The decomposition of the time reversal operator ͑DORT͒ method is a selective detection and focusing technique using an array of transmit-receive transducers. It relies on the theory of iterative time reversal mirrors which was presented by Prada et al. ͓C. Prada, J. L. Thomas, and M. Fink, J. Acoust. Soc. Am. 97, 62-71 ͑1995͔͒. The time reversal operator was defined as K*()K(), where is the frequency, * means complex conjugate, and K͑͒ is the transfer matrix of the array of L transducers insonifying a time invariant scattering medium. It was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities, each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers. The DORT method consists in determining these eigenvectors and using them for the selective focusing. This paper presents a complete analysis of this method in the case of two scatterers. The mathematical expressions of the eigenvectors are given and several experimental results are described. In particular, the effectiveness of the method to focus selectively through an inhomogeneous medium is established.
The fabrication and modeling of novel, capacitive, ultrasonic air transducers is reported. Transmission experiments in air at 11.4, 9.2, and 3.1 MHz are shown to correspond with theory. The transducers are made using surface micromachining techniques, which enable the realization of center frequencies ranging from 1.8 to 11.6 MHz. The bandwidth of the transducers ranges from 5% to 20%, depending on processing parameters. Custom circuitry is able to detect 10 MHz capacitance fluctuations as small as 10−18 F, which correspond to displacements on the order of 10−3 Å, in a bandwidth of 2 MHz with a signal to noise ratio of 20 dB. Such detection sensitivity is shown to yield air transducer systems capable of withstanding over 100 dB of signal attenuation, a figure of merit that has significant implications for ultrasonic imaging, nondestructive evaluation, gas flow and composition measurements, and range sensing.
The successful modeling and fabrication of capacitive ultrasonic air transducers is reported. Emission and reception in air at 11.4, 9.2, and 3.1 MHz is demonstrated. Furthermore, transmission experiments through air–glass–air (70 dB of signal loss) at 3.8 and 5.1 MHz are reported. The transducers are made using surface micromachining techniques, which enable the realization of center frequencies ranging from 1.8 to 11.6 MHz. A theory explaining both the static and dynamic operation of the devices is presented. In addition to agreeing well with the experiments, the theory predicts that displacements on the order of 10−3 angstroms (with potential for 10−5 angstroms) are detectable with a 20-dB signal-to-noise ratio. Such detection sensitivity is shown to yield air transducer systems capable of withstanding over 100 dB of signal attenuation, a figure of merit that has significant implications for ultrasonic imaging, nondestructive evaluation, gas flow and composition measurements, and range sensing. [This work has been supported by a grant from ONR.]
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