Keywords

1 Opening Remarks

The temperature signals of macroscopic objects can be observed by infrared imaging because all objects with nonzero temperatures emit electromagnetic energy, known as thermal radiation [1,2,3]. The Wien law [4] implies that within an extensive temperature range (\(10^0\sim 10^3\) K), the radiation-spectrum peak of an ideal black body locates in the infrared region. This intrinsic property is extensively applied in industry reconnoiter, military detection, and daily life. Naturally, the technology of thermal illusion [5,6,7,8,9] has attracted much attention due to its promising prospect in illusion or camouflage, namely, misleading or camouflaging thermal signals. The former (“illusion”) means that an existing object exists in infrared imaging, replacing another non-existing object [5,6,7]. In contrast, the latter (“camouflage”) represents that the thermal infrared pattern of an existing object blends into the background as if the object does not exist [8, 9]. Meanwhile, various challenges arise in designing infrared illusion, mainly resulting from complex surroundings, multifold heat-transfer modes, and fabrication difficulties.

Recent progress on infrared illusion focuses on regulating surface temperatures \(T_{\textrm{sur}}\) and designing surface emissivities \(\varepsilon _{\textrm{sur}}\), which play two key roles in infrared imaging. On the one hand, with the successful development of thermal metamaterials [10,11,12,13,14,15,16,17], temperature distributions can be tailored at will with elaborate microstructure designs. Based on it, the thermal illusion has been achieved within fixed or varying backgrounds. However, there are two weaknesses of this method in the existing studies: firstly, most of them are confined to conductive systems [18,19,20,21], neglecting thermal convection and radiation; secondly, the surface structures are still identifiable from the background in the visible-light view [22,23,24], which make them hard to be concealed under multiband detections. On the other hand, tuning emissivities can disguise an actual object into a fake one in the infrared camera. For self-adapting control, phase-change materials are widely adopted [25,26,27,28]. But these materials are not common and usually call for additional installations to input stimulus, adapting to changing circumstances (say, changing temperatures). Besides, if ambient temperatures vary sharply or even out of the region of phase-change temperature, its effect will become invalid. So both of these two methods of infrared illusion have some limitations. Furthermore, these two tailoring methods are mutually independent and scarcely coupled due to the lack of a practical and synergistic platform.

Fig. 13.1
figure 1

Adapted from Ref. [29]

Schematic diagram showing the proposed thermal metasurface. The units are arranged in three arrays (Array I, Array II, and Array III), which can form three different images (specific gestures) in the infrared camera (the third column). Meanwhile, they are similar in the visible-light view (the second column).

Full size image

To overcome the limitations and promote the integration of tuning \(T_{\textrm{sur}}\) and \(\varepsilon _{\textrm{sur}}\) in a single platform, we design an omnithermal restructurable thermal metasurface for infrared illusion; see Fig. 13.1. We can achieve characteristic infrared patterns by tailoring each block unit and assembling them in a specific array. We consider the three heat transfer modes, conduction, convection, and radiation (omnithermotics), which dominate surface temperatures. With the radiation-cavity effect, say, the dependence of effective emissivity on the sizes, shapes, and proportion of surface cavities, the specific emissivity can be achieved on each unit within a wide temperature range. Therefore, this single platform can tailor the surface temperature and emissivity synergistically. The unit-discretization operation in the \(x-y\) plane not only provides flexibility in designing fake temperature signals (hence yielding infrared illusion) but also makes different arrays almost identical (thus causing similarity in visible light) despite different properties (\(T_{\textrm{sur}}\) and \(\varepsilon _{\textrm{sur}}\)). As a result, both illusions in infrared view and similarity in visible-light view are achieved simultaneously, as schematically shown in the middle and right columns of Fig. 13.1.

2 Theoretical Foundation

According to the Stefan−Boltzmann law [30], the total thermal radiative energy density \(I_{\textrm{bb}}\) of a black body is related to the biquadrate of surface temperature \(T_{\textrm{sur}}\),

$$\begin{aligned} \begin{aligned} I_{\textrm{bb}}= \int \limits _{0}^{\infty }u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda =\int \limits _{0}^{\infty }\frac{2\pi h c^2}{\lambda ^5}\frac{1}{e^\frac{hc}{\lambda k_B T_{\textrm{sur}}}-1}d\lambda =\left( \frac{2\pi ^5k_B^4}{15c^2h^3}\right) T_{\textrm{sur}}^4 =\sigma T_{\textrm{sur}}^4, \end{aligned} \end{aligned}$$
(13.1)

where \(\lambda \) is radiative wavelength and \(u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) \) is the black-body spectral radiance, described by the Plank law. Here, h is the Plank constant, c is the velocity of light in vacuum, \(k_B\) is the Boltzmann constant, and \(\sigma \) is the Stefan−Boltzmann constant. We consider a scene that an infrared camera captures the infrared signals of an object in a far field for identification, the actually received spectral radiance deviates from the result described by Eq. (13.1). Spectral directional emissivity \(\varepsilon _{\textrm{sur}}(\lambda ,\,T_{\textrm{sur}},\theta , \phi )\) can describe this deviation, which is defined as the spectral-radiance ratio of actual objects to black bodies at temperature \(T_{\textrm{sur}}\), wavelength \(\lambda \), and direction angles \(\theta \) and \(\phi \). But in most practical situations without elaborate directed thermal emission, the diffuse-emitter approximation is reasonable enough. So we can simplify the surface emissivity to \(\varepsilon _{\textrm{sur}}(\lambda ,\,T_{\textrm{sur}})\). Then the actual radiative energy density \(I_{\textrm{ac}}\) can be written as

$$\begin{aligned} \begin{aligned} I_{\textrm{ac}} =\int \limits _0^{\infty }\varepsilon _{\textrm{sur}}\left( \lambda ,\,T_{\textrm{sur}}\right) u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda =\int \limits _0^{\infty }\varepsilon _{\textrm{sur}}\left( \lambda ,\,T_{\textrm{sur}}\right) \frac{2\pi h c^2}{\lambda ^5}\frac{1}{e^\frac{hc}{\lambda k_B T_{\textrm{sur}}}-1}d\lambda . \end{aligned} \end{aligned}$$
(13.2)

As we concern the total thermal radiative energy instead of the spectral radiance, the full wavelength emissivity \(\varepsilon _{\textrm{sur}}(T_{\textrm{sur}})\) makes sense. It can be defined as

$$\begin{aligned} \begin{aligned} \varepsilon _{\textrm{sur}}(T_{\textrm{sur}}) =\frac{I_{\textrm{ac}}}{I_{\textrm{bb}}}=\frac{\int _0^{\infty }\varepsilon _{\textrm{sur}}\left( \lambda ,\,T_{\textrm{sur}}\right) u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda }{\int _0^{\infty } u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda }=\frac{\int _0^{\infty }\varepsilon _{\textrm{sur}}\left( \lambda ,\,T_{\textrm{sur}}\right) u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda }{\sigma T_{\textrm{sur}}^4}. \end{aligned} \end{aligned}$$
(13.3)

Except for the intrinsic emissivity affects thermal radiation, both the signal collection range and resolution of the infrared camera should also be considered. According to the practical situations, the signal collection range \((\lambda _1,\,\lambda _2)\) covers the main emission band. Then the full wavelength emissivity \(\varepsilon _{\textrm{sur}}(T_{\textrm{sur}})\) can be adopted in this scene. Combing with Eqs. (13.2) and (13.3), the reading temperature \(T_{\textrm{read}}\) is given as [8]

$$\begin{aligned} \begin{aligned} T_{\textrm{read}}=C\times I_{ac}&=C\int \limits _{\lambda _1}^{\lambda _2}\varepsilon _{\textrm{sur}}\left( \lambda ,\,T_{\textrm{sur}}\right) u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda \\&\approx C\varepsilon _{\textrm{sur}}\left( T_{\textrm{sur}}\right) \int \limits _{\lambda _1}^{\lambda _2}u_{bb}\left( \lambda ,\,T_{\textrm{sur}}\right) d\lambda \\&\approx C\varepsilon _{\textrm{sur}}\left( T_{\textrm{sur}}\right) \int \limits _{\lambda _1}^{\lambda _2}\frac{2\pi h c^2}{\lambda ^5}\frac{1}{e^\frac{hc}{\lambda k_B T_{\textrm{sur}}}-1}d\lambda , \end{aligned} \end{aligned}$$
(13.4)

where C is a built-in conversion parameter of the infrared camera. Equation (13.4) indicates that the two factors dominate the infrared imaging, namely, the camera capacity \(\left[ C,\, \left( \lambda _1,\,\lambda _2\right) \right] \) and the surface properties \(\left( T_{\textrm{sur}},\,\varepsilon _{\textrm{sur}}\right) \). Here, we focus on modulating the characteristic radiative spectrum, which depends on the surface properties \(\left( T_{\textrm{sur}},\,\varepsilon _{\textrm{sur}}\right) \). Within a limited surface temperature region, the full wavelength emissivity \(\varepsilon _{\textrm{sur}}(T_{\textrm{sur}})\) is regarded as \(\varepsilon _{\textrm{sur}}\), independent on \(T_{sur}\). It is noted that if the surface temperature varies sharply, the coupling relation between \(\varepsilon _{\textrm{sur}}\) and \(\lambda \) should be underlined. And while the surface temperature difference is large enough between units, the coupling relation between \(\varepsilon _{\textrm{sur}}\) and \(T_{\textrm{sur}}\) should also be taken into consideration. Our strategy for controllable infrared illusion consists of tuning \(T_{\textrm{sur}}\) and \(\varepsilon _{\textrm{sur}}\) individually and assembling them in any specific way.

Fig. 13.2
figure 2

Adapted from Ref. [29]

Different tuning methods. a and b A cuboid as a block unit. Conductive flow is comparable with convective and radiative flow in (a), but dramatically different in (b). c Assembly of the units, which construct the whole metasurface.

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For the first step, let us consider a three-dimensional bulk as a unit, as illustrated in Fig. 13.2a. We set its sides to be thermally insulated and place a homothermal source at the bottom. The heat flows in the bulk along the z axis and dissipates into the surroundings from the top surface due to convection and radiation. This process includes the three basic modes of heat transfer. In a steady state, the temperature of the top surface \(T_{\textrm{sur}}\) can be determined by the conservation law of heat flow,

$$\begin{aligned} \boldsymbol{J}_{\textrm{cond}} = \boldsymbol{J}_{\textrm{conv}} + \boldsymbol{J}_{\textrm{rad}}, \end{aligned}$$
(13.5)

where \(\boldsymbol{J}_{\textrm{cond}}\), \(\boldsymbol{J}_{\textrm{conv}}\), and \(\boldsymbol{J}_{\textrm{rad}}\) are conductive, convective and radiative heat flow density, respectively. We set the unit’s height as \(H_b\) and thermal conductivity as \(\kappa _b\). The convective coefficient and radiative emissivity of the surface are \(h_b\) and \(\varepsilon _b\), respectively. Besides, the source and room temperatures are given as \(T_0\) and \(T_{\textrm{air}}\). We can write down the expressions of \(\boldsymbol{J}_{\textrm{cond}}\), \(\boldsymbol{J}_{\textrm{conv}}\), and \(\boldsymbol{J}_{\textrm{rad}}\) as

$$\begin{aligned} J_{\textrm{cond}}&=\kappa _b\nabla T|_{\textrm{bulk}} =\kappa _b\frac{T_0-T_{\textrm{sur}}}{H_b}, \end{aligned}$$
(13.6a)
$$\begin{aligned} J_{\textrm{conv}}&= h_b (T_{\textrm{sur}}- T_{\textrm{air}}), \end{aligned}$$
(13.6b)
$$\begin{aligned} J_{\textrm{rad}}&= \varepsilon _b \sigma (T_{\textrm{sur}}^4-T_{\textrm{air}}^4)=\varepsilon _b \sigma (T_{\textrm{sur}}^2+T_{\textrm{air}}^2)(T_{\textrm{sur}}+T_{\textrm{air}})(T_{\textrm{sur}}-T_{\textrm{air}})\nonumber \\&=R_b(T_{\textrm{sur}}) (T_{\textrm{sur}}- T_{\textrm{air}}), \end{aligned}$$
(13.6c)

where \(R_b(T)=\varepsilon _b \sigma (T_{\textrm{sur}}^2+T_{\textrm{air}}^2)(T_{\textrm{sur}}+T_{\textrm{air}})\), representing the radiative ability of the surface. Combining Eqs. (13.5)–(13.6c), we can deduce the temperature of the top surface \(T_{\textrm{sur}}\) as

$$\begin{aligned} T_{\textrm{sur}} = \frac{\kappa _b T_0/H_b+\left[ h_b+R_b(T_{\textrm{sur}})\right] T_{\textrm{air}}}{\kappa _b/H_b+h_b+R_b(T_{\textrm{sur}})}. \end{aligned}$$
(13.7)

Hereto, we obtain the general solution of the top-surface temperature of a unit. To obtain the value of \(T_{\textrm{sur}}\), an iteration of \(R_b(T_{\textrm{sur}})\) should be executed by calculator. Compared with the method reported in Ref. [19] where only \(\kappa _b\) is tuned, the present scheme has four parametric freedoms for handling. They are \(\kappa _b\), \(h_b\), \(\varepsilon _b\), and \(H_b\), involving the three basic modes of heat transfer. \(\kappa _b\) and \(H_b\) play the roles in controlling conductive flow. \(h_b\) and \(\varepsilon _b\) correspond to convective and radiative flows, respectively. These four parameters can be expressed as

$$\begin{aligned} \kappa _b&=\frac{H_b\left[ h_b(T_{\textrm{sur}}-T_{\textrm{air}})+ \varepsilon _b \sigma \left( T_{\textrm{sur}}^4-T_{\textrm{air}}^4\right) \right] }{T_0-T_{\textrm{sur}}}, \end{aligned}$$
(13.8a)
$$\begin{aligned} H_b&=\frac{\kappa _b(T_0-T_{\textrm{sur}})}{h_b(T_{\textrm{sur}}-T_{\textrm{air}})+ \varepsilon _b \sigma \left( T_{\textrm{sur}}^4-T_{\textrm{air}}^4\right) }, \end{aligned}$$
(13.8b)
$$\begin{aligned} h_b&=\frac{\kappa _b(T_0-T_{\textrm{sur}})/H_b-\varepsilon _b \sigma \left( T_{\textrm{sur}}^4-T_{\textrm{air}}^4\right) }{T_{\textrm{sur}}-T_{\textrm{air}}}, \end{aligned}$$
(13.8c)
$$\begin{aligned} \varepsilon _b&=\frac{\kappa _b(T_0-T_{\textrm{sur}})/H_b-h_b(T_{\textrm{sur}}-T_{\textrm{air}})}{\sigma \left( T_{\textrm{sur}}^4-T_{\textrm{air}}^4\right) }. \end{aligned}$$
(13.8d)

We can see if the surface temperature \(T_{\textrm{sur}}\) of each unit is preset to create specific infrared illusion, only three of them are independent. Also, these four parameters can be tuned arbitrarily and simultaneously to achieve the designed \(T_{\textrm{sur}}\) of each unit. Thus, the tuning strategy is flexible. We suppose that \(\varepsilon _{\textrm{b}}\) (equivalent to \(\varepsilon _{\textrm{sur}}\)) is uniform in each unit and approximate to that of a black body, the reading temperature can be estimated by Eq. (13.4) as

$$\begin{aligned} T_{\textrm{read1}}(x,\,y)\approx C \times \int \limits _{\lambda _1}^{\lambda _2}\frac{2\pi h c^2}{\lambda ^5}\frac{1}{e^\frac{hc}{\lambda k_B T_{\textrm{sur}}}-1}d\lambda \approx T_{\textrm{sur}}(x,\,y), \end{aligned}$$
(13.9)

where \((x,\,y)\) refers to the central position of each unit.

It is noted that tuning \(\varepsilon _b\) plays a limited role in controlling \(T_{\textrm{sur}}\) due to its maximum value 1, especially in low temperature regions. However, when \(T_{\textrm{sur}}\) is nearly uniform in each unit under some circumstances, tuning surface emissivity is another effective method for creating illusion because \(\varepsilon _{\textrm{sur}}\) becomes a major impact beyond \(T_{\textrm{sur}}\) in Eq. (13.4). For example, according to Eq. (13.7), if \(\kappa _b\) is far greater than \(h_b\) and \(R_b(T_{\textrm{sur}})\), \(T_{\textrm{sur}}\) will reach \(T_0\). Inversely, it will reach \(T_{\textrm{air}}\), as shown in Fig. 13.2b. Then, tailoring emissivity is the only way for creating infrared illusion in the infrared imaging. On the basis of Eq. (13.4), the reading temperature in this case is

$$\begin{aligned} T_{\textrm{read2}}(x,\,y)\approx \varepsilon _{\textrm{sur}}(x,\,y)\times C \times \int \limits _{\lambda _1}^{\lambda _2}\frac{2\pi h c^2}{\lambda ^5}\frac{1}{e^\frac{hc}{\lambda k_B T_{\textrm{sur}}}-1}d\lambda \approx \varepsilon _{\textrm{sur}}(x,\,y)\cdot {T_{\textrm{sur}}}. \end{aligned}$$
(13.10)

The final step is to assemble these units in a specific array to create the infrared illusion in infrared imaging, see Fig. 13.2c. Each unit can be regarded as a pixel. The fake surface temperature of each pixel should be distinguishable enough to make the illusion valid in infrared imaging. Therefore, the contrast ratio should be larger than the intrinsic resolution of the infrared camera under any conditions. The contrast ratio of imaging is based on the maximum and minimum values of reading temperatures. We can define the contrast ratio C as

$$\begin{aligned} C= \frac{T_{\textrm{read}}|_{\textrm{max}}-T_{\textrm{read}}|_{\textrm{min}}}{T_{\textrm{read}}|_{\textrm{max}}+T_{\textrm{read}}|_{\textrm{min}}}. \end{aligned}$$
(13.11)

We have two ways for tailoring \(T_{\textrm{read}}\). If the three modes of heat transfer are comparable, tuning \(T_{\textrm{sur}}\) solely is enough. According to Eq. (13.9), Eq. (13.11) can be written as

$$\begin{aligned} C_1 =\frac{T_{\textrm{sur}}|_{\textrm{max}}-T_{\textrm{sur}}|_{\textrm{min}}}{T_{\textrm{sur}}|_{\textrm{max}}+T_{\textrm{sur}}|_{\textrm{min}}}. \end{aligned}$$
(13.12)

Otherwise, tuning \(\varepsilon _{\textrm{sur}}\) is necessary to present a distinguishable temperature distribution in the infrared camera. So from Eq. (13.10), Eq. (13.11) can be written as

$$\begin{aligned} C_2 =\frac{\varepsilon _{\textrm{sur}}|_{\textrm{max}}-\varepsilon _{\textrm{sur}}|_{\textrm{min}}}{\varepsilon _{\textrm{sur}}|_{\textrm{max}}+\varepsilon _{\textrm{sur}}|_{\textrm{min}}}. \end{aligned}$$
(13.13)

The contrast ratio is related to the ratio of the surface temperature or the extremum difference of the effective emissivity, representing an intrinsic character of a sort of specifically-designed thermal metasurfaces. The flexible combination of units contributes to the reconfigurability, and does not affect the contrast ratio C. So, once we design the units completely, the thermal metasurface will always meet the resolution requirement of the detector.

3 Finite-Element Simulation

We perform finite-element simulations based on the commercial software COMSOL Multiphysics. The simulations focus on tuning the temperature \(T_{\textrm{sur}}\). Here, we keep \(H_b\) fixed and tailor \(\kappa _b\), \(h_b\), and \(\varepsilon _b\) not to break the geometric construction of metasurfaces. Firstly, the metasurface is constituted with \(15\times 30\) units, as shown in Fig. 13.2c. They are cubes of 1 cm length. Then, we classify the total 450 units into 6 groups, as demonstrated in Fig. 13.3a. Each group is designed independently to obtain six patterns of \(T_{\textrm{sur}}\). Here, we expect to create an illusion of “FUDAN”. When tuning \(\kappa _b\), we keep \(h_b\) and \(\varepsilon _b\) as constants. So as the other two parameters. Then, the six groups are assembled, as shown in Fig. 13.3a. For simplification, we heat the entire lower surface with a homothermal heat source \(T_0\) and keep the room temperature \(T_{\textrm{air}}\) at 300 K. The laterals of the surface are thermally contacted with neighboring units to mimic the real situation. Figure 13.3b–d, respectively, show the results of tuning \(\kappa _b\), \(h_b\), and \(\varepsilon _b\) at \(T_0=350\) K, while Fig. 13.3e–g are those at \(T_0=700\) K. We can see that convection and radiation play minor roles under low-temperature surroundings. In particular, the effect of thermal radiation is nearly indistinguishable. When \(T_0\) goes higher, they make sense gradually. We calculate the contrast ratio C with the simulation data at 350 and 700 K. It is 2.96 and 15.23% when tuning \(\kappa _b\), and 0.20 and 2.28% when tuning \(\varepsilon _b\). The amplification of tuning \(\varepsilon _b\) is about twice bigger than that of tuning \(\kappa _b\), confirming that radiation plays an increasingly important role with the temperature rising.

Fig. 13.3
figure 3

Adapted from Ref. [29]

Simulation results of tuning temperature \(T_{\textrm{sur}}\). a Six groups and arrays with letters “FUDAN”. b–g Temperature distributions with different tuning methods. \(T_0\) is set at 350 K and 700 K. For tuning thermal conduction, \(\kappa _b\) is set as 0.5, 1, 2, 3, 4, and 5 W m\(^{-1}\) K\(^{-1}\) for six groups while \(h_b\) is 50 W m\(^{-2}\) K\(^{-1}\) and \(\varepsilon _b\) is 1. For tuning thermal convection, \(h_b\) is 5, 10, 20, 30, 40, and 50 W m\(^{-2}\) K\(^{-1}\) while \(\kappa _b\) is 1 W m\(^{-1}\) K\(^{-1}\) and \(\varepsilon _b\) is 1. For tuning thermal radiation, \(\varepsilon _b\) is 0.1, 0.2, 0.4, 0.6, 0.8, and 1 while \(\kappa _b\) is 1 W m\(^{-1}\) K\(^{-1}\) and \(h_b\) is 50 W m\(^{-2}\) K\(^{-1}\). h–j Comparisons between theoretical values and simulation values of \(T_{\textrm{sur}}\), corresponding to the data extracted from b–g.

Full size image

It has been proved that the expected patterns can be observed by tuning the three heat-transfer modes individually. Convection and radiation dominate at low and high temperatures, affecting the contrast ratio of the pattern in the infrared camera. Figure 13.3h–j show the comparisons of \(T_{\textrm{sur}}\) between theoretical data and simulation results under three tuning modes. They echo well at low temperatures and show a little shift when they are high because the thermal interaction between different units appears. More heat exchange in the \(x-y\) plane impacts \(T_{\textrm{sur}}\). When the condition goes to extremes (say, \(T_{\textrm{sur}}\) reaches \(T_0\) or \(T_{\textrm{air}}\)), we have to tune the effective emissivity.

4 Laboratory Experiment

As shown in Fig. 13.3d, tuning radiation with emissivity at low-temperature conditions has little effect on infrared illusion. However, the engineered emissivities can impact apparent temperature distribution. Here, we resort to the surface-cavity effect [31, 32] to modulate \(\varepsilon _{\textrm{sur}}\). The cavity structures on the surface promote the block to a higher radiant exitance. Hence, the apparent temperature in infrared imaging will be deviated from the actual, forming an illusion pattern. Now, we are in the position to design a surface cavity structure. For simplification, we adopt the cylindrical structure as it is easy to manufacture, as demonstrated in Fig. 13.4a. The heat transfer process is between the surface cavity and the free space, in which the angle factor of the cavity can be omitted. According to Ref. [31], the effective emissivity of an isolated cylindrical cavity \(\varepsilon _e\) depends on its area ratio of mouth and inwall, which can be expressed as

$$\begin{aligned} \varepsilon _e=\left[ 1+\frac{S_0}{S_1}\left( \frac{1}{\varepsilon _b}-1\right) \right] ^{-1}, \end{aligned}$$
(13.14)

where \(S_0\) and \(S_1\) are the area of mouth and inwall, respectively, and \(\varepsilon _{\textrm{sur}}\) is the intrinsic surface emissivity. Owing to the high thermal conductivity and regular shape of the blocks, the surface temperature can be considered a constant. The plat surface allows the energy to transfer into the environment, so the thermal interaction between cavities occurs only. Thus, a quantitative emissivity expression of the whole surface of the block can be derived as

$$\begin{aligned} \varepsilon _{\textrm{sur}}=\varepsilon _e' \approx f\varepsilon _e+(1-f)\varepsilon _0 =f\left[ 1+\frac{S_0}{S_1}(\frac{1}{\varepsilon _b}-1)\right] ^{-1}+(1-f)\varepsilon _b. \end{aligned}$$
(13.15)

The area proportion of the cavity f and inherent area ratio \(S_0/S_1\) enable us to tailor the effective emissivity of the surface to form specific apparent temperature distribution in infrared imaging.

Fig. 13.4
figure 4

Adapted from Ref. [29]

Experimental measurements for different effective emissivities \(\varepsilon _{\textrm{sur}}\). a Cavity structure (upper panel) and effective emissivity principle. The effective emissivity of a flat surface with cavity (upper panel) is equivalent to \(\varepsilon _{\textrm{sur}}\) of another flat surface (lower panel), which is quantitatively expressed in Eqs. (13.14) and (13.15). The first column of We performfinite, c, and d shows the photo of experimental apparatus for a human pattern, a machine-gun pattern, and an “FD” pattern, respectively. And the other three columns display the experimental measurements, each for one observation angle (0\(^{\circ }\), 30\(^{\circ }\), or 60\(^{\circ }\)). Note that the experimental apparatus is placed in a heat bath of 50 \(^{\circ }\)C. The unit of numerical values in the color bars is \(^{\circ }\)C.

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We examine the practical effects directly with an infrared camera FLIR E60, whose resolution is 0.1 K. We use a \(10\times 15\) array and two groups of tailored units for designing feature patterns for simplification. Copper cubes with 2 cm in length are employed as block units. The thermal conductivity of copper is about 397 W m\(^{-1}\) K\(^{-1}\), to homogenize \(T_{\textrm{sur}}\). Group I is not hollow with an intrinsic emissivity of 0.2, while group II is trepanned with a cylindrical hole. The hole is 0.4 cm in radius and 1 cm in depth. According to Eq. (13.15), the effective emissivity is about 0.6. Besides, we design an acrylic plat with \(15\times 20\) square holes for encoding the block units. They can be inserted in the holes for fixation. We design infrared patterns of a human, a machine gun, and the letters “FD”, respectively, as shown in Fig. 13.4b–d by manually rearranging these units. This operation can also be mechanically executed with additional active installations, thus forming an active restructurable metasurface. We place the encoded surface in a water bath with a temperature of 50\(\mathrm{^oC}\). The room temperature is about 20\(\mathrm{^oC}\). After the system reaches a steady state, the infrared camera helps to detect the feature patterns. The metasurfaces of different arrangement ways in visible-light view are hard to distinguish (similarity). At different angles to observe, we find its robustness in both infrared and visible-light views, see Fig. 13.4b–d. It is worth mentioning that when the surface is coated with an anti-reflection film, we find that the feature pattern disappears. The reading temperatures get a little higher than the previous, confirming that the cavity engineering method helps change the imaging.

5 Discussion

Object emissivity and surface temperature determine the imaging pattern of infrared cameras. We have demonstrated two tuning methods by simulation or experiment of emissivity and temperature on the same platform to achieve infrared illusion and visible-light similarity. Reference [19] has given a feasible way to tune temperature by manipulating conduction processes. In addition to this, how to practically control convective and radiative flows need further study to satisfy theoretical predictions by Eqs. (13.8a)–(13.8d). Tuning \(T_{\textrm{sur}}\) only works with the system in the steady state, while tuning \(\varepsilon _{\textrm{sur}}\) works in both steady and transient states. We should note that emissivity plays two roles in the tailoring process. On the one hand, it guides the radiative flow to change the surface temperature. On the other hand, it helps conceal the actual temperature \(T_{\textrm{sur}}\) to cheat the infrared camera by displaying an apparent temperature. So, we perform the variable-controlling method in the above simulations and experiments. This platform is a flexible and applicable tool for infrared illusion. In different temperature regions, targeted tuning methods are available. Besides, the encoding and assembling process on unit cells is non-invasive and repeatable. Its flexibility with block assembly makes the illusion applicative to diverse situations. Moreover, infrared cameras usually have some limitations in dimensional resolution; the illusion pattern quality can be improved when the sizes of units are comparable with dimensional resolution. The proposed restructurability is essentially distinguished from the common reconfigurability or adjustability [33]. The former is property-invariant but structurally rearrangeable, while the latter is structure-invariant but property-adjustable. The proposed restructurable metasurface exhibits both illusions in infrared light and similarity in visible light. The “similarity” can be upgraded to “indistinguishability” as long as the surface is structured carefully, as implied by Fig. 13.4b–d, which should be useful for real applications.

Also, as a direct application, we suggest using our scheme to realize infrared anticounterfeiting. As we know, anticounterfeiting is extensively applied in industry, military, and daily life. The common strategies are based on optical holograms [34,35,36], which naked eyes or detectors can find. Nevertheless, such technologies tend to be defeated because the typical pattern can be forged. Recently, flourishing research on optical metasurfaces has been involved in this traditional field [37,38,39,40]. Light’s amplitude, phase, and polarization can be tailored arbitrarily with carefully designed two-dimensional microstructures. So, its intrinsic signal is characteristic and hard to be replicated. However, we only need to capture emissive electromagnetic-wave information for identification. Intuitional insight is to tailor the characteristic radiative signals for anticounterfeiting, which does not need additional incident lights. The encryption process can be executed on our proposed metasurfaces, while decoding is achieved by using infrared imaging. The key secret is hard to be forged because of its similarity in visible-light view. Moreover, restructurability raises the difficulty level for falsifying. This kind of anticounterfeiting strategy has applicability in non-invasive and quick-recognition scenes.

6 Conclusion

We have proposed a practical scheme for achieving infrared-light illusion and visible-light similarity. The tuning of surface temperature and emissivity can be executed synergistically. Compared with existing thermal metamaterials, our scheme considers all the three basic modes of heat transfer (omnithermotics), thus expanding the scope of applications. Also, we have introduced the cavity effect to tailor the emissivity, simplifying the manufacture. We hope this scheme can not only overcome some challenges in designing infrared illusion but also has direct applications in industry and commerce.

7 Exercise and Solution

Exercise

  1. 1.

    Discuss the effective emissivity of a cylindrical cavity with radius r and depth h.

Solution

  1. 1.

    According to Eq. (13.14), we can derive

    $$\begin{aligned} \varepsilon _e&=\left[ 1+\dfrac{\pi r^2}{2\pi r h+\pi r^2}\left( \dfrac{1}{\varepsilon _b}-1\right) \right] ^{-1} =\left[ 1+\dfrac{1}{2h/r+1}\left( \dfrac{1}{\varepsilon _b}-1\right) \right] ^{-1} \nonumber \\ {}&\quad =\left[ 1+\dfrac{1}{2\delta +1}\left( \dfrac{1}{\varepsilon _b}-1\right) \right] ^{-1}, \end{aligned}$$
    (13.16)

    where \(\delta =h/r\) is the depth-radius ratio. Then, we can define a cavity factor as \(F=\varepsilon _e/\varepsilon _b\),

    $$\begin{aligned} F=\frac{\varepsilon _e}{\varepsilon _b} =\left[ \varepsilon _b+\dfrac{S_0}{S_1}\left( 1-\varepsilon _b\right) \right] ^{-1} =\left[ \varepsilon _b+\dfrac{1}{2\delta +1}\left( 1-\varepsilon _b\right) \right] ^{-1}. \end{aligned}$$
    (13.17)

    For the same \(\varepsilon _b\), the larger \(\delta \), the larger F. For the same \(\delta \), the smaller \(\varepsilon _b\), the larger F.