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Abstract
With the advent of the hypersonic era, diverse combat methods of hypersonic precision-guided weapons have been gradually developed. This study focuses on the precise design of a conformal infrared dome to accommodate different working conditions. To achieve this, an adaptive optimization technology for configuring conformal infrared domes is proposed, employing a multi-objective genetic algorithm. The technology enables the dome to dynamically balance its aerodynamic and imaging performance, taking into account the specific characteristics of each working condition. Moreover, it streamlines the design process of the conformal infrared domes. By optimizing the design with von Karman surfaces, we can overcome the limitations associated with the traditional quadric configuration. In order to evaluate its performance, a comparison was made with a conventional ellipsoid dome. The results indicate that, under the same working conditions, the air drag coefficient of the optimized infrared dome is reduced by 34.29% and that the peak signal-to-noise ratio of the distorted image from the infrared detection system is increased by 1.7%. We have demonstrated the effectiveness of the optimization method to balance aerodynamic performance and optical performance. Hopefully, our new method will improve the comprehensive performance of the infrared dome as well as the guidance capability of infrared detection technology.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Infrared detection technology offers excellent features such as high-precision guidance, all-weather functionality, and strong resistance to interference. It has been widely recognized as the primary method for achieving precise guidance under hypersonic conditions [1,2]. The infrared detection system, particularly the infrared dome, plays a central role in hypersonic infrared precision guidance systems. Serving as a crucial optical component, the dome is installed at the front end of the infrared detection system. Its interior houses the imaging detection system, comprising an optical system, and a detector [3,4]. An optimal infrared dome should simultaneously exhibit favorable aerodynamics, optics, aerothermal properties, and aero-optics [5,6]. The design of such a dome not only affects the imaging quality and guidance accuracy of the infrared detection system but also impacts its speed, range, and maneuverability. Therefore, the key to advancing hypersonic infrared precision guidance technology lies in obtaining an infrared dome with superior comprehensive performance, which can enhance the overall combat capability of the infrared detection system.
Currently, conformal design is the predominant approach for optical dome design in a hypersonic environment. The conformal infrared dome substantially reduces the air drag coefficient of the infrared detection system, thereby improving its aerodynamic performance [7]. However, the conformal optical dome introduces different dynamic aberrations, thereby diminishing the imaging quality of the infrared detection system [8]. Additionally, the hypersonic flight induces aero-optical effects, further degrading the imaging quality of the infrared detection system [9,10]. The aforementioned statement suggests that the enhancement of the aerodynamic performance of the conformal infrared dome comes at the expense of its imaging detection capabilities. Simultaneous significant improvements in both aspects of the optical dome’s performance are not feasible. Presently, research on the design of conformal optical dome configurations is primarily based on fixed surfaces, such as ellipsoidal, quadric, tangent pointed arch, von Karman, and other domes. The fixed design approach for conformal optical domes achieves outstanding performance in a specific working environment. Among these configurations, the ellipsoid design is the most widely adopted and well-established for conformal infrared domes [7]. The ellipsoid dome is specifically designed to ensure optimal imaging detection performance, albeit at the cost of compromised aerodynamic performance improvement [6]. Consequently, it is most suitable for combat environments with low mobility requirements. Conversely, numerous infrared domes with pointed arch configurations are engineered to enhance the aerodynamic performance of the infrared detection system. Notably, the American OPTIMAX Company and the American SURMET Company design and manufacture conformal infrared domes that prioritize aerodynamics, such as pointed arch configurations [11,12]. However, these designs neglect the degradation of imaging detection performance, limiting their suitability to operations with high penetration requirements, often necessitating higher demands for internal detection systems [13,14]. As mentioned earlier, the current design technology for conformal infrared domes primarily focuses on a single characteristic, lacking comprehensive consideration of both aerodynamic and imaging performance. Additionally, the fixed design approach fails to accommodate diverse and evolving working environments. Consequently, when the working environment changes, a separate redesign of the conformal dome configuration is necessary for each specific characteristic, resulting in a complex and time-consuming process.
In recent years, hypersonic precision guidance technology has been gradually improved in various countries. The combat environment and methods of hypersonic infrared detection systems have also gradually diversified. Clearly, a conformal dome with a single performance consideration fails to meet the needs of modern warfare. The application of the fixed conformal infrared dome scheme has strong limitations, and it is only suitable for certain types of combat conditions, given the contradiction between infrared detection performance and aerodynamic performance. Achieving accurate alignment of the conformal infrared dome is crucial for ensuring precise guidance of the infrared detection system across different operational scenarios. However, the design process for a conformal infrared detection system is challenging. The existing fixed method for designing conformal infrared domes entails laborious and time-consuming efforts to accurately address each specific combat condition individually. Consequently, in order to adapt to the evolving landscape of diverse hypersonic flight platforms and effectively enhance the infrared dome’s overall combat capabilities in modern warfare, it is imperative to explore new approaches. The adaptive optimization technology of the conformal infrared dome is essential because it can simplify the design process of the conformal infrared dome, and the technology also achieves an adaptive balance of imaging detection performance and aerodynamic performance.
The von Karman curve is a fluid dynamics concept. It helps reduce the air resistance and the impact of the load efficiently. A conformal infrared dome configuration tends to be more suitable for hypersonic applications. D Feng et al. proposed a novel wave rider generated from axisymmetric supersonic flows past a pointed von Karman ogive. This device possessed higher lift-to-drag ratios, smaller trim drag, and larger internal volume than the conventional wave rider [15]. In recent years, the von Karman surface has been successfully employed in the design of domes. For instance, Zhao Rui et al. investigated the factors affecting the pulsating pressure environment on the outer wall of the von Karman domes. Xiaoqiang Fan et al. examined the fluid velocity and pressure of the external fluid of the von Karman domes [16]. Lin JU et al. studied the dynamic aberration characteristics of the von Karman infrared domes and put forward a preliminary correction scheme [8,17]. Furthermore, Lin JU and colleagues put forward an imaging prediction model for infrared detection systems operating in hypersonic environments. They conducted extensive research investigating the influence of aerodynamic optical effects on both urban and rural areas [5,10]. Arguably, most of the existing works on the von Karman domes have focused on aerodynamics, with limited research on the application of von Karman to infrared domes. The existing research on the von Karman infrared dome is aimed at the imaging characteristics of the dome itself. It does not consider the influence of aero-optical effects on imaging in the hypersonic flight environment. Moreover, it ignores its aerodynamic characteristics. Nevertheless, the most important application of the von Karman surface is under hypersonic conditions, given its aerodynamic advantages. Therefore, it is imperative to investigate the conformal dome optimization technique, which can comprehensively take care of the imaging degradation and the aerodynamic performance of the von Karman conformal infrared dome under hypersonic conditions.
In this paper, we proposed an adaptive optimization technology for infrared dome configuration based on a multi-objective genetic algorithm. The von Karman surfaces have been applied to optimize conformal infrared domes. Firstly, we established the evaluation model of the aerodynamic performance and assessed the imaging performance of the conformal infrared dome. We use the air drag coefficient and peak heat flux as the aerodynamics evaluation indicators. Imaging evaluation indicators such as wave aberration, dot plot radius, and peak signal-to-noise ratio were utilized to assess the imaging characteristics of the von Karman infrared dome in hypersonic conditions. Subsequently, we introduced and developed a design model for a composite conformal infrared dome. To derive optimized parameters, we employed a parameterized composite conformal dome. Finally, we explored the correlation between optimization parameters and objectives in the optimization process. We obtained the adaptive optimization scheme of the conformal infrared dome drawing on the multi-objective genetic algorithm. We further verified the effectiveness of the adaptive optimization technology by comparing it with the traditional ellipsoid dome having an aspect ratio of 1.5 under the same working conditions.
2. Performance evaluation model of the conformal infrared dome
In this paper, we propose the optimization technique considering both aerodynamic performance and optical performance to improve the performance of the conformal infrared dome comprehensively. We establish a conformal infrared dome aerodynamic performance and imaging performance evaluation model and clarify the optimization goal.
2.1 Aerodynamics characteristics of the conformal infrared dome
The aerodynamic performance of the conformal infrared dome is assessed based on the air drag coefficient and peak heat flux density. In scenarios where the working flight status and cross-sectional area of the conformal dome remain constant, the air drag coefficient is the sole determinant of its aerodynamic resistance [18]. Hence, the aerodynamic resistance coefficient of the dome serves as a direct indicator of its aerodynamic performance, making it a suitable evaluation criterion. A lower air drag coefficient indicates the superior aerodynamic performance of the conformal dome.
Moreover, the conformal dome is directly exposed to the hypersonic fluid environment, leading to significant aerodynamic heating [19]. Intense aerodynamic heating can destroy the infrared dome structure and cause aero-optical effects that degrade infrared dome imaging [5]. The heat flux density is a measure of heat transfer per unit area over a specific time period, representing the thermal exchange between the surrounding fluid and the dome. The elevated temperature experienced by the dome due to the external flow field results in a higher absolute value of the heat flux. Consequently, the peak heat flux density serves as an indicator of the aerodynamic performance. A lower peak heat flux signifies the superior aerodynamic performance of the optical dome.
2.1.1 Air drag coefficient
We can divide the aerodynamic resistance into two components, namely, the pressure resistance and the friction resistance. When the dome is flying at hypersonic speed, the head of the dome produces a high-pressure airflow caused by the shock layer, and the tail produces expansion waves due to the vortex, forming a low-pressure zone. A pressure difference is formed due to these pressure components acting on the dome. This leads to a force opposite the direction of the motion of the dome, which causes pressure resistance. In addition, the interaction between the shock layer and the boundary layer and the state of fluid separation also influence the pressure resistance. Frictional resistance refers to the tangential component of resistance resulting from the action of air viscosity on the surface of the dome. Its magnitude is strongly correlated with the state of the flow field boundary layer. The primary factor influencing frictional resistance is the velocity gradient of the boundary layer, with a turbulent boundary layer exhibiting a higher velocity gradient compared to a laminar boundary layer. Therefore, the frictional resistance on the surface of the turbulent layer tends to be relatively high. When a dome flies in a hypersonic flight state, the total aerodynamic resistance it receives can be expressed as [18],
where c0 represents the air drag coefficient, ρ ∞ represents the freestream density, V ∞ represents the freestream velocity, and S represents the cross-sectional area of the dome. If the working flight status and the cross-sectional area of the conformal dome are the same, only the air drag coefficient can influence its aerodynamic resistance. The smaller the air drag coefficient of the conformal dome is, the better its aerodynamic performance.2.1.2 Peak heat flux density
We cannot obtain the calculation of the heat flux density on the wall of the conformal infrared dome directly through its flow field calculation. The results obtained from the fluid domain calculation serve as a basis for conducting subsequent calculations on boundary layer heat transfer. In this study, we employ the axisymmetric comparison method to evaluate the three-dimensional boundary layer heat transfer of the conformal infrared dome. This method has demonstrated its effectiveness as one of the most efficient approaches for engineering computation.
We divide the calculation of the surface heat flux density of the conformal infrared dome into two parts, namely, the calculation of the heat flux density of the stagnation point and the heat flux density of the non-stagnation point area. The von Karman domes are pointed arches, and their peak heat flux density occurs at the stagnation point. There are many formats of the empirical formulas of stagnant heat flux density. They include the Fay-Riddell formula, the Kemp-Riddell formula, the modified Lees formula, the Cohen formula, the Sutton formula, and others. In this paper, we adopt the Fay-Riddell formula to calculate the stagnant heat flux density of the conformal infrared dome. The corresponding stagnation point heat flux density qwe can be expressed as [20–22],
2.2 Imaging characteristics of the conformal dome
For evaluating the imaging quality of an infrared detection system, we combined three parameters: dot plot radius, wave aberration, and peak signal-to-noise ratio (PSNR). The dot plot radius is a parameter that describes the inherent aberration characteristics caused by the conformal dome itself. A smaller dot plot radius value with a smoother transition indicates a reduced dynamic aberration introduced by the optical dome, resulting in improved imaging performance. Wave aberration and PSNR quantify the impact of aero-optical effects on image degradation. A smaller PV value of wave aberration at the exit pupil of the infrared detection system, accompanied by a gradual transition from the center to the edge, signifies higher imaging quality of the infrared detection system. Moreover, the received image demonstrates higher PSNR values with better imaging quality of the infrared detection system.
2.2.1 Dot plot radius on the imaging surface of the infrared detection system
We obtain a spot diagram on the imaging surface to analyze the aberrations introduced by the von Karman dome in the CODEV software. This is done by tracing the target light rays passing through the infrared dome to the imaging surface of its internal imaging system. We apply the root mean square radius (RMS) and geometric radius (GEO) of the dot plot as evaluation metrics to analyze the aberrations quantitatively induced by the von Karman dome [8].
2.2.2 Wave aberration at the exit pupil of the infrared detection system
In hypersonic conditions, the conformal dome is subject to aero-optical transmission effects, which consequently impact the quality of the acquired target image. To account for the influence of aero-optical transmission effects, the total optical path (OPL) was determined using the principles of ray tracing. The wave aberration, namely W j, of the exit pupil can be calculated as follows [10]:
2.2.3 PSNR of the target image
The conformal dome heated to a high temperature emits a large amount of infrared radiation under hypersonic conditions. Consequently, an aero-thermal radiation effect arises, wherein the stray infrared rays emitted by the von Karman dome are traced to determine the irradiance received by the infrared detector. We can obtain a distorted image of the infrared detection system using photoelectric conversion.
The evaluation of distorted image quality was conducted using the PSNR, which is widely recognized as a common and objective parameter for imaging assessment. The PSNR value is determined as follows: [10]
where M indicates the pixel number in the images, and MSE indicates the mean squared error in the images.3. Imaging characteristic analysis of the von Karman infrared dome
In this paper, we use the von Karman surface to determine the optimal configuration for the infrared dome foundation. The imaging and aerodynamic properties of the von Karman infrared dome infrared detection system were considered as the necessary theoretical foundation for optimization. However, the imaging results influenced by aero-optical effects under hypersonic conditions are often ignored by the existing research on the characteristics of the von Karman infrared dome. In the following, we present a complete prediction of the von Kamen infrared dome imaging in a hypersonic environment.
3.1 Dot plot radius on the imaging surface of the infrared detection system
Table 1 presents the configuration parameters for the von Karman dome and its imaging system. In order to attribute all aberrations in conformal optical systems solely to the conformal domes, an ideal lens is typically used to replace the internal imaging system. To capture high-resolution images of a wide range of targets, the internal imaging system adopts a scanning working method. Additionally, the position of the rotation center is characterized by the distance between the rotation center and the dome apex, denoted as x0. The entrance pupil diameter of the imaging system is represented by D0. The optical axis ray (OAR) is defined as the ray perpendicular to the aperture stop, passing through its center. The viewing angle is determined by the angle between the OAR and the symmetry axis of the conformal dome. The maximal viewing angle is defined as the FOR [8].
Table 1. The configuration parameters of the von Karman dome and its imaging system
Table 2. The boundary conditions of the hypersonic environment
In the design of the conformal infrared dome, the dome aspect ratio F is an important parameter. In Fig. 1 below, we show a plot of the point diagram formed by the light passing through the von Karman dome with different aspect ratios to the imaging surface under different viewing angles.
Fig. 1. The spot diagram of the imaging surface of the von Karman dome infrared detection system with different aspect ratios
At a viewing angle of 0°, a “vacuum” zone appears in the center of the spot diagram formed on the imaging surface of the imaging system inside the von Karman dome. We know that the light cannot reach the center of the imaging surface. This can be explained by the configuration of the sharp leading edge of the von Karman dome. It causes many central rays to be divided, and some of them are totally reflected. As a result, the rays cannot enter the imaging system to reach the center of the imaging surface. As the viewing angle increases, the spot diagrams on the imaging surface of the internal imaging system of the von Karman dome with different aspect ratios decrement in the meridian and arc deviance directions significantly. However, the change tends to be more prominent in the meridional direction. As the aspect ratio increases, the spot diagram formed on the imaging surface will gradually decrease in the meridional direction and increase in the arc-missing direction.
Figure 2 depicts the RMS and GEO of the dot plot as a function of the viewing angle. The point array obtained from imaging with the Von Karman dome exhibits significant changes when the scanning angle is below 15°, indicating the pronounced dynamic aberration introduced at smaller scanning angles. Correcting the aberration introduced by the Von Karman dome becomes challenging until the scanning angle of view reaches 15°. Hence, optimizing the Von Karman dome configuration for the small angle field of view becomes a focal point. Additionally, the maximum value and range of RMS and GEO of the dot plot, along with the aspect ratio of the Von Karman dome, increase.
Fig. 2. The RMS and GEO of Spot Diagrams of the von Karman Dome Imaging Systems with Different Aspect Ratios
3.2 Wave aberration at the exit pupil of the infrared detection system
In Fig. 3, we show the simulation for the wave aberration at the exit pupil of the von Karman dome infrared detection system under hypersonic conditions. This is achieved by employing the ray tracing principle [10]. Note that the boundary conditions are shown in Table 2. The aero-optical effect leads to large wavefront distortion. We know that the PV value of the von Karman infrared dome infrared detection system is much higher than that of the traditional spherical [10]. Moreover, as the aspect ratio of the von Karman dome increases, the wave aberration undergoes significant changes from the center position of the exit pupil to the edge position. Consequently, the PV value of the wave aberration will be higher.
Fig. 3. The wave aberration at the exit pupil of the von Karman dome infrared detection system with different aspect ratios. a. F = 1.0; b. F = 1.3; c. F = 1.7; d. F = 2.0
3.3 PSNR of the target image
The target image used in our study was the USAF1951 test card, as depicted in Fig. 4. In Fig. 5, we show the distorted images and the PSNR values of the von Karman dome infrared detection systems with different aspect ratios. We observe that the PSNR of the target image described by the von Karman dome infrared detection system with different aspect ratios seems to be slightly different. In the case of the dome aspect ratio F = 1.0 and F = 2.0, the image quality degradation turns out to be the most serious. This means that the design of the small or large aspect ratio may lead to a more serious aero-optical effect. Accordingly, it is important to focus on the design of the aspect ratio in designing a conformal infrared dome.
Fig. 5. The distorted images and its PSNR values of the von Karman dome infrared detection systems with different aspect ratios. a. F = 1.0; b. F = 1.3; c. F = 1.7; d. F = 2.0
4. Composite conformal infrared dome model
As is shown in the previous research, the aberration induced by the ellipsoidal dome is within the correctable range. This arguably ensures the image quality. The blunt surface shape significantly increases the missile resistance during the flight to reduce the aerodynamic performance. The aerodynamic performance of the missile is improved by the scan of the von Kaman conformal dome significantly. In contrast, the sharp front-end structure introduces large dynamic aberrations in a small angle viewing field [7,17]. It is difficult to correct the introduced aberration of the von Kaman conformal dome using current correction technology. In this study, we focus on the von Karman dome as the subject of our research. Our objective is to propose a method that involves replacing a section of the von Karman surface, specifically the portion responsible for imaging under a small angle view field, with an ellipsoidal surface. By combining the advantages of both shapes, we aim to optimize the conformal dome configuration. Additionally, we systematically modify the conformal dome configuration by adjusting the composite parameters. As a result, the aerodynamics and imaging performance are changing accordingly.
By the composite method, we obtain the composite conformal dome. In Fig. 6, we show the parametric diagram of the composite dome. The green part here is the composite surface. We can define the original diameter of the dome’s bottom as D and the distance from the top of the dome to the ground as the dome length L. The length of the replaced von Karman surface is represented by the replacement length L v, the composite surface length is represented by the composite length L c, and the composite position diameter is represented by the composite interface diameter D c. The angle between the tangent of the composite position and the x-axis is represented by $\gamma $.
The initial configuration, prior to optimization, corresponds to the von Karman dome. The configuration of the conformal infrared dome based on the von Karman design can be represented as:
where $\varphi = arccos\left( {1 - \frac{{2x}}{L}} \right).$The mathematical expression for the basic shape of the dome von Kaman surface is fv(x), which can be expressed as follows:
The mathematical expression for the spliced surface is f c(x), which is given by the following:
Thequantity S e is the edge slope of the composite position which can be given as follows:
The two surfaces based on the principle of equal tangent slopes at the joining position are determined by the following equations:
This condition determines the basic von Karman dome surface, and the composite surface expression can be expressed as:
Some parameters could influence the configuration of the composite conformal dome. They include a basic surface length of the dome L, bottom diameter D, replacement length L v, and composite length L c. The aspect ratio is often the design parameter in the dome shape design. Hence, the formulation of the optimized parameters of the composite conformal dome involves the basic surface aspect ratio ${F_v} = L/D$, the composite surface aspect ratio ${F_c} = {L_c}/{D_c}$, and the composite surface length L v. In Fig. 7, we show the schematic diagram of the influence of optimized parameters on the shape of the dome. The larger the F v and F c are, the sharper the tip of the composite conformal infrared dome is. Moreover, the larger the Lv is, the smoother the front end of the composite conformal dome becomes.
Fig. 7. The schematic diagram of the influence of designed parameters on the shape of the dome. a. The influence of Fv; b. The influence of Fc; c. The influence of Lv
5. Adaptive optimization technology based on genetic algorithm
Here, we use the multi-objective genetic algorithm to realize the self-adaptive optimization technology. The genetic algorithm is a powerful parallel global randomized search method used to solve problems that lies at the convergence of life sciences and engineering sciences. Furthermore, it forms a random iteration and evolution based on natural selection and population genetics. The genetic algorithm is a versatile search method that employs adaptive control of the search process to discover optimal solutions. It operates by iteratively combining characteristics from a set of input vectors known as individuals, with the goal of achieving convergence by progressively enhancing the traits of the top-performing individuals [18].
It is essential to ascertain the relationship between the design parameters and the optimization objective to obtain the fitness of the genetic algorithm. We have analyzed the aerodynamic performance and imaging performance of the composite conformal infrared dome with different design parameters. Tables 2 and 3 show the hypersonic boundary conditions and infrared detection system parameters of the composite conformal infrared dome in our simulations.
Table 3. The infrared detection system parameters of the composite conformal infrared dome
5.1 Influence of optimization parameters on the aerodynamic performance of conformal infrared dome
Fluent ANSYS is a widely acknowledged software for fluid dynamics simulation. In this study, we utilized this software to conduct simulations on the aerodynamic performance of the optical dome.
5.1.1 Air drag coefficient
The designing parameters F v, F c, and L v change separately, while other parameters are unchanged. In Fig. 8 below, we show the effect of the designed parameters on the aerodynamic drag coefficient. We observe that the aerodynamic drag coefficient decreases when the designed parameters F v and F c increase, but it increases along with L v. Moreover, the designed parameter F v has the most significant impact on the aerodynamic drag coefficient. This is followed by the parameter L v, and then F c.
Fig. 8. The effect of the designed parameters on the drag coefficient, a. The influence of Fv, b. The influence of Fc; c. The influence of Lv
5.1.2 Peak heat flux density
Changes in the designed parameters F v, F c, and L v simulate the heat flux density of the dome while other conditions remain unchanged. Figure 9 depicts the effect on the peak heat flow. In terms of heat flow distribution, a sharper dome design results in a more concentrated high heat flux at the front end. Consequently, this leads to an increase in the peak heat flux. Moreover, the heat flux increases along with the designed parameters F v and F c from the perspective of peak heat flow, and it decreases when L v increments. The designed parameters F v and L v have a greater impact on the heat flux density, whereas the quantity F c has little impact on it.
Fig. 9. The result of the effect on the peak heat flow, a. The influence of Fv, b. The influence of Fc; c. The influence of Lv
5.2 Influence of optimization parameters on imaging characteristics of conformal infrared domes
5.2.1 Dot plot radius on the imaging surface of the infrared detection system
When other parameters are unchanged, separately changing Fv, Fc, and Lv give rise to the RMS and GEO of the spot diagram on the imaging surface for the typical parameter dome under different viewing angles. This is shown in Fig. 10. Our findings indicate that modifying the designed parameters directly affects the peak values of RMS and GEO, which, in turn, reflect the impact on the imaging quality of the dome. It has been observed that smaller RSM and GEO peaks correspond to superior overall imaging quality of the dome. Besides, the designed parameters have a relatively strong influence on the GEO in the spot diagram for the imaging surface. Consequently, the GEO peak value selection follows the single evaluation criterion for aberration induced by the dome. The designed parameter Fc has a significant impact on the RMS and GEO of the spot diagram, whereas the two quantities Fv and Lv show a relatively small impact on it.
Fig. 10. The spot diagram on the imaging surface of the typical parameter dome under different viewing angles, a. Influence on the RMS of spot diagram; b. Influence on the GEO of the spot diagram
5.2.2 Wave aberration at the exit pupil of the infrared detection system
When other parameters are unchanged, changing Fv, Fc, and Lv separately leads to the PV value of wave aberration at the exit pupil of the composite dome infrared detection system. This is shown in Fig. 11. We observe that the PV value increases along with the designed parameters F v and F c. It decreases when L v increases. Moreover, the designed parameters F v and Fc show a significant impact on the PV value of wave aberration.
Fig. 11. The effect of the designed parameters on the PSNR of the target image, a. The influence of Fv, b. The influence of Fc; c. The influence of Lv
5.2.3 PSNR of the target image
When other conditions are unchanged, a change in the designed parameters, F v, F c, and L v, simulates the PSNR of the target image. This is shown in Fig. 12. The influence of F v and L v on PSNR first increases and then decreases. It has a great impact on the heat flux density, while the quantity F c has little influence on it. The choice of Fv should be between 1.4 and 1.8 in the design of composite parameters. The LV value should be smaller than 35 mm.
Fig. 12. The result of the effect on the peak heat flow, a. The influence of Fv, b. The influence of Fc; c. The influence of Lv
5.3 Adaptive scheme based on multi-objective genetic algorithm
We also clarify the influence of design parameters on the aerodynamic and optical characteristics of the conformal infrared dome. Here, we apply the genetic algorithm to determine the designed parameters following the influence law and obtain the best conformal infrared dome configuration.
To configure the dome, a multi-objective genetic algorithm is employed, which considers multiple objectives simultaneously. The determination of the optimal shape configuration solution relies on assigning relative weights to each configuration objective. The set of Pareto-optimal solutions obtained through the multi-objective genetic algorithm represents the optimal trade-offs between the objectives. From this set, we select the best Pareto-optimal solution by assigning appropriate weights across all conditions. As is known, each Pareto-optimal solution is optimal for the assigned weights to all objectives. Nevertheless, it is not necessarily the optimal solution for the objectives under all weighted conditions. In Fig. 13, we show a schematic diagram of the concerned configuration process here.
We analyzed the target values for the dome shape and compared them to each other. Here, the minimization of all objective values is desirable. Every objective value in each generation of solutions is meant for sorting each target value from the best to the worst. As is known, the lowest objective value is considered the best. We plot all objective values on a separate axis forming the Pareto front. We adjust the relative weights of the optimization goal and change the objective function to derive different optimal solutions. We combine these solutions to generate the Pareto-optimal front. Natural selection is carried out following evaluation. We sort the target dome from most back toward least fit. The fittest half of the data “survives” has a chance to reproduce and influence the next generation in the multi-objective genetic algorithm. We finally discard the rest of the curves.
6. Shape configuration method based on the genetic algorithm
As an illustration, we can utilize the provided operational boundary conditions from Table 2 to employ the proposed optimization method and identify the optimal conformal optical dome for a combat environment. Through simulations, we have evaluated the aerodynamic and imaging performance of the optimized optical dome under identical combat conditions, comparing it with the ellipsoidal fairing.
Based on our comments in Section 5, the designed parameters impact the aerodynamic drag coefficient and the GEO of the point map on the imaging surface significantly, but they have a relatively small impact on the heat flux density. Considering the typical operating conditions of air-to-air vehicles on hypersonic flight platforms, where the work environment is primarily focused on rapid penetration. We find that the weight of the optimization objective of aerodynamic performance and imaging detection performance turns out to be 3:2. We design the parameters as F v = 1.71, F c = 0.76, and L v = 26.26 mm. In Fig. 14, we show the 3D configuration of the optimized dome.
In Fig. 15, we show the heat flux distribution of the dome after configuration. We observe that the peak value of heat flux distribution is 8.56 × 10−5, which corresponds to an air drag coefficient of 0.2721. We show in Fig. 16 the percentage reduction in the air drag coefficient of the optimized dome compared with elliptical domes having different aspect ratios. In comparison to oval domes with various aspect ratios, the designed dome demonstrates a substantial decrease in the aerodynamic drag coefficient. The reduction ranges from a maximum of 69.8% to a minimum of 24%. Furthermore, when compared to the conventional ellipsoid dome, our configuration method markedly enhances the aerodynamic performance of the conformal dome. Compared with the most widely used ellipsoid dome with an aspect ratio of 1.5, we are able to reduce the air resistance coefficient of the conformal infrared dome by 34.29% after design.
Fig. 16. The percentage reduction in the air drag coefficient of the optimized dome compared to elliptical domes with different aspect ratios
In Fig. 17, we show the simulation results for the RMS and GEO of the spot diagram on the imaging surface of the conformal infrared dome after design, the traditional ellipsoidal dome, and the von Karman dome. We observe that the geometric aberrations of the designed infrared dome seem to be reduced at all viewing angles compared with the von Karman dome. We find that the RMS and GEO peaks of the imaging plane spotgrams are reduced by 55.9% at the highest. Moreover, the RMS and GEO of the imaging plane spotograms evolve more gently with the viewing angle. Nevertheless, compared with the traditional ellipsoid dome with good imaging quality, the geometric aberration induced by the infrared dome after design still significantly changes with the viewing angle. This indicates that the shape composite design method can correct the dynamic aberration induced by the von Karman curved dome preliminarily. However, it fails to meet the standard of the traditional ellipsoid dome.
Furthermore, we have considered the effect of aero-optics on the degradation of conformal infrared dome imaging. Considering the hypersonic environment, we show in Fig. 18 the wave aberration at the exit pupil of the infrared detection system after it is affected by the aero-optical effect. Compared with the wave aberration at the exit pupil of the traditional ellipsoid dome infrared detection system, there is still some small gap. The current technology has been able to correct the imaging of the infrared detection system of the ellipsoid dome, and it has also been put into application. Accordingly, it is possible to further correct the aberration of the infrared dome after design.
Fig. 18. The wave aberration at the exit pupil of the infrared detection system, a. The Optimized dome, b. Ellipsoid dome; c. Von Karman dome
Figure 4 displays the original image utilized for testing purposes. In Fig. 19, we present the resulting distorted image obtained from the infrared detection system, along with its corresponding PSNR. Our observations indicate that the image quality received by the infrared detection system, following the design process, exhibits an improvement of approximately 10% compared to the undesigned von Karman dome infrared detection system. Furthermore, it demonstrates a 1.7% enhancement compared to the infrared detection system with an elliptical dome.
Fig. 19. The distorted images of the ellipsoid, von Karman, and the designed infrared dome are shown as follows: a) the optimized dome, b) the ellipsoid dome, and c) the von Karman dome.
We have found that the designed dome improves aerodynamic performance without compromising optical performance compared to the ellipsoidal dome. In contrast, compared to the undesigned von Karman dome, the designed dome significantly enhances optical performance while retaining its high aerodynamic performance. These findings demonstrate that our adaptive technology effectively balances the aerodynamic and optical performance of the conformal infrared dome, resulting in an optical dome with superior overall performance and enhanced adaptability to the working environment.
Another notable feature of this optimization scheme is its ability to optimize the configuration of the conformal optical dome based on different working conditions and characteristics. To illustrate the adaptability of our optimization method to the working environment, we conducted an optimization of the conformal optical fairing for an alternative working condition. The flight conditions of this new working environment are the same as those of working condition 1, but the primary objective is high-precision tracking. As a result, the weight assigned to the optimization targets of aerodynamic performance and imaging detection performance is set to a ratio of 2:3. The analysis results of the optimized fairing’s aerodynamic performance and imaging capability are presented in Fig. 20. We observe that the peak value of heat flux distribution is 7.79 × 10−5, corresponding to an air drag coefficient of 0.3152. In comparison to the optimized conformal dome under condition 1, the newly optimized conformal dome exhibits lower geometric aberration peaks with smoother changes as the viewing angle varies. Additionally, the PV value of the wave phase difference is reduced, while the PSNR value of the acquired target is improved. In response to the new working environment, the aerodynamic performance of the newly optimized conformal dome is slightly compromised, while the imaging capability is strengthened. These comparisons demonstrate that when the working environment changes, we can obtain conformal optical domes with different combinations of aerodynamic performance and imaging capability tailored to the specific working characteristics.
Fig. 20. The analysis results of the aerodynamics and imaging performance of the optimized conformal dome under the second typical operating environment are presented as follows: a) the heat flux distribution of the configured dome, b) and c) the geometric aberration results of the designed dome, d) the wave aberration at the exit pupil of the infrared detection system, and e) the distorted image comparison between the ellipsoidal, von Karman, and designed infrared domes.
In conclusion, our proposed adaptive technology enables the achievement of a conformal optical dome configuration that effectively balances aerodynamics and optical performance under varying operating conditions. The optimized conformal dome exhibits superior overall performance and proves to be better suited for the given operating conditions.
7. Conclusion
In conclusion, we have formulated an evaluation model to assess the imaging and aerodynamic performance of a conformal infrared dome under hypersonic conditions. By conducting measurements under hypersonic conditions, we examined the imaging characteristics of the von Karman infrared dome. The presence of a sharp leading edge in the von Karman configuration resulted in notable degradation of imaging quality. Even the “vacuum” position, which infrared rays cannot reach, would appear as the small field angle. Under hypersonic conditions, the image quality of the infrared detection system in the von Karman dome is significantly degraded compared to that of the traditional spherical and ellipsoidal domes. Moreover, we find that the larger the aspect ratio of the von Karman infrared dome is, the larger the PV value of wave aberration at the exit pupil becomes. Accordingly, the more significant the change from center to edge becomes, the lower the peak signal-to-noise ratio of the received image turns out to be.
We have proposed the composite design scheme, and the von Karman surface has been applied to design the configuration of the hypersonic conformal infrared dome. Moreover, based on the genetic algorithm, we have realized the conformal infrared dome design technology, which can adaptively balance the aerodynamic and optical performance. Here, we have presented a design example. By comparing the infrared dome to a traditional ellipsoid dome with an aspect ratio of 1.5, we reduce the air resistance coefficient by 34.29% after design. By implementing this approach, the aerodynamic performance of the infrared dome can be significantly enhanced. Although the peak signal-to-noise ratio experiences only a marginal improvement in the hypersonic environment, the overall image quality from the infrared detection system of the designed dome does not exhibit a substantial decrease when influenced by the comprehensive aero-optical effect. These results illustrate the capability of the technology to dynamically balance the aerodynamic and imaging performance of a conformal infrared dome.
In summary, the conformal infrared dome adaptive technology proposed in this paper can effectively improve the aerodynamic performance of the conformal infrared dome. It ensures the imaging quality of its infrared detection system and improves the comprehensive performance of the infrared dome. We expect this technology may be first applied to hypersonic air-to-air guidance weapons to improve their combat capability comprehensively as well as the hypersonic diversified environment combat adaptability.
Acknowledgements
The authors wish to thank the anonymous reviewers for their valuable suggestions.
Disclosures
The authors declare there is no conflict of interest.
Data availability
The data presented in this study are available on request from the corresponding author.
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