Foreword

To my knowledge, this is the first book ever published dedicated to the topic of aperture synthesis (or interferometry) for the remote sensing of the Earth. Much of its contents can, however, be applied to other types of microwave radiometers and applications. The author, Prof. Ignasi Corbella of the Polytechnic University of Catalunya (UPC), Barcelona (Spain), is, in my humble opinion, the engineer, among all I know, who best understands aperture synthesis for Earth Observation, a field that started in the 1980s. Readers of this book will have the privilege to learn directly from him.

In fact, I started learning microwave theory having Ignasi as teacher at UPC back in 1983, and he was also the supervisor of my master's thesis in 1986, and of my PhD in 1996. Therefore, it is an honor to write this foreword to his book some 41 years after I attended his lessons at UPC. From 1993 till 1999, he was involved in several studies and experiments to develop the Microwave Imaging Radiometer with Aperture Synthesis (MIRAS) within contracts with the European Space Agency (ESA) I was responsible for. Since 2000 till today, Prof. Corbella has been part of the team supporting, in many aspects, ESA's Soil Moisture and Ocean Salinity (SMOS) mission, which carries MIRAS as its only payload. It is the SMOS mission, in which I am involved from ESA side, which has allowed us to enjoy this very long professional link and friendship.

The development of MIRAS is a story truly worth telling. It all started with the work of David LeVine (NASA-GSFC) and Carl Swift (University of Massachusetts at Amherst) in the late 1980s on the Electronically Scanning Thinned-Array Radiometer (ESTAR). ESTAR was a one-dimensional interferometer presenting a new technological solution to deploy a very large L-band antenna in space, to make observations in the 1400-1427 MHz protected band, to provide global maps of soil moisture and ocean salinity. Inspired by this research, and following some work carried out by the French Space Agency (CNES), in 1992, ESA decided to initiate the development of a two-dimensional interferometer: MIRAS.

During the first 10 years of MIRAS, Prof. Corbella was involved in the theoretical aspects, the calibration, and the image processing of the instrument. In principle, although aperture synthesis had never been applied to remote sensing, it was a matter of translating the knowledge accumulated in radio-astronomy to the field of Earth Observation. Given this, we were all quite confident that the new type of radiometer should work very finely.

Radio-astronomy was (and is) based on a theorem that was first formulated by the Dutch physicist Pieter Hendrik van Cittert in 1934, and four years later proved in a simpler way by another Dutch physicist, Frits Zernike. Zernike was a prominent scientist who was awarded the Nobel Prize in 1953 for having invented the Phase-Contrast Microscope. The so-called Van Cittert-Zernike theorem, or in short, the VCZ theorem, was the theoretical basis of radio-astronomy, and in turn, of ESA's initiative to embark on two-dimensional aperture synthesis for remote sensing.

Nobody would have anticipated that such solid theoretical grounds were going to be shaken by the development of MIRAS, to the point of proving them completely inadequate for the application of interferometry to Earth Observation.

Based on the so-far successful breadboarding of MIRAS subsystems and the scientific need to monitor soil moisture and ocean salinity, ESA's Earth Science Advisory Committee recommended the implementation of the SMOS mission on April 27, 1999, as second Earth Explorer Opportunity Mission.

By 2002, the breadboarding activities (MIRAS Demonstrator Pilot Project - MDPP) were running in parallel with the Phase B of the SMOS project. The prototype built within the MDPP consisted of three linear arrays of four receivers each which could be mechanically moved along three horizontal tracks 120° equi-spaced from each other. The MDPP also included the optical harness, the correlator, and the internal calibration subsystems.

In December 2002, the MDPP demonstrator was brought inside the Electro Magnetic Compatibility (EMC) chamber of INTA (Instituto Nacional de Técnica Aeroespacial, Madrid) for the very first end-to-end test. The imaging algorithm, based on the VCZ theorem, was predicting high correlation values due to the high emissivity of the microwave absorber material (at room temperature) of the walls of the EMC chamber. To our surprise, the correlations were two orders of magnitude (!) smaller than those predicted by the VCZ theorem. After carefully assessing the breadboard, and realizing that the hardware was working well, we had to accept that the value of the correlations was real. As mentioned, SMOS was already in Phase B .

The UPC team, led by Prof. Corbella, was responsible for processing the data from the INTA test. Therefore, we all packed the hardware and went on Christmas Holidays with the heavy weight of the insignificant correlation values on our shoulders.

It was during the Christmas of 2022 that Ignasi set himself into resolving the mystery. He found a paper on noise waves and passive linear multiports of 1991 which gave the expression of the correlation of the outgoing noise waves of a passive microwave circuit. Such problem resembled the configuration of the MDPP breadboard inside the EMC chamber. The article referred to a theorem stated by a Dutch engineer, Hendrik Bosma, in his PhD thesis of 1967. According to Bosma's theorem, the correlation of the noise waves coming out of a passive microwave circuit in thermal equilibrium with its terminations, as the MDPP breadboard inside the EMC chamber, had to null.

Based on these findings, Prof. Corbella carefully reformulated the basic measurement of interferometry, the correlation between the output signals of two receivers forming a baseline, considering the presence of the neighboring receivers as well as the physical temperature of the receivers and the target. By February 2003, he had come with a new equation, more general than the CVZ theorem, which could explain the correlations in the INTA chamber as well as those measured by radio-telescopes (for large antennas and spacings, in wavelength units, the new formulation reduced to the CVZ theorem). Later the same year, Prof. Corbella had derived the polarimetric version of his equation. The new equation, which I very deservedly coined as the Corbella Equation, was first published in TGARS, August 2004.

The fact that the VCZ theorem could not explain all interferometric experiments, like the test of the MDPP breadboard in the EMC chamber (by two orders of magnitude), was further evidenced when the opposite test was carried out: the imaging of the Cold Sky at the Dwingeloo radio-observatory facility in The Netherlands. In the Dwingeloo experiment, four receivers were manually moved along three arms to get an image of the Cold Sky. While the VCZ theorem was predicting now very low correlations based on the low brightness temperature of the Cosmic Microwave Background Radiation (CMBR), around 2.7 K, the expected values according to the Corbella equation were two orders of magnitude larger in this case. The measurements were perfectly in accordance with Corbella's predictions and, once again, about two orders of magnitude away from the VCZ theorem-predicted values.

The Corbella Equation was then adopted to process the data of the SMOS mission instead of the VCZ theorem. The calibration approach had to be adapted, and, fortunately, the Flat Target Response of the instrument could be obtained by using the CMBR and the subsequent Flat Target Transformation could be devised to remove the -Tr term Corbella had introduced into the VCZ equation. With the data processing and calibration following his equation, Ignasi had brought the SMOS project back on track half way through Phase B.

It is worth noting that it took some time for some engineers to accept and understand the profound implications of the "Corbella Equation." After all, the VCZ theorem, established by renowned (Nobel Prize awarded) scientists, had been working perfectly well in radio-astronomy for decades. It was only a matter of making new experiments in new conditions (as taking the MDDP breadboard inside the INTA EMC chamber), realizing of other scientists' research (as Bosma's PhD thesis), and having a clear and humble mind to put the pieces of the puzzle together. This ultimately culminated in a scenario where David beat Goliath with a new more general formulation of aperture synthesis.

This book starts with a tedious Chapter 1 on probability concepts and stochastic processes, Hilbert transform, and analytic signals. However, the usefulness of its contents will be much appreciated throughout the rest of the book, as they will be frequently called upon to make progress in the formulation of the different flavors of interferometers.

Chapter 2 introduces the basic concepts of radiometry. Prof. Corbella has made an effort to explain interferometry and all its equations in a way that collapses to the case of a conventional total power radiometer. In this respect, it makes interferometry easier to digest for engineers knowledgeable in conventional radiometry.

The Corbella Equation is derived in Chapter 3. This chapter can be considered central and including the nucleus of the aperture synthesis theory applied to remote sensing. An engineer confronted with the design of this type of radiometers should absorb these contents thoroughly. This chapter introduces also...