Abstract
In the conventional pulse-echo method or acoustical holography, it is difficult to obtain high resolutions in lateral and longitudinal directions simultaneously. We have developed a new acoustic imaging method to improve both resolutions. This method is similar to holography but uses an impulsive sound. When a point source at a point P projects an impulsive sound p(t), the signal reflected from a point O at a object and received at Q is expressed by Eq. (1), where r_0 and r_i are the distances as shown in Fig. 1. These signals are recorded with a multi-channel data recorder and an image of the object is reconstructed with the aid of a computer. If a point O', coincides with O, the summed signal B expressed by Eq. (2) becomes maximum and is expressed by Eq. (3). Then we define that the magnitude of an image at a point O' is expressed by the rms value of B within the pulse duration. We can obtain an image of an object by calculating Eq. (4) at all points in space. In this paper, we have reconstructed an image in the x-z plane of a point source by calculating Eq. (4a). As shown in Fig. 2, a reconstructed image of a point source at O is expressed by Eq. (7) in acoustical acoustical holography. The lateral resolution is 0. 6λL/a as is well know, where λ is wave length, L is the distance from a source to the receiving plane and 2a is the aperture of a receiving plane. On the other hand, the range resolution is 2. 4λL^2/a^2 even when a^2/L>>λ and is worse than the lateral one by a factor of 4L/a. Moreover, a discrete arrangement of receivers with a large interval in between causes the appearance of diffracted images of higher order with equal magnitude to the real image. In this imaging method, when a point source projects a very short pulse expressed by Eq. (11) where T_p is pulse duration, the image distribution on the z-axis is expressed by Eq. (12). Then the range resolution depends on only pulse length cT_p. For example, if p(t)=1, T_p=n/f (n is a multiple of 0. 5), the range resolution is 1. 5 nλ as shown in Eq. (14). We calculated the image distribution on a line parallel to the x-axis at L where L=2a=100λ and N=11. As shown in Fig. 6, the lateral resolution is about 1. 25λ when p(t)=1 and n=1. When a source projects a pulse expressed by Eq. (15), the relation between waveform of pulse and image distribution in Fig. 7. Fig. 8 shows the lateral resolution when (p(t)=1, n=1) and (T_p=1. 5/f, τ=0. 6/f). Experiments were performed in air using a small speaker as an object. A block diagram for experiments is shown in Fig. 11. The speaker projected a sinusoidal pulse of about one cycle (wave length λ=34 mm). Fig. 12 shows the clear image of the speaker. Figs. 14 and 15 show the separated images of two speakers located with a separation of 75 mm in lateral and longitudinal directions respectively.
