The optics of ellipsoidal domes

Abstract

An ellipsoidal dome is a conformal optical element used to replace a hemispherical dome on a missile to enhance its performance by reducing its aerodynamic drag. Conformal optics are a general class of optical systems in which the optical elements are shaped to optimize something other than image quality, such as aerodynamics. An ellipsoidal dome has lower aerodynamic drag than a comparably sized hemispherical dome. On a missile, lower drag improves its aerodynamic performance by increasing its range and fuel efficiency but degrades the quality of the transmitted wavefront. In particular, an ellipsoidal dome introduces a varying aberration component that depends on the orientation of the aperture stop, which is pivoted about a fixed axis inside the dome. The transmitted ray bundle is incident only on a portion of the dome surface, and the included area lacks axial symmetry. To better understand the imaging characteristics of an ellipsoidal dome in this application, the first- and third-order optical properties of a constant thickness dome are investigated. Particular emphasis is placed on the geometry and symmetry of an ellipse, which impose certain constraints on the form of the aberration coefficients. The geometry is defined in terms of the aerodynamic fineness ratio, outer diameter, and center thickness of the dome. Emphasis is placed on third-order astigmatism and coma, which are shown to be the dominant aberration terms. The effects of varying the fineness ratio, thickness, and index of refraction of a dome are also investigated.