrix elements. Assuming reciprocity, target vectors and covariance matrices capture statistical inter-relationships between polarimetric channels.

• The system uses a 4x4 real matrix M for Stokes scattering.
• The Mueller or Kennaugh matrix contains 16 numbers.

Normalised backscatter coefficient measures surface scattering properties independently of sensor footprint or geometry. While radar cross-section measures total target response, extended distributed targets like the Earth's surface require normalisation by geometric area.

• A 3/2 ratio relates backscattering to total scattering cross-sections for Rayleigh scatterers.

Scattering behavior depends on the relative size of the target object compared to the incident wavelength, categorized into Rayleigh, Mie, and optical regions. When targets are much smaller than the wavelength, Rayleigh scattering dominates. When comparable in size, Mie scattering creates resonant peaks and troughs.

• The scattering cross-section drops off with the inverse fourth power of wavelength.

Scattering and Emission from Natural Surfaces

Key derived parameters help interpret physical properties of Earth targets. You can examine unpolarised total power, polarimetric ratios, coherence, entropy, and target decomposition.

• The span measures unpolarised total power.
• Co-pol and cross-pol ratios indicate vegetation cover.
• Polarimetric phase difference classifies single-bounce versus double-bounce scattering.
• Polarimetric entropy and coherence magnitude range from 0 to 1.

Surface roughness is evaluated relative to the wavelength using statistical limits like the Rayleigh and Fraunhofer criteria. The Rayleigh criterion states that a surface is smooth if phase differences from height deviations are less than one quarter of a wavelength. The Fraunhofer criterion applies a stricter limit of one eighth of a wavelength for modeling scattering behavior.

• The Rayleigh roughness criterion uses a pi / 2 phase difference limit.
• The Fraunhofer roughness criterion uses a pi / 8 phase difference limit.

Wind-induced capillary waves on the ocean act as a Bragg surface, creating resonant coherent scattering sensitive to wind speed and direction. Small capillary waves combine constructively, producing high normalized radar cross-section values.

Sea water contains 3.2 percent salt content. A representative SAR image pixel size is 25 meters, while illustrative ocean ripples have a wavelength of 2.5 centimeters. The illustrative NRCS contribution of a single small ripple is negative 45 dB, and the resulting coherent NRCS when resonant scattering occurs reaches negative 5 dB.

Liquid water content is the dominant factor determining the dielectric properties and microwave penetration depth of soils. As soil moisture increases, the real part of the dielectric constant increases from dry soil toward the high value of liquid water.

The approximate real dielectric constant for air is 1, while dry soil has a value of 4. Water at frequencies near 1GHz has an approximate real dielectric constant of 80.

4. Microwave Systems, Passive Imaging, and Active Radar

Microwave systems utilize antennas, heterodyne receivers, and calibration methods to operate passive radiometers and active radar instruments for environmental monitoring.

Most microwave remote sensing systems are comprised of an antenna for collecting radiation, a receiver for amplification and detection, and a specialized data handling system. The antenna points toward a narrow range of look angles to collect radiation, while the receiver amplifies and detects signals across specific frequency ranges. Active systems additionally require a pulse generator and transmitter, often sharing the same antenna for transmission and reception. There is up to six orders of magnitude difference in wavelength between microwaves and optical ranges.

The Antenna and Receiver

Microwave antennas use various configurations such as parabolic reflectors, simple dipoles, or array antennas to focus and direct electromagnetic radiation. Parabolic antennas focus energy onto a detector or waveguide, using solid metal or wire mesh reflectors. Simple dipoles offer minimal directivity but respond to specific polarizations. Array antennas utilize multiple transmitters or receivers, including slotted waveguides and phased arrays, to enable electronic steering.

The radar imager onboard the Magellan space probe to Venus used a 2.3 m circular parabolic dish. The Envisat ASAR phased array system relied on 320 Transmit/Receive Modules.

• Use a parabolic reflector or wire mesh where size permits for high-frequency microwaves above 10 GHz.
• Employ an array of transmitting or receiving units when low-frequency microwaves below 10 GHz make optical-type focusing impractical.

Heterodyne receivers convert high-frequency radio signals down to lower intermediate frequencies to simplify amplification and filtering. Because direct amplification at high microwave frequencies is difficult, a non-linear circuit mixer combines the radio-frequency signal with a constant-frequency signal generated by a local oscillator, producing a lower frequency component proportional in power to the original signal.

Coherent measuring systems record both the amplitude and phase of incident radiation by splitting signals into in-phase and quadrature components. By mixing incoming signals with reference frequencies locked to a stable local oscillator and phase-shifted by pi over two, the system converts sinusoidal signals into complex exponential formats represented by real in-phase and imaginary quadrature channels.

• Pass incoming measured signals through a low-noise amplifier.
• Mix the signal with a reference frequency from a stable local oscillator down to an intermediate frequency.
• Mix the signal with two oscillator outputs separated by pi over two to generate in-phase and quadrature channels.

Calibration quantitatively characterizes instrument performance by relating raw voltage outputs to physical properties using internal, external, or target-based references. Because instrument characteristics change over time due to environmental drift, launch vibrations, and thermal shifts, calibration feeds known signals into components.

Tropical rain forests like the Amazon and Congo basins are used as distributed targets because they show remarkably stable radar cross-sections over extended periods.

• Perform internal calibration by feeding an electrically generated signal or internal reference pulse directly into the amplifiers.
• Execute hot-cold calibration in passive systems by observing blackbody emitters at two known temperature extremes.
• Utilize microwave corner reflectors or active transponders externally to calibrate end-to-end active radar systems and antenna patterns.

Passive Imaging Principles

Passive microwave sensors are sensitive to surface temperature, roughness, salinity, and moisture, offering advantages in power efficiency and cloud penetration, but suffer from poor spatial resolution. Spaceborne systems yield coarse spatial footprints of tens of kilometres.

The top-of-the-atmosphere brightness temperature observed by a passive radiometer is modeled by combining direct surface emission, atmospheric transmissivity, upwelling radiation, and scattered background radiation. Below 20 GHz, the atmosphere becomes largely transparent, and the scattered term is dominated by the 3 Kelvin cosmic background radiation rather than atmospheric emission.

While thermal infrared is preferred for sea surface temperature, passive microwaves are essential for estimating ocean salinity through low-frequency measurements. Ocean surface brightness temperature is a function of physical temperature and salinity, where salinity influences emissivity only at long microwave wavelengths below 6 GHz. The Soil Moisture and Ocean Salinity mission achieved a 50 km spatial resolution target using an L-band frequency of 1.4 GHz.

Passive rainfall mapping uses low-frequency emission over oceans and high-frequency ice scattering over land and oceans to estimate precipitation rates. 78 percent of all precipitation falls on the ocean compared to 22 percent on land.

• Apply the emission method over oceans at frequencies below 50 GHz where sea surface emission is low and contrast with precipitating clouds reaches 50K or more.
• Apply the scattering method for frequencies higher than 50GHz by measuring the scattering index based on the difference between brightness temperature and background surface radiation.

Active Radar and Altimetry

Active microwave remote sensing bypasses the limitations of passive sensors by generating its own microwave illumination and measuring the returning echo's time delay, intensity, and polarisation.

Active systems measure distance via the two-way travel time delay and extract surface properties from backscattered echo characteristics at the speed of light of 186,000 miles a second from platforms flying around 800 km high. Bats act as natural active remote sensing systems using echolocation.

The radar equation determines the proportion of transmitted energy returned from a target, demonstrating that received signal power drops off inversely with the fourth power of range, meaning doubling the range reduces return power by a factor of sixteen. Range resolution in radar is limited by pulse duration, creating a design conflict resolved by using a linear frequency modulated or chirped pulse.

Radar altimeters use precise time-delay measurements of nadir-directed echoes to determine surface topography and average height variations with centimetre-scale precision. The TOPEX/POSEIDON mission altimeter achieved a precision of 2 cm and a single-pass accuracy of about 13 cm. Greenland contains 9 percent of frozen fresh water, while Antarctica holds 91 percent, and complete melting would cause a 72m sea level rise.

Scatterometers are specialized active microwave instruments designed to measure radar cross-sections accurately rather than focusing purely on range timing. The Tropical Rainfall Measuring Mission Precipitation Radar operated a 2.1 m square active phased-array antenna at 13.8 GHz across a 215 km swath with 250 m range resolution.

Across-track Synthetic Aperture Radar interferometry resolves directional ambiguities in radar imagery to produce high-precision digital elevation models. The Shuttle Radar Topography Mission used Space Shuttle Endeavour in 2000 to collect global DEM data across 80 percent of Earth's land surface between 60 degrees North and 54 degrees South during an 11-day mission with a 60-meter antenna mast.

• Acquire single look complex data from two parallel passes.
• Perform accurate co-registration of the images so they overlap by 90% or more.
• Cross-correlate the co-registered images to generate an interferogram.
• Apply flat-Earth correction to convert the raw interferogram relative to a reference surface.
• Perform phase unwrapping to convert cyclic phase differences into absolute phase differences.
• Infer pixel height and true location using the unwrapped phase and look angle relationships.

Conclusion

Microwave remote sensing combines fundamental electromagnetic physics, advanced polarimetry, and sophisticated instrument design to observe the Earth across all weather conditions and lighting states.

To apply these principles effectively in your work, follow these rules.

1. Match your frequency and wavelength to the specific physical property you want to measure.
2. Account for complex dielectric constants and surface roughness before you interpret backscatter coefficients.
3. Utilize polarization states and scattering matrices to distinguish volume scattering from surface and double-bounce effects.
4. Calibrate your active and passive systems rigorously to convert raw digital numbers into meaningful geophysical units.
5. Combine synthetic aperture radar imagery with interferometric and altimetric techniques when you map surface deformation and topography.

10 Key Ideas

1. Microwave remote sensing relies on electromagnetic principles established in the 19th century to measure physical properties and penetrate clouds and dry soils without relying on solar illumination.
2. Heinrich Hertz experimentally confirmed James Clerk Maxwell's electromagnetic theory by demonstrating that electric force propagates through space as waves at the speed of visible light.
3. Increasing the number of in-phase point sources across an aperture focuses most radiated energy into a single narrow beam with minimal sidelobes.
4. Radar polarimetry and scattering models characterize target structures using Stokes vectors, scattering matrices, and surface roughness criteria like the Rayleigh and Fraunhofer limits.
5. As soil moisture increases, the real part of the dielectric constant increases from dry soil toward the high value of liquid water.
6. Microwave antennas use parabolic reflectors, simple dipoles, or array antennas to focus radiation, while heterodyne receivers convert high-frequency signals down to lower intermediate frequencies.
7. Calibration quantitatively characterizes instrument performance by relating raw voltage outputs to physical properties using internal, external, or target-based references.
8. Passive microwave sensors are sensitive to surface temperature, roughness, salinity, and moisture, yet yield coarse spatial footprints of tens of kilometres.
9. Active radar systems measure distance via the two-way travel time delay and extract surface properties from backscattered echo characteristics where received signal power drops off inversely with the fourth power of range.
10. Across-track Synthetic Aperture Radar interferometry resolves directional ambiguities in radar imagery by generating interferograms and performing phase unwrapping to produce high-precision digital elevation models.