## Abstract

Millimeter-wave (MMW) radiometry has been used in a vast and growing assortment of applications. Several MMW discriminators have been proposed and achieved good results in material classification and recognition. However, these discriminators are difficult to measure accurately in the real world. In this article, we defined two discriminators, emissive degree of polarization (EDoP) and reflecting DoP (RDoP), and proposed a physically based method using the characteristic of weak correlation of the emission part and reflection part of MMW radiation as an optimization criterion to obtain the optimal estimation of RDoP. Most measurement errors, such as the thermal noise of the radiometer, radiative transfer, antenna pattern, and calibration error, will not affect our method, and thus it is easy to implement in the real world. The effectiveness of our method has been verified by experiments. Our method only needs to measure the brightness temperature of horizontal polarization and vertical polarization. Based on RDoP, more information such as other discriminators, physical temperature, equivalent permittivity, reflectivity, and surrounding brightness temperature can be retrieved. Potential applications include liquid ingredient analysis, terrain monitoring, and security checks.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

All substances at a finite absolute temperature radiate electromagnetic energy. This phenomenon is called thermal radiation. Millimeter-wave (MMW) radiometry measures the electromagnetic radiation in the MMW band, and the sensors employed are referred to as radiometers [1]. With the ability to penetrate through a variety of common substances (e.g., atmosphere, fog, clouds, clothing, and to some extent rain) independently of the time of day, MMW radiometry has been used in a vast and growing assortment of applications, such as remote sensing [1,2], security checks [3,4], terrain monitoring [5,6], and target detection [7,8].

When a scene, such as terrain, is observed by an MMW radiometer, the radiation received by the antenna is partly self-emission by the object and partly reflecting radiation originating from the surroundings, such as that from the atmosphere. Through proper choice of radiometer parameters (wavelength, viewing angle, and especially the polarization), it is sometimes possible to establish useful relations between the magnitude of the energy received by the radiometer and specific object parameters of interest. In the field of remote sensing, MMW polarimetric radiometry has been successfully used for obtaining the parameters of wind fields, snow, ice, and hurricanes [9,10]. With the increase in the sensitivity and spatial resolution of radiometers, MMW polarimetric radiometry has achieved good results in surface orientation estimation [11,12], complex permittivity estimation [13,14], object enhancement [3,15,16], and image segmentation [17,18]. Another important application of MMW polarimetric radiometry is material classification and recognition. Previous studies showed that there are obvious differences between the polarization brightness temperature (TB) of different objects [15,19,20]. However, TB is related to physical temperature, surroundings, and incident angle, and thus cannot be directly used for material classification and recognition. In order to overcome this problem, some TB-derived feature discriminators have been proposed and achieved good results in experiments. For example, passive degree of polarization (PDoP) [21] is used for the classification of surface features such as water, concrete, and soil. Meanwhile, linear polarization ratio (LPR) [22] and linear polarization difference ratio (LPDR) [7] are used for the recognition of metal objects. However, these discriminators are difficult to measure accurately in the real world. This is because 1) object temperature is needed in the measurement, which is usually difficult to obtain; 2) the attenuation and reradiation of radiative transfer will cause measurement errors; and 3) high-accuracy calibration of the radiometer is needed. These three problems limit the real-world application of these discriminators. Ref. [22] proposed that, when the physical temperature of the object and the environment where the radiometer is located are the same, the measurement of object temperature can be replaced by the radiometer indication of a radar-absorbing material (RAM), and calibration is unnecessary. However, this assumption has strong limitations, for example, it is not applicable in long-distance applications. In addition, the temperature inconsistency between the object and the RAM will also bring errors.

In this article, referring to the definition of the degree of polarization (DoP) in the visible and infrared spectral band [23–25], we define the DoP of the emission part and reflection part of MMW radiation as emissive DoP (EDoP) and reflecting DoP (RDoP). We find that incorrect estimation of RDoP will lead to incorrect estimation of the emission and reflection parts of MMW radiation, which in turn increases the relevance of the emission and reflection parts. Therefore, the optimal estimation of the RDoP is obtained when the relevance of estimated emission and reflection is minimum. Based on this finding, we propose a new method for estimating RDoP. RDoP is also a discriminator, and theoretical calculations show their ability to be used for material classification and recognition. Furthermore, through simple mathematical operations, they can be converted into other discriminators. The contributions of our work are summarized as follows:

- 1) Our method only needs to measure the TB of the horizontal polarization and vertical polarization of an object. Other prior information, such as physical temperature, complex permittivity, and surrounding TB, is not required.
- 2) The measurement error of the TB caused by radiative transfer, antenna pattern, and calibration will not affect the estimation of RDoP. The influence of the thermal noise of the radiometer on the estimation can be eliminated, and thus our method does not require high performance of the radiometer.
- 3) Based on the RDoP, information such as physical temperature, equivalent permittivity, reflectivity, and surrounding TB can be retrieved from the measured TB.
- 4) Our method aids the application of discriminators in the real world. Future applications of our method include liquid ingredient analysis, terrain classification and recognition, and security checks.

## 2. Theory

#### 2.1 Basic theory

Figure 1 shows an illustration of MMW radiometry: a dual-polarization radiometer is measuring an object with physical temperature $T_{obj}$, and $\theta$ is the incident angle. According to the Rayleigh-Jeans approximation, the radiation intensity can be described with the TB in the MMW band. As shown in Fig. 1, the radiation received by the radiometer is partly due to self-emission by the object and partly due to the reflecting and scattering radiation originating from the surroundings; thus, the TB with horizontal polarization and vertical polarization can be respectively expressed by

$T_{E}^h$ and $T_{E}^v$ are the self-emission part of horizontal polarization and vertical polarization respectively, and can be expressed by

where the superscript $p$ denotes $h$ or $v$, and $e_p$ are the emissivity of $p$ polarization. $T_{R}^h$ and $T_{R}^v$ are the reflecting part (both reflecting and scattering radiation are called ’reflecting part’ in this article) of horizontal polarization and vertical polarization respectively, and can be expressed by [1]:We divide the total radiation of an object (i.e., $T_h+T_v$) into an emission part $T_E=T_{E}^h+T_{E}^v$ and a reflection part $T_R=T_{R}^h+T_{R}^v$. Referring to the definition of the DoP in the visible and infrared spectral band [23,24], we define the DoP of the emission part and reflection part of MMW radiation as emissive DoP (EDoP, $p_e$) and reflecting DoP (RDoP, $p_r$):

#### 2.2 Statement of problem

For an object with smooth surface, Eq. (1) can be rewritten as:

According to conservation of energy, the relationship between emissivity and reflectivity can be expressed as $e_p+r_p=1$. From Eq. (4) and Eq. (5), we can get the physical model of RDoP and EDoP for a smooth object:

Many researchers use MMW radiometry for material classification and recognition. However, as shown in Eq. (5), because TB is related to surrounding TB and the object’s temperature, it cannot be directly used for classification and recognition. Some TB-derived feature discriminators, such as LPR, LPDR, and DoSP, have a common characteristic, that is, they are only related to reflectivity or emissivity. So they are used to exclude the influence of $T_{obj}$ and $T_{inc}$. RDoP and EDoP also have the characteristic, as exemplified by Eq. (6).

Figure 2 shows the theoretical calculations of the EDoP and RDoP for several common materials at 94 GHz. We can find that the EDoP and RDoP of different materials are obviously different at most incident angles, and thus both the EDoP and RDoP can be used as the basis of material classification or recognition. Other discriminators have also been proved to have the ability of classification or recognition [7,21,22].

However, these discriminators have a common problem, that is, they are difficult to measure accurately in the real world. Firstly, to obtain these discriminators, in addition to measuring $T_h$ and $T_v$, we must also measure $T_{obj}$ or $T_{inc}$. For example, from Eq. (5) and Eq. (6), we can get the measurement formulas for the EDoP and RDoP:

In general, especially in remote applications, it is difficult to measure $T_{obj}$ or $T_{inc}$. Secondly, the atmospheric radiation and attenuation between the object and radiometer will cause measurement errors of $T_h$ and $T_v$, and then lead to errors of $p_e$ and $p_r$. Thirdly, accurate calibration is needed when measuring $T_h$ and $T_v$, which will increase the complexity and cost of the measurement system. Finally, Eq. (7) is valid for only smooth objects, which is a strong limitation for practical application.

The above four problems limit the real-world application of discriminators. In the next subsection, we will introduce the finding that the inaccurate estimation of RDoP leads to crosstalk between the estimation of $T_E$ and $T_R$. Based on this finding, we propose a new method for measuring RDoP.

#### 2.3 Correlation and crosstalk

From Eq. (1) and Eq. (4), we can deduce that

This is a general result for both smooth and roughness objects, enabling the separation of $T_E$ and $T_R$ from the measured $T_h$ and $T_v$ with the given $p_e$ and $p_r$.

If we want to calculate $T_E$ and $T_R$ from the measured $T_h$ and $T_v$ by Eq. (8), we must first know the accurate estimations of $p_e$ and $p_r$. However, estimation error is inevitable. Let

where $\widehat {p}_e$ and $\widehat {p}_r$ are the estimations of $p_e$ and $p_r$, respectively; and $\epsilon _e$ and $\epsilon _r$ are the estimation errors of $p_e$ and $p_r$, respectively. From Eq. (8), the estimations of $T_E$ and $T_R$ can be calculated bySubtracting Eq. (8) from Eq. (10) yields the relationship between estimations and true values:

For the sake of simplicity, Eq. (11) can be expressed as follows:

We can observe from Eq. (12) that if there are no estimation errors for $p_e$ and $p_r$ (i.e., $\epsilon _r=\epsilon _e=0$), then $c_{11}=c_{22}=1$ and $c_{21}=c_{12}=0$. Otherwise, the wrong estimations for $p_e$ and $p_r$ will cause crosstalk between $\widehat {T}_E$ and $\widehat {T}_R$ which in turn changes their correlation.

Covariance can be used to describe the degree of correlation between two variables. Using Eq. (2) and Eq. (3), the covariance of time series of $T_E$ and $T_R$ can be expressed by

#### 2.4 Estimation of RDoP

In this subsection, we propose a method for estimating RDoP based on the above analysis of correlation and crosstalk. Since the covariance of a constant and a variable is 0, $cov(T_{obj},T_{inc})=0$ when we utilize natural phenomena or artificial means to make $T_{inc}$ fluctuate for a period of time while $T_{obj}$ keeps constant. At this time, $cov(T_E,T_R) = 0$, in other words, there is weak correlation between the emission part and reflection part of MMW radiation.

Using $cov(T_E,T_R)=0$, Eq. (15) is reduced to

We can see from Eq. (16) that when $T_{obj}=\rm {C}$ (C denotes a constant), if we make an accurate estimate of $p_r$ (i.e., $\epsilon _r=0$), then $cov(\widehat {T}_E,\widehat {T}_R)=0$ no matter whether the estimation of $p_e$ has error. Therefore, the optimal estimation of $p_r$ can be expressed as

To summarize, our method for estimating $p_r$ mainly includes the following steps:

- 1) Over a period of time $t\in [0,T]$, we utilize natural phenomena or artificial means to make $T_{inc}$ fluctuate while $T_{obj}$ remains constant.
- 2) We measure $T_h$ and $T_v$ in the time series of $t\in [0,T]$.

## 3. Real-world considerations

In real-world applications, the observed power of a radiometer represents all radiation incident upon the antenna, integrated over all possible directions and weighted according to the antenna directional pattern; this may cause inaccuracy in the measurement of $T_h$ and $T_v$. Other factors also play an important role in the measurement, including the noise generated inside the receiver, calibration errors, as well as atmospheric effects. This section will analyze the impact of these factors.

#### 3.1 Radiometer noise

Radiometer noise can be characterized as Gaussian white noise with a standard deviation defined as radiometer sensitivity. Taking the radiometer noise into account, the measured $T_h$ and $T_v$ can be expressed as follows:

where $N_h$ and $N_v$ are the noises of horizontal polarization channel and vertical polarization channel, respectively.By plugging Eq. (18) into Eq. (10) to calculate the noise-polluted $\widehat {T}_E'$ and $\widehat {T}_R'$, we can derive their covariance:

We can find from Eq. (19) that the radiometer noise will reduce the covariance and affect the estimation of $p_r$ or $p_e$. Fortunately, sensitivity (i.e., $\sigma _{N_h}$ and $\sigma _{N_v}$) can be easily obtained by measuring in advance or directly estimating from $T_h'$ and $T_v'$. Therefore, the influence of radiometer noise can be eliminated by

whereNaturally, if the sensitivity of the radiometer is very poor and cannot sense even the changes of $T_{inc}$, our noise elimination method also cannot work. Therefore, the changes of $T_{inc}$ should be greater than the sensitivity of the radiometer. This is easy to implement since the sensitivity of most radiometers is within 1 K.

#### 3.2 Other factors

The influence of factors such as the atmosphere, antenna pattern, and calibration error can be described by

where $a_h$, $a_v$, $b_h$, and $b_v$ are influence coefficients of error that will be described in detail later.By plugging Eq. (22) into Eq. (10) to calculate the error-polluted $\widehat {T}_E'$ and $\widehat {T}_R'$, we can derive their covariance:

We can see from Eq. (23) that influence coefficients $b_h$ and $b_v$ will not affect $cov(\widehat {T}_E,\widehat {T}_R)$, but $a_h$ and $a_v$ will cause an offset of $cov(\widehat {T}_E,\widehat {T}_R)$. Because $\sigma _{T_h}$ and $\sigma _{T_v}$ are unpredictable, this offset cannot be estimated and eliminated. Fortunately, as will be analyzed later, the influence coefficients usually meet $a_h=a_v$, and thus Eq. (23) can be reduced to

As seen from Eq. (17), the coefficient $a_h^2$ does not affect the estimation of $p_r$.

The rest of this subsection will discuss the influence coefficients in detail.

### 3.2.1 Atmosphere

When the radiometer is far from the object, atmospheric radiation and attenuation cannot be ignored. Thus, the actual measured TB should be corrected to

where $L$ and $T_{atm}$ are the loss factor and atmospheric radiation between the object and radiometer, respectively.By comparing Eq. (25) and Eq. (22), we can find that $a_h=a_v=1/L$ and $b_h=b_v=T_{atm}$. Therefore, atmospheric radiation and attenuation does not affect the estimation of $p_r$. Similarly, fabric and plastic bottles will cause radiation attenuation and reradiation, the physical model of which is the same as Eq. (25), and therefore will not affect the estimation of $p_r$. In sum, our method is suitable for remote applications, liquid ingredient analysis, and security checks.

### 3.2.2 Antenna

Affected by antenna pattern and antenna efficiency, the measured TB consists of three parts: (a) energy received through the antenna beam covered by the object, i.e., the quantity of interest; (b) energy received from directions outside the object; and (c) thermal radiation energy emitted by the antenna structure itself. These three parts can be expressed as follows [1]:

By comparing Eq. (26) and Eq. (22), we can find that

Therefore, antenna pattern and antenna efficiency do not affect the estimation of $p_r$.

### 3.2.3 Calibration errors

Most radiometer receivers are linear systems in the sense that the output indication $V$ is directly proportional to the measured TB:

Hence, it is sufficient to measure $V$ for each of two known values of TB to determine the constants $k$ and $c$:

where $V_{H}$ and $V_C$ are output indications for unpolarized calibration sources $T_H$ and $T_C$, respectively. The superscripts $H$ and $C$ stand for hot and cold, respectively.However, the TBs of calibration sources used in the calibration usually have errors. Let

where $T_H'$ and $T_V'$ are the TBs of calibration sources used in Eq. (29); $T_H^{ture}$ and $T_V^{ture}$ are the true TBs; and $\epsilon _H$ and $\epsilon _V$ are the errors. Through using $T_H'$ and $T_V'$, the measured TB with error can be expressed asTherefore, the influence coefficients of calibration errors are

We can see that calibration errors do not affect the estimation of $p_r$. That is, we only need two unpolarized calibration sources, and we do not need to know their true brightness temperature. This greatly reduces the difficulty of calibration. For example, RAM at room temperature can be used as a hot calibration source, and the atmosphere is a convenient and easily available cold calibration source.

In sum, various errors in the above analysis will affect the accuracy and precision of measured $T_h$ and $T_v$. If we use Eq. (7) to calculate $p_r$ and $p_e$, considerable errors will occur, which is one of the reasons why discriminators are difficult to apply in practice. However, our method is not affected by these errors, and thus will promote the application of discriminators.

## 4. Experiment

In this section, we will introduce more details and verify the feasibility of our method through an experiment. The experiment was conducted outdoors. As shown in Fig. 3, a 94 GHz dual-polarized radiometer was used to collect the $T_h$ and $T_v$ data over a period of time. Detailed information of radiometer is shown in Table 1. During the measurement process, we manually moved RAM in the order of position ①$\rightarrow$②$\rightarrow$③$\rightarrow$②$\rightarrow$①. When an RAM is in position ① and ③, $T_{inc}$ comes from atmospheric radiation and is a low brightness temperature. On the contrary, when the RAM is in position ②, $T_{inc}$ comes from the RAM whose emissivity is about 1, and thus $T_{inc}$ is a high brightness temperature. By controlling the position of an RAM, we made $T_{inc}$ fluctuate.

Figure 4 shows the measurement results of $T_h$ and $T_v$. The measurement object is water with a calm surface. The incident angle of measurement is $45^\circ$. The integration time of the radiometer is 1 ms, and the total measurement time is 18 s, that is, the data size is 18000 for both $T_h$ and $T_v$. We can infer from Fig. 4 that the RAM was in position ① for $t=0\sim 5\textrm {s}$, then in position ② for $t=6.5\sim 7\textrm {s}$, in position ③ for $t=8\sim 10\textrm {s}$, and then back to position ② for $t=10\sim 12.5\textrm {s}$, and finally position ① for $t=13\sim 18\textrm {s}$. In such a short time of 18 s, we can think that $T_{obj}$ remained unchanged.

Then, using Eq. (10), we calculated $\widehat {T}_E(t)$ and $\widehat {T}_R(t)$ for $t\in [0,18]$s with the traversal of $\widehat {p}_r\in [-1,0]$ and $\widehat {p}_e\in [0,1]$. Then we calculated the covariance of $\widehat {T}_E(t)$ and $\widehat {T}_R(t)$, i.e., $cov(\widehat {T}_E(t),\widehat {T}_R(t))$. Considering the radiometer noise, $\widehat {\sigma }_{N_h}=0.6314$-K and $\widehat {\sigma }_{N_v}=0.3251$-K were estimated by calculating the standard deviations of $T_h(t)$ and $T_v(t)$ for $t\in [0,5]$s, respectively, and input into Eq. (20) to eliminate the radiometer noise. The final result of $cov(\widehat {T}_E(t),\widehat {T}_R(t))$ as a function of $\widehat {p}_r$ and $\widehat {p}_e$ is shown in Fig. 5. From Eq. (17), we can get the optimal estimation of ${p}_r$, which is marked with a red line in Fig. 5. We find that $\widehat {p}_r^{optimal}=-0.2990$ and is independent of $\widehat {p}_e$. This is consistent with the analysis in subsection 2.4.

We chose water as the measurement object because the complex permittivity model of water has been well studied. We can calculate the complex permittivity of water through the model, then calculate the reflectivity according to Fresnel’s law, and finally calculate the RDoP from Eq. (4). This physical-model-derived RDoP (${p}_r^{exact}$) is regarded as the theoretical exact value to gauge the quality of the experimental result. The complex permittivity of water is related to frequency and physical temperature. According to the semiempirical model in Ref. [1], the complex permittivity of water is 7.80$-$12.77i for 94 GHz and 290.5 K, and the corresponding ${p}_r^{exact}=-0.3085$. Compared with the exact value, the error of $\widehat {p}_r^{optimal}=-0.2990$ is about 3$\%$. Because our method only requires that $T_{inc}$ changes when $T_{obj}$ keeps constant, using the data of 5$\sim$7s, 10$\sim$12s, and 12$\sim$14s respectively, we also got the similar results, and the errors are all about 3$\%$.

We also used the traditional method to estimate $p_r$. With the data shown in Fig. 4 and $T_{obj}=290.5$ K, we calculated $p_r$ by Eq. (7). The mean of estimations of $p_r$ is -0.2698, and its error is 13$\%$. This result shows that the traditional method not only needs more prior information, but also has greater error.

Similarly, we measured the RDoP of water with two incident angles: $30^\circ$ and $60^\circ$. All results are shown in Table 2. We can see that the error decreases as the incident angle increases. This is because the polarization characteristics of the object decrease with the decrease in incident angle. Methods that use polarization characteristics to obtain object information all face the problem of increasing error at small incident angle; such methods include the surface normal vector estimation method [12] and complex permittivity estimation method [14]. However, large incident angles may also cause problems. One problem is that when the incident angle is too large, the beam coverage of the radiometer antenna becomes wider. In such a case, the measured data is not the data under a single incident angle, but the mean value of data under a wide range of incident angles. In addition, achieving object alignment is more difficult when the incident angle is large, and thus the operation is more likely to introduce errors. Therefore, although feasible in theory, it is not recommended to use our method at incident angles outside of $[30^\circ ,60^\circ ]$ unless the accuracy and resolution of the radiometer have been greatly improved.

In the MMW band, it is often quite difficult to measure a physical quantity accurately. Reference [1] shows that the semiempirical model represents the complex permittivity of water to within 3$\%$ over 30$\sim$100 GHz, and thus ${p}_r^{exact}$ is not absolutely accurate. Therefore, the estimation results of $p_r$ with error less than 5$\%$ are satisfactory. As shown in Fig. 2, since this error is much smaller than the difference of $p_r$ between different materials, our estimation method is sufficient for material classification and recognition.

## 5. Discussion

So far, we have introduced the estimation method of RDoP. This section will show how to use just the estimated RDoP to extract more information, thereby illustrating the broad potential of our method.

#### 5.1 Information extraction

For an object with a smooth surface, the reflectivity is given by Fresnel’s law [1]:

From Eq. (34), we can find that both EDoP and RDoP are functions of three quantities, i.e., $\epsilon '$, $\epsilon ''$, and $\theta$. As $\theta$ is usually known to the observer, there are only two unknown quantities ($\epsilon '$ and $\epsilon ''$). To estimate $\epsilon '$ and $\epsilon ''$, we need at least two independent equations, that is, we need to estimate both EDoP and RDoP first, and then use Eq. (34) to estimate $\epsilon '$ and $\epsilon ''$. However, our method can only estimate RDoP.

Fortunately, in our previous work [14] we found

Therefore, we can use Eq. (37) with the estimated RDoP to estimate the equivalent permittivity, and then use Eq. (36) to calculate the reflectivity and EDoP.

Table 3 shows the estimated equivalent permittivity from the experimental results $\widehat {p}_r^{optimal}$. Both theory and experiment show that each discriminator, including $p_r$ and $p_e$, is governed by the incident angle. If objects of the same material are observed at different incident angles, they may be classified as having different materials. However, from Table 3, we can see that the equivalent permittivity is almost not influenced by incident angle, and thus, compared with those discriminators, it may be more suitable for material classification and recognition. In our other work, we will discuss the characteristics of equivalent permittivity in detail.

The estimated EDoP calculated from the estimated equivalent permittivity by Eq. (36) and the theoretical exact value of the EDoP $\widehat {p}_e^{exact}$ calculated from $\epsilon =7.80-12.77$i are also shown in Table 3. The error of the estimated EDoP comes from two parts: the error of $\widehat {p}_r^{optimal}$, as shown in Table 2, and the error of Eq. (36), that is, the equivalent permittivity used in Eq. (36) instead of complex permittivity. The error of Eq. (35) increases with the incident angle, and thus the error of the estimated EDoP is smaller when the incident angle is small. This is consistent with the results presented in Table 3.

The conversion from RDoP and EDoP is valuable because more information can be obtained. For example, by using Eq. (7), the physical temperature of the object and the environmental TB can be retrieved by the EDoP and RDoP:

Figure 6 shows the retrieved results based on the data shown in Fig. 4 and the estimated RDoP and EDoP of $\theta =45^\circ$. We can see that the estimated $T_{obj}$ fluctuates around 285 K. An interesting phenomenon is that the fluctuation becomes larger at $t\in [5,14]$s, when $T_{inc}$ is changing rapidly. Therefore, to use our method to obtain the object temperature, it is recommended to use the data when $T_{inc}$ is stable, i.e., when $t\in [0,4]$s or $t\in [14,18]$s. The mean value of the estimated $T_{obj}$ of $t\in [0,4]$s is 285.2 K, and thus the error is about 5 K compared with its actual temperature of 290.5 K. This error is calibration error. As previously analyzed in subsection 3.2, calibration error does not affect the accuracy of the estimated RDoP and EDoP, but will affect that of $T_h$ and $T_v$, and then cause errors in $T_{obj}$ and $T_{inc}$.

The retrieved $T_{inc}$ shown in Fig. 6(b) is in accordance with the change in RAM position. However, theoretically, when an RAM is in position②, $T_{inc}$ should be the physical temperature of the RAM, i.e., about 290 K (but this is not coincident with Fig. 6(b)). This is because only part of the antenna beam is covered by the RAM due to the beam efficiency of the antenna, as shown in Fig. 3.

#### 5.2 Conversion between discriminators

There are other discriminators in addition to the EDoP and RDoP. The application scenarios of different discriminator are also different. For example, LPR [22] and LPDR [7] have been proven to be suitable for the classification of metals and nonmetals, and the PDoP [21] has been proven to be suitable for the classification of different nonmetal objects. The formulas for converting the RDoP to other discriminators are

Equations (39)–(41) are deduced by comparing their own definitions. Therefore, our method can be applied to more application scenarios.

#### 5.3 Application examples

The key of our method is to utilize natural phenomena or artificial means to construct application scenarios, in which $T_{obj}$ remains constant while $T_{inc}$ fluctuates. Here are some potential application scenarios.

### 5.3.1 Illumination of noise source

As shown in Fig. 7, the fluctuating radiation produced by noise source irradiates on the object. Since the radiation energy of the noise source is concentrated in the MMW band, the $T_{obj}$ of the object will not be affected. Using our estimation method, we can get discriminators to recognize or classify the object. This process can be used in nondestructive liquid ingredient analysis and security inspection.

### 5.3.2 Illumination of the sun

As shown in Fig. 8, when the sun rises or sets and passes through the incident direction, the strong MMW radiation of the sun will lead to the sudden change in $T_{inc}$. For a radiometer with angular resolution of $2^\circ$, the time for the sun to pass through the reflecting beam is 8 min since the angular velocity of the sun is about $15^\circ /\textrm {h}$. In this process, we can think that $T_{obj}$ has almost no change. Therefore, in this scenario, our method can be used to extract the information of terrain, such as temperature monitoring and detection of oil or ice.

## 6. Conclusion

We have proposed and demonstrated a new information extraction method using polarized MMW radiation. Two discriminators, the EDoP and RDoP, are used to characterize the polarization of the emission part and reflection part of MMW radiation. We find that the wrong estimation of the EDoP and RDoP will increase the correlation between the estimated emission part and reflection part. Therefore, using the lowest correlation as an optimization criterion, we can obtain the optimal estimation of RDoP. We also theoretically prove that the measurement error of TB caused by radiative transfer, antenna pattern, and calibration will not affect our method, and the thermal noise of the radiometer can be eliminated mathematically. The effectiveness of our method has been verified by experiments. Fig. 2 shows the material classification and identification potential of RDoP. Our method is suitable for the whole millimeter wave band. However, materials have different RDoP characteristics in different frequency and different incident angles. In our future work, we will show the multi incident angles and multi frequency measurement results of typical liquids to find the best measurement angle and band of our method.

In addition, we provided the formulas for conversion between discriminators, and proposed a method to further estimate the equivalent permittivity, physical temperature of an object, surrounding TB, and reflectivity. Hence, the application potential of our method is expanded. More detailed analysis of these applications will be carried out in the future.

As shown in the first example of subsection 5.3, based on our method, object classification and recognition can be realized by noise source illumination, which has high application potential in non-destructive liquid component analysis. In the second example, our method is realized by utilizing the rise and fall of the sun, which has strict restrictions on the time and observation direction, and thus is limited in practical applications. In the future, we need to further explore the natural phenomena to meet the needs of our method and thereby expand its application. In addition, in the terahertz and infrared field, radiation is also composed of self-emission part and reflecting part. Therefore, our method may provide some references for information extraction of terahertz and infrared signal.

## Funding

China Postdoctoral Science Foundation (2020M682412); National Natural Science Foundation of China (61871438).

## Disclosures

The authors declare no conflicts of interest.

## Data availability

Data underlying the results presented in this paper are available in Dataset 1 in Ref. [26].

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