Inverse Filtering to Minimize the Effect of Mechanical Aberration in Focusing Piezoelectric Transducers
The resolution of acoustic images from a “positively scanning transmitter” system is limited by the size of the focal spot of the acoustic beam. Frequently a spatial focusing electrode pattern, such as a Fresnel zone plate, is used to excite the piezoelectric transducer of such a system. However, the transformation of that electrode pattern to the acoustic pattern actually generated is not exact. This effect, called mechanical aberration, is a result of wave generation and propagation in the piezoelectric plate and can be represented by a spatial transfer function. The aberration enlarges the focal spot and decreases the resolving power of the instrument.
The resolution can be improved by inverse filtering. The approach is to assume that a desired acoustic pattern has already been generated by an unknown electrode pattern. The electrode pattern is found by inverse filtering. If this electrode pattern is then used to excite the piezoelectric plate, it will produce very nearly the desired acoustic pattern. The actual pattern will usually not be exactly the same as the desired pattern because frequency cutoff in the transducer may prevent the propagation of high spatial frequencies necessary for the two patterns to be exactly the same.
KeywordsSpatial Frequency Focal Spot Piezoelectric Transducer High Spatial Frequency Fresnel Zone
Unable to display preview. Download preview PDF.
- 1.K. Wang, and G. Wade, “Threshold Contrasts for Various Acoustical Imaging Systems,” Acoustical Holography, V. 4, G. Wade Ed., Plenum Press, N.Y., 1972.Google Scholar
- 3.M. Mortezaie, G. Wade, and B. Noorbehesht, “Near Field Acoustic Pattern of Fresnel Zone Plate Transducers,” International Workshop on Physics and Engineering in Medical Imaging, 1982. IEEE Trans. on Computer Science (in press).Google Scholar
- 4.B. Noorbehesht, M. Mortezaie, G. Wade, and C. Schueler, “Effect of Mechanical Aberration on Resolution of Fresnel Zone Plate Transducers,” Acoustical Imaging, Vol. 11, J. Powers, Ed., Plenum Press, New York, 1981.Google Scholar
- 6.Generalization to two dimension may be achieved by taking advantage of the crystallographic symmetry of the piezoelectric ceramics. The two dimensional transfer function H(f ,f ) or H(fr ,f) (in the polar coordinates) may be obtained from H(fx ) by a rotation of H(fx ) around the H(fx ) axis. This is mathematically equivalent to replacing fx in H(fx ) by fr. Due to the symmetry, there is no dependence on f. It should be noted that h(r,) cannot be obtained from h(x) by simple rotation of h(x) about the h(x) axis.Google Scholar