The underwater imaging sonar system with an acoustic lens is again receiving considerable attention because it does not require a complex beam-forming circuit. The lens system used in this type of sonar was designed by the ray theory or by a hybrid method of the ray and wave theories. In this report, a basic analysis was performed by an analytical method using a wave theory and by a numerical method using the parabolic equation (PE) method, to determine the convergent characteristics of a biconcave lens. The pressure field focused by the biconcave lens was measured in a water tank. The biconcave lens used in the experiment is made of acrylic resin with a radius of 20 cm and a radius of curvature of 20 cm. Measurements was conducted in a water tank at a frequency of 500 kHz. Sound pressure fields around the focal region measured by the experiments agreed well with the calculated ones by the analytical and PE methods.
The underwater sonar system using an acoustic lens is receiving attention again because it does not need a complex electrical circuit and exhibits reduced volume and cost. However, in our former experiments, singlet spherical or aspherical lenses could not concentrate sound at a focal point completely because of aberrations. In this study, we tried to design a lens that can remove spherical and coma aberrations in a paraxial area using a ray tracing method, and two types of lens were designed. One is a biconcave acoustic lens with the refractive index of n=0.56, which corresponds to an acrylic resin, and the other is a biconvex acoustic lens with n=1.5, which corresponds to a silicon rubber. These lenses are evaluated by comparing of their sound pressure fields with those of a spherical lens and a plano-concave elliptic lens as calculated by a two-dimensional finite difference time domain (2D-FDTD) method. As a result, the biconcave aplanatic lens shows the best performance among these four lenses.
We designed several shapes of aplanatic Fresnel acoustic lenses to correct spherical and coma aberrations. These lenses were made of room temperature vulcanizable (RTV) silicone rubber, and were designed by combining several aplanatic lenses. The converged sound pressure fields of these lenses were calculated numerically with the two-dimensional finite difference time domain (2D FDTD) method. The focal sound pressures of these lenses were 8 -9 dB larger than those of aplanatic biconvex lenses. Comparing several aplanatic Fresnel lenses, the best convergence was achieved by the lens having the smoothest first surface. We assumed the reason for this advantage was the smooth first surface itself. Thus to smooth the first surface and to enlarge the focal sound pressure, small steps on the first surface were removed by two methods. The first method approximates the first surface to a polynomial equation. The second method changes the curvature of the aplanatic lenses to minimize the small steps; this method is called bending. The evaluation of the lenses made by the two methods showed that the resolutions of these lenses were higher than 1 . The lens made by bending showed higher sound pressure than the lens made by the approximated surface.
A convex acoustic lens using room temperature vulcanizing (RTV) silicone rubber, whose acoustic impedance is similar to that of water, is a typical acoustic lens. A phase-continuous Fresnel lens was proposed to thin the shape of the lens because a convex acoustic lens has large attenuation due to its thickness. However, a Fresnel lens based on a convex spherical acoustic lens could not concentrate sound pressure completely on the focal point because of a spherical aberration. We designed an aspherical Fresnel lens by ray theory to remove the spherical aberration. A two dimensional finite difference time domain (2-D FDTD) method was used to survey the sound pressure field focused by the acoustic lens under condition in which the angle of incidence and the aperture were varied. Results showed that the aspherical Fresnel lens can concentrate greater sound pressure than the spherical Fresnel lens at normal and small angles of incidence.
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