A theoretical investigation of acoustic wave interactions with turbulent premixed flames was performed. Such interactions affect the characteristic unsteadiness of combustion processes, e.g., combustion instabilities. The small perturbation method (SPM) was utilized to evaluate the scattered fields as a result of the flame-wave interaction at the instantaneous wrinkling surface of a randomly moving turbulent flame. Stochastic analysis of ensemble-averaged net acoustic energy was conducted to examine coherent and incoherent acoustic energy amplification /damping by the interaction. Net acoustic energy flux out of the flame is due to two factors: the acoustic velocity jump due to unsteady heat release from flame. The other is the flames unsteady motion. Five(5) dimensionless parameters that govern this net acoustic energy were determined: rms height and correlation length of flame front, incident wave frequency, the ratio of flames diffusion time to flame fronts correlation time, and incidence angle. The dependence of net acoustic energy upon these dimensionless parameters was illustrated and discussed by numerical simulations in case of Gaussian statistics of flame front. The laminar flame response to equivalence ratio perturbations was also examined, showing that the overall heat release response is controlled by the superposition of three disturbances: heat of reaction, flame speed, and flame area. Heat of reaction disturbances dominate the flame response at low Strouhal numbers, roughly defined as (frequency x flame length)/(axial flow velocity). All three disturbances play equal roles at Strouhal numbers of O(1). In addition, the mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio.

This dissertation focuses on the scattering phenomena by well-polished optical mirror surfaces. Specifically, predicting image degradation by surface scatter from rough mirror surfaces for a two-mirror telescope operating at extremely short wavelengths (9nm~30nm) is performed. To evaluate image quality, surface scatter is predicted from the surface metrology data and the point spread function in the presence of both surface scatter and aberrations is calculated. For predicting the scattering intensity distribution, both numerical and analytic methods are considered. Among the numerous analytic methods, the small perturbation method (classical Rayleigh-Rice surface scatter theory), the Kirchhoff approximation method (classical BeckmanKirchhoff surface scatter theory), and the generalized Harvey-Shack surface scatter theory are adopted. As a numerical method, the integral equation method (method of moments) known as a rigorous solution is discussed. Since the numerical method is computationally too intensive to obtain the scattering prediction directly for the two mirror telescope, it is used for validating the three analytic approximate methods in special cases. In our numerical comparison work, among the three approximate methods, the generalized Harvey-Shack model shows excellent agreement to the rigorous solution and it is used to predict surface scattering from the mirror surfaces. Regarding image degradation due to surface scatter in the presence of aberrations, it is shown that the composite point spread function is obtained in explicit form in terms of convolutions of the geometrical point spread function and scaled bidirectional scattering distribution functions of the individual surfaces of the imaging system. The approximations and assumptions in this iv formulation are discussed. The result is compared to the irradiance distribution obtained using commercial non-sequential ray tracing software for the case of a two-mirror telescope operating at the extreme ultra-violet wavelengths and the two results are virtually identical. Finally, the image degradation due to the surface scatter from the mirror surfaces and the aberration of the telescope is evaluated in terms of the fractional ensquared energy (for different wavelengths and field angles) which is commonly used as an image quality requirement on many NASA astronomy programs.