## 1 Introduction
### Diagnostics Based on Microwave Radiometry  
Figure 2 shows the spectral energy density of passive radiation (\(B_{v}\)) at body temperature, which is typical of the human core within \(T_{core}=\) (37-38) \({}^{\circ}\)C at rest. The maximum value of \(B_{v}\) is reached at the frequency \(\
u_{\max}\simeq 1.82\times 10^{13}\) Hz, which corresponds to the wavelength \(\lambda_{\max}=1.64\times 10^{-5}\) m. Instruments use different microwave bands, which are marked with vertical lines in this figure. For example, the broadband radiothermometer RTM-01-RES can operate in the range of 1-5 GHz depending on the type of radio sensor (the green bar in Figure 2); the radiometer's small antenna (approximately 2 cm) provides reliable measurements in the range of 1.4-1.427 GHz from depths up to 2.3 cm (see the brown line) [41]. Antenna-applicator and sensor measure the internal (microwave) and skin (infrared) temperature at one point simultaneously in about 3 s (including the processing time). The intensity of microwave radiation in the operating range is \(10^{6}\)-\(10^{8}\) times less than in the IR range (see Figure 2), which gives us skin temperature based on IR thermography. Therefore, there is a direct dependence of the radiation intensity on temperature in the microwave range in accordance with the Rayleigh-Jeans formula  
\[B_{v}=\frac{k_{B}\
u^{2}}{c^{2}}\,T, \tag{1}\]  
where \(k_{B}\) is the Boltzmann constant, and \(c\) is the speed of light. The linear dependence of \(B_{v}\) on \(T\) underlies the temperature measurement due to the proportionality between \(T_{B}\) and \(B_{v}\) under a narrow operating frequency range. The diagnostic capabilities of microwave radiometry extend to a significant number of diseases of various organs/tissues (Figure 3). The original studies were on the brain [7; 25],  
Figure 2: The spectral density of electromagnetic radiation \(B_{v}\) at temperature \(T=37\)\({}^{\circ}\)C (blue line): the left axis is the dependence \(B_{v}(v;T)\), \(v\) is the radiation frequency (\(|v|=\) Hz). The magenta line shows the range for microwave radiation. Other colored lines are explained in the text. arthritis of various joints [11], and breast [10]. Because many diseases are associated with inflammatory processes, a local increase in internal temperature (at a depth of several centimeters) and the corresponding specific gradients of temperature fields can be detected by MWR measurements. It is noteworthy that this method allows for a reduction in the number of errors and an increase in the informative features of X-ray and ultrasound diagnostic methods in the early stages of acute inflammatory diseases of the kidneys and prostate [42] (see Figure 3, pointers 8 and 9). Brain activation due to local changes in blood flow during the metabolic activity of neurons is accompanied by changes in temperature and electrical conductivity, which can be tracked by real-time MWR measurements [30]. Microwave radiometry can provide additional clinical monitoring of deep temperatures during surgical operations on the brain, as lowering the temperature of the involved organs significantly increases the risk of pathological consequences [3]. Brain activation due to local changes in blood flow during the metabolic activity of neurons is accompanied by changes in temperature and electrical conductivity, which can be tracked by real-time MWR monitoring [30]. Traumatic brain injuries (TBI) alter the temperature distribution due to disruption of normal blood circulation, and special studies show the ability of MWR to fix even small TBI [43]. Separately, we single out non-invasive radiometric sounding for thermal monitoring of deep brain temperature in infants [44]. Some joint diseases are accompanied by inflammatory processes, which makes MWR an effective tool for the early diagnosis of arthritis in various joints [29; 45]. Local temperature changes in the pathophysiology of arthritis and arthrosis reflect inflammation even in the absence of clinical signs and can be diagnosed by MWR before pain occurs [46].