[pt] Esta dissertação tem por objetivo analisar, a partir da Teoria Geométrica da Difração, o efeito de espalhamento mútuo entre as superfícies refletoras no diagrama de irradiação de antenas Cassegrain. São apresentados resultados numéricos evidenciando todas as contribuições de campos difratados de até 3ª. ordem. / [en] It is the purpose of this dissertation to analyse, via the Geometrical theory of Diffraction, the effect of mutual scattering between reflector surfaces on the radiation pattern of Cassegrain antennas. Numerical results highlight the contributions of the complete set of up to 3(rd) order diffracted fields.

Focal plane corrected Cassegrain type optical systems have been widely used in various fields. The axial alignment of complex optical systems is not easy and a practical alignment method is needed for such systems. Tilts, decenters and axial motion of elements or group of elements in the system are the typical alignment parameters. Interferometric measurement is an effective way to see the errors caused by the misalignment of each element in an optical system. In this thesis, alignment of a Cassegrain type telescope will be examined by using interferometric measurements and modulation transfer function simulations.

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.