FR3054674A1 - HYPERFREQUENCY RADIOMETRIC IMAGING SYSTEM AND IMAGING METHOD THEREOF - Google Patents

Abstract

The subject of the invention is a microwave radiometric imaging system (1) comprising an array (2) of microwave reception antennas (2a) for acquiring the brightness temperature of an object, said system (1) further comprising a passive analog coding module (3), an analog digital converter module (4) and a digital processing module (5), the passive analog coding module (3) generating on each output an encoded analog output signal, each output of the passive analog coding module (3) being connected to an analog-to-digital converter of the analog-digital converter module (4) for generating at the output of the digital-to-analog converter module (4) M digital signals, each output of the analog-digital converter module (4) being connected to the digital processing module (5) configured to perform a thermal image reconstruction of the imaged object by the antenna array (2) by processing digital signal based on interferometric aperture synthesis.

Description

Holder (s): microwave characterization center Simplified joint-stock company, NATIONAL CENTER FOR SCIENTIFIC RESEARCH Public establishment, UNIVERSITY OF LIMOGES Public establishment, ATOMIC AND ALTERNATIVE ENERGY COMMISSION Public establishment.

Extension request (s)

Agent (s): CABINET CHAILLOT.

MICROWAVE RADIOMETRIC IMAGING SYSTEM AND ASSOCIATED IMAGING METHOD.

FR 3 054 674 - A1 (5 /) The subject of the invention is a microwave radiometric imaging system (1) comprising an array (2) of microwave reception antennas (2a) for acquiring the brightness temperature of a object, said system (1) further comprising a passive analog coding module (3), an analog to digital converter module (4) and a digital processing module (5), the passive analog coding module (3) generating on each outputs a coded analog output signal, each output of the passive analog coding module (3) being connected to an analog digital converter of the analog digital converter module (4) to generate at the output of the analog digital converter module (4) M digital signals, each output of the analog to digital converter module (4) being connected to the digital processing module (5) configured to perform a thermal image reconstruction of the object imaged by the antenna network es (2) by digital signal processing based on an interferometric aperture synthesis.

i

MICROWAVE RADIOMETRIC IMAGING SYSTEM AND METHOD

ASSOCIATED IMAGING

The present invention relates to the field of imaging, and relates in particular to a microwave radiometric imaging system with aperture synthesis and to an associated imaging method.

Security systems for the detection of hidden objects such as metal detection portals, portable metal detectors, or even security scanners, are increasingly used to secure public places, such as performance halls, stadiums, stations, airports, or even educational establishments, in order to detect possible weapons that could be carried by people seeking to enter these public places.

In commonly used systems, an electromagnetic field is generated, which is backscattered by any metallic weapon-type object placed in the backscatter field of the electromagnetic field. The electromagnetic enables metallic.

These state-of-the-art systems have two main drawbacks. On the one hand, they make it possible to detect only objects which are not transparent with respect to the electromagnetic wave generated, and which have dielectric properties sufficiently different from those of the human body. They are therefore likely to let through plastic weapons or explosives, which poses a security problem. On the other hand, they generate an electromagnetic field on the inspected person, which can pose health or even safety problems for people sensitive to the fields.

Electromagnetic object or carrying a pacemaker.

The radiometry, which designates measurement of Intensity radiation electromagnetic, East mainly used to measure the temperature of a

dissipative body.

The physical principle used for this type of measurement is the electromagnetic radiation of thermal origin emitted by any body whose temperature is different from absolute zero. The power of electromagnetic noise, in relation to body temperature, comes from the random agitation of the microscopic electric dipoles of molecules. The intensity of the radiation of a body then has three contributions: its self-emission proportional to its intrinsic physical temperature (contribution of emissivity ε), reflection of the waves generated by the external sources of illumination (contribution of reflectivity R) , and the transmission of the waves emitted by the scene located in the background (contribution of transmittance t), with ε + R + t = 1.

Each contribution depends on the physical and geometric characteristics of the materials, the temperature Tmes of an object measured by radiometry depending on the temperature of the object Tobj, the temperature of the illumination source Till and the temperature of the back Tarr plane, with Tmes = s * Tobj + R * Till + t * Tarr.

A large majority of metals have low or zero emissivity and transmittance at frequencies corresponding to millimeter waves. For a plastic object with a low dielectric constant, the temperature measured by a radiometric receiver at frequencies corresponding to millimeter waves comes mainly from the waves emitted by the scene in the background. For a natural person, at 90 GHz, its emissivity is around 50%, its transmittance is almost zero and its reflectivity is therefore also close to 50%.

Thus, it is possible by radiometry to distinguish a metal or plastic object carried by a person.

Indeed, detection by radiometry at frequencies corresponding to millimeter waves makes it possible to distinguish metal or plastic objects from a person's body. In addition, detection by radiometry at frequencies corresponding to millimeter waves is completely passive: no wave is emitted, and detection is made safe in terms of electromagnetic radiation for the persons inspected, and a greater range of objects can be detected.

An example of such a detector by radiometry at frequencies (30-300 GHz) corresponding to millimeter waves is for example the Millicam camera (registered trademark), developed by the company MC2-Technologies.

The disadvantage of such a millimeter camera is that the image is obtained by a mechanical displacement in two dimensions of a millimeter sensor (measuring the power of the electromagnetic noise generated by the person in the range of millimeter waves). This mechanical movement limits the acquisition time of the camera, and therefore limits the number of people who can be checked in a given time interval.

To achieve a compatible real-time refresh rate, it is necessary to simultaneously acquire signals from a large network of sensors. This requires an RF signal acquisition chain for each sensor, and therefore a large footprint and very high production and maintenance costs for the overall system.

The publication “Code-modulated interferometric imaging System using phased arrays”, Vikas Chauhan et al., Passive and active millimeter-wave imaging XIX, Proc. SPIE Vol. 9830. describes an interferometric imaging system using an antenna array, the signals from the antenna array being phase coded so that the signals are orthogonal to each other, then summed, converted from analog to digital, then finally processed to find by synthesis of interferometric aperture the brightness temperature of the imaged object at frequencies corresponding to millimeter waves, which represents the image of the object.

The system described in this publication has the advantage for the user to perform passive detection, however the phase coding of the signals from the sensor network means that the detection chain up to the analog / digital converter is not not passive: active components are required to phase code each signal, so as to make the signals orthogonal to each other two by two.

The invention aims to overcome the drawbacks of the prior art and relates to a microwave radiometric imaging system in which the coding of the signals is passive.

The subject of the present invention is therefore a microwave radiometric imaging system comprising a network of N microwave reception antennas for acquiring the brightness temperature of an object in the microwave domain according to the interferometric aperture synthesis technique, characterized by said system further comprises a passive analog coding module, an analog to digital converter module and a digital processing module, the passive analog coding module comprising N inputs connected to the N antennas and M output channels connected to the analog to digital converter module , with N >> M> 1, each input channel of the passive analog coding module receiving a radio frequency (RF) signal from an antenna of the antenna array and passively coding the RF signal which it carries between the input and the output, the coded signal on one channel being decorrelated from the coded signals on the other channels, each channel being t sent to a single output of the passive analog coding module in order to generate an analog output signal on each output of the passive analog coding module, each output of the passive analog coding module being connected to an analog to digital converter of the analog to digital converter module to generate at the output of the analog to digital converter module M digital signals, each output of the analog to digital converter module being connected to the digital processing module configured to perform a thermal image reconstruction of the object imaged by the antenna array by digital processing signals based on an interferometric aperture synthesis.

The analog to digital converter module can include one or more analog to digital converters.

According to a particular embodiment, the passive analog coding module comprises at least one passive analog coder, each passive analog coder consisting of one of a planar monolayer or multilayer cavity, a volume oversized cavity, a chaotic planar monolayer cavity or multilayer, a chaotic volume cavity, delay lines summed by a summator, filters with frequency coding summed by a summator.

According to a particular embodiment, each analog to digital converter of the analog to digital converter module is one of a 1-bit comparator, an analog to digital converter composed of a stage of stage and a digitization on several bits of sampling.

According to a particular embodiment, the processing performed by the digital processing module is a decoding performed by at least one of a suitable filtering, a time reversal, a matrix inversion by the least squares method, a regularized matrix inversion.

According to a particular embodiment, a first RF signal conditioning chain comprising at least one RF low noise amplifier is disposed between each antenna of the antenna array and the corresponding input of the passive analog coding module.

According to a particular embodiment, the first signal conditioning chain comprises a first RF low noise amplifier, a frequency step-down and a second RF low noise amplifier, connected in this order in series from the antenna to the corresponding input of the passive analog coding module.

According to a particular embodiment, the first signal conditioning chain comprises a two-way unipolar switch associated with a load, preferably of 50 Ohms, a low noise RF amplifier and an isolator, connected in this order in series from the antenna to the corresponding input of the passive analog coding module

According to a particular embodiment, a second signal conditioning chain is disposed between the output of the passive analog coding module and the analog converter module digital conditioning chain, the second signal comprising a low noise RF amplifier in series with a filter demodulator bandpass

IQ, each filter of and an IQ demodulator comprising an intermediate (IF) in series with a low noise IF amplifier, the signal of the local oscillator of the IQ demodulator being supplied by a voltage controlled oscillator associated with a phase locked loop .

According to a particular embodiment, the digital processing module comprises at least a first slave programmable pre-broadcast matrix (FPGA) for decoding the signals coming from the analog digital converter module and performing a calibration, at least one master programmable pre-broadcast matrix (FPGA) for synchronizing the at least one first programmable prediffused matrix (FPGA) and performing an inverse Fourier transform on the signals decoded by the at least one first programmable prediffused matrix (FPGA), at least one digital signal processor to perform image processing on the inverse Fourier transform performed by the master programmable pre-scattered matrix (FPGA), and optionally a computer for displaying the image and driving the master programmable pre-scattered matrix (FPGA) and the at least one first slave preprogrammed matrix (FPGA).

According to a particular embodiment, the digital processing module is configured to perform the following steps:

frequency channel - deconvolve signals from the analog to digital converter module;

- correlate pair by pair the signals from the deconvolution of the previous step;

- calculate the visibility function of the antenna array from said pair-to-pair correlation; and - reconstruct the brightness temperature characterizing the area to be imaged detected from said visibility function by inverse Fourier transform or matrix inversion.

According to a particular embodiment, the digital processing module is configured to perform the following steps:

- direct estimation of visibility functions by multiplication of each signal received from the analog to digital converter module by its conjugate;

- reconstruction of the brightness temperature detected from characterizing the area to be imaged, said visibility function by inverse Fourier transform or matrix inversion.

The subject of the invention is also a method of imaging an object by a passive microwave radiometric imaging system as described above, characterized in that it comprises:

- Passively acquiring the brightness temperature of an object in the microwave domain by the antenna array of the passive microwave radiometric imaging system;

- the calculation of the visibility function from the acquired signals, by one of:

- the pair-to-pair deconvolution of the acquired signals and the calculation of the visibility function from said pair-to-pair correlation, or - the direct estimation of the visibility function by multiplication of each signal received from the analog-to-digital converter module by sound conjugate and - the reconstruction of the brightness temperature characterizing the area to be imaged detected from said visibility function by inverse Fourier transform or matrix inversion.

To better illustrate the object of the present invention, there will be described below, by way of illustration and not limitation, preferred embodiments, with reference to the accompanying drawings.

In these drawings:

- The imaging figure is a radiometric diagram that microwave functional of a system according to the present invention;

- Figures 2a, 2b, and 2c respectively represent three variants of the passive analog coding module of the imaging system of Figure 1;

- Figure 3 is a block diagram of the signal conditioning chains upstream and downstream of the passive analog coder of the imaging system of Figure 1;

- Figure 4 is a block diagram of a digital processing module of the imaging system of Figure 1; and ίο Figure 5 is a block diagram of a particular embodiment of the digital processing module of a radiometric imaging system according to the present invention.

Referring to Figure 1, it can be seen that there is shown an imaging system 1 according to the present invention.

The imaging system comprises a network, in the mode of in FIG. 1, of microwave reception antennas 2, a passive analog coding module 3, an analog to digital converter module 4 and a digital processing module 5, in order to image the area to be imaged 6.

The antenna array 2 is a schematic embodiment shown rectangular and uniform, the antennas 2a being arranged equidistant inside a rectangle, and generating microwave signals if, s2, sn, ..., sm. The invention is not however limited in this respect, and the antenna array 2 is not necessarily uniform and / or rectangular: an antenna array 2 in T or in Y is also envisaged in the context of the present invention. The arrangement of the antennas in the antenna array 2 can also be arbitrarily distributed.

The smallest spacing between antennas in the antenna array 2 fixes the maximum size of the observable area to be imaged 6. The larger spacing gives the spatial resolution (pixel size of the antenna array image obtained)

The antennas of the are arranged to be able to implement a radiometry technique (SAIR).

π interferometric aperture synthesis

The antenna array 2 is functionally connected to the passive analog encoder 3.

The passive analog encoder 3 is a device which makes it possible to reduce the number of radio frequency signals originating from the antennas of the antenna array 2 to be processed, by coding analogically on one or more outputs of the passive analog encoder 3 several inputs of the passive analog encoder 3. Each input of the passive analog encoder 3 (corresponding to an antenna of the antenna array 2) passes through a single channel of the passive analog encoder 3 and undergoes a passive transformation thereon, each signal undergoing in the analog encoder passive 3 a different transformation, illustrated in Figure 1 by the corresponding channel (impulse response) cl, c2, into, ..., cm.

The passive analog encoder 3 analogically codes the information received from each antenna of the antenna array 2: the signals received by the antennas 2a are convolved by the impulse responses (orthogonal or uncorrelated with each other) from the passive analog encoder 3. Next, a summation, which can be direct or through one or more summers.

The coded signal on each channel of the passive analog encoder 3 is decorrelated from the other channels: a time or frequency diversity is created. Ideally, the autocorrelation of the code should tend towards a Dirac in the time domain, and the intercorrelation of two signals coded on two different channels of the passive analog encoder 3 should tend towards 0.

It is important to note that in the context of the present invention, the passive analog coder 3 does not require control electronics to code the signals received by each antenna of the antenna array 2. The coding is intrinsic to the passive component, which has decorrelated transfer functions for each of its channels. It is therefore not necessary to generate codes electronically.

Several passive analog encoders can be envisaged in the context of the present invention.

According to a first variant envisaged, the passive analog encoder is implemented by an oversized planar or volume, monolayer or multilayer cavity. An oversized cavity is a resonant cavity which has sufficient modal diversity for the different transfer functions to be decorrelated and for autocorrelation to be optimal. Its quality factor must be as high as possible so that the spectral occupancy of each mode is as fine as possible, the objective being to avoid modal overlap in frequency which would cause a loss of diversity and therefore a degradation of the properties of correlation.

The expression "oversized cavity" means a minimum operating frequency> 3 * f0 to 6 * f0, fO being the operating frequency of the fundamental mode of the oversized cavity. In addition the

dimensions of the cavity oversized must be very greater than the speed light c divided by fO, c / f 0. he East note that the volume of the cavity

oversized depends on the number of antennas, the bandwidth used and its quality factor. Those skilled in the art will be able to optimize these parameters by electromagnetic simulation. Such optimizations can be made based on the publication by D. A. Hill "Electromagnetic Fields in Cavities: Deterministic and Statistical Theories, 2009, IEEE Press" (Electromagnetic fields in cavities: Deterministic and statistical theories). Software which can be used for such simulations are for example CST microwave studio®, FEKO® or even HFSS® software from the company ANSYS.

According to a second variant envisaged, the passive analog coder is implemented by a planar or volume chaotic cavity, monolayer or multilayer.

A chaotic cavity is an oversized cavity as in the first variant, in which the modal diversity has been improved by the shape of the cavity or by the addition of diffusers therein to give it ergodic properties. Modal degeneration is made minimal (number of modes at the same minimum frequency) compared to an oversized cavity. In addition, the diffusion of the field is increased in a chaotic cavity compared to an oversized cavity.

In the first and second variants, the cavities can be planar (metallized printed circuit) or solid, monolayer or multilayer.

For the first and second variants, it is possible to use a single output of the cavity on which all the outputs are coded, or to use more than one output, in order to associate with the frequency diversity a spatial diversity.

The advantage of the first and second variants is that the responses of the cavity remain stable over time, unlike an architecture using control electronics to code the signals, which is a sensitive point in the field of application of the invention, namely microwave radiometry.

Another advantage of the first and second variants is that passive coding is carried out instantaneously, once again unlike the use of control electronics for coding signals on several symbols, where the coding duration depends on the modulation speed phase.

FIG. 2a schematically represents by way of nonlimiting example a chaotic cavity 7, of parallelepiped shape, the chaotic character being obtained by adding a spherical diffuser 7a in one of the corners of the chaotic cavity 7.

According to a third variant shown in Figure 2b, the passive analog encoder 3 is produced by association of microwave or optical delay lines and one or more summers. For this variant, each input of the passive analog encoder 3 corresponding to an antenna of the antenna array 2 is sent on a channel Cl, .., Cn, each channel Cl, .., Cn having a delay different from that of the other channels .

The output channels of the channels Cl, .., Cn are sent to an adder S, the output of the adder S corresponding to the output of the passive analog encoder 3.

It should be noted that the passive analog coder 3 could have several outputs, each associated with a summator, each input then being directed to one of the outputs (one of the summers) of the passive analog coder 3.

According to a fourth Figure 2c, the analog coder: association of filters of several summers S. For the passive analog coder of the antenna array 2 is transfer function Cl s variant shown on the .que passive 3 is achieved by passive coding and d 'one or this variant, each input corresponding to an antenna; sent on a filter of

Cn, each channel Cl

Cn having a frequency coding different from that of the other channels.

At the output, the output channels of each transfer function filter Cl, Cn are sent to an adder S, the output of the adder S corresponding to the output of the passive analog encoder 3.

It should be noted that the passive analog coder 3 could have several outputs, each associated with a summator, each input then being directed to one of the outputs (one of the summers) of the passive analog coder 3.

For each variant, it is therefore possible to have in the passive analog coding module 3 either a passive analog coder having one or more outputs, or several passive analog coders each having one or more outputs, each passive analog coder in this case associated with a sub-network of the antenna network.

Each output of the passive analog coding module is connected to an input of the analog digital converter module 4.

The analog to digital converter module 4 comprises as many channels as there are inputs, each channel carrying an analog to digital converter. In a 1-bit approach, each analog-to-digital converter can for example be constituted by a 1-bit comparator.

It should be noted, as shown in FIG. 3, that signal conditioning chains are preferably arranged upstream and downstream of the passive analog coding module 3.

A first signal conditioning chain is arranged between each antenna of the antenna array 2 and the passive analog coding module 3.

In a first variant represented in FIG. 3, the first signal conditioning chain comprises a two-way unipolar switch (SPDT) 8

associated with a load 9, of preference of 50 Ohms, a amplifier low noise RF 10 and, of way optional, an insulator 11, mounted in this order in series since the antenna towards Entry correspondent of

passive analog coding module 3.

According to a second variant not shown, the first signal conditioning chain can comprise a first low noise RF amplifier, a frequency step-down and a second low noise RF amplifier, connected in this order in series from the antenna to the corresponding input of the passive analog coding module.

A second signal conditioning chain is disposed between the passive analog coding module 3 and the analog digital converter module 4, and comprises a low noise RF amplifier 12 in series with a bandpass filter 13 and an IQ demodulator 14, each channel. of the IQ demodulator 14 comprising an intermediate frequency (IF) filter 15 in series with a low noise IF amplifier 16, the signal of the local oscillator of the IQ demodulator 14 being supplied by a voltage controlled oscillator 17 associated with a locking loop phase 18, the signals I and Q coming from the second conditioning chain being subsequently digitized by the analog-to-digital converters of the analog-to-digital converter module 4.

The first and second signal conditioning chains make it possible to have a sufficient signal level upstream of the analog-to-digital converter module 4.

If we now refer to Figure 4, we can see that there is shown a block diagram of an embodiment, given by way of example but not limiting, of the digital processing module 5 according to the present invention.

The inputs of the digital processing module 5 are connected to the output or outputs of the analog digital converter module 4.

Each input of the digital processing module 5 corresponds to an input of the transmitter / receiver (transceiver) type of a programmable prediffused matrix (FPGA) 19 associated inter alia with a block of dynamic random access memory (DDR) 20, an Ethernet corn port 20 and analog digital converters (DAC) 12 to 16 bits 23, the whole of the digital processing module 5 being synchronized by a clock 22.

The VHDL code of FPGA 19 is programmed to decode the digitized signals coming from each output of the analog to digital converter module 4, which corresponds to an output of the passive analog coding module 3. The VHDL code also includes in situ calibration operations making it possible to correct the variations in the transfer function of each channel from the passive analog coding module 3 due to temperature variations or to low frequency noise from the low noise amplifiers 10, 12, 16. This calibration step may require, among other things, checking microwave switches, the polarization of low noise amplifiers 10, 12, 16, hence the presence of DACs 23.

Depending on the number of passive analog coders in the passive analog coding module 3 and the complexity of the code implemented, several FPGAs can be used in the digital processing module 5, knowing that one FPGA will be taken as master and the other slave FPGAs for synchronization.

Such an embodiment is shown in Figure 5, and includes 4 slave FPGAs 24, 25, 26 and 27, to decode the signals of all the channels and carry out an in-situ calibration, as indicated above, and a Master FPGA 28 associated with a digital signal processing device (DSP) 29, the master FPGA 28 being configured to synchronize and carry out the inverse Fourier transform processing, as indicated in more detail below, the DSP 29 being for a final image processing. A PC 30 makes it possible to control the assembly and to display the image on a monitor (not shown) and to provide additional processing to the image.

The various calculations used to reconstruct the image of the area to be imaged will now be described in more detail.

As indicated above, the object of the imaging system 1 according to the present invention is to measure the visibility function which, in the ideal case, is the Fourier transform of the image of the brightness temperature of the area to be imager 6, which corresponds to the image of the area to be imaged observed.

The signals received by each antenna 2a of the antenna array 2 are coded by the transfer functions of the passive analog coding module 3.

In what follows, for the sake of simplification of the equations, certain relations will be expressed in the frequency domain.

Thus, we consider that a signal emitted s (t) has spectrum S (f):

S '. fl. F if i i (1) where F [] denotes the Fourier transform.

In an example of the digital processing developed below, only one output channel of the passive analog encoder 3 and N input channels corresponding to the N antennas are considered, but the equations can be easily generalized in the case of an N system. inputs to M outputs of the passive analog encoder. The single signal thus measured at the output of the passive analog coding module 3 is given by the equation:

S _meS ^) = ^ sJt) ^ C _n Ct) ⁽²⁾ n

where s _mes (t) represents the signal measured at the output of the analog digital converter module 4, s _an (t) the signal received by the antenna n and c _n (t) the nth impulse response of the oversized cavity, and where l operator (*) is the convolution operator. This operation can also be written in the form of a simple multiplication in the frequency domain:

S _m , (f) = YSJf) »C _n (f) (3) n

The first and second conditioning chains and the analog to digital converter module 4 can be modeled by a transfer function taking into account the transfer functions of all the elements. This allows the complex signal measured to be transposed into baseband for digital processing.

We denote by H _rec the transfer function of this modeled set. Thus the baseband signal s _bd (t) measured is therefore written:

w it '; - mi »sb> d Π, ¹ » ₍ , Ή (4) g,., .. jf: .s ..... i î 'if; · - 5 ,, „; fi. <(5)

For simplicity of writing, this equation can be represented in the form of a matrix product:

Su = < ^(6} where C _rec = C (f) H _rec (f) is the transfer function of the set measured at the output of the set. The measured baseband signal therefore depends on the signals actually measured by the antennas and transfer functions of the passive analog coding module 3 and of the set of conditioning chains + analog digital converter module 4.

The digital processing module 5 comprises three essential steps, the deconvolution of the signals measured by the antennas, the calculation of the visibility functions and the reconstruction of the brightness temperature characterizing the area to be imaged 6. Three possible methods of reconstructing the noise temperature of a source are described below.

1.1 - Deconvolution of the signals received by the antennas

The system of equations (6) is a linear system with more unknowns than equations. In the case where we consider a coder with N input channels and M output channels, C _rec will be a matrix Μ χ N, Sta a vector of length M and S _a is a vector of length N with N> Μ , M being the number of output ports of the passive analog coding module 3 and N being the number of antennas of the antenna array 2. In this example, it is assumed that M = 1.

If [C _rec C * _re c] is invertible, then the system admits an infinity of solutions, and we say of this system that it is badly posed. There are several methods allowing the deconvolution of the signals picked up by the antennas 2a, the simplest method being that of time reversal. However, this method only compensates for the phase due to the response of the passive analog coding module 3. The regularization method with minimum standard makes it possible to compensate for both the phase and the amplitude of C _rec · The regularization of MoorePenrose allows minimization of the I ₂ standard defined by:

v i (7) s ,, j · '' Z__f

P, - J

This term most often relates to the energy of the signal S _a . This method, commonly known as the least squares method, makes it possible to minimize this energy. The explicit solution is therefore written:

i ç ,, ~ î, if) ¹ (θ)

However, if the signals are noisy, the term C _re cC * rec may be poorly conditioned, so the reverse can cause significant estimation errors of C ⁺ rec and therefore of the signals received by the antennas 2a.

In order to limit the noise level, the Tikhonov sense regularization technique can be used. It makes it possible to minimize the objective function admitting for explicit solution:

c + = _eit (7..if. {. · η>. ⁽⁹⁾ where I is an identity matrix and μ is the regularization parameter for thresholding level of noise. It avoids inversion errors too low values of the additive noise and of the intercorrelation noise between the channels of the passive analog coding module 3. The disadvantage of this method is the appropriate choice of the regularization parameter. Iterative, fast and efficient regularization methods can also be used, such as conjugate gradient algorithms (see K.-C. Toh and S. Yun, "An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems", Pacific Journal of Optimization, vol. 6, no. 615 -640, p. 15, 2010) which solve problems of the “basic pursuit” type, algorithms of the Hogbom's Clean type (see T. Fromenteze, E. Kpre, D. Carsenat, and C. Decroze, “Clean Deconvolution Applied to Passive Compressed Beamforming ", Progress in

Electromagnetics Research C, vol. 56, pp. 163-172, 2015).

Unlike the regularization methods of standard I ₂ , these methods do not admit of explicit solutions. The convergence and stop conditions of the algorithm are set by the user. It is recalled that the deconvolution process will be all the more efficient the higher the bandwidth of the passive analog coding module 3 (and therefore of the reception chain). This is a priori not compatible with the conventional SAIR technique, which must respect the channel coherence band. The system must not have sufficient time resolution to distinguish the time difference between two source-antenna paths.

In this model, we will use the method of least squares for which μ = 0. The signals measured by the antennas can therefore be estimated via the equation:

(10) d „- * · ^ν “ ··

(.

Ideally, the product C ⁺ recpC _re c = U so the reconstructed signal is perfectly identical to that received by the antennas. The phase and quadrature components for antenna i are given by:

ffi. = api (11) (12)

1.2 - Calculation of the complex visibility function

The complex signal thus estimated can be used for the calculation of the visibility function on each channel (I, Q), namely V _z and V _Q. For each spatial frequency (Uij, Vij) associated with the pair of antennas (i, j), the visibility function is calculated by the correlation of the complex signals:

d

- "/ μι λ id (13;

(14;

where the operator <' ^{i |} duj. <! > temporal. This is the correlation operation. The complex visibility function can therefore be obtained by the following equation:

Λ represents the integration to make mathematically a

Vl f>. ri - V / li i fi. i (15)

This operation can be done both in the time domain and in the frequency domain: it is just appropriate to replace the temporal dimension by the frequencies.

The coding of the signals received by the channel functions inevitably generates errors on the phase and on the module of the reconstructed visibility function. The more pronounced peaks which appear in the visibility functions module of the system according to the invention are due to the autocorrelation functions of the channels of the passive analog coding module 3. They appear in the spatial decorrelation function also called “Washing of the fringes " This function can be described in general by the following equation:

ι., '. ιΐ-'''! I /.(/-/:/)1./ ¹ * f // (16) with ⁽¹⁷⁾

Ideally Ii and Ij are identity matrices. However, in practice, the estimation is not perfect, which makes the “Washing of the fringes” function complex and then comes to weight the values of the visibility function. These complex coefficients strongly attenuate the modulus of the visibility function of the system according to the invention.

For a better reconstruction of the brightness temperature, the spatial decorrelation function must be taken into account. Another solution making it possible to minimize the influence of the spatial decorrelation function is the direct estimation of the visibility functions, as described below.

- Direct estimation of the complex visibility function

In the above, the visibility function has been calculated in two distinct steps, the first step being a deconvolution process to estimate the signals received by the antennas, encoded by the channels of the passive analog coding module 3 and the second step being the calculation of complex visibilities. It is possible to find the visibility functions by multiplying the signal received behind the analog-to-digital converter by its conjugate. This amounts to calculating the power of the signal measured at the output of the receiver. The mathematical development reveals the term of the visibility function useful for the reconstruction of the temperature.

P s - .. i · .S ',,.

(18)

We consider the very simple case of two antennas receiving the signals S _a2 and S _a2 . The visibility function associated with this antenna couple is denoted V ₁₂ = <S _a2 . S * _a2 >. The signal received at the component output is such that:

di., | t (., (19)

The power is given by:

; C ,, î 'w-l iF.-i f L, ·, s' „. i g ',,,, - r ,,, .y • <' 1.. i .1 .., S. I F (2o:

JV-1

Vc

O Q * · '>', <S i

Equation (18) shows that the power spectral density of the received signal contains a continuous component linked to the individual power received by each channel of the passive analog coding module 3 as well as inter-channel interactions which include the information relating to the degree spatial coherence. Thus, it suffices to measure beforehand all the combinations C _re ci-C * _re cj linked to the antenna torque (i, j) to estimate the visibility functions linked to this couple. The summation over time or frequencies becomes deconvolution.

the operation of after ν, ίρ ,,. ρ ,,; F (21 ’(22;

The visibility functions thus estimated, the reconstruction of the image is done by an inverse Fourier transform or by matrix inversion. The second is to solve the linear equation:

F = G.T (23) where G represents the system matrix linking the space of the object T to the space of the measure V. The dimensions of G depend on the number of functions of spatial frequencies and the number of pixels. Minimum standardization methods solve this type of equation.

T = G ⁺ .F (24) with G ⁺ the inverse of G.

A more generalized method allows a reconstruction of the image of the area to be imaged from the measured signal power. The following paragraph describes the principle of reconstruction.

- Deconvolution of the image of the area to be imaged

A more generalized method would allow the image signal of the area to be imaged to be reconstructed just from the signal power measured at the receiver output (antenna array 2). It follows from equation 22 that the terms of the visibility function appear in the expression of the measured signal strength.

These terms are weighted by the terms:

F-recij U reci · Urecj which are linked to the responses of the passive analog coding module 3 and of the antenna array 2. Consequently, if all the combinations are known beforehand and integrated into the characterization matrix of the system, there n There is more need for deconvolution of the received signals, even less for the visibility function. That said, it is advisable to define a system matrix simulating the impulse response of the whole system according to the invention.

(25) where ζ is a spatial variable linked to the coordinates of each pixel.

Ρ ^ ζ) and F ^) are the radiation patterns of the pair of antennas i, j whose relative positions create the spatial frequency u _tj .

Rrecÿ (f) is the spatial decorrelation function linked to the pair of antennas i, j.

The measured signal power can therefore be written in matrix form by the equation:

P = G JF (26)

p ,, IX, ·

G'Ii.L) (ïll.2) (, 'fft dit. 2) fi'i .Y /. Q '. GLY, ^f . (F.

where Q represents the number of pixels of the reconstructed image and Nf, the number of frequency points. Measuring the matrix G of the system amounts to simulating all the possible delays as a function of the position of the pixel and of the pair of antennas considered, while taking into account all the elements involved in the reception chain. The advantage of this method is the generalized inversion of the matrix of the system which makes it possible to reconstruct the brightness temperature without any hinge operation.

Its drawback, on the other hand, is the inversion of the matrix G such that: 3 = G ¹ ~ F. Indeed, the size of the matrix G increases with the number of pixels and the number of frequency points.

Once the signals have been decoded and corrected (visibility function of the system reconstructed after correction of the variations in the transfer function of each channel), a fast inverse Fourier transform (IFFT) is performed to return to the “dirty” image. This operation of IFFT can be done in different ways, this being carried out by FPGA in the example of Figures 4 and 5. The “dirty” image thus produced is “cleaned” by application of different treatments (for example: a CLEAN algorithm), like among others the deconvolution of the PSF (transfer function of the optical system), filtering, contrast enhancement. These processing operations can be carried out by the DSP 29 in FIG. 5 or by means of a processor on the PC 30. The entire digital processing chain is controlled by the PC 30 via an Ethernet corn port 21.

An experiment was carried out by the Applicants, at 3 GHz, on a bandwidth of 1 GHz, with a system having the same architecture as that shown in FIG. 1, and an area to be imaged containing two point sources of white noise. The network was a network of 16 T-antennas, the passive analog coding module consisting of an oversized cavity of lm3, 16 channels to 2.

By the first method implemented in the digital processing module (deconvolution of signals and calculation of the complex visibility function), the image of the noise sources is obtained with a resolution identical to that calculated theoretically (of the order of 30 cm with the size of the antenna network considered).

Claims (7)

1 - Microwave radiometric imaging system (1) comprising a network (2) of N microwave reception antennas (2a) for acquiring the brightness temperature of an object in the microwave domain using the interferometric aperture synthesis technique, characterized in that said system (1) further comprises a passive analog coding module (3), an analog to digital converter module (4) and a digital processing module (5), the passive analog coding module (3) comprising N inputs connected to the N antennas and M output channels connected to the analog digital converter module, with N >> M> 1, each input channel of the passive analog coding module (3) receiving a radio frequency (RF) signal from an antenna (2a) of the antenna array (2) and passively coding the RF signal which it carries between the input and the output, the coded signal on one channel being decorrelated from the coded signals on the other channels, each channel being sent to a single output of the passive analog coding module (3) in order to generate on each output of the passive analog coding module (3) an analog output signal, each output of the passive analog coding module (3) being connected to an analog to digital converter of the analog to digital converter module (4) for generating at the output of the analog to digital converter module (4) M digital signals, each output of the analog to digital converter module (4) being connected to the digital processing module (5) configured for perform a thermal image reconstruction of the object imaged by the antenna array (2) by digital signal processing based on an interferometric aperture synthesis. 2 - microwave radiometric imaging system (1) according to claim 1, characterized in that the passive analog coding module (3) comprises at least one passive analog coder, each passive analog coder consisting of one of a monolayer or multilayer planar oversized cavity, a volume oversized cavity, a monolayer or multilayer planar chaotic cavity, a volume chaotic cavity, delay lines summed by a summator, frequency coded filters summed by a summator. 3 - microwave radiometric imaging system according to one of claims 1 and 2, characterized in that each analog to digital converter of the analog to digital converter module (4) is one of a 1-bit comparator, an analog to digital converter composed of a sampling stage and a multi-bit digitization stage. 4 - microwave radiometric imaging system according to one of claims 1 to 3, characterized in that the processing carried out by the digital processing module (5) is a decoding carried out by at least one of a suitable filtering, a time reversal, a matrix inversion by the least squares method, a regularized matrix inversion. 5 - Radiometric imaging system microwave according to 1 'a of claims 1 to 3, characterized by the made that a first chain of packaging of signal RF including at least a weak amplifier noise RF (10) is arranged between each antenna (2a) of the antenna array (2) and the corresponding input of the passive analog coding module (3). 6 - microwave radiometric imaging system (1) according to claim 5, characterized in that the first signal conditioning chain comprises a first low noise RF amplifier, a frequency step-down and a second low noise RF amplifier, mounted in this order in series from the antenna (2a) to the corresponding input of the passive analog coding module (3). Microwave radio frequency imaging system (1) according to claim 5, characterized in that the first signal conditioning chain comprises a bi-directional unipolar switch (8) associated with a load (9), preferably 50 Ohms, an amplifier low noise RF (10) and an isolator (11), connected in this order in series from the antenna (2a) to the corresponding input of the passive analog coding module (3). 8 - microwave radiometric imaging system (1) according to one of claims 1 to 7, characterized in that a second signal conditioning chain is disposed between the output of the passive analog coding module (3) and the analog to digital converter module (4), the second signal conditioning chain comprising an RF low noise amplifier (12) in series with a bandpass filter (13) and an IQ demodulator (14), each channel of the IQ demodulator (14 ) comprising an intermediate frequency filter (IF) (15) in series with a low noise amplifier IF (16), the signal of the local oscillator of the IQ demodulator (14) being supplied by a voltage controlled oscillator associated with a loop phase locked (17). 9 - microwave radiometric imaging system according to one of claims 1 to 8, characterized in that the digital processing module (5) comprises at least a first programmable prediffused matrix (FPGA) slave (24-27) for decoding the signals coming from the analog-to-digital converter module (4) and performing a calibration, at least one master programmable pre-broadcast matrix (FPGA) (28) for synchronizing the at least one slave first programmable pre-broadcast matrix (FPGA) (24- 27) and perform an inverse Fourier transform on the signals decoded by the at least one first programmable prediffused matrix (FPGA) slave (24-27), at least one digital signal processor (29) for performing image processing on the inverse Fourier transform carried out by the master programmable diffused matrix (FPGA) (28), and optionally a computer (30) to display the image and control the matrix programmable master (FPGA) matrix (28) and the at least one first programmable master (FPGA) slave matrix (24-27). 10 - Radiometric microwave imaging system (1) according to one of claims 1 to 9, characterized in that the digital processing module (5) is configured to perform the following steps: - deconvolve the signals coming from the analog to digital converter module (4); - correlate pair by pair the signals from the deconvolution of the previous step; - calculate the visibility function of the antenna array (2) from said pair-to-pair correlation; and - reconstruct the brightness temperature characterizing the area to be imaged detected from said visibility function by inverse Fourier transform or matrix inversion. 11 - Microwave radiometric imaging system (1) according to one of claims 1 to 9, characterized in that the digital processing module (5) is configured to perform the following steps: - direct estimation of visibility functions by multiplication of each signal received from the analog to digital converter module by its conjugate; - the reconstruction of the brightness temperature characterizing the area to be imaged detected from said visibility function by inverse Fourier transform or matrix inversion. 12 - Method for imaging an object by a passive microwave radiometric imaging system (1) according to one of claims 1 to 11, characterized in that it comprises: - Passively acquiring the brightness temperature of an object in the microwave domain by the antenna array (2) of the passive microwave radiometric imaging system (1); - the calculation of the visibility function from the acquired signals, by one of: - the pair-to-pair deconvolution of the acquired signals and the calculation of the visibility function from said pair-to-pair correlation, or - the direct estimation of the visibility function by multiplication of each signal received from the analog-to-digital converter module by sound conjugate, and - the reconstruction of the brightness temperature characterizing the area to be imaged detected from said visibility function by inverse Fourier transform or matrix inversion. 1/7 σα c φ sz 3 VS 3 = r ξ Ξ. o C? Q- m 5 c —1 .q ’ 3 ô fD _ VS 3 ° - ro rt- fD 2/7 fD Μ ω "J ω 3Π 4/7 5/7 ω υυ NJ 6/7 ω ιη 7/7 Ό Q> Μ (JJ -ο ο η ~ σ ο > NJ σι