Basic geometry and aberration characteristics of conicoidal conformal domes.

ABSTRACT

This paper investigated the geometry and aberration characteristics of conicoidal conformal domes. First, on the basis of previous research, we got the expression that was suitable for describing the external surface of the conicoidal conformal dome. Based on the theory of differential geometry, this paper first proved that the Dupin index line of a quadric surface was an ellipsoid and the radius of curvature had extreme values in the meridian plane and sagittal plane. Then the uniform formulas of curvature which were suitable for ellipsoid, paraboloid, and hyperboloid were deduced in the meridian plane and sagittal plane, respectively. Meanwhile, the angle between the axis of imaging systems and the surface normal was calculated. With the help of computers, the plots of curvature differences and the angle in the case of different edge slopes, fineness ratios, and the locations of the rotational center were obtained. Finally, we analyzed the Zernike polynomial coefficients of Z4, Z5, and Z8, which represent defocus, astigmatism and coma, respectively for the model established in CODE V. The research indicates that the dynamic ranges of defocus, astigmatism, and coma increase with the growing of edge slopes and fineness ratios, but have little change with the variation of the rotational center positions. Moreover, the curves of Z5 and Z8 have turning points, and the curves of curvature differences and angle difference are only similar to the curves of Z5 and Z8 when the look angle changes after the turning point. For the look angle changing from zero to the turning point, the curves of Z5 and Z8 change rapidly. This is mainly caused by the significant variations of the symmetry of the conformal dome participating in imaging. Therefore, the aberrations with small scanning angles should be given more attention when designing the conformal systems.