**1. Introduction**

The interceptor mounted with inferred detector moves at speed of the supersonic, and an aerodynamic window will be formed at the face of the detector. Supersonic flows produce time- and position-dependent density fields, which directly lead to changes in optical properties dominated by the refractive index. When light passes through a field of varying refractive index, the initial optical path changes, causing distortions and phase errors in the light. This causes optical distortions such as blurring, shifting, jitter, loss of brightness, and loss of resolution. These image distortions

are often referred to as the aero-optical effect (AOE). The aberration will affect the image quality of the aeronautical optical sensor, seriously affect the guidance accuracy, and even cause the interceptor to fail. The study of the principle of aero-optical effects and the measurement of aero-optical aberrations are of great importance for the endo-atmospheric aircraft. Consequently, it is necessary to study the influence of the supersonic flow fields on optical propagation and imaging in order to acquire higher guidance accuracy. The research on the aero-optical transmission not only has theoretical merit, but also has important merits in the instruction of the optical system design and restoration of the turbulence-degraded images.

Unlike atmospheric optics, aero-optics is near-field optics [1], which includes turbulent boundary layers, wake layers, and shear layers. Sutton [2] carried out detailed studies of the fundamentals and applications of aero-optics. Aero-optics is a phenomenon of fluid-optic interactions. The refractive index of air and many other fluids is linearly related to the fluid's density through the Gladstone-Dale relationship. In general, supersonic flows are turbulent. Density fluctuations are the root cause of optical aberrations. Liepmann first studied the aero-optical effects on turbulence in 1952 [3]. After this, methods for simulating and measuring aero-optical effects have been widely developed, and research in aero-optics has a history of almost 60 years. However, there are many difficult problems in numerical modeling of aero-optical images based on computational simulation of flow fields and optic transmission, which can be used to adjust imaging sensors' measurement, predict potential distortion, and improve guidance accuracy. It is worth our attention that this effectively reduces experimental costs and helps guide wavefront sensor design in the field of adaptive optics. There is still a difficult problem in aero-optical research, and a lot of researchers around the world have fared better in such field.

In the 1990s, researchers improved dynamic measurement and analysis of aerooptical interactions to obtain wavefront phase variance, Strehl ratio, and optical transmission function (OTF) to compensate for images degraded by turbulence. Shack-Hartmann wavefront sensors [4] have been used to measure wavefront distortion for many years. The sensor frequency has recently reached 1Mz [5, 6], almost meeting the requirements of dynamic wavefront phase measurement. Jumper [4] provided a brief perspective on traditional approaches to measure and quantify aerialoptical interactions. Meanwhile, the theory of numerical analysis from aero-optics is integrated into the CFD codes. Sutton [3, 7–9] pointed out that the procedure of aerooptic, and he devoted efforts to aero-optical performance predictions and analyzed the effect of nonuniform turbulence on the point-spread function (PSF) for imaging through turbulent flow fields. Clark and Farris [10] employed CFD codes and wave optics to provide a numerical method for calculating the aero-optical performance of a hypersonic flow field. Lockheed Martin Aeronautics has published a CFD-based aerooptical analysis of unstable aerodynamic flow fields [11, 12] that has been successfully applied to programs such as ARROW, THAAD, and ENDO LEAP. Catrakis et al. [13] studied aero-optical interactions along the propagation path in shear layers of turbulent compressible separation through direct imaging experiments of refractive-index fields, and the amount and RMS values of the differences in the optical path of interaction, that are a function of the distance traveled in the direction of the beam and a function of the laser aperture size. Roberto et al. [14] described an experimental imaging technique in which the refractive index field and the propagation optical wavefront can be measured simultaneously and based on the results of quantitative image analysis of the refractive index field and the calculated optical wavefront. Frumker et al. [15] proposed a general method to calculate the average MTF flux for a

### *Perspective Chapter: Computational Modeling for Predicting the Optical Distortions… DOI: http://dx.doi.org/10.5772/intechopen.106591*

supersonic flying spherical dome using Code V and FLUENT. Monteiro and Jarem [16] studied the mutual interference function in the theory of strong fluctuations when light passes through a nonuniform layer of optical turbulence of gas, and deduced the point scattering function, optical transfer function, and related imaging equations. Michael [17] solved the Laplacian and Runge-Kutta integral parabolic beam equations along the beam path in aero-optics using higher-order compressed differentials. Zhang and Fan [18] and Wang et al. [19–21] used a grid-based model to study aero-thermal optical effect and aerodynamic optical effect near side-mounted optical windows. Juan and David et al. [22] performed a 1:1 scale validation study of a computational fluid dynamics-based aero-optics model in a wind tunnel experiment and found that the overall performance of the CFD-based predictive model was better. These studies facilitated the study of aero-optics. Numerical simulation of aero-optics propagation and imaging is an important topic in the experimental study of aero-optics physics in the wind conditioning process, and the two are considered complementary to each other.

This chapter makes use of the CFD grid model respectively with geometrical optics and information optics in order to describe a computation model of the light propagation through the supersonic flow field. The CFD grid model is thought of as the foundation of the computational simulation. The first method is based on geometrical optical so as to build up a ray tracing model for optic transmission through the supersonic flow fields. By tracking the ray path in the turbulent flow field, the wavefront aberrations can be calculated and the aero-optical performances were predicted. The algorithms in the cases of the normal incidence and the oblique incidence are worked out, and accurate ray tracing is done well. Provided data from CFD numerical simulations on certain conditions, the optical path differences (OPDs), wavefront phase variances, and the Strehl ratios used for measuring the effect of the high-speed flow fields on the optical intensity are calculated. In addition, the maximum offset angles of the line of sight (LOS) are figured out. The influences of the initial incident angle, the altitude, and the Mach number on the optical transmission through the high-speed flow fields are discussed. The results show the coincident with the prior knowledge on the characteristics of aero-optical phenomena. The second method integrates the CFD grid model with angular spectrum propagation model so as to study the aero-optical imaging through the supersonic flow fields directly. In this point of view, the aero-optical propagation is viewed as the optic angular spectrum of plane wave transmitting grid by grid, and the total optical transfer function of such flow fields can be derived and further digital image processing method is utilized to simulate the aero-optical imaging through supersonic flow fields. Finally, theoretical studies of the side-mounted IR window aero-optical imaging are made and figure out a way to model the imaging through the hypersonic flow fields.

Three kinds of computational simulation methods of aero-optics have been developed: One is to use the ray tracing method, which uses the wave delay phenomenon to measure the change in the direction of the light, but it cannot give the light deviation or the blurring of the uncertain image. One is physical optics, which predicts diffraction caused by interference between light waves; the other is wave optics, which calculates the transmission between wavefronts along the optical path and calculates the complex amplitude distribution on each wavefront. Aero-optics itself studies the interaction of light and fluids, and the application of optics theory is associated with numerical simulation methods of fluids. The density and other related data are obtained through the CFD method to simulate the flow field, and the refractive index field is calculated. Combining geometric optics theory and wave optics to

quantitatively study the occurrence of light wavefront through the flow field has always been the focus of aero-optics computational simulation research. The wavefront can accurately compensate for the imaging. In adaptive optics applications, such as the Shack-Hartmann wavefront sensor, the wavefront is directly measured and used to reconstruct the wavefront. The geometry of the turbulent degraded light wavefront accurate prediction of the structure is crucial for inferring and controlling the aero-optical phenomena existing in aerospace applications and assisting in the design of optical systems.

The arrangement of this chapter is described as follows. The first section is the introduction to research on the computational study of aero-optical transmission through supersonic flow fields. In Section 2, the computational fluid dynamics model is analyzed and the Gladstone-Dale relationship used for transforming the density fields into the refractive index fields is figured out. Then, the method based on geometrical optics used for modeling aero-optical transmission is illustrated in detail in Section 3. The corresponding computational results are also given out in Section 3. In Section 4, the method using the angular spectrum propagation model for studying the aero-optical imaging is shown and the simulation results are presented. In the end, the conclusions are described.
