Active microwave remote sensing
The monostatic active type creates its own electromagnetic energy which is propagated from the sensor toward the ground and through their interaction a backscatter is produced and returned to the sensor. The transmitter and the receiver are collocated in the same system in contrary to the bistatic type where they are separated by a distance of the order of the expected target distance.
Active microwave remote sensing is performed using a RAdio Detection And Ranging (RADAR) system, which is a radio device composed of a transmitter, responsible of the illumination of the ground using an artificial radiation, and a receiver, which measures the backscattered signal after the interaction with the ground .
Active microwave remote sensing using radars fall into three categories:
ii) Synthetic aperture radars (SARs), widely used in active remote sensing applications, create their own illumination, propagate it toward the Earth’s surface and measure the strength and round-trip time of the backscattered response. SAR systems are capable of achieving high spatially resolved images, but are strongly impacted by the surface topography (rougher areas will induce brighter pixels on the image),
iii) Scatterometers are essentially dedicated instruments to map the ocean wind circulation and some other geophysical variables from space. They actively transmit electromagnetic pulses toward the Earth’s surface and measure the backscattered response to derive the surface properties. Due to their relatively coarse spatial resolution (of the order of radiometer’s), scatterometers are mainly sued to provide a global coverage mapping, and
iii) Altimeters, usually employed in combination with radars, are especially intended to provide auxiliary data to the radar’s output such as wind speed or sea surface roughness. By exploiting the ranging capability of the radar, altimeters are capable of measuring the precise satellite’s altitude and mapping the surface topography profile in the flight direction. However, altimeters’ measurements are highly aﬀected by the surface roughness, which renders them mostly eﬀective over smooth surfaces such as oceans and low relief land surfaces.
Passive microwave remote sensing
The passive type measures the self-emitted microwave radiation from objects on the ground as a result of sun illumination by means of a radiometer. The measured spectral brightness by radiometers is expressed by the Rayleigh-Jeans law derived from the Planck’s law (1.1) in the regime kT ≫ hc/λ,
A radiometer is thus a sensor capable of converting the receiver’s output voltage Vout into an eﬀec-tive apparent temperature TM L. TM L represents the brightness distribution of the incident radiation (containing the scene self-emitted radiation and other emissions) carried by the solid angle subtended by the main lobe of the receiving antenna. The physical temperature is afterwards deduced by means of the relationship linking the power generated by a matched load as function of its physical temperature.
Spaceborne radiometers are highly accurate but at the expense of a coarse spatial resolution (typically 25 to 50 km in L-band) essentially dictated by the antenna’s diameter; the larger the antenna’s diameter is, the higher the achieved spatial resolution will be. For this reason, enhancing the radiometer’s spatial resolution requires the use of very large antennas (typically a 16m-diameter low-orbit antenna to achieve a 10-km spatial resolution at around 1.4 GHz) unsuitable for a spaceborne use. This limitation was overcome by the introduction of the Synthetic Aperture technique .
Aperture synthesis is an interferometric technique similar to Earth rotation synthesis employed in radioastronomy in which the signals received by a pair of small antennas are processed in such a way to synthesize a single large antenna of narrow beamwidth with the intent of observing typically punctual celestial sources . Instead of looking upward, Earth rotation synthesis was readapted to Earth remote sensing by looking downward and dealing with large thermal sources. Thanks to this technique, limitations on antenna size in satellite-based passive radiometers were overcome . Aperture synthesis uses the basic idea that the coherent product (cross-correlation) of the received signals by a pair of diﬀerent antennas defines a sample point in the Fourier transform of the brightness temperature map of the observed scene. Thus, instead of a power measurement in real aperture systems, a synthetic aperture radiometer measures the cross-correlation product between the measured signals by a pair of antennas (figure 1.1), where V (u, v) is the so-called visibility function, (u, v) = (x1 − x2, y1 − y2)/λ is the baseline vector normalized by the wavelength, (ξ, η) is the direction cosine of the incident wave and TB (ξ, η) is the brightness temperature distribution of the scene. The Fourier-transform relationship linking the visibil-ities to the brightness temperature distribution is straightforward from (1.6) and is classically known as the Van Cittert–Zernike theorem.
When observing a scene using synthetic aperture systems, the Fourier-transform of the brightness temperature map of the observed scene is constructed by cross-correlating the pair of signals collected by an array of antennas of various baselines (spacings between the antennas). Then, using inversion and regularization techniques, the brightness temperature distribution of the scene can be reconstructed  and the spatial resolution of the reconstructed image is found to be directly dictated by the longest baseline of the array instead of the antenna diameter in real aperture systems.
However, employing aperture synthesis by means of small antennas to bypass the need of large an-tennas comes at the cost of a reduced accuracy in addition to a complex electronic hardware, data processing, and calibration procedures. Fortunately, one shows that the radiometric accuracy of inter-ferometric systems can be improved by increasing the time-bandwidth product to approach real aperture radiometers .
More generally in aperture synthesis, a tradeoﬀ between the spatial resolution (dictated by the longest baseline) and the radiometric sensitivity (dictated by the maximal integration time) is always set depending on each mission’s objectives. The optimality of an interferometric configuration relies on the trade-oﬀ between filling as much as possible the (u, v)−plane and reducing the minimal required number of radiating elements for mass optimization.
One of the famous applications of the synthetic aperture technique are the Electronically Scanned Thinned Array Radiometer (ESTAR), the Microwave Imaging Radiometer with Aperture Synthesis (MIRAS), and the Atacama Large Millimeter Array (ALMA) in Chile  used for radioastronomical observations.
ESTAR is a 1D push-broom system composed of an array of antennas oriented in the flight-direction which employs a combination of real aperture and interferometric imaging methodologies (figure 1.2).
The imaging in the along-track direction is performed through a classical real aperture technology, whereas in the cross-track direction a synthetic aperture technique is employed. This configuration was for the first time tested on board of the NASA P-3B Orion aircraft, incorporating a ESTAR instrument developed as part of the cooperative research between the NASA and the university of Massachusetts, between July 8-20, 1999 as an experiment (Southern Great Plains (SGP)) to demonstrate the feasibility of aperture synthesis for remote sensing purposes . As firstly developed, the ESTAR system consisted of a L-band (1.4 GHz) instrument composed of five real « stick » antennas providing the resolution in the along-track direction, and the equivalent beam synthesized by means of seven unique baselines of width at half power of 7◦ produces the resolution in the other direction.
ESTAR allowed for the first time to show the feasibility of synthetic aperture for the measurement of soil moisture and ocean salinity .
The MIRAS instrument on board of the SMOS mission employs a 2D interferometry in both direc-tions by collocating a set of small antennas to achieve the best trade-oﬀ between the instrument weight and the spatial resolution.
MIRAS operates in the L-band (1.4 GHz) and is composed of 69 dual-polarized antennas arranged along a three-arm Y-shaped configuration . Using a 2D synthetic aperture, this configuration allows to synthesize an equivalent 8m-diameter real aperture antenna and a mean ground spatial resolution of 40-50 km.
MIRAS constituted the first spaceborne demonstration of the feasibility of a 2D interferometry to Earth observation and provided a new means for the measurement of soil moisture and ocean salinity .
ALMA is a complete astronomical imaging and spectroscopic instrument incorporating an array of up-to 80 12m-diameter antennas at diﬀerent baseline configurations raging from 15 m to 18 km (figure 1.4). By combining the signals from diﬀerent antenna-pairs, ALMA continuously synthesizes very narrow beams yielding the provision of radio-astronomical images of resolution as fine as 0.005″.
History of microwave remote sensing
The first radio experiment was conducted by Heinrich Hertz, 1886, where he experimentally demon-strated the Maxwell’s electromagnetic theory. His experiment allowed the discovery of radio waves and showed that reflections could be received from metallic and nonmetallic objects. In 1903, Christian Hulsmeyer obtained a patent for the detection of ships using radars.
The pulse radar system was originally developed by A. H. Taylor and the U. S. Naval Research Laboratory to detect and track ships and aircrafts. While the first practical radar system for aircraft detection was designed by Sir Robert Watson-Watt in 1937.
During World War II, the first military reconnaissance imaging radars employed the plan-position indicator (PPI) to produce an accurate ground mapping. Later in 1950s, the use of real aperture side-looking airborne radar (SLAR) has led to even finer resolution ground maps compared to PPI systems.
In June 1951, Carl A. Wiley invented a new system called « Doppler beam-sharpening », which ex-ploited the Doppler shifts of the returned signals to significantly improve the resolution. This technique led afterwards to the current synthetic aperture radar (SAR). During 1950s and 1960s, Goodyear Aircraft introduced numerous advancements in SAR technology.
Early experiments using artificial Earth satellites had demonstrated that the Doppler frequency shifts of signals traveling through the ionosphere and atmosphere were stable enough to permit fine and achievable resolutions even at ranges of hundreds of kilometers. The application of SAR systems to Earth remote sensing and geoscience radar reconnaissance was primarily deployed with the first radar mapping mission launched in 1967 using the Westinghouse AN/APQ 97 system and the development of multi-channel airborne SAR systems. Later, the Apollo Lunar Sounder experiment launched in 1972 constituted the first use a SAR system on board of a spaceborne instrument.
In the recent past, SAR and InSAR (interferometric SAR) remote sensing technologies have been largely widespread. While the U.S. haven’t had any operational civilian satellites carrying a SAR system since the short-lived SEASAT program launched in 1978, many non-U.S. spaceborne SAR systems have been deployed for the imaging of the Earth’s surface, namely the ESA satellites ERS-1, ERS-2, ENVISAT and the Canadian satellites Radarsat-1 and Radarsat-2.
Table of contents :
1 STATE OF THE ART: AN OVERVIEW OF RECENT MISSIONS
1.2 Introduction to microwave remote sensing
1.2.1 Why microwave remote sensing ?
1.2.3 Aperture Synthesis
1.3 History of microwave remote sensing
1.4 Rationale for the use of L-Band
1.5 Earth observation using microwave remote sensing
1.5.1 Science motivation
1.5.2 Soil Moisture (SM)
1.5.3 Sea Surface Salinity (SSS)
1.6 Retrieval algorithmic schemes
1.6.1 Iterative approach
1.6.2 Soil moisture retrieval
1.6.3 Sea Surface Salinity retrieval
1.6.4 Neural Network approach for SM retrieval
1.7 Dedicated L-band Earth observation missions
1.7.1 Soil Moisture and Ocean Salinity (SMOS) mission
1.7.3 Soil Moisture Active and Passive (SMAP) mission
2 EARTH OBSERVATION USERS’ NEEDS
2.2.1 Study of climate change
2.2.2 Weather prediction & forecasting
2.2.3 Drought and flood monitoring
2.2.4 Disaster management
2.2.5 Agriculture and water resources management
2.2.6 Forest stocks and carbon concentration assessment
2.2.7 Ocean management
2.4 Users’ needs
3 TEMPORAL CORRELATION IMAGING: GENERALIZATION OF THE VAN CITTERT–ZERNIKE THEOREM
3.2 Spatio-temporal interferometry
3.3 Generalization of the Van Cittert-Zernike theorem
3.3.3 Electric field
3.3.4 Correlation function
3.4 Similar concepts
3.4.1 Very Long Baseline Interferometry (VLBI)
3.4.2 2D Doppler-Radiometer
4 FOURIER CORRELATION IMAGING: ANALYTICAL DERIVATION
4.2 Theoretical model
4.2.1 Electric field
4.2.2 Fluctuations of sources
4.3 Fourier Correlation Imaging
4.3.2 Electric field spectrum
4.3.3 Correlation function
4.3.4 Properties of the correlation function
4.3.5 General expression of the correlation function
4.3.6 Simplified expression of the correlation function
4.3.7 Study of the HOI kernel
4.3.8 Analytical inversion of the correlation function
4.3.9 Estimation of the geometric resolution
4.4 Appendix: Thermal fluctuations and their fundamental laws
5 FOURIER CORRELATION IMAGING: NUMERICAL DERIVATION
5.2 Numerical quadrature of the highly oscillatory integral kernel
5.2.2 Theoretical model
5.2.3 Quadrature methods for highly oscillatory integrals
5.2.4 Analytical derivations of the quadrature
5.2.5 Quadrature simulation results
5.3 Numerical processor: derivation & results
5.3.2 Numerical simulations using frequency translation
5.3.3 Numerical simulations using the quadrature of the HOI kernel
5.3.4 Numerical simulations in the ultra-sound regime
5.3.5 Discussion on the FDT assumption
CONCLUSIONS & PERSPECTIVES