Title: A device system and method for non-invasive temperature measurements

Scope of the invention

The present invention relates to a system, method and handheld device for measuring the internal temperature of a body.

Background

It is well-known that the internal temperature of the body is a significant clinical parameter when assessing the health status of a patient. Suitable devices for temperature measurements should be accurate even with minimal operator training and they should be easy to use even on children and patients which are not able to remain still. Furthermore, a suitable device should be compact and rugged to withstand routine clinical use while maintaining accurate readings. Today, mainly two methods based on either contact thermometry or infrared radiation are available each with several drawbacks.

Contact thermometry is commonly used either orally or rectally, where rectal measurement is considered as a best effort or reference measurement for clinical temperature measurement in general. Traditionally mercury thermometers were use, but these have relatively recently been replaced by cheap and reliable electrical thermometers. These have especially become widespread due to their ease of use and accurate digital read out combined with the elimination of the risk of breakage and mercury contamination. In either case, both oral and rectal contact measurements are time consuming and require significant patient cooperation.

Infrared thermometry requires shallow access to the internal temperature due to high absorption of infrared radiation in tissue. Accordingly, the technique is commonly applied in the ear or on the forehead where there is a shallow access to significant blood flow, which is assumed to be at the internal temperature of the patient. Due to mentioned absorption accurate readings depend heavily on correct contact conditions.

As studies have shown the method therefore requires significant operator skill to obtain reliable measurements, even more so if the patient is not fully cooperating (see for example Y. Amoateng-Adjepong, J. Del Mundo, and C. A. Manthous, "Accuracy of an Infrared Tympanic Thermometer", Chest. 1999,i 15:1002-1005. Also available via the hyperlink: http://www.chestiournal.ora/content/vol115/issue4/index.shtm n

Summary of the invention

In order to overcome the drawbacks of the presently available devices, the present invention relates to a handheld portable device for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, at least one receiver, a self contained power source, such as a battery and a front end comprising at least one reception circuit and at least one antenna, wherein the total receiving cross section of the antenna area is less than 0,04m ² , such as less than 0,01m ² , such as less than 0,0025 m ² and optionally means for recording data

The size of the total receiving cross section of the antenna area significantly affects the possible size of the device. As a handheld device suitable for routine clinical use, the total possible size of the device is limited. On the other hand, a preferred antenna should not be significantly smaller than the size of the wavelength of the measured radiation at least in one dimension. To minimise the wavelength and hence the dimension of the antenna and to improve the coupling of radiation from the body into the antenna the device may have a dielectric medium in the antenna with a refractive index above unity and in the range of that of the body, implying that the wavelength considered here may be smaller than in air for a given frequency. Accordingly, it is preferred that the total receiving cross section of the antenna area is less than 0,04m ² , such as less than 0,03m ² , such as less than 0,02m ² , such as less than 0,01 m ² , such as less than 0,005 m ² , such as less than 0,0025m ² , such as less than 0,0001 m ² .

All bodies (humans, animals, meat, rocks, wood, fluids, gases, etc.) with finite temperature emit electromagnetic radiation, so called thermal emission, which is related to the temperature of the body. This is well known from Infrared thermography where the radiation in the infrared (IR) band is measured and typically the surface

temperature of the emitting body is inferred. The source of the thermal radiation extends some distance into the emitting body. The depth distribution of the emission is referred to as the emission profile. The depth which the emission profile extends into the body depends on the wavelength of the radiation and on the dielectric properties of the body. In the infrared range this depth is extremely shallow in the case of living bodies, and the inferred temperature is therefore that of the surface. Getting reliable readings with IR thus typically depends on placing the thermometer over a blood vessel or on viewing the inner part or the ear.

Due to the longer wavelength in the GHz range and the deeper emission profile, measurement of the body temperature with the present invention does not depend on placing it over or near particular spots on the body. The tolerance with respect to translation of the device along the surface of the body is speculated to be many centimetres or comparable to the body size, while the distance between body and antenna is speculated to be up to approximately 0.5 cm. This implies that accurate placement of the present device is not critical. Accordingly, the present invention provides a compact device for internal temperature measurement which only needs to be held close to the patient, such as close to the chest or the stomach. However, it is speculated that measuring the core temperature of the extremities may also yield valuable information. Furthermore, in many cases clothing may even be tolerable while still obtaining reliable readings. Therefore, the present invention provides a device which in its application is relatively insensitive to the handling by the operator and which may be applied almost without the patient noticing. Accordingly this device has none of the drawbacks of current technology. The device may also be used with animals, foods and in many other contexts where the sub-surface temperature is of interest. Especially for applications where mobility and/or compactness of the device is important.

As it turns out, the preferred embodiment of the present invention comprises attractive features for GHz radio thermometry in general, so in a second aspect the present invention relates to a system for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, comprising at least one receiver, and a front end comprising at least one

reception circuit and at least one antenna; wherein said reception circuit comprises partial reflection means.

In a third aspect, the present invention relates to a system for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, comprising at least one receiver, and a front end comprising at least one reception circuit capable of assuming at least one state, and at least one antenna; wherein the front end and/or receiver comprises an active noise source and the number of state(s) enables the elimination of the uncertainty of the spectral density/noise temperature of said active noise source and/or enables the determination of the spectral density/noise temperature of said active noise source. In this respect the system will be robust for routine use as the need for separate calibration of the active noise source is eliminated.

In a fourth aspect, the present invention relates to a system for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, comprising at least one receiver and a front end comprising at least one reception circuit capable of assuming at least one state, and at least one antenna; wherein the receiver comprises an active noise source Preferably said active noise is the low noise amplifier of most common receiver designs. Accordingly, requirements of complexity and power consumption may be relaxed as no additional components are needed.

In a fifth aspect, the present invention relates to a method for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body with a handheld portable device with a self containing power source, such as a battery, and at least one antenna, wherein the total receiving cross section of the antenna area is less than 0,04m ² , such as less than 0,01 m ² , such as less than 0,0025 m ²

In a sixth aspect, the present invention relates to a method for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, utilizing a finite reflection unrelated to the coupling to said body, thereby enabling partial reflection of the noise signal from at least one noise source and/or enabling partial reflection of the noise signal emitted from said body.

In a seventh aspect, the present invention relates a method for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, by including at least one active noise source and allowing for at least one measurable state enabling the elimination of the uncertainty of the spectral density/noise temperature of said active noise source and/or enabling the determination of the spectral density/noise temperature of said active noise source.

Finally, the present invention relates a method for measuring the internal temperature of a body by measuring thermal noise radiation at frequencies in the GHz range emitted from said body, by including at least one active noise source in a receiver.

List of figures

Figure 1 Relative permittivity as a function of frequency for muscle tissue.

Figure 2 Conductivity as a function of frequency for muscle tissue.

Figure 3 Real part of the refractive index for a wave in a medium (muscle tissue) with the relative susceptibility and conductivity given in Figure 1 and Figure 2.

Figure 4 Emission profiles for a number of frequencies from 0.6 to 2.2 GHz. The profiles are plotted against distance into the body. The labels on the curves indicate frequency in GHz.

Figure 5 Skin depth versus frequency.

Figure 6 Differences between emission profiles at a number of frequencies and a reference emission profile at 2.2 GHz.

Figure 7 Differences between emission profiles at a number of frequencies and a reference emission profile at 4 GHz.

Figure 8 Weight function in convolution integral for estimate of internal body temperature composed of the weighted difference between two radiation temperatures, one at 2.2 GHz. The curves are labelled with the frequency in GHz at which the second radiation temperature was recorded.

Figure 9 Weight function in convolution integral for estimate of internal body temperature composed of the weighted difference between two radiation temperatures, one at 4 GHz. The curves are labelled with the frequency in GHz at which the second radiation temperature was recorded.

Figure 10 Weight function resulting from estimating the body temperature from the radiation temperature in three frequency bands centred on 1 , 3 and 4.4

GHz.

Figure 11 Front end with antenna, two single throw switches, two circulators, two matched loads, and an impedance mismatch on the transmission line between the circulators.

Figure 12 Front end with one circulator found in the prior art.

Figure 13 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface with: T _s = 37 ⁰ C, T ₁ =T ₂ = 20 ⁰ C,

δr = 0.01°, Ap _r = 0.01, G = l-p _r , AV = 0.01. The curves are labelled with the values of p _s .

Figure 14 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface with: 7; = 37°C, T ₁ =T ₂ = 2O ⁰ C,

δr = 0.01°, Ap _r = 0.01, G = l-p _r , AV = 0.02. The curves are labelled with the values of p _s .

Figure 15 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface, p _s . T _c = 37°C, T ₁ = T ₂ +5° = 25 ⁰ C,

δr = 0.01°, δ/? _r = 0.01, G = \-p _r , δ7 = 0.01. The curves are labelled with the values of p _s .

Figure 16 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface, p _s . T _c = 37 ⁰ C, T ₁ =T ₂ +5° = 25 ⁰ C,

δr = 0.01°, Ap _r = 0.01, G = l-p _r , AV = 0.02. The curves are labelled with the values of p _s .

Figure 17 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface, p _s . T _c = 37 ⁰ C, T ₁ = T ₂ +10° = 3O ⁰ C,

δr = 0.01°, Ap _r = 0.01, G = l-p _r , AV = 0.01. The curves are labelled with the values of p _s .

Figure 18 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface, p _s . T _c = 37 ⁰ C, T ₁ =T ₂ + 20° = 4O ⁰ C,

δr = 0.01°, Ap _r = 0.01, G = l-p _r , AV = 0.01. The curves are labelled with the values of p _s .

Figure 19 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface, p _s .T _c = 37°C, T ₁ =T ₂ -5° = 15 ⁰ C,

δr = 0.01°, Ap _r = 0.01, G = l-p _r , AV = 0.01. The curves are labelled with the values of p _s .

Figure 20 The uncertainty in the measured body temperature plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface, p _s . T _c = 37°C, T ₁ =T ₂ = 2O ⁰ C,

δγ = 0.01°, Ap _r = 0.2, G = l-p _r , AV = 0.003. The curves are labelled with the values of p _s .

Figure 21 Front end FE1 , comprising antenna, three single throw switches, three circulators, two matched loads and an active noise source. Numbered elements: 1 : single throw switch connecting antenna to rest of front end. 2: single throw switch. 3: single throw switch.4: Matched load at temperature T ₂ . 5: Active noise source. 6: Matched load at temperature

T ₁ . 7: Antenna. 8: Receiver. 9: Body

Figure 22 Front end FE2, comprising antenna, three single throw switches, two circulators, and two matched loads. Numbered elements: 1 : single throw switch connecting antenna to rest of front end. 2: single throw switch. 3: single throw switch. 4: Matched load at temperature T ₂ . 6: Matched load at temperature T ₁ . 7: Antenna. 8: Receiver which is also an active noise source. 9: Body.

Figure 23 The uncertainty in the measured body temperature plotted against the spectral power density, TN, of the active noise source for a range of reflection coefficients at the body to antenna interface with:

Z] = IT ₂ = 20 ⁰ C, δr = 0.01°, G = l, δV = 0.01.

Figure 24 The uncertainty in the body temperature plotted against the spectral power density, T _N , of the active noise source for a range of reflection coefficients at the body to antenna interface with: T ₁ = T ₂ = 20 ⁰ C, δr = 0.01°, G = I, δV = 0.02.

Detailed description

Definitions

Body: An object of which measurement of the sub-surface and/or internal temperature is required.

Front end: The front end consists of the following two components: at least one antenna, and at least one reception circuit. Preferably, the front end consists of one of each component. However, in the following it should be understood that the single components may be substituted by multiple components without departing from the scope of the invention.

The receiver circuit may assume one or more states, and therefore the front assumes corresponding states also referred to as front end states.

Reception circuit: The components between the antenna(s) and the receiver(s). This set of components makes it possible to set the device in various states. These states combine signals from the body and other sources in a variety of ways, which collectively permit the body temperature to be inferred (measured).

Circulator means: In the present context circulator means is understood as a circulator, which is a device with multiple ports, commonly 3, wherein substantially all radiation impinging on port 1 exits at port 2, substantially all radiation impinging on port 2 exits at port 3 and so forth. The radiation impinging on the last port commonly exits at port 1. However, for some front end designs a circulator means in combination with a matched load may be substituted by an isolator as discussed in the definition of circulator means.

Alternatively, similar functionality may be obtained by utilizing a directional coupler. As the directional coupler performs symmetrically its utilization will commonly entail redesigning of the reception circuit to accommodate this compared to the reception circuit with a circulator.

However, it is within the scope of the present invention to replace circulators with one or more directional couplers, perhaps in conjunction with additional loads and/or switches, to obtain:

a) the functionality of a reception circuit with a number of measurable states to enabling the elimination of the uncertainty of the reflection/transmission coefficient between the antenna(s) and the body, and/or

b) the functionality of a reception circuit with a number of measurable states enabling the elimination of the uncertainty of one or more active noise sources.

Preferably a circulator means is a circulator and therefore the term circulator is used interchangeably with the term circulator means.

Internal temperature: The internal temperature is preferably understood as the core temperature or an approximation to same. However, alternatively internal temperature is understood as temperature profile, i.e. temperature as a function of depth.

Device features

As a handheld device, a preferred embodiment of the invention comprises means for analysing data, i.e. computation means either static or programmable.

Furthermore, in a preferred embodiment the device comprises a user interface. In its simplest form the user interface may inform the operator of the result of a measurement. Other relevant types of information are battery status and feedback on the reliability of a measurement. The user interface may also inform the operator of calibration status and time since last calibration or time till next suggested recalibration. It may also allow the entry of patient information so that measurements may be logged directly on the device according to the patient. As an alternative, the device may further comprise means for scanning a patient identification device, thus enabling a safe link

between the patient's file and obtained temperature reading. This will also allow the device to report any changes relative to previous measurements. Finally, patient information may also be utilized as a part of the data processing in the event that it is found that the measurements are affected by such, or it may be used to select different measurement parameters such as frequency band.

In one preferred embodiment of the invention, the device comprises means for communication with external computation and/or storage means. The communication may be performed wirelessly and/or via a cable, such as a cable or connector integrated into a cradle.

Frequency band

The longer the wavelength is (or equivalent^ the lower the frequency) the greater the depth of the emission profile. In the case of Radio waves in the 0.1 to 20 GHz range the depth of the emission profile extends from several centimetres to fractions of a centimetre into living bodies.

As discussed below, the emission profile becomes increasingly shallow with increased frequency. On the other hand low frequencies require a large antenna due to the increased wavelength, so a suitable compromise resides in the range between about 0.1 GHz to about 20 GHz. Accordingly, in a preferred embodiment of the invention radiation is collected in one or more frequency bands centred in the range 0.1 GHz to 20 GHz, such as centred in the range 0.5 GHz to 15 GHz, preferably centred in the range 0.5 GHz to 10 GHz, more preferably centred in the range 0.5 GHz to 5 GHz, most preferably centred in the range 0.5 GHz to 3 GHz, such as centred in the range 0.5 GHz to 2 GHz. With the development towards more sensitive receivers it may be preferable to measure in a higher frequency range to minimize the device. Accordingly for another preferred embodiment of the invention radiation is collected in one or more frequency bands centred in the range such as centred in the range 10 GHz to 20 GHz, such as centred in the range 15 GHz to 20 GHz, or in another preferred embodiment of the invention radiation is collected in one or more frequency bands centred in the range 10 GHz to 15 GHz, such as in the range 5 GHz to 10 GHz.

However, by measuring at higher frequencies the temperature of the surface of the body, i.e. the skin, is measured. It may therefore turn out that measurements above this range are beneficial to determine the skin temperature which may then be used in conjunction with one or more measurements at other frequencies to determine the internal temperature. However, measurements of the surface temperature may also be valuable in themselves for some applications, such as the quantification of frost bite, hypothermia, state of a wound, surface infection, agitation, stress. Accordingly, in one preferred embodiment radiation is collected in one or more frequency bands in the range 20 GHz to 50 GHz.

In setting the bandwidth for collecting radiation a trade off between low signal power for a narrow band and higher sensitivity to external noise sources in a wide band has to be considered. Accordingly, in the preferred embodiment radiation for at least one frequency band is collected in a frequency band less than 3 GHz wide, such as a frequency band less than 2,5 GHz wide, such as frequency band less than 1.5 GHz wide, such as frequency band less than 1 GHz wide, such as frequency band less than 0.75 GHz wide, such as frequency band less than 0.5 GHz wide, such as frequency band less than 0.25 GHz wide, such as frequency band less than 0.15 GHz wide, such as frequency band less than 0.1 GHz wide, such as frequency band less than 0.05 GHz wide, such as frequency band less than 0.01 GHz wide, such as frequency band less than 0.005 GHz wide.

Depth selectivity

Multiple antennas may be applied to obtain depth selectivity. Such antennas will conventionally require spatial separation of at least a few centimetres to give relevant depth resolution, but with well-designed radiation pattern this requirement may be relaxed to some degree. Added to this is the necessary spatial extent of the individual antennas to obtain sufficient coupling between body and antennas and suitable radiation patterns from the antennas in the body, which will be discussed below. However, with sufficiently sensitive receiver electronics smaller antennas with less optimal coupling may be applied allowing for the design of a compact thermometer. Accordingly, in a preferred embodiment depth resolution is achieved by spatial distribution of at least two antennas. Each or some of these antennas may be

connected to an individual reception circuit and some or each reception circuit may have a dedicated receiver. However, it is preferred that the antennas are connected to the same reception circuit either simultaneously and/or sequentially, e.g. by switching means preferably by one or more single throw switches. At least it may be advantageous for the said switch to have an open position where it is not connected to an antenna so that substantially all signal propagating towards the switch from the reception circuit side is reflected.

Alternatively, depth selectivity may be obtained by measuring at multiple frequencies. Due to the varying depth profile as a function of frequency, measurement at two or more frequencies may be used to retrieve the temperature at a specific depth or depth interval. As this only requires a single antenna, in the most preferred embodiment of the invention the device comprises only one antenna or the device comprises only two or more antennas connected to perform substantially as a single antenna. Depth selectivity is achieved by measuring noise power in at least two frequency bands. This embodiment is compact and therefore well suited for a portable device.

The physical basis for depth selectivity by measuring multiple frequencies may be understood as follows. The thermal electromagnetic radiation is emitted from a finite volume of the body, i.e. not simply from the surface of the body.

The fraction of emission at frequency, v = ωjlπ , coming from the depth between z and z+δz is f(z,ω)x&. The function i{z,ώ) is the emission profile of the body at frequency ω/2π . The device estimating the body temperature based on radiation collected in a narrow frequency band around the frequency ω/2π would thus estimate a weighted mean of the body temperature with f(z,ω) as the spatial weighting function. That is, it would provide the temperature estimate

where the integral is from the surface of the body to some depth where in practice the emission profile function has dropped to zero. For a uniform body the emission profile is an exponential, maximum at the surface and falling off into the body. This implies

that the temperature near the surface is weighted more than the temperature deeper in the body. It can be expected that for a living body this leads to a temperature estimate which is systematically lower than the internal temperature. This can be alleviated by inferring the temperature from the emission in one, two or more frequency bands. In the following the discussion is limited to considering two narrow spectral bands, but the principle applies also to the use of multiple wide bands, or to a spectrally resolved broad band.

In the subsequent calculations the approach is illustrated by assuming a body where the relative dielectric constant and conductivity as functions of frequency are as given in Figure 1 and Figure 2 showing typical functions for muscle tissue.

The plane wave propagating along the z direction is then given by

with

where N, ε, ε ₀ , σand øare respective y the refractive index, relative and vacuum permittivity, conductivity and angular frequency. With the relative permittivity and the conductivity given in Figure 1 and Figure 2, the real part of the refractive index is as shown in Figure 3. The emission profiles are given by

f (z, ω) = αexp {-ccz) (4)

Where the absorption coefficient, a, is given by

(X = Tk _1n , . (5)

The emission profiles for a set of frequencies are plotted in Figure 4. The skin depth, d =l/a , plotted versus frequency in Figure 5, is the characteristic distance which the emission profiles extend into the body.

To get an estimate of the internal temperature of the body the estimator

is used. It is composed of the weighted difference between the radiation temperatures recorded in two separate frequency bands labeled a and b. The resulting temperature estimate, T _ab , is the weighted average of the body temperature profile,

where the weight function, g _ab (z) , is given by

Examples of weight functions are plotted in Figure 6 to Figure 9. Figure 6 and Figure 7 show the weight functions as unnormalized, whereas the same weight functions are shown normalized in Figure 8 and Figure 9.

The standard deviation (STD) uncertainty in this estimate is

where σ _a is the STD uncertainty in the estimate of the radiation temperature in frequency band a and similarly for b. Assuming that σ _a = σ _b = σ _ϋ expression (9) simplifies to

For the frequencies 1 GHz and 2.2 GHz it is found that cτ _ab /σ ₀ ~ 2 , which reduces to 1.44 if the frequencies 1 GHz and 4 GHz are used.

It is noted that combining measurements at two frequencies with the relative weights indicated here, zero weight is given to the temperature at the surface of the body. The weight function does, however, have a non zero gradient at the body surface giving finite weight to the body temperature immediately below the surface. This may be improved further with a temperature estimator composed of a weighted difference between the radiation temperatures recorded in three distinct frequency bands, labelled a, b and c. This estimator is given by

T _αbc = αT _α -bT _b -cT _c (11) where

The corresponding weight function is

g _a ic (z) = αexp(-α _fl z)-&exp(-α _fe z)-cexp(-α _c z) . (13) It is plotted in Figure 10.

The drawback of the later estimator is a significantly increased uncertainty in the estimate compared with previously discussed estimators based on one or two frequency bands. Using frequencies 1 , 3 and 4.4 GHz it is found that σ _αb /σ ₀ « 3.6.

Whether two three or more frequency bands are preferred depends on the relative value of uncertainty in the estimate of the weighted average of the body temperature on the one hand, and the depth localisation of the temperature measurement on the other. This choice may further depend on the application, price and other factors.

Dielectric medium

To obtain good coupling between the thermal radiation emitted within the body and the antenna and to achieve a good spatial profile of the antenna sensitivity, said antenna must have an impedance matched to the body and a cross section able to fit at least a significant fraction of one wavelength of said radiation, i.e. for antenna with a circular cross section the diameter must be at least a significant fraction of one wavelength. For emission at 1 GHz this corresponds to approximately 30 cm if operated in air, and such a large diameter is not preferable for a handheld device. In some cases coupling losses incurred by using a smaller antenna may be tolerated. However, in a preferred embodiment the antenna(s) further comprises at least one dielectric medium and it is preferred that the said dielectric medium substantially fills the antenna cavity and/or aperture. Preferably, the dielectric medium has similar relative dielectric permittivity and magnetic permeability as the object to be measured, which results in the best coupling of the wave energy from the body to the antenna. It follows that for clinical measurements the dielectric medium should have a refractive index close to those for fat and muscle, such as those shown in Figure 3 for muscle tissue. The refractive index is generally required to be on the order of 3 to 8 and the wave length and required dimension of the antenna aperture is accordingly reduced by the same factor. Commonly, it is preferred to minimize the conductivity to avoid losses in the antenna.

In one embodiment it is preferable to combine a compact antenna with depth selectivity achieved by multiple frequencies as this combination provides for the potentially most compact device. However, as multiple frequencies are used, the selected properties of the dielectric medium/media will generally have to be a compromise that best fits the frequency dependence of the electromagnetic properties of tissue.

Front end

The following section describes various designs of a front end for a device according to the invention. The front end includes the antenna and the reception circuit enabling nuisance parameters, such as reflection coefficient at the interface between body and antenna, to be determined in addition to the parameter of interest, the temperature of the body. The receiver could simply be an assembly of a low noise amplifier (LNA), sets of band pass filters and detector diodes, a recording system and a computational

unit. It's purpose is to record the power impinging on it in various frequency bands for one or more states of the front end. Extensive literature exists in the art regarding different designs of the antenna, front end of which many will be applicable within the scope of the present invention. However, the front end design disclosed here is particular suitable for a handheld device as it obtains high accuracy with low number of components and with minimal power consumption. The main concept preferred for the device according to the invention is that the front end allows that at least one noise signal or part thereof is reflected off the body. In a preferred embodiment the said noise signal is at least partially generated by the said body and/or by at least one noise source. Preferably the said noise signal generated by the body is reflected off the said body by incorporating reflection means in the reception circuit and/or antenna(s).

A variety of front end designs may be constructed to obtain the main concept, wherein a noise signal is reflected off the body in order to eliminate the reflection between antenna and body as an unknown by:

A) partial reflection in front end, preferably in the reception circuit, or

B) noise sources,

D) active noise sources, either separate or using noise from the receiver amplifier or

E) combination of all of the above.

The generally preferred front end design for the invention comprises:

Antenna connection: A connection to an antenna or an antenna array configured to act as a single antenna. Preferably, the connection to the antenna(s) comprises a switch to engage or disengage the connection to the said antenna. The switch is preferably a single throw switch.

Transmission lines: The front end preferably comprises transmission lines, preferably short for minimum attenuation.

Circulator means: The front end preferably comprises one or more circulator means, wherein said circulator means preferably comprises at least one of the following: a circulator, an isolator and a directional coupler. It should be noted that an isolator is often constructed by combining a circulator and a matched load. Accordingly, an isolator combined with means for determining the temperature of said isolator, or at least the temperature of the matched load of said isolator, is equivalent to a circulator statically connected to a matched load.

As discussed in the definition of circulator means above, a directional coupler may perform some of the same tasks of a circulator, commonly with increased signal loss. However, this device may be a suitable replacement for some applications.

Preferably a circulator means is a circulator and therefore the term circulator is used interchangeably with circulator means.

Noise sources: The front end preferably comprises one or more noise sources. The said noise sources may comprise one or more of the following: a matched load, the receiver, a secondary receiver, an amplifier, and a noise generator. The noise source(s) is preferably a matched load and as such noise sources are interchangeably referred to as matched loads in the following, wherein the noise temperature is equivalent to the temperature of the load. However, it is to be understood that these matched loads may be substituted by other means for generating a noise signal.

Noise source control: It is preferred that the device comprises means for establishing and/or setting the spectral power density/noise temperature of at least one noise source. Preferably said means for establishing the spectral power density/noise temperature of the at least one noise source comprises means for measuring the temperature of said noise source. Furthermore, it is preferred that the device further comprises at least one heater for heating the noise source and that the said means for

establishing the spectral power density/noise temperature and the said heater are connected to a feedback loop. In this way a specific spectral power density/noise temperature may be set and maintained.

A receiver: At least one receiver recording the power in one, two or more frequency bands. The receiver could simply be a low noise amplifier

(LNA), sets of band pass filters and detector diodes, recording system and computational unit. Measuring in one frequency band and subsequently determining the signal in two or more sub-bands, e.g. by Fourier analysis, is considered equivalent to measuring in said bands directly.

Reflection means: The front end preferably comprises partial reflection means, preferably located in the reception circuit, giving rise to a reflection coefficient/?,. . Preferably the said reflection means is an impedance mismatch, but it may also be realized using a directional coupler with an open end and a matched load. The latter embodiment introduces more loss compared to an impedance mismatch. Preferably said reflection means has a reflection coefficient in the order of 10%, or 20% or 30% or 40% or 50% or 60% or 70% or 80% or 90%. Most preferably the reflection coefficient is between 50%-70%.

Configuration: It is preferred that each circulator means is connected to at least one noise source and anti reflection means such as an impedance matched load and/or is connected to means for connecting to at least one noise source. Said connection means is preferably a switch, such as a single throw switch. Preferably, said noise source further comprises anti reflection means such as found in an impedance matched load.

In a preferred embodiment the said means for connecting is configured relative to the circulator means so that the thermal noise radiation from the said noise source is guided away from the at least one receiver. This allows the said noise signal to be reflected off the body in line with the main concept preferred for the design of the front end according to the

invention. Accordingly, it is preferred that said thermal noise radiation from the noise source is subsequently reflected at least once and then guided toward the at least one receiver.

In one embodiment of the invention it is preferred that at least one of the means for connecting comprises a switch preferably a single throw switch. However, for some embodiments according to the invention it is preferable that at least one of the means for connecting comprises a switch for connecting sequentially to two or more noise sources. In both cases it may be advantageous that the switch further comprises the means for disconnecting the circulator means from any noise source leaving this port of the circulator means open. In this way substantially all of the signal entering this port will be reflected.

It is preferred that the partial reflection means is located between two circulator means as this allows for mixing of the signal from noise sources connected to each circulator. By using switches this mixing may be varied resulting in an extra number of states and hence possibilities to take measurements which provide constraints (equations), which may be advantageous when unknowns, such as the coupling between body and antenna, are to be determined.

Examples

The scope of the invention is further illustrated by means of the following examples. These examples should in no way be understood as to limit the invention as defined by the attached claims.

A variety of front ends may be designed with the same or substantially the same functionality as the front ends shown in the following examples. Accordingly, the limitation of the present invention should be understood as the functionality described by the mathematical equations rather than the specific front end design. Furthermore, the functionality described by the equations should be considered as an outline description which can be further refined to take more effects into account, such as

including absorption in the mathematical description of the antenna (see example 1 b). It may be possible to add or subtract mathematical complexity by considering contributions from effects ignored here and/or the same or substantially the same functionality may be achieved by adding additional components, such as an extra circulator, without departing from the scope of the invention.

In the following most equations are the result of derivations. The details of these derivations may be found in the section List of derivations below.

Example 1

A front end according to the preferred embodiment of the invention is illustrated in Figure 11. This shown embodiment consists of: an antenna, short transmission lines, two single throw switches, two circulators, two matched loads maintained at temperatures T ₁ and T ₂ , and a receiver recording the power in one, two or more frequency bands. There is an impedance mismatch on the transmission line between the circulators giving rise to a reflection coefficient of p _r .The gain of the receiver system to the right of the dashed line is denoted G . In the absence of signal from the left of the dashed line the receiver reading will be V _r . The receiver reading is denoted

V _ab where the first and second subscript denotes the state of respectively the first and the second switch, o for open, c for closed.

The receiver readings of the four states of the front end are related to the body temperature and a number of system parameters as follows

V ₀₀ =V^GT ₁ (14)

V _0C =V _r +GT ₂ (15)

V _cc =V _r +G(τ _s T _{s + Ps} T ₂ ) (16)

Here the transmission coefficients are related to the reflection coefficients byτ+p = l . It is assumed that T ₁ and T ₂ are known by separate contact temperature measurements. It is also assumed that the transmission line reflection coefficient p _r is known by design or separate measurement, and that this value is constant.

The gain can be estimated by the relation

while the transmission between body an antenna is estimated by

The body temperature can then be estimated from the relation

For integration into a battery powered compact device it is of value to minimize power consumed to heating elements. It is therefore valuable to note that T ₁ or T ₂ can be kept at ambient temperature most of the time. It is only necessary to establish a difference between T ₁ and T ₂ when calibrating the system, that is when estimating the value of the system gain G .

It is assumed that it is not necessary to calibrate the device at every temperature reading. When not calibrating both T ₁ and T ₂ may be at ambient temperature. To get the best estimate of τ _s it is preferable that T ₂ is not significantly above ZJ . When calibrating, it is therefore preferable to raise T ₁ rather than T ₂ above ambient.

Generally, it is therefore preferred that the noise temperature of at least one noise source is kept at ambient temperature, and it is furthermore preferred that the noise temperature of at least one noise source is kept at ambient temperature and raised

from this temperature when performing a calibration of the device. Furthermore, to reduce power requirements even further, it may be preferable to place matched load(s), which are required to have a temperature raised or reduced from ambient, externally such as in a cradle. The device may then only need to be connected to these loads when placed in a cradle which draws its power from the mains. In the front end of the present example the loads are also used to absorb signal impinging on them. Accordingly, if a load is to be placed externally it is necessary to have another internal load in the device and allow switching means to connect to the external load when the device is in the cradle. Such a setup with external loads may be applicable for any front end design and will commonly be advantageous if loads/noise sources with higher power requirements are required but only periodically used. Furthermore, instead of applying heating it may be advantageous to apply cooling instead, in this example preferably reducing T ₂ below ambient temperature.

The energy to raise a load from ambient temperature may be supplied by the body to be measured or the operator, which in clinical operation is expected to be warmer than ambient temperature. Accordingly, in one embodiment it is preferable that at least one noise source with a noise temperature different from room temperature can receive its thermal energy from the operator and/or the body to be measured.

Due to the advantages with regard to power consumption, the present front end design is particularly suitable for the portable device of the present invention.

If required, the reflection coefficient for the transmission line impedance mismatch, p _r , can be estimated by letting the device view a body with known temperature, T ₀ .

The reflection p _r can then be estimated by the following relations:

Accordingly, in a preferred embodiment the device comprises means for calibration such as a reference object with known temperature/noise temperature.

A variety of front ends may be designed with the same or substantially the same functionality as the front end shown in Figure 11. Accordingly, the limitation of the present invention should be understood as the functionality described by the mathematical equations above rather than specific front end design. Also the functionality described by the above equations should be considered as an outline description which can be further refined to take more effects into account. It may be possible to add or subtract mathematical complexity by considering contributions from effects ignored here and/or the same or substantially the same functionality may be achieved by adding additional components, such as an extra circulator, without departing from the scope of the invention.

Example 1 b

Assume now that the antenna has a transmission coefficient of τ _a and an emission coefficient of ε _a =\-τ _β . The readings are then related to the system parameters and body temperature as follows:

V ₀₀ =V^GT ₁ (23)

V _0C =V _r +GT ₂ (24)

V _cc =V _r +G(T _s τ _s t _a +T ₂ [p _s τ _a +ε _a )) (25)

The reflection at the interface between body and antenna is estimated with the expression

while the body temperature is estimated by

Viewing a body with known temperature r _c the transmission line reflection can be estimated by

with

Example 1 c Consider the limiting case, where there is no reflection in the transmission line, i.e. where p _r = 0. In this case the expression for V _co simplifies. For convenience the other three expressions for receiver readings are repeated:

As before the gain is estimated by

The estimate of the transmission from body to antenna is altered and is now given by

The body temperature can then e estimated from the relation

In contrast to the front end with a finite transmission line reflection, here it is necessary to maintain a difference between T ₁ and T ₂ every time the transmission between body and antenna is estimated. In practice this will have to be done at every temperature reading since it cannot be assumed that the transmission from body to antenna is constant. Accordingly, this front end has a significant drawback compared to the front discussed in examples 1-1b.

This setup corresponds to the front end previously described in art (D.V. Land, "AN EFFICIENT, ACCURATE AND ROBUST RADIOMETER CONFIGURATION FOR MICROWAVE TEMPERATURE MEASUREMENT FOR INDUSTRIAL AND MEDICAL APPLICATIONS", Journal of Microwave Power & Electromagnetic Energy Vol. 36, No. 3, 2001) and sketched in Figure 12.

Example 1d

Consider the limiting case where the reflection in the transmission line is close to unity and hence τ _r « 1. In this case the expression for V _co simplifies. For convenience the other two required expressions for readings are repeated:

V ₀₀ =V^GT ₁ (38)

V _0C =V _r +GT ₂ (39)

V _C0 =V _r +GT _s (40)

As before the gain is estimated by

Note that in this limit it is not necessary o estimate the transmission at the interface between the body and the antenna. The body temperature can be estimated from the relation

This front end corresponds to the loading of a cavity (switch 1 closed and 2 open) with only a small leak towards the receiver. The advantage of this design is that it is not necessary to estimate the transmission from body to antenna. Accordingly, in a preferred embodiment of the invention at least a part of the reception circuit, or the antenna(s) and/or a combination thereof form a cavity. The disadvantage is that the gain will be very low (recall that the gain used here includes the transmission r _r ) and hence the signal to noise ratio will be poorer than in the designs described above. Its realization also depends crucially on being able to keep the absorption very low in the components forming part of the cavity.

Example 2 comparative receiver sensitivity

Referring to the front end described in Example 1 and Figure 11 , recall that the receiver readings of the four states of the front end are related to the body temperature and a number of system parameters as follows

V ₀₀ =V _{r +} GT ₁ (43)

V _0C =V _r +GT ₂ (44)

V _cc =V _r +G{τ _s T _s + _Ps T ₂ ) (45)

Furthermore as shown above, the gain can be estimated by the relation

the transmission between body and antenna is estimated by

and the body temperature can be estimated from the relation

The accuracy of the inference of the body temperature is affected by detector noise in the readings and uncertainties in the values of the matched load temperatures and in the transmission line reflection coefficient. The expression for the uncertainty in the inferred body temperature is readily derived from the expressions above.

In Figure 13 the uncertainty in the inferred body temperature is plotted against the transmission line reflection coefficient for a range of reflection coefficients at the body to antenna interface. Here it is assumed that the two matched loads have the same temperature (for instance the ambient temperature to avoid the need to heat one load) and that these temperatures are known with an accuracy of 0.01 degrees. The uncertainty in the knowledge of the reflection coefficient at the impedance mismatch in the transmission line IsAp ₁ . = 0.01. In accounting for the uncertainty in the gain estimate it is assumed that the gain is estimated in a separate measurement where the temperature of matched load 1 is increased by 10 degrees above that of matched load 2.

The gain is set equal to the transmission coefficient at the transmission line impedance mismatch. This implies that at 100% transmission a change of 1 in the reading corresponds to a change of 1 degree in the spectral power density at the dashed line (see Figure 11). All readings are assumed to have the same noise level, given byδV .

A receiver with a god low noise amplifier at the input with a noise figure of 0.8 dB will have a noise temperature of just under 360 degrees. Assuming for this receiver that the

bandwidth per band is 0.2 GHz and the integration time is 6 seconds then the receiver noise gives rise to an RMS uncertainty in the readings of 0.01 degrees. These are the assumptions on noise and uncertainties used in Figure 13.

With a bandwidth of 0.1 GHz per band and an integration time of 3 second the uncertainty in the readings double to 0.02 degrees. The resulting uncertainty in the inferred body temperature is shown in Figure 14.

From Figure 13 and Figure 14, it is clear that high transmission between body and antenna is important for keeping the uncertainty in the inferred body temperature low. Assuming the transmission can be kept above 70% (corresponding to a reflection coefficient below 0.3) the optimum transmission line reflection coefficient is in the range 0.4 to 0.7.

By increasing the temperature of matched load one by 5 degrees above that of matched load two the uncertainty of the inferred body temperature is changed, particularly at low levels of transmission line reflectivity. The results are shown in Figure 15 and Figure 16.

At low reflection at the body to antenna interface there is an improvement in the accuracy of the body temperature estimate of 25 to 30%. At higher reflection at the body to antenna interface there is a greater benefit from the raised temperature of matched load one. Increasing the temperature difference to 10 degrees, the accuracy improves still further (see Figure 17). Increasing the temperature difference to 20 degrees yields only a small further improvement (see Figure 18).

As noted above, the temperature of matched load two should not be above matched load 1. The motivation for this is illustrated in Figure 19 where the temperature of load two is 5 degrees above that of load one. It is seen that this can lead to very large uncertainties in the inferred body temperature.

If the uncertainty of the reflectivity at the impedance mismatch in the transmission line is high then the optimum design shifts towards the cavity design corresponding to a low

transmission coefficient at the impedance mismatch in the transmission line as demonstrated in Figure 20.

The cavity design suffers from the reduced throughput from antenna to receiver, reflected in a low gain. To compensate for this and reach the reasonably low levels of uncertainty in the estimates of the body temperature, presented in Figure 20, the reading uncertainty has been reduced to 0.003 degrees corresponding to a receiver noise figure of 0.8 dB, a bandwidth of 0.5 GHz and an integration time of 30 seconds. This integration time may render the device unsuitable for some applications. Reasonable performance also depends on achieving low reflectivity at the body to antenna interface.

Example 3

In the previous example any of the matched loads may be replaced with a different noise source active or inactive as long as it exhibits similar behaviour with respect to spectral power density/noise temperature and absorption of impinging radiation. In this example two front ends with separate active noise source such as a noise tube, a secondary receiver, an amplifier, and another type of noise generator or in the form of the noise emitted backward from the receiver, e.g. from an amplifier within the receiver. In contrast to previous examples, it is not assumed that the spectral power density of the noise source can be inferred from a contact measurement of the temperature of the noise source or similar direct measurement. The purpose of the active noise source is to probe the transmission between the body and antenna. Two examples of how the front end can be designed to achieve this are shown in Figure 21 (referred to as Front end 1 (FE1)) and Figure 22 (referred to as Front end 2 (FE2)). Accordingly, in a preferred embodiment the device according to the invention comprises at least one active noise source, wherein the possible front end states preferably enables the elimination of the spectral power density/noise temperature of said active noise source and/or enables the determination of the spectral density/noise temperature of said active noise source.

The two frond ends, FE1 and FE2, defined by the diagrams in Figure 21 and Figure 22, have 8 states defined by the states of the single throw switches. Each switch can be either open (O) or closed (C). The switches are referred to by the numbers assigned to

them in the figures. OCO implies that switch 1 is open, 2 is closed and 3 is open, while CCC implies that all switches are closed. The receiver reading depends on the state of the front end. The two front ends can realize the same set of 6 receiver reading dependencies (i.e. how the readings depend on the temperatures and transmission coefficient between body and antenna). For both front ends there are two sets of two states which give rise to the same reading, thus there are only 6 independent states. The expressions for the receiver readings for the various states, for the two front ends are given in Table 1.

Table 1 Expressions for receiver readings for the different states of the two front ends, FEl and FE2. The state is determined by the state of the three switches. OCO implies that switch 1 is open, 2 is closed and 3 is open.

Here the transmission coefficient is related to the reflection coefficient byτ+p = 1. It is assumes that T ₁ and T ₂ are known by separate contact temperature measurements. T _N is the unknown noise power coming from the active noise source. It is assumed to be

considerably higher than ambient temperature, but it is not assumed to be known. In estimating system performance a value is assumed, but this does not enter into the estimates of the body temperature.

The gain can be estimated by the relation

while the transmission between body and antenna is estimated by

The body temperature can then estimated from the relation

Alternatively the transmission between body and antenna is estimated by

and the body temperature can th be estimated from the relation

It is possible to use expression (51) with (54), and (53) with (52), but this leads to increased uncertainty in the estimate of the body temperature. At very high T _N (in excess of 1000 degrees) this increase in the uncertainty disappears asymptotically.

For integration into a battery powered small unit it is of value to minimize power consumed to heat elements. It is therefore valuable to note that T ₁ or T ₂ can be kept at ambient temperature all the time. It is only necessary to establish a difference between

T ₁ andT ₂ when calibrating the system, that is when estimating the value of the system gain G . It is assumed that it is not necessary to calibrate the thermometer at every temperature reading. When not calibrating both T ₁ and T ₂ can be at ambient temperature.

The accuracy of the inference of the body temperature is affected by detector noise in the readings and uncertainties in the values of the matched load temperatures. The expression for the uncertainty in the inferred body temperature is readily derived from the expressions above.

In Figure 23 the uncertainty in the inferred body temperature is plotted against the spectral power density, T _N , of the active noise source for a range of reflection coefficients at the body to antenna interface. It is assumed that the two matched loads have the same temperature (for instance the ambient temperature to avoid the need to heat one load) and that these temperatures are determined with an accuracy of 0.01 degrees. In accounting for the uncertainty in the gain estimate it is assumed that the gain is estimated in a separate measurement where the temperature of matched load 1 is increased by 10 degrees above that of matched load 2.

The gain is set equal to 1. This implies that a change of 1 in the reading corresponds to a change of 1 degree in the spectral power density at the dashed line (see Figure 21). All readings are assumed to have the same noise level, given byδV .

A receiver with a god low noise amplifier at the input with a noise figure of 0.8 dB will have a noise temperature of just under 360 degrees. Assuming for this receiver that the bandwidth per band is 0.2 GHz and the integration time is 6 seconds then the receiver noise gives rise to an RMS uncertainty in the readings of 0.01 degrees. These are the assumptions on noise and uncertainties used in Figure 23.

Raising T ₁ OrT ₂ has little effect provided T _N is higher than T ₁ and T ₂ .

With a bandwidth of 0.1 GHz per band and an integration time of 3 second the uncertainty in the readings double to 0.02 degrees. The resulting uncertainty in the inferred body temperature is shown in Figure 24.

From Figure 23 and Figure 24 it is it is seen that high transmission between body and antenna is important for keeping the uncertainty in the inferred body temperature low. It is also noted that there is an optimum value for T _N around 50 degrees above T ₁ and T ₂ .

List of derivations

Derivation 1 Here the expressions are derived for the state dependent readings for the front end described in example 1 and Figure 11. The states of the front end refer to the states of the switches.

General for all states of the front end:

There is emission from the receiver, either originating from the receiver itself or being reflected at the interface to the receiver. This emission is fully absorbed by matched load 1 , and thus does not need to be considered further. Thermal emission from

matched load 1 exits circulator 1 at port b. At the transmission line impedance mismatch T ₁ P ₁ . power is reflected back towards circulator 1 , exiting it at port c and entering the receiver. This thermal noise contribution to the receiver reading is included in the receiver baseline reading, V _r . A thermal noise spectral power density of T{V _r passes from the right to the left of the transmission line impedance mismatch and enters circulator 2 at its port c.

The gain G is defined as the reading increase resulting per unit noise spectral power density passing towards the receiver at the dashed line located between the two circulators and to the left of the impedance mismatch.

Front end state oo, both switches are open:

The noise ^originating from matched load 1 and entering circulator 2 at port c is reflected at both open switches and exits circulator 2 at port c. T ₁ T ₁ . reaches the dashed line and contributes GT ₁ -^tO the receiver reading. T{V _r xp _r \s reflected back toward circulator 2 and reemerges at the dashed line giving a further contribution to the receiver reading of GT ₁ T ₁ . xp _r . Of this T(c _r Y.p) is reflected, goes round the circulator and contributes a further GT ₁ T ₁ . x/? _r ² to the reading. Taking the infinite series of partial reflections into account the total contribution from the thermal emission from matched load 1 to the receiver reading is

AV ₀₀ = GT ₁ T _r X(I ₊ P ₊ Pl ₊ Pl _{+ ^} ) = GT ₁ Tj(I-P _r ) =GT ₁ (55)

Basically what happened was that with both switches open circulator 2 acted as a perfect cavity with only one port. The temperature of this port will increase till it is in thermal equilibrium with the temperature of the port it is attached to, i.e. it will rise to the temperature of matched load 1.

The reading for the state oo is thus

V ₀₀ =V _{r +} GT ₁ (56)

Front end state oc, first switch open, second closed:

The noise origination from matched load 1 and making it to circulator 2 is absorbed in matched load 2 and plays no further role. The emission at temperature T ₂ from matched load 2 reaches the dashed line and contributes Gr ₂ to the reading. A fraction is reflected at the impedance mismatch, enters circulator 2 at port c, exits at port a, and is then absorbed in matched load 2. So in this case there is not an infinite sum of reflections making it to the receiver.

The reading for the state oc is thus

V _0C =V _r +GT ₂ (57)

Front end state cc, both switches are closed:

The noise originating from matched load 1 and making it to circulator 2 is absorbed in matched load 2 and plays no further role. The emission at temperature T ₂ from matched load 2 exits circulator 2 at port b, is reflected at the interface between antenna and body with a spectral power density of p _s T ₂ . Here it is added to the thermal emission from the body which at this point has spectral power density τ _s T _s . The sum enters circulator 2 at port b, exits at port c and reaches the dashed line, making a contribution of G(τ _s T _s +p _s T ₂ )\o the receiver reading. A fraction is reflected at the impedance mismatch, enters circulator 2 at port c, exits at port a, and is then absorbed in matched load 2. So in this case there is not an infinite sum of reflections making it to the receiver.

The reading for the state cc is thus

V _cc =V _r +G{τ _s T _s +p _s T ₂ ) . (58)

Front end state co, first switch closed, second open:

The noise T ₁ T ₁ . originating from matched load 1 and entering circulator 2 at port c is reflected at the open switch 2, returns to the circulator and exits it at port b, is reflected at the interface between antenna and body with a spectral power density o\p _s T _λ τ _r . Here it is added to the thermal emission from the body which at this point has spectral power density T _S T _S . The sum enters circulator 2 at port b, exits at port c and reaches the dashed line, making a contribution of G(τ _s T _s +p _s T{u _r )\.o the receiver reading. Noise with spectral power density (τ _s T _s +p _s T _x τ _r )xp _r is reflected back toward circulator 2 and reemerges at the dashed line, after reflection at the interface between body and antenna, giving a further contribution to the receiver reading of G(τ _s T _s +P ₅ T ₁ T ₁ )Xp ₅ P ₁ ..

Taking the infinite series of partial reflections into account the total contribution to the receiver reading from the thermal emission from matched load 1 and from the body is

δV _∞ = G[T ₆ T ₅ + P _x T ₁ T^x(I ₊ p _sPr +p _s ² p _r ² ₊ p)p\ +...) = G{τ _s T _s +p _s T,τ,.)/(l-p _s p _r ) (59)

The reading for the state co is thus

Derivation 2

Derivation of expression for the reflection coefficient at the interface between body and antenna for the front end described in example 1 and Figure 11.

V ₀₀ =K ₊ GT ₁ (61)

V _0C =V _{r +} GT ₂ (62)

V _cc =V _{r +} G{τχ. +p _s T ₂ ) (63)

Rearranging equation (64):

Inserting expression (61) solved for V _r

Multiplying out

Obtain expression for Gτ _s T _s from expressions (63) and (61)

Inserting expression for Gτ _s T _s in equation (67) to eliminate T ₃ from the equation

Rearrange with terms containing p _s placed on the left

Reduce

Solve for p _s

And hence the transmission is

Derivation 3

Derivation of expression for estimating the transmission line reflection from signals obtained when viewing a body with known temperature for the front end described in example 1 and Figure 11.

Derivation 4

Derivation of expression for the reflection coefficient at the interface between body and antenna in the case of an absorbing antenna for the front end described in example 1 and Figure 11.

Readings:

Now:

Rearranging equation and inserting (79) and (80):

Placing terms containing p _s on the left

Reducing

And solving for p _s to get

Derivation 5

Deriving expression for estimating the body temperature in the case of an absorbing antenna for the front end described in example 1 and Figure 11.

Derivation 6

Derivation of expression for estimating the transmission line reflection from signals obtained when viewing a body with known temperature in the case of an absorbing antenna for the front end described in example 1 and Figure 11.

Derivation 7

Derivation of equation (6), the temperature estimator based on radiation temperatures measured in two narrow frequency bands a and b:

where

g _ab (z) = aa _a exp(-a _a z)-ba _b exp(-a _b z) (89)

The requirement that the estimate should be exact in the case of a homogeneous temperature in the body leads to the constraint

a-b-l. (90) The requirement that the weight function g _ab should vanish at the body surface leads to the constraint

aa _a -ba _b =0. (91)

Eliminating b

aa _a +(a+ϊ)a _b =0. (92) Solving for a

Solving for b

Derivation 8 Derivation of equation (12), the coefficients for the temperature estimator based on radiation temperatures measured in three narrow frequency bands a, b and c:

where

The requirement that the estimate should be exact in the case of a homogeneous temperature in the body leads to the constraint

a-b-c = l . (97)

The requirement that the weight function g _abc and its derivative should vanish at the body surface leads to the constraints

aa _a -ba _b -ca _c = 0

(98) aa _a a _a -ba _b a _b -ca _c a _c = 0

With the following steps

b(a _a - a _b ) + c(a _a - a _c ) = -a _a b(a _a -a _b )a _b + c(a _a -a _c )a _c =0 (99) c{a _a -a _c )(a _c -a _b ) = a _a a _b the expressions for the coefficients are obtained