Liu, G. R.

The inverse problem of determining the size, shape and orientation of a submerged object using the scattered field data is studied. Based on the physical optics approximate, the profile function of the object is found directly proportional to its ramp response that is the second integral of the impulse response. Through analyzing the feature of the ramp response in different computed frequency ranges, it is found that the low-frequency data are essential to the shape of the underwater object while the high-frequency data are very important to the size of the object. Therefore, when employing the high-frequency data to compute the ramp response, the edge of the object can only be highlighted in the illuminated region at certain aspect. Based on this finding, a new method is developed to estimate the size of underwater objects. The present method uses different frequency ranges to determine different parameters of the underwater objects so as to achieve the best accuracy. A number of examples are presented to demonstrate the effectiveness of the present method in using the ramp response technique to identify the size of both rigid and elastic bodies.

The inverse problems in the area of the acoustic scattering often concern the determination of the size, shape, and orientation of an object using the scattered field data. This paper presents a method to retrieve the shape information of an underwater object using illuminated lengths, which can be obtained from the ramp response signatures of the object. An ellipsoidal object submerged in water is considered. Both the low and high backscattered frequency data have been employed to calculate the illuminated lengths. The calculated results show that the illuminated lengths will be more accurate, if only the high-frequency-range data are employed. For ellipsoidal objects, any three illuminated lengths that are not of a same plane can in theory fully determine the shape of the ellipsoid. As the calculated illuminated lengths contain numerical errors, the calculated results of the three semiaxes of the ellipsoid will deteriorate and become unreliable, especially when the three incident directions of the illuminated lengths become close. The reason is that the condition number of the coefficient matrix becomes big in such situations, which leads to an increase of the relative error upper limit in the calculated results. To avoid such errors in close incident wave cases, it is found that the use of more than three incident waves works very well in the shape identification of an underwater object.