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Accurate characterization of full-chain infrared multispectral imaging features under an aerodynamic thermal environment

Ning Yang, Ying Yuan, Chao Zhang, Xin Liu, Xiaorui Wang, and Yi Li

Open Access Open Access

Abstract

The detection performance of infrared imaging systems during high-speed flight is significantly impacted by aero-optical and aero-thermal radiation effects. However, traditional numerical calculations struggle to balance accuracy and efficiency, and there is a lack of a comprehensive model for infrared imaging in an aerodynamic thermal environment. In this study, we propose a calculation method based on Cellular Automata (CA) ray tracing, which allows for parallel calculation of aero-optical and aero-thermal radiation effects by combining optical field transport rules with the cellular space obtained by interpolation under fluid-solid boundary constraints. Using this method, we extend the traditional imaging feature prediction model of the infrared imaging system to obtain an accurate characterization model of the full-chain imaging features adapted to the aerodynamic thermal environment. Finally, we investigate the characteristics of infrared multispectral imaging system in various spectral bands under the influence of aero-optical and aero-thermal radiation effects. With this full-chain imaging model, the key elements of the imaging system under aerodynamic thermal environment can be globally optimized.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

When operating under high-speed flight conditions, the aero-optical and aero-thermal radiation effects can cause the imaging results to become blurred, jittery and saturated, ultimately leading to a significant reduction in the performance of the infrared imaging system [1]. To overcome these challenges and maintain detection capability, researchers have explored various approaches, including optical window optimization [2], active cooling [3,4], and back-end algorithm correction [5–7], etc.

Several studies have been conducted on the numerical calculation of aero-optical and aero-thermal radiation effects [8–16]. Fan [11] used ray tracing to complete the numerical calculation of the radiation characteristics of optical windows. Wang [12,13] used ray tracing based on the fourth-order Runge-Kutta method to complete the accurate numerical calculation of aero-optical and aero-thermal radiation effects. Luo [14,15] established a differential ray equation solution format based on Cellular Automata to achieve efficient numerical calculation of aero-optical effects. Ju [16] studied the influence of aero-optical and aero-thermal radiation effects on the degradation of imaging quality under time-varying conditions based on the ray tracing method.

While these studies have made some progress in the field of accurate numerical calculation of aero-optical and aero-thermal radiation effects, there is still a lack of research on an accurate characterization model for system-level full-chain imaging features in aerodynamic thermal environments. The existing research is insufficient to support the global optimization of infrared imaging systems in aerodynamic thermal environments.

To accurately characterize the full-chain imaging features in the aerodynamic thermal environment, this study extends the original full-chain imaging model by incorporating the interaction mechanism between the optical field and the fluid-solid-thermal coupling medium. The resulting full-chain imaging model is adapted to the aerodynamic thermal environment and provides a comprehensive understanding of the imaging features. To address the challenges of low calculation efficiency and incomplete imaging chain information in the existing numerical calculation of aero-optical and aero-thermal radiation effects, this study proposes a multi-physics field, multi-medium coupled aero-optical and aero-thermal radiation effects calculation method based on Cellular Automata ray tracing. This method provides a complete integration of the effects of fluid-solid-thermal coupling media on optical field transmission, while enabling parallel, flexible, and extensible calculations of aero-optical and aero-thermal radiation effects. Based on the full-chain imaging model and the proposed calculation method, the key elements of the imaging system under the aerodynamic thermal environment can be optimized globally.

2. Accurate characterization model for full-chain imaging features under aerodynamic thermal environments

Due to the influence of aerodynamic thermal effect, the shock layer and optical window outside the imaging system of a high-speed aircraft are transformed into non-uniform media. This results in multi-dimensional characteristics such as refractive index, absorption characteristics, and radiation characteristics becoming non-uniform in spatial and temporal domains [16]. Consequently, the complex amplitude of infrared radiation of the target and background changes when it passes through the inhomogeneous medium, leading to blurred, jittery, distorted, and saturated imaging results [1]. Figure 1 illustrates the imaging process of an infrared imaging system under an aerodynamic thermal environment.

 figure: Fig. 1.

Fig. 1. Imaging process of an infrared imaging system under an aerodynamic thermal environment.

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To accurately characterize imaging features under aerodynamic thermal conditions, two crucial steps must be taken. Firstly, a mathematical model of the vehicle's flow and temperature fields must be created to calculate the aero-optical and aero-thermal radiation effects. Secondly, the interaction between this radiation and the imaging chain must be modeled, taking into account the target/background, atmosphere, optical system, and imaging sensor array. By considering all factors, an accurate characterization model can be achieved to optimize imaging system design and improve target detection and recognition.

2.1 Model for the interaction between the optical field and the medium under aerodynamic thermal environment

The inhomogeneous shock layer and optical window under the aerodynamic thermal environment lead to aero-optical and aero-thermal radiation effects [12]. To accurately calculate the impact of aero-optical and aero-thermal radiation effects on imaging quality under aerodynamic thermal conditions, a characterization model of the optical field, medium, and their interaction in the aerothermal environment must be established.

The light field function E(x,y,z,θ,φ,λ,t) characterizes the state of the light field in space, where E, (x,y,z), (θ,φ), λ and t characterize the intensity, position, transmission direction, spectral information and time-varying characteristics of the light field, respectively. The description of the light field intensity characteristics is done using radiometry in the conventional full-chain imaging model. To ensure that the results of the aero-optical and aero-thermal radiation effects calculations can be coupled with the conventional imaging chain, the E in the light field function is replaced here by the radiance L [17]. Using the optical cosine D = (Dx,Dy,Dz) to characterize the transmission direction of the light, the optical field function can be expressed as Lt(r,D,λ). Figure 2(a) shows the light field of a plane wave characterized by an array of light rays, where L(r,D,λ) is the entire vector light field and Lm(rm,Dm,λm) is the local light field vector represented by the m-th ray.

 figure: Fig. 2.

Fig. 2. (a) High-dimensional light field represented by a ray array; (b) Transmission process of light field vector in fluid-solid-thermal coupling medium.

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The medium through which light travels can have a significant impact on the position r, direction D, and radiation information Lλ of the light field function. As shown in Fig. 2(b), the resulting light field Lout(rout,Dout,λ) is affected by the aerodynamic thermal environment. To accurately model this impact, it is necessary to establish a targeted state function F for the medium and corresponding interaction rules. By doing so, we can better understand and predict the behavior of light in different environments.

The impact of the medium on the position and direction information of the light field function can be obtained by combining the refractive index field nλ(s) of the medium with the ray equation

$$\frac{d}{{ds}}\left( {n(s)\frac{{d{\mathbf r}}}{{ds}}} \right) = \nabla n(s)$$
where n(s), r and ds are the refractive index at spatial location s, the position vector, and the tiny line element in the transmission path, respectively [11]. The impact of the medium on the radiation dimension of the light field can be obtained using the radiation characteristics of the medium combined with the radiation transmission equation
$$\frac{{d{L_\nu }(s )}}{{ds}} = {k_\nu }(s )\cdot \left( {\frac{{{j_\nu }}}{{{k_\nu }}}(s )- {L_\nu }(s )} \right)$$
where kν(s) and jν(s) are the extinction coefficient and the coefficient of radiation source function at position s, respectively, Lν is the spectral radiance and ν is the wave number [12]. When both the shock layer and the optical window are in local thermal equilibrium, the radiation transmission equation [12] can be simplified as
$$\frac{{d{L_\nu }(s )}}{{ds}} = {k_\nu }(s )\cdot ({{L_{b\nu }}(s )- {L_\nu }(s )} )$$
where Lbν is the blackbody radiation function. The integral form solution of the radiation transmission equation can be expressed as
$$\left\{ \begin{array}{l} {L_\nu }({{s_1}} )= {L_\nu }({{s_0}} )\exp [{ - {\tau_\nu }({s_0},{s_1})} ]+ \int_{{s_0}}^{{s_1}} {{k_\nu }(s ){L_{b\nu }}(s )\exp [{ - {\tau_\nu }(s,{s_1})} ]ds} \\ {\tau_\nu }({s_0},{s_1}) = \int_{{s_0}}^{{s_1}} {{k_\nu }(s )ds} \end{array} \right.$$
where s0 and s1 represent the starting and ending position of the integration path for the radiation transmission equation, respectively.

The shock layer and optical window serve as fluid-solid coupling media, with vastly different intrinsic properties between the two regions. As such, it is necessary to model these regions separately and incorporate boundary constraints, such as surface functions fin and fout as well as the BRDF (bidirectional reflectance distribution function) at the interface. This ensures that precise fluid-solid coupling can be achieved during subsequent processing.

The state function of the medium, initially obtained, can be described as F(x,y,z,nλ,kλ,T), where kλ and T represent the spectral extinction coefficient and temperature at various positions within the medium. However, due to the spatial inconsistencies present in the terms of the medium state function F(x,y,z,nλ,kλ,T), a point-by-point solution of the combined ray equation and radiation transmission equation is necessary. This solution must be conducted in conjunction with the medium equation F and the light field function L. Finally, the combined equation can be expressed as

$$\left\{ \begin{array}{l} {{\mathbf L}_{in}}({{\mathbf r}_{in}},{{\mathbf D}_{in}},\lambda )\\ {\mathbf F}({x,y,z,{n_\lambda },{k_\lambda },T} )\\ {f_{in}} = \sum\limits_i {{f_{in\_i}}({s \in {S_i}} ),BRDF({f_{in}})} \\ {f_{out}} = \sum\limits_i {{f_{out\_i}}({s \in {S_i}} ),BRDF({f_{out}})} \\ \frac{d}{{ds}}\left( {n(s)\frac{{d{\mathbf r}}}{{ds}}} \right) = \nabla n(s)\\ \frac{{d{L_\nu }(s )}}{{ds}} = {k_\nu }(s )\cdot ({{L_{b\nu }}(s )- {L_\nu }(s )} ),\nu = {1 / \lambda } \end{array} \right.$$
where Si corresponds to different areas on the optical window, with different surface functions fin and fout under different areas.

2.2 Numerical calculation method of aero-optical and aero-thermal radiation effects based on cellular automata

The equation governing the interaction between the optical field and medium in an aerodynamic thermal environment is complex, as it entails the coupling of multiple physical fields and media. Consequently, traditional ray tracing techniques are not applicable for solving this equation directly.

Cellular automata (CA) typically comprise cellular space and rule functions. By defining specific computational domains, setting appropriate rule functions, and specifying initial conditions, boundary conditions, and neighborhood constraints, it is possible to simulate a wide range of complex systems [14,15]. To calculate aero-optical and aero-thermal radiation effects, a computational domain can be generated by integrating information from multiple physical fields within the same cellular space and applying specific boundary constraints.

The cellular space in CA is characterized by various properties, including coordinates (i,j,k), refractive index nλ, spectral extinction coefficient kλ, and temperature T, among others, as defined by the established combined equations. The rule functions, such as the ray equation and radiation transmission equation, are applied to these properties, while the boundary conditions, such as the fluid-solid boundary function and BRDF at the interface, are also specified. This approach enables highly parallel calculations of aero-optical and aero-thermal radiation effects, as all light vectors fall within the same calculation domain and are subject to identical constraints.

Figure 3(a) shows the process of generating a CA space using physical field data obtained by CFD (computational fluid dynamics) combined with measured data, where the fluid-solid regions are integrated in the same computational domain for the actual calculation. Figure 3(b) displays the basic 3-dimensional cell and its 3-dimensional Moore-type neighbors. Figure 3(c) illustrates the process of solving the combined equation point by point using CA. This method utilizes the properties of neighboring points to obtain the properties of the current computational location, resulting in an efficient and highly parallel solution of the combined equations. Figure 3(d) showcases the calculation at the fluid-solid boundary. To ensure high accuracy in the fluid-solid coupling solution, the fluid-solid boundary is solved analytically with the help of interface functions fin and fout, as well as the BRDF. When a boundary flag appears in the neighborhood state of the trace point, the calculation mode switches to the analytical solution mode, and the current calculation position is updated to the fluid-solid boundary, thus completing the calculation at the fluid-solid boundary. Here, Nout represents the normal direction at the interface.

 figure: Fig. 3.

Fig. 3. (a) CA space generation using CFD data and measured data; (b) 3D cell with its 3D Moore-type neighbors; (c) Ray tracing calculation using CA properties; (d) The solution at the fluid-solid boundary.

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To solve the combined equation, the ray equation is solved point by point to determine the path of the ray, followed by solving the radiation transmission based on the ray path. Due to the non-uniform distribution of extinction coefficients and temperatures along the path, a segmented numerical integration of the tracing path is necessary to achieve more precise results. To enhance computational accuracy and efficiency, the fourth-order Runge-Kutta method combined with the gradient-centered difference of the 3D cell is utilized to format the solution of the ray equation [12,15], which can be expressed as

$$\left\{ \begin{array}{l} {{\mathbf r}_{i + 1}} = {{\mathbf r}_i} + \frac{h}{6}({{\mathbf K}_1} + {{\mathbf K}_2} + {{\mathbf K}_3} + {{\mathbf K}_4})\\ {{\mathbf T}_{i + 1}} = {{\mathbf T}_i} + \frac{h}{6}({{\mathbf L}_1} + {{\mathbf L}_2} + {{\mathbf L}_3} + {{\mathbf L}_4})\\ {{\mathbf K}_1} = {{\mathbf T}_i},{{\mathbf L}_1} = n({{\mathbf r}_i})\nabla n({{\mathbf r}_i})\\ {{\mathbf K}_2} = {{\mathbf T}_i} + h{{\mathbf L}_1}/2,{{\mathbf L}_2} = n({{\mathbf r}_1})\nabla n({{\mathbf r}_1})\\ {{\mathbf K}_3} = {{\mathbf T}_i} + h{{\mathbf L}_2}/2,{{\mathbf L}_3} = n({{\mathbf r}_2})\nabla n({{\mathbf r}_2})\\ {{\mathbf K}_4} = {{\mathbf T}_i} + h{{\mathbf L}_3},{{\mathbf L}_4} = n({{\mathbf r}_3})\nabla n({{\mathbf r}_3})\\ \frac{{dn({\mathbf r})}}{{dl}} = \frac{{n(CA{{({\mathbf r})}_{l + 1}}) - n(CA{{({\mathbf r})}_{l - 1}})}}{{2{h_{CA,l}}}},(l = x,y,z)\\ n({\mathbf r}) = \sum\limits_m {{w_m}n({CA{{({\mathbf r})}_m}} ),{w_{CA,m}} \propto {1 / {norm({{\mathbf r} - Pos({CA{{({r})}_m}} )} )}}} \end{array} \right.$$
where,
$$\left\{ \begin{array}{l} {{\mathbf r}_1} = {{\mathbf r}_i} + h{{\mathbf K}_1}/2\\ {{\mathbf r}_2} = {{\mathbf r}_i} + h{{\mathbf K}_2}/2\\ {{\mathbf r}_3} = {{\mathbf r}_i} + h{{\mathbf K}_3} \end{array} \right.$$
h, hCA,l, dn(r)/dl, n(r), CA(r), CA(r)m, Pos(CA(r)m) are tracing step, cellular size on the l-axis, refractive index gradient along the l-direction, refractive index, index of cell, index of neighbor cells, and the corresponding spatial location of neighbor cells, respectively.

Figure 4 depicts the comprehensive calculation process of aero-optical and aero-thermal radiation effects. Initially, the CA space is generated based on various input parameters, such as CFD physical field data, fluid-solid constraints, relevant measured data, and calculation accuracy, etc. These input parameters include physical field point cloud data, gas component content, optical window refractive index, thermo-optical coefficient, and fluid-solid boundary point cloud data. Subsequently, the initial conditions and rule functions are established, including the initial light field state, control equations, and termination conditions. Ray-tracing calculations are then performed in the CA space. Once all ray calculations are completed, the light field distribution Lout(rout,Dout,λ) is obtained, taking into account the influence of aero-optical and aero-thermal radiation effects.

 figure: Fig. 4.

Fig. 4. The overall calculation process for aero-optical and aero-thermal radiation effects.

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Efficient and parallel computation of combined equations can be achieved through the use of cellular automata. The current results yield the light field state Lout(rout,Dout,λ), taking into account the influence of the aerodynamic thermal environment. However, to accurately characterize the imaging features integrated in the aerothermal environment, the results must be coupled and computed with existing modules for target/background, atmospheric transport, optical systems, imaging sensor arrays, and image processing.

2.3 Full-chain imaging model adapted to aerodynamic thermal environment

The imaging results in an aerodynamic thermal environment are affected by various factors, including atmospheric transport, aero-optical and aero-thermal radiation effects, optical systems, imaging sensor arrays, image processing, and other components [17].

To achieve accurate integration between the aero-optical and aero-thermal radiation effects module and other modules, additional light tracing coupling calculations are required for the optical system, imaging sensor array, and other components. The calculation of the aero-optical and aero-thermal radiation effects, Lout(rout,Dout,λ), can be divided into two parts: L(r,λ) for calculating the focal plane radiant flux, and Ray(r,D,λ) for calculating the point spread function (PSF) at the focal plane.

Figure 5(a) illustrates the ray tracing calculation using L(r,λ) to determine the spectral radiant flux on the imaging sensor array. After obtaining L(r,λ) by separating Lout(rout,Dout,λ), the optical window is then discretized into an array of small surface elements As,i, and the radiation flux Ps,i (λ) emitted by each small surface element As,i to different stereo angles can be expressed as

$${P_{s,i}}(\lambda ) = \int_{{\varphi _1}}^{{\varphi _2}} {\int_{{\theta _1}}^{{\theta _2}} {{L_{s,i}}(\theta ,\varphi ,\lambda )} \Delta {A_{s,i}}(\theta ,\varphi )\sin \theta d\theta d\varphi }$$
where Ls,i(θ,φ,λ), ΔAs,i(θ,φ), θ and φ are the spectral radiance, projected area, zenith angle and azimuth of the small surface element, respectively. The results for the spectral radiant flux received from the small surface element i at the location of the sensor array (m,n) are
$${P_{m,n,i}}(\lambda ) = \sum\limits_i {{\tau _{opt}}(\lambda ){P_{s,i}}(\lambda )} |{{P_{s,i}}(\lambda ) \in Det(m,n)} $$
where τopt(λ) is the spectral transmittance of the optical system.

 figure: Fig. 5.

Fig. 5. The aero-optical and aero-thermal radiation effects calculation results coupled with the optical system and imaging sensor array. (a) Calculating radiant flux; (b) Calculating PSF.

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In Fig. 5(b), the ray-tracing calculation of the PSF on the imaging sensor, obtained through Ray(r,D,λ), is presented. By merging the optical system and the imaging sensor array, a PSF that integrates the spatial sampling effect of the sensor array can be obtained.

The result of coupling the aero-optical and aero-thermal radiation effects module with other modules can be expressed as

$$\left\{ \begin{array}{l} {P_{\det }}(\lambda ) = {\tau_a}(\lambda ){\tau_{opt}}(\lambda ){P_{In}}(\lambda )\ast PS{F_{a,\lambda }} + {P_a}(\lambda )\\ {U_{\det }} = \int\limits_\lambda {{P_{\det }}(\lambda ){R_v}(\lambda )} d\lambda + {U_n}\\ G = \left\{ \begin{array}{l} {G_{\min }},{U_{\det }} < {U_{\min }}\\ \frac{{{U_{\det }} - {U_{\min }}}}{{{U_{\max }} - {U_{\min }}}} \times ({G_{\max }} - {G_{\min }}) + {G_{\min }},{U_{\min }} \le {U_{\det }} \le {U_{\max }}\\ {G_{\max }},{U_{\min }} < {U_{\det }} \end{array} \right. \end{array} \right.$$
where PIn(λ), τopt(λ), τa(λ), PSFa,λ, Pa(λ) are the spectral radiant flux of the image plane without aero-optical and aero-thermal radiation effects interference, optical system transmittance, spectral transmittance, PSF and spectral radiant flux due to aero-optical and aero-thermal radiation effects, respectively. Rν(λ), Un, Pdet, Udet are the voltage spectral responsivity of the imaging sensor, noise voltage, spectral radiant flux received by the sensor under the impact of aero-optical and aero-thermal radiation effects and output voltage, respectively. Gmin, Gmax, Umin, Umax are the upper and lower limits of image quantization and the upper and lower limits of voltage, respectively. G represents the quantized output of the grayscale image.

Since then, a precise model for characterizing integrated imaging features in aerodynamic thermal environments has been developed. By integrating the various components of the imaging chain, it is now possible to accurately characterize imaging features under specific operating conditions.

3. Simulation and analysis

3.1 Testing of the computational method

This section conducts accuracy and calculation speed tests on the calculation method described above, with a computer configured as Inter Core i5-11600KF CPU @3.9 GHz (RAM 32 GHz). A gradient refractive index medium is selected, which can be described as

$$n(z) = n(0){({1 - {\beta^2}{z^2}} )^{{1 / 2}}}$$
where n(0) = 1.667, β=0.001. The transmission path of light in this medium can be analytically derived [18].

As shown in Fig. 6, the calculation error results indicate that using refractive index difference instead of refractive index for differentiation leads to a decrease in the calculation accuracy of the fourth-order Runge-Kutta method. However, under the current calculation conditions, where the wavelength of the light is in the range of 1-15µm, the calculation error still meets the requirements for calculation accuracy.

 figure: Fig. 6.

Fig. 6. Comparison between ray tracing results and analytical results in a medium with gradient refractive index. (a) Comparison between tracing path and ideal path; (b) Computation error results under different cellular sizes and tracing step lengths.

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Here a computational domain of 100 × 100 × 100 mm was set up with a cellular size of 0.1 mm. The computation time, computation error and number of tracing steps under different tracing step lengths are shown in Table 1. The computation time refers to the time taken for a single ray to traverse the computational domain. Under the current computing conditions, the average per-step computation time is 3.030e-4 s. It can be observed that the current calculation method's speed is comparable to that reported in Ref. [15]. Considering the addition of path radiance integration during actual calculations, the final calculation speed may decrease slightly, but overall, it still exhibits relatively high computational efficiency.

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Table 1. The computation results under different tracing step lengths

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All quantities in this computational method are solved in a unified cellular space, and there is no need for a very complex data structure, which provides a rather concise approach to solving the problem of low computational efficiency in ray tracing for aero-optical and aero-thermal radiation effects.

3.2 Simulation of radiation characteristics of aero-optical and aero-thermal radiation effects

To analyze the influence of different optical window shapes and flight conditions on the spectral radiation characteristics of aero-optical and aero-thermal radiation effects, we have presented the simulation parameters in Table 2 for comparative purposes.

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Table 2. The simulation parameters

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Figure 7 depicts the aerodynamic thermal radiation distribution characteristics of ellipsoidal and hemispherical optical windows at different flight speeds. The radiation content of the shock layer and optical window varies depending on the flight conditions and the type of optical window used, thus requiring customization for specific calculation conditions.

 figure: Fig. 7.

Fig. 7. Radiation content of the shock layer and optical window in different spectral bands at 10 km altitude. (a) optical window 1; (b) optical window 2.

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Figure 8 illustrates the spectral radiation characteristics of a hemispherical optical window under different conditions, resulting from aero-optical and aero-thermal radiation effects. The peak wavelengths of 2.7 and 4.3 µm, which are commonly used for aircraft wake detection, exhibit strong gas radiation [19–21]. However, under high-speed flight conditions, aerodynamic thermal radiation reduces the signal-to-clutter ratio of the target in this band, thereby diminishing the imaging system's detection capability. Therefore, optimizing the detection band based on the target's radiation characteristics is crucial.

 figure: Fig. 8.

Fig. 8. The spectral radiation characteristics of optical window 2 under different flight speed. (a) spectral radiance in 3500∼3850 cm-1; (b) spectral radiance in 2200∼2400 cm-1; (c) spectral radiance in 800∼1250 cm-1; (d) spectral radiance in 2300∼3300 cm-1.

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3.3 Simulation and degradation evaluation of multi-spectral imaging features under aerodynamic thermal environment

The imaging process of the infrared imaging system under the aerodynamic thermal environment is shown in Fig. 1, and the corresponding full-chain imaging simulation process is shown in Fig. 9.

 figure: Fig. 9.

Fig. 9. The full-chain imaging simulation process under aerodynamic thermal environments.

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To quantitatively evaluate the impact of aero-optical and aero-thermal radiation effects on imaging quality, we have chosen a standard 4 bars target [22] as the simulation scene. The simulation parameters are presented in Table 3, where the integrated irradiance of the original target on the imaging sensor, after accounting for atmospheric transmission and MTF (Modulation Transfer Function), is represented by Eint. This approach enables us to accurately assess the influence of aero-optical and aero-thermal radiation on the imaging system's performance.

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Table 3. Simulation parameters of standard 4 bars target scene

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Figure 10(a) and Fig. 10(c) show the spectral radiation of the original standard 4 bars target at 2200∼2400 and 3500∼3850 cm-1, respectively, under the simulation conditions of Table 3. Figure 10(b) and Fig. 10(d) depict the imaging simulation results, taking into account aero-optical and aero-thermal radiation effects, at a flight speed of 3 Ma.

 figure: Fig. 10.

Fig. 10. (a) The spectral radiation of the original standard 4 bars target at 2200∼2400 cm-1; (b) The imaging simulation results at 2200∼2400 cm-1; (c) The spectral radiation of the original standard 4 bars target at 3500∼3850 cm-1;(d) The imaging simulation results at 3500∼3850 cm-1.

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To account for the imaging system's decreased detection capability, we have selected the local signal-to-clutter ratio (SCR) [19] and local Structural Similarity (SSIM) [23] as the image quality evaluation metrics. Specifically, we have chosen a 2-fold pixel region (128 × 128 pixels) around the target as the local area for evaluation. Here, SCR is defined as

$$SCR = \frac{{{{\bar{G}}_T} - {{\bar{G}}_B}}}{{{\sigma _B}}}$$
where $\bar{G}$T and $\bar{G}$B are the mean grey scale values of the target and background in the local area, and σB is the standard deviation of the background area. SSIM is defined as
$$SSIM({G_a},{G_b}) = {[l({G_a},{G_b})]^\alpha }{[c({G_a},{G_b})]^\beta }{[s({G_a},{G_b})]^\gamma }$$
where Ga and Gb are the gray image results before and after adding aero-optical and aero-thermal radiation effects, respectively [23].

The image quality degradation results for different flight conditions under the Table 3 calculation conditions can be seen in Table 4 and Table 5.

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Table 4. Evaluation results at a saturation threshold of 1.5×max(Eint)

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Table 5. Evaluation results at a saturation threshold of 5×max(Eint)

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At the current standard 4 bars target temperature, saturation is very easy to occur in the 2200∼2400 and 3500∼3850 cm-1 bands when the saturation threshold is 1.5×max(Eint).When the saturation threshold is 5×max(Eint), the image still has a high local SCR at 3 Ma and can complete the target detection task, and at 4 Ma and above, the target extraction capability has been lost due to aerodynamic thermal saturation. Because of the high temperature of the currently selected target, the saturation threshold is higher in 800∼1250 and 2300∼3300 cm-1, and there is no obvious saturation in the simulation image results.

3.4 Imaging simulation of actual scene under aerodynamic thermal environment

For the simulation, a cloud background scene was selected and the corresponding parameters are listed in Table 6, where Eint is the integrated irradiance on the imaging sensor array without the effect of aero-optical and aero-thermal radiation effects.

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Table 6. Simulation parameters of actual scene

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Figure 11 displays the simulation results of the aero-optical and aero-thermal radiation effects on the image for the Table 6 simulation parameters. The grayscale levels in the displayed images are re-quantized to 0-255 grayscale levels according to the grayscale extreme values of the original image. It is evident that under these conditions, the background information in the image has been largely lost at 4 Ma, and the image has been saturated in a large area at 5 Ma, rendering the target identification and localization task impossible. These simulation results are consistent with the evaluation results obtained under the standard 4 bars target scene conditions.

 figure: Fig. 11.

Fig. 11. Original image (a) and simulation results after adding aero-optical and aero-thermal radiation effects; (b) 3 Ma; (c) 4 Ma; (d) 5 Ma.

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4. Conclusion

Under high-speed flight conditions, the imaging performance of infrared imaging systems is significantly degraded due to the aero-optics and aero-thermal radiation effects caused by the aerodynamic thermal environment. The aero-optical effects cause blurring, shifting, and distortion of the imaging results, while the aero-thermal radiation effects saturate the imaging results, leading to the loss of target signal in severe cases.

To address the issues of low computational efficiency and incomplete imaging chain in existing numerical methods, this study proposes a novel approach that utilizes a cellular automata model to fuse multi-physical fields, multi-medium, and multi-chain elements for calculating aero-optical and aero-thermal radiation effects. Furthermore, to achieve efficient and accurate end-to-end simulation of the aero-optics and aero-thermal radiation effects on imaging degradation characteristics, this study extends the modules of aero-optics and aero-thermal radiation effect based on the original full chain model of infrared imaging systems. The expansion considers the interaction between the light field and medium, and establishes an accurate characterization model of full-chain imaging features suitable for aerodynamic thermal environments. The improved full-chain imaging model developed in this study significantly enhances the environmental adaptability of the original full-chain imaging model, making it suitable for more complex high-speed aerodynamic environments. These improved methods and models are logically connected and together constitute the core contribution of this study.

Funding

Fundamental Research Funds for the Central Universities; National Natural Science Foundation of China (62005204, 62005206, 62075176).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. Z. Xing, X. Y. Chen, Z. Y. Peng, Z. W. Yang, H. L. Zhang, Z. F. Xing, and N. Zhang, “Research progress and thinking of infrared aero-optical effect,” Infrared and Laser Engineering. 51(4), 108–124 (2022). [CrossRef]  

2. F. Y. Dang, S. Q. Chen, W. Zhang, H. Wang, and Z. G. Fan, “Optimized design method for the inner surface of a conformal dome based on the ray tracing approach,” Appl. Opt. 56(29), 8230–8239 (2017). [CrossRef]  

3. G. Fu, S. H. Yi, X. H. Wang, L. He, and Y. Ge, “Experimental study on supersonic film cooling on the surface of a blunt body in hypersonic flow,” Chin. Phys. B 23(10), 104702 (2014). [CrossRef]  

4. S. H. Yi and H. L. Ding, “Research progress of optical aperture with supersonic film cooling under hypersonic flight environment,” Air Space Defense. 4(4), 1–13 (2021).

5. T. T. Zhang, S. H. Yi, Y. Z. Zhu, and L. He, “Reconstruction and calibration on aero-optical wavefront aberration based on background oriented schlieren based wavefront sensing,” Acta Phys. Sin. 64(8), 084201 (2015). [CrossRef]  

6. H. L. Ding, S. H. Yi, Y. Y. Wu, F. Zhang, and L. He, “Investigation on correction method of aero-optical transmission effects imaging deviation based on BOS technique,” Infrared and Laser Engineering. 47(4), 206–213 (2018).

7. X. H. Zhao, S. H. Yi, H. L. Ding, T. C. OuYang, and Y. Shi, “Hypersonic flow field imaging quality characteristics and its correction method,” Aerosp. Sci. Technol. 95(1), 105459 (2019). [CrossRef]  

8. M. D. White, “High-order parabolic beam approximation for aero-optics,” J. Comput. Phys. 229(15), 5465–5485 (2010). [CrossRef]  

9. S. Gordeyev, E. Jumper, and T. E. Hayden, “Aero-optical effects of supersonic boundary layers,” AIAA J. 50(3), 682–690 (2012). [CrossRef]  

10. S. K. Yang, S. Seong, D. Ryu, S. W. Kim, H. Kwon, S. H. Lin, H. Jeong, H. B. Kong, J. W. Jae, and J. H. Jong, “Ray tracing simulation of aero-optical effect using multiple gradient index layer,” Electro-optical and Infrared Systems: Technology and Applications XIII. 9987, 99870R (2016). [CrossRef]  

11. Z. G. Fan, C. P. Yu, H. S. Xiao, and W. Zhang, “Numerical simulation of thermal radiation effect about optical dome in aerodynamic thermal environment,” Journal of Applied Optics. 33(4), 649–653 (2012).

12. H. Wang, S. Q. Chen, W. Zhang, F. Y. Dang, L. Ju, X. M. Xu, and Z. G. Fan, “Evaluating imaging quality of optical dome affected by aero-optical transmission effect and aero-thermal radiation effect,” Opt. Express 28(5), 6172–6187 (2020). [CrossRef]  

13. H. Wang, S. Q. Chen, H. J. Du, F. Y. Dang, L. Ju, Y. Ming, R. D. Zhang, X. T. Shi, J. Q. Yu, and Z. G. Fan, “Influence of altitude on aero-optic imaging quality degradation of the hemispherical optical dome,” Appl. Opt. 58(2), 274–282 (2019). [CrossRef]  

14. L. Luo, H. Xia, J. S. Liu, J. L. Jia, and W. K. Xie, “Cellular automata ray tracing in two-dimensional aero-optical flow fields,” Acta Phys. Sin. 69(19), 194201 (2020). [CrossRef]  

15. L. Luo, J. Liu, J. Fei, J. L. Fei, H. Xia, and W. K. Xie, “Cellular automata ray tracing in flow field near the optical window of the optical dome,” Results Phys. 25(8), 104319 (2021). [CrossRef]  

16. L. Ju, Z. G. Fan, B. Liu, M. Yue, X. T. Shi, and X. S. Li, “Time characteristics of the imaging quality degradation caused by aero-optical effects under hypersonic conditions,” IEEE Photonics J. 14(5), 1–9 (2022). [CrossRef]  

17. H. Yuan, X. R. Wang, B. T. Guo, D. Ren, W. G. Zhang, and K. Li, “Performance analysis of the infrared imaging system for aircraft plume detection from geostationary orbit,” Appl. Opt. 58(7), 1691–1698 (2019). [CrossRef]  

18. Y. T. Qiao, “The solution of the ray-path differential equation in the axial gradient-index media,” Acta Optica Sinica. 4(1), 89–92 (1984).

19. H. Yuan, X. R. Wang, Y. Yuan, K. Li, C. Zhang, and Z. S. Zhao, “Space-based full chain multi-spectral imaging features accurate prediction and analysis for aircraft plume under sea/cloud background,” Opt. Express 27(18), 26027–26043 (2019). [CrossRef]  

20. H. L. Zhu, Y. J. Li, T. L. Hu, and P. Rao, “Key parameters design of an aerial target detection system on a space-based platform,” Opt. Eng. 57(02), 1–10 (2018). [CrossRef]  

21. X. Y. Ni, S. T. Yu, X. F. Su, and F. S. Chen, “Detection spectrum optimization of stealth aircraft targets from a space-based infrared platform,” Opt. Quantum Electron. 54(3), 151 (2022). [CrossRef]  

22. H. B. Fan, L. Tang, and S. C. Pan, “A design of standard 4 bars target for IR imaging simulator,” Infrared Technology. 29(7), 386–388 (2007).

23. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. on Image Process. 13(4), 600–612 (2004). [CrossRef]  

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (11)
Fig. 1.
Fig. 1. Imaging process of an infrared imaging system under an aerodynamic thermal environment.

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Fig. 2.
Fig. 2. (a) High-dimensional light field represented by a ray array; (b) Transmission process of light field vector in fluid-solid-thermal coupling medium.

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Fig. 3.
Fig. 3. (a) CA space generation using CFD data and measured data; (b) 3D cell with its 3D Moore-type neighbors; (c) Ray tracing calculation using CA properties; (d) The solution at the fluid-solid boundary.

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Fig. 4.
Fig. 4. The overall calculation process for aero-optical and aero-thermal radiation effects.

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Fig. 5.
Fig. 5. The aero-optical and aero-thermal radiation effects calculation results coupled with the optical system and imaging sensor array. (a) Calculating radiant flux; (b) Calculating PSF.

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Fig. 6.
Fig. 6. Comparison between ray tracing results and analytical results in a medium with gradient refractive index. (a) Comparison between tracing path and ideal path; (b) Computation error results under different cellular sizes and tracing step lengths.

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Fig. 7.
Fig. 7. Radiation content of the shock layer and optical window in different spectral bands at 10 km altitude. (a) optical window 1; (b) optical window 2.

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Fig. 8.
Fig. 8. The spectral radiation characteristics of optical window 2 under different flight speed. (a) spectral radiance in 3500∼3850 cm-1; (b) spectral radiance in 2200∼2400 cm-1; (c) spectral radiance in 800∼1250 cm-1; (d) spectral radiance in 2300∼3300 cm-1.

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Fig. 9.
Fig. 9. The full-chain imaging simulation process under aerodynamic thermal environments.

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Fig. 10.
Fig. 10. (a) The spectral radiation of the original standard 4 bars target at 2200∼2400 cm-1; (b) The imaging simulation results at 2200∼2400 cm-1; (c) The spectral radiation of the original standard 4 bars target at 3500∼3850 cm-1;(d) The imaging simulation results at 3500∼3850 cm-1.

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Fig. 11.
Fig. 11. Original image (a) and simulation results after adding aero-optical and aero-thermal radiation effects; (b) 3 Ma; (c) 4 Ma; (d) 5 Ma.

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Tables (6)

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Table 1. The computation results under different tracing step lengths

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Table 2. The simulation parameters

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Table 3. Simulation parameters of standard 4 bars target scene

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Table 4. Evaluation results at a saturation threshold of 1.5×max(Eint)

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Table 5. Evaluation results at a saturation threshold of 5×max(Eint)

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Table 6. Simulation parameters of actual scene

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Equations (13)

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d d s ( n ( s ) d r d s ) = ∇ n ( s )
d L ν ( s ) d s = k ν ( s ) ⋅ ( j ν k ν ( s ) − L ν ( s ) )
d L ν ( s ) d s = k ν ( s ) ⋅ ( L b ν ( s ) − L ν ( s ) )
{ L ν ( s 1 ) = L ν ( s 0 ) exp ⁡ [ − τ ν ( s 0 , s 1 ) ] + ∫ s 0 s 1 k ν ( s ) L b ν ( s ) exp ⁡ [ − τ ν ( s , s 1 ) ] d s τ ν ( s 0 , s 1 ) = ∫ s 0 s 1 k ν ( s ) d s
{ L i n ( r i n , D i n , λ ) F ( x , y , z , n λ , k λ , T ) f i n = ∑ i f i n _ i ( s ∈ S i ) , B R D F ( f i n ) f o u t = ∑ i f o u t _ i ( s ∈ S i ) , B R D F ( f o u t ) d d s ( n ( s ) d r d s ) = ∇ n ( s ) d L ν ( s ) d s = k ν ( s ) ⋅ ( L b ν ( s ) − L ν ( s ) ) , ν = 1 / λ
{ r i + 1 = r i + h 6 ( K 1 + K 2 + K 3 + K 4 ) T i + 1 = T i + h 6 ( L 1 + L 2 + L 3 + L 4 ) K 1 = T i , L 1 = n ( r i ) ∇ n ( r i ) K 2 = T i + h L 1 / 2 , L 2 = n ( r 1 ) ∇ n ( r 1 ) K 3 = T i + h L 2 / 2 , L 3 = n ( r 2 ) ∇ n ( r 2 ) K 4 = T i + h L 3 , L 4 = n ( r 3 ) ∇ n ( r 3 ) d n ( r ) d l = n ( C A ( r ) l + 1 ) − n ( C A ( r ) l − 1 ) 2 h C A , l , ( l = x , y , z ) n ( r ) = ∑ m w m n ( C A ( r ) m ) , w C A , m ∝ 1 / n o r m ( r − P o s ( C A ( r ) m ) )
{ r 1 = r i + h K 1 / 2 r 2 = r i + h K 2 / 2 r 3 = r i + h K 3
P s , i ( λ ) = ∫ φ 1 φ 2 ∫ θ 1 θ 2 L s , i ( θ , φ , λ ) Δ A s , i ( θ , φ ) sin ⁡ θ d θ d φ
P m , n , i ( λ ) = ∑ i τ o p t ( λ ) P s , i ( λ ) | P s , i ( λ ) ∈ D e t ( m , n )
{ P det ( λ ) = τ a ( λ ) τ o p t ( λ ) P I n ( λ ) ∗ P S F a , λ + P a ( λ ) U det = ∫ λ P det ( λ ) R v ( λ ) d λ + U n G = { G min , U det < U min U det − U min U max − U min × ( G max − G min ) + G min , U min ≤ U det ≤ U max G max , U min < U det
n ( z ) = n ( 0 ) ( 1 − β 2 z 2 ) 1 / 2
S C R = G ¯ T − G ¯ B σ B
S S I M ( G a , G b ) = [ l ( G a , G b ) ] α [ c ( G a , G b ) ] β [ s ( G a , G b ) ] γ
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