Theory for random arrayspredicts a mean sidelobe level given by the inverse of the number of elements. In practice, however, the sidelobe level fluctuates much around this mean. In this paper two optimization methods for thinned arrays are given: one is for optimizing the weights of each element, and the other one optimizes both the layout and the weights. The weight optimization algorithm is based on linear programming and minimizes the peak sidelobe level for a given beamwidth. It is used to investigate the conditions for finding thinned arrays with peak sidelobe level at or below the inverse of the number of elements. With optimization of the weights of a randomly thinned array, it is possible to come quite close and even below this value, especially for 1D arrays. Even for 2D sparse arrays a large reduction in peak sidelobe level is achieved. Even better solutions are found when the thinning pattern is optimized also. This requires an algorithm that uses mixed integer linear prog...

¯ A method is presented which optimizes weights of general planar 1D and 2D symmetric full and sparse arrays. The objective is to ønd a weighting of the array elements which gives the minimum sidelobe level of the array pattern in a speciøed region - the stopband. The sidelobe level is controlled on a discrete set of points from this region. The method minimizes the Chebyshev norm of the sidelobe level. The method is based on linear programming and is solved with the simplex method. The method removes the large AEuctuation in sidelobe level which characterizes random sparse arrays. Examples of optimal weighted 1D and 2D planar arrays are presented. I. Introduction 2D arrays in ultrasound represent a technological challenge not the least because of the high channel count [7]. For this reason sparse array methods, where elements are removed by thinning, are considered to be necessary [8]. However this will result in an often unacceptably high sidelobe level. Two dioeerent approaches to...

this paper developments in transducers and beamformers and their relationship will be discussed. COMPOSITE ARRAYS The advent of piezocomposites has been the main recent development in transducer technology. A piezocomposite is a combination of a piezoelectric ceramic and a polymer which forms a new material with different piezoelectric properties. Piezocomposites have improved the performance of Proc. 15th Int. Congress on Acoustics, Trondheim, Norway, 26-30 June 1995 2 commonly used arrays such as the mechanically scanned annular array and the linear phased array of Fig. 1 upper panels, in the following ways [2]: 1. Acoustic impedance is reduced giving a better impedance match with tissue. This results in a reduction in reverberation level in the near field as the transducer surface to a less extent reflects back incident energy. 2. The composite materials make the radiators closer to the ideal of a vibrating piston. Primarily this is due to the suppression of unwanted surface waves propagating laterally over the transducer.

Sparsely sampled irregular arrays and random arrays have been used or proposed in several fields such as radar, sonar, ultrasound imaging, and seismics. We start with an introduction to array processing and then consider the combinatorial problem of finding the best layout of elements in sparse 1-D and 2-D arrays. The optimization criteria are then reviewed: creation of beampatterns with low mainlobe width and low sidelobes, or as uniform as possible coarray. The latter case is shown here to be nearly equivalent to finding a beampattern with minimal peak sidelobes. We have applied several optimization methods to the layout problem, including linear programming, genetic algorithms and simulated annealing. The examples given here are both for 1-D and 2-D arrays. The largest problem considered is the selection of K = 500 elements in an aperture of 50 by 50 elements. Based on these examples we propose that an estimate of the achievable peak level in an algorithmically optimized array is inverse proportional to K and is close to the estimate of the average level in a random array. Active array systems use both a transmitter and receiver aperture and they need not necessarily be the same. This gives additional freedom in design of the thinning patterns, and favorable solutions can be found by using periodic patterns with different periodicity for the two apertures, or a periodic pattern in combination with an algorithmically optimized pattern with the condition that there be no overlap between transmitter and receiver elements. With the methods given here one has the freedom to choose a design method for a sparse array system using either the same elements for the receiver and the transmitter, no overlap between the receiver and transmitter or partial overlap as in periodic arrays.

Theory for random arrays predicts a mean sidelobe level given by the inverse of the number of elements. In this paper 1 two optimization methods for thinned arrays are given: one is for optimizing the weights of each element, and the other one optimizes both the layout and the weights. The weight optimization algorithm is based on linear programming and minimizes the peak sidelobe level for a given beamwidth. It is used to investigate the conditions for finding thinned arrays with peak sidelobe level at or below the inverse of the number of elements. With optimization of the weights of a randomly thinned array it is possible to come quite close and even below this value, especially for 1D arrays. Even for 2D sparse arrays a large reduction in peak sidelobe level is achieved. Even better solutions are found when the thinning pattern is optimized also. This requires an algorithm that uses mixed integer linear programming. In this case solutions with lower peak sidelobe level than the i...

ke to thank my supervisor, Professor Sverre Holm, for his encouragement and assistance through this work. Also thanks to Dr. Geir Dahl for his contribution of ideas to the optimization methods. Oslo, May 1996 Bjørnar Elgetun Contents 1 Introduction 5 1.1 Medical ultrasound . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Objective of this thesis . . . . . . . . . . . . . . . . . . . . . . 7 2 Ultrasound imaging 8 2.1 The ultrasound imaging system . . . . . . . . . . . . . . . . . 8 2.1.1 The ultrasound transducer . . . . . . . . . . . . . . . . 9 2.1.2 Di#erent transducer types . . . . . . . . . . . . . . . . 10 2.2 3D imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Technical considerations . . . . . . . . . . . . . . . . . 12 3 Ultrasound wave propagation 14 3.1 Ultrasound waves . . . . . . . . . . . . . . . . . . . . . . .

Existing 3D ultrasound systems are based on mechanically moving 1D arrays for data collection and post-processing of data to achieve 3D images. To be able to both collect and process 3D data in real-time, a scaling of the ultrasound system from 1D to 2D arrays is necessary. A typical 2D-system uses 1D arrays with about 100 receive and transmit channels. Scaling of this system to get a 3Dsystem with as good performance as the 2D-system implies a squaring of the number of channels, i.e. a 10.000 channel system. To reduce cost and complexity of such a system, removal of array elements or equally channels is possible. Arrays with removed elements are known as sparse arrays. At the University of Oslo, there are two ongoing projects which aim to find optimal 2D sparse layouts through optimization and simulation. The goal is to minimize the number of channels without compromising image quality. To verify this work and to critically test system performances, an extensive evaluation program is...