J. M. Richardson

Acoustic Imaging of Solid Objects in Air Using a Small Set of Transducers

We describe an a1 gori thm that enables 3-dimensional acoustic imaging of simple objects in a ir using an array containing o nly a small number of transducers. Each transducer provides a pulseecho measurement in an appropriate incident direction. Our probabilistic imaging procedure uses entire waveforms (i.e., they are not limited to simple time-of-flight measurement), and are based on the Kirchhoff approximation together with the assumption that the scatterer is a rigid body. We further assume that the body is flat-bottomed with its upper surface represented by a singlevalued elevation function. The imaging algorithm employs an iterative technique involving artificial smoothing initially, followed by incremental unsmoothing and linearization with respect to elevation function c orrections. We present the results of preliminary testing of this technique using synthetic data.

Statistical Flaw Detection: Theory

In this paper we discuss the problem of flaw detection using ultrasound. We describe the decision theoretic optimal algorithm for interior flaw detection in the presence of noise. Based on this algorithm, an efficient sub-optimal algorithm is derived that can be implemented in real time. Finally, we present some results of computer simulation tests comparing the new algorithm with a more traditional video detection scheme based on peak waveform thresholding. Preliminary evaluation of the new detection scheme under laboratory experimental conditions is described in a companion paper [Elsley, Fertig, and Richardson (1983)]. We first start with a brief statement of the specific detection problem we are addressing.

The Automation of the Born Inversion for Ultrasonic Flaw Sizing

The Born approximation has been widely employed as a basis for determining flaw sizes using individual pulse-echo waveforms together with the assumption of an ellipsoidal flaw geometry. A major difficulty in implementing such algorithms has been the determination of the time delay corresponding to the flaw centroid. However, both the time delay calculation and the flaw size determination itself can be performed in an optimal fashion using statistical estimation techniques with an appropriate error model. We will discuss the application of these techniques to an automated flaw-sizing algorithm requiring a minimum of operator input, and will compare the results obtained by this method with those obtained by previous operator-intensive methods.

Application of the Phase Closure Technique to Passive Acoustic Imaging Through Inhomogeneous Media

We consider the problem of passive acoustic imaging of a spatially uncorrelated noise source through an inhomogeneous medium. The measurement system consists of an array of transducers whose signals are processed in a manner similar to that used in radio interferometry of celestial sources. Using a philosophy similar to that of radio astronomers in the field of very long baseline interferometry, we make use of a quantity known as the closure phase. Under certain assumptions, this quantity is independent of the effect of phase shifts in the intervening medium, but yet contains useful information about source structure. There is, of course, an important distinction between the acoustic case and radio astronomy. In the former case, the distorting medium is present in the entire region between the source and the imaging system, whereas in the latter case, the distorting medium is the earth’s atmosphere, representing a thin sheet of material at one end of the propagation path. Nevertheless, in the acoustic case, the closure phase is still a useful quantity for imaging purposes, provided that the time delay for a given path depends primarily on the receiver position and is independent of (or weakly dependent on) source position transverse to the line of sight, and that the medium does not change appreciably during the observation time. To investigate the applicability of the phase closure technique to the acoustic case, we have performed a series of numerical experiments in which a simple source is viewed through an inhomogeneous medium. These calculations support the theoretical predictions.

Statistical Flaw Detection in a Scanning Mode

The purpose of this paper is to describe an extension to an integrated model for assessing the performance of a given ultrasonic inspection system for detecting internal flaws. The integrated model is described in Fertig, Richardson, and Elsley (1984). The modified model incorporates the use of multiple waveform information obtained in a scanning mode. It is demonstrated that the proper use of this information can enhance the detectability of interior flaws. The next section describes the noise model for the scanning experiment. Section 3 develops an approximation to a decision theoretic solution to the detection problem and Section 4 provides a computer simulation.

Statistical Flaw Detection: Application to Flaws Below Curved Surfaces

The detection of the presence of flaws in structural materials is the most important function which Non-Destructive Evaluation (NDE) performs. As structures are designed to higher performance criteria and as safety and life cycle cost factors become more important, it becomes necessary to detect smaller and more difficult to find flaws. This paper presents a practical approach to the optimum detection of flaws in the presence of noise signals. A decision theoretic approach (described in more detail in a companion paper by Fertig, et al.1) is used to derive a detection algorithm which is adapted to the noise environment in which a particular measurement is being made. An automatic procedure for characterizing the noises and developing the optimum detection algorithm is presented. Two implementations of this approach have been tested on experimental data and show substantial improvement over conventional detection techniques. One is a flexible algorithm used for research purposes, and the other is a real-time algorithm suitable for field implementation.

Statistical Approach to the Automation of Flaw Detection

The detection of flaws in the presence of noise and other interfering signals can be enhanced by specifically taking into account the nature of these noise signals and designing a detection algorithm which performs optimally in the presence of that noise. In this paper, we present results of the application of this technique to a variety of specimens and show improvement in flaw detectability in the presence of grain scattering noise. We also discuss the use of this approach as a first step in the automation of flaw detection by virtue of its ability to recommend and evaluate measurement setups, perform optimum detection and provide confidence measures of the results.

Acoustic imaging in three dimensions

An algorithm and method of implementation are described for obtaining high-resolution, three-dimensional acoustic images of simple objects in air using only a small number of transducer positions. Each transducer position provides a single large bandwidth pulse-echo waveform along a specified incident direction. Probabilistic estimation procedures using the full waveforms are used to reconstruct a three-dimensional image of the objects in the observed volume. Prior information about the physics of the scattering process, the statistical nature of the noise and the acoustic reflectivity of the target object are used to obtain resolution of the order of the smallest wavelength present in the acoustic pulses. Results of both synthetic and experimental tests of the algorithm are presented, as well as a brief description of the experimental apparatus and the algorithm used.

Probabilistic image reconstruction using experimental ultrasonic data

Ultrasonic pulse-echo measurements at a center frequency of 2.25 MHz have been made of a multiwire target in water (consisting of 3 thin parallel wires separated by 0.8 mm), and a prolate spheroidal void in titanium, whose major axes were 800 x 1600 microns. The data consisted of digitized r.f. waveforms corresponding to 4 incident directions, obtained using a transducer array. Calibration of the acoustical system response functions for the two experiments discussed above were based on similar measurements of a thin single wire, and of a spherical void in titanium, respectively.

Probabilistic Approach to Inverse Problems in Ultrasonics

problems pertaining to the longitudinal-to- longitudinal pul se-echo scattering of elastic waves from scatterers of restricted types under farfield conditions. The treatment is limited to cases in which either the Born or K irchhoff approximations can be applied. The approach in all cases is probabilistic, i.e., with a priori statistical models of both measurement errors and possible scatterers as a basis, the procedure is to determine the most probable scatterer given the results of measurement. We consider several nonGaussian , nonparametric statistical scatterer models while the measurement error is represented only by additive Gaussian random noise. Computational results using synthetic test data will be presented for the foll owing scatterer model s : (a) Gaussian randan process in space, (b) positive inhomogeneity that is otherwise Gaussian, (c) weakly scattering inclusion with unknown uniform material and unknown boundary, (d) general void, and (e) planar crack with unknown outline. Dependence of results on incident direction d iversity, bandwidth, and certain model parameters will be di scussed. We have recent1 y investigated several inverse