Low Acoustic Velocity Research Articles

Nearly Spherical Lenses

A unidirectional geometrically perfectly focusing lens can be made by shaping appropriately the interface between homogeneous lens media. For good geometric focusing over a wide angle, the lens should be as spherical as possible. A single component lens that focuses a perfect image of an object at infinity is a conic section of eccentricity 1/n, where n is the index of refraction of the lens material. The limitation on n due to the lack of transmissive materials with very low acoustic velocity requires that such a lens be quite aspherical. This difficulty is not inherent in multicomponent lenses. Perfectly focusing shapes have been determined for two-component lenses with spherical outer surface. The meridional and sagittal focusing properties of these lenses have been studied for obliquely situated objects. With a proper choice of lens parameters, the internal interface is not required to deviate from sphericity by more than about 2%, so that the attainment of a perfect geometric focus in the forward direction does not seriously degrade the imaging of objects situated at very wide angles.