2166 IEEE TRANSACTIONS ON MAGNETICS, VOL. 31, NO. 3. MAY 1995

Near Field Weighting Functions for Microwave Radiometric Signals

K. Ridaoui, A. Mamouni, R. Ait Abdelmalek, B. Bocquet, Y. Leroy Institut d'Electronique et de Microelectronique du Nord

D6partement Hyperfrkquences et Semiconducteurs Domaine Universitaire et Scientifique de Villeneuve d'Ascq

Avenue Poincare - B.P. 69 - 59652 Villeneuve d'Ascq CCdex FRANCE

I.E.M.N. -U.M.R C.N.RS. 9929

Abstract - After being used extensively for remote sensing, microwave radiometry is also applied for non-invasive thermometry in medecine and industry. Several works have already shown the interest of such technique for thermological applications.

I. INTRODUCTION

Microwave radiometry is being used in order to measure the near field thermal noise transmitted by lossy materials in the microwave frequency range. The corresponding applications are devoted to non-invasive thermometry in medecine and industry[1]-[3].

Such methods of investigation need to compute the radiometric signals in order to forcast the influence of the material under test, of the frequency and the caracteristics of the antenna which is being used as a probe in radiometric operation. Methods of computation are also needed in order to define the data processing in the synthesis of the radiometric images [4].

11. PRINCIPLE OF MICROWAVE RADIOMETRY

In most cases, the antenna @robe) is a rectangular wavegude aperture, filled with a low loss dielectric, the permittivity of wich achieves a fair matching at the discontinuity probe-material. The probe, placed flush to the surface under investigation is connected to the low noise- high gain radiometric receiver (Fig. 1).

1 PROBE I

Fig. 1 . Principle of microwave radiometry

Every subvolume AVi of the lossy material, coupled to the probe, delivers to this device a noise power proportional to its absolute temperature Ti and to its weighting function Ci(f) with respect to the probe. Then we have, for a limited bandwith around the frequency f :

with G(f) being the transmittance of the receiving system According to principle of detailed balancing and reciprocity theorem , a weighting functions Ci(f) is proportional to the power dissipated in AVi when the antenna (probe) is active,then we have :

111. NEAR FIELD COMPUTATION

As a consequence of relation (2), the computation of the weighting functions Ci(f) needs at first the knowledge of the near field distribution Ei(f) radiated by the antenna in the lossy material in active process. The determination of the electric field distribution requires that we consider the discontinuity between the two media, taking into account the mode matching technique of the transverse field components. Our solution includes an analytical calculation associated with an iterative method. This method has already been defined and tested in the case of homogeneous lossy material coupled to a radiometric probe [5]. Here, we consider the case of multilayered structures ( complex permittivities E; with j = 2,3,4 ...), coupled to the probe (rectangular waveguide aperture : size a, b and permittivity E ~ ) . This situation is encountered when microwave radiometry is used in medecine for non-invasive thermometry of subcutaneous tissues ( Fig.2 ). The mode of incident wave is TE,,. The discontinuities of the interfaces generate reflected discrete mode in the waveguide ( characterized by a coupling function poo.) and continuous transmitted (+) and reflected (-) modes m the

0018-9464195$04,00 O 1995 IEEE

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TEo4 @Eo0

e 2 5

a=22 mm

(probe) and qle2+, q q t e 4 + , *

2 9 E y ( ~ ) , E ~ ( ~ ) , H ~ ( ~ ) , E ~ ( ~ )

q m + qtm3+ qm4+ qm+

,qte3-,qtec= the transverse fields components of the continuous modes qte2- q m - qm4- qm+ in medium j.

IV. ESTIMATION OF THE COUPLED VOLUME

Information about the temperature profile in depth is obtained by means of radiometric data where the volume of material corresponds to Merent penetrations. This volume depends on radiation pattern of the antenna and the experimental conditions. In order to follow theses properties, we have already [6] defined the coupled volume by the next relation :

(sj Eoo( ;)( 1 + P00) = I J (&+ +q;-

0 (3 W '

dpdq

+ 7 ( q y + &'"-) E;"' dpdq .

f ..\

H , , ( : j ( i - p , ) = j j ( q g - q ~ - ) H ~ m

b = l l m m

(3) 26T i=I - 1- at z=zi , j=2 or 3 or 4

5ci - (P 12 1 ( q ~ + q 7 - ) E ~ ( z ) + ( q j m + + q ~ - ) E ~ m ( ~ ) ] i=I

The temperature resolution 6T of the radiometric receiver .exp(Tiy jzj)dpdq is given by :

1 In the next step, the continuity equations are transformed

.exp(Tiy j+lzj)djxiq .

T+T, 6 T = - J 3 (4)

where T is the temperature of the material under test ,Ts, Af, z are respectively the noise temperature, bandwith and integration time of the receiver.

Equation (3) shows that the coupled volume increases with the emissivity, with AT and with the temperature resolution of the receiver respectively.

As an example, we give in Fig3 the coupled volumes in plane XOZ in the case of structure related to living tissues [7]. The model considers a 2" skin layer followed by

I (4;:' - qT- 1 H:e + (qjm' - qy- ) H y ("1 exp ( T iy j z ) dpdq

:[ q7:l - 47; ) Hy+I ( z ) + (qz; - qz;

HF1 (31 .exp(Ti~ j+Iz j ) ~ J Q .

2168

breast tissues for the same length of probe aperture (a=22mm), but for different width b, at 3.05 GHz. This example shows that the modification of the geometry of the probe changes the shape of the coupled volume. This new process should be of interest in the research of a parameter in order to modify the depth of the radiometric investigations.

Fig. 3. Example of coupled volumes in the case of bilayered living tissue

the noise superimposed to the signal is partially cancelled by a Wiener filtering.

We point out some results of such simulations applied to thermal structures ( cylinders of diameter D at a depth Z ) with a temperature difference AT=5O C with respect to the surrounding tissues ( bolus 1 cm, skin 2mm, fat jmm, muscle ) at 3GHz. The figures 4a, 5a point out the first generation radiometric images. The figures 4b and 5b, second generation radiometric images, point out an important improvement in spatial resolution.

However, studies are still necessary in order to apply this method to experimental radiometric data.

IV. RADIOMETRIC M G I N G

The aims of the radiometric measurements is to retrieve the temperature profile in depth. Previous works have shown that is possible when two conditions are fulfilled. The first

Fig. 4. Simulation of radiometric images in the case of one thermal object

a) fmt generation b) second generation

one is to dispose of more than several radiometric data by centimeter square of the area under investigation. The second one is to be aware of the weighting functions corresponding to every positionning of the radiometric probe.

Several attempts have been proposed in the past [2] [3] [SI. For example, in [SI the combination of radiometric measurements at two frequencies leads to a retrieval of size, depth and temperature of the compact thermal structures with some a-priori hypothesis about their shape ( the first generation radiometric imaging ). However, this method suffers of a spatial resolution which is limited to the retrieval of structures with a size greater than two centimeters.

A more powerful method of retrieval has been proposed recently [4], which is based on the fact that the radiometric data result from the physical temperatures are convoluted with the weighting functions in the corresponding parts of the volume. In consequence, the Fourier transform of the radiometric data and the weighting functions leads to the two-dimension spatial spectrum of the physical temperature

Fig. 5. Simulation of radiometric images in the case oftwo thermal objects

a) fmt generation b) second generation .

and then to the corresponding temperature profile. Morever,

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V. CONCLUSION [3] F. Bardati,V. J. Brown, and G. Di Bemando, "Multifrequency microwave radiometry for retrieval of temperature distributions in the humain neck" Journal ofphotographic science, vol. 39, pp. 157- 160, 199 1.

[4] B. Bocquet, R Ait-Abdelmalek and Y. hroy, "Deconvolution and Wiener filtering of short-range radiometric images," Electronics Lefters, vol. 29

This paper presents a modal method for computation of the near field weighting functions applied to multilayered structure. From this kind of data, we point out that the coupled volume as a function of the size of the radiometric probe and that the second generation radiometric imaging is able to improve the spatial resolution.

1628-16299 1993.

[5] A. Mamouni, Y. hroy, B. Bocquet, JC. Van de velde, and Ph. Gelin, "Computation of near field microwave radiometric signals, defmition and experimental verifications," IEEE Trans. MIT, vol. 39, no. 1, pp. 124-132, 1991.

[6] B. Bocquet, P. Dehour, A. Mamouni, JC. Van de velde, and Y. Leroy, "Near field microwave radiometric weigthing functions for multilayered materials,"JEWA,vol. 7,110. 11,pp. 1497-1514, 1993.

171 D. Land. and A. M. Cambell, "A quick accurate method for measuring the microwave dielectric properties of small tissue samples," Phys. Med Biol., vol. 37, no. 1,pp. 193-210, 1992.

[81 B. Bocquef J. c. van de 'IAn

example of thermometry in volume by microwave radiometry," LEE.?? Biomed. Eng, vol. 40, no. 9, pp. 990-992, 1993.

REFERENCES

[I ] Y. Leroy, A. Mamouni, JC. Van de velde, B. Bocquet, and B. Dujardin, "Microwave radiometry for non-invasive thermometry," Automedica, Gordon & Breach science Publishers Inc. vol. 8, pp. 181-202, 1987.

[2] S. Mizushina, Y. Hamamura, and T. Sugiura, "A three band microwave radiometer system for non invasive measurement of temperature," lEEE MTsDiegest, pp. 171-174,1986.

A. Mamouni, and y.