1985 年 41 巻 5 号 p. 308-315
Since materials with a continuous variation of refraction index are not available for the construction of spherical Luneburg lens, the desired continuous variation of index with radius is approximated by a number of constant-index spherical layers. There are several methods for determining the index difference between adjacent layers and their radii. The common method for step-index division is to choose equal index increments in which the outer part of the lens is more precisely divided than the inner part but here most of the acoustic power passes the inner part of the lens. This paper describes a step-index method which equally distributes the acoustic power incident on the lens. A wave solution has been obtained for the acoustic field in spherical multi-layered lens. The relative pressure and the relative intensity were computed along the axis of the lens. The pressure focal point and the intensity focal point were obtained and they were used for the comparison of the focusing properties. In the case of 3, 4, and 6 layered lens, the focusing properties of the new lenses were compared with those of the Morgan lenses which have equal index increments. Although the focal points of pressure and intensity did not coincide for the equal-index-increment lens, they almost coincided for the new lens of 3 layers with K_0a 30-40 (k_0: wave number, a : radius of lens). It is shown that increasing the number of steps does not improve the focusing properties but choosing the thickness and the specific acoustic impedance of the outermost layer is effective in improving of the focusing properties of the multi-layered lens.