Thomas G. Kincaid

The application of finite element method analysis to eddy current nondestructive evaluation

The finite element method for the computation of eddy current fields is presented. The method is described for geometries with a one-component eddy current field. The use of the method for the calculation of the impedance of eddy current sensors in the vicinity of defects is shown. An example is given of the method applied to a C-magnet-type sensor positioned over a crack in a plane-conducting material.

On Optimum Waveforms for Correlation Detection in the Sonar Environment: Reverberation‐Limited Conditions

This study is concerned with optimum waveforms for correlation detection in the sonar environment. The selection of optimum waveforms for combating random multipath under noise‐limited conditions was considered previously [T. G. Kincaid, J. Acoust. Soc. Am. 43, 258–268 (1968)]. In this paper, the same problem is considered under reverberation‐limited conditions. The optimum waveforms are required to maximize the ratio of expected signal to expected reverberation plus noise under a fixed‐energy constraint. Necessary and sufficient conditions for the optimum waveforms are derived. As under noise‐limited conditions, it has only been possible to develop a technique for finding waveforms that satisfy a necessary condition. However, it is conjectured that this technique produces optimum waveforms. Conjectured optimum waveforms are found for selected examples, and their performance is compared to that of two conventional (CW and chirp) waveforms.

Optimum Waveforms for Correlation Detection in the Sonar Environment: Noise‐Limited Conditions

Sonar systems currently in use and under development attempt to discover the presence of an underwater target by transmitting an acoustic pulse and detecting the echo with a correlation receiver. This receiver correlates its input with time and frequency translates of a stored reference waveform, usually the same as the transmitted waveform. Owing to the presence of random multipath, there is usually not a single echo, but a multiplicity of echoes with random attenuations, time delays, and frequency shifts. Under these conditions, the detection capability of the correlation receiver is shown to be dependent upon the transmitted and reference waveforms. Necessary and sufficient conditions for optimum waveforms under a maximum signal‐to‐noise ratio criterion with an energy constraint are derived. A technique for finding waveforms that satisfy only a necessary condition is demonstrated, but it is conjectured that it produces the optimum waveforms. Conjectured optimum waveforms are derived for selected exampl...

Eddy-Current Probe Design

This paper describes theoretical and experimental work directed toward finding the optimum probe dimensions and operating frequency for eddy current detection of half-penny surface cracks in nonmagnetic conducting materials. The study applies to probes which excite an approximately uniform spatial field over the length of the crack at the surface of the material. In practical terms, this means that the probe is not smaller than the crack length in any of its critical dimensions.

Partially-Coherent Ultrasonic Imaging

An important problem in ultrasonic imaging is target detection under non-ideal imaging conditions. One example of this occurs in nondestructive testing (NDT) where cracks or inclusions must be found in the presence of normal material inhomogeneities (including surface roughness). The material inhomogeneities may create spatial variations in sound speed [1] as well as multi-path pulse distortion and speckle-like “material noise”. Furthermore, the ultrasonic pulse reflected from the target depends on the target shape and composition. Although this work is motivated by problems in NDT, the concept of partially-coherent imaging may also find applications in medical imaging and sonar.

Ultrasonic Synthetic-Aperture Holographic Imaging †

Ultrasonic reflection imaging has become an important tool in NDE [1,2,3]. The lateral resolution of such images is limited by the aperture size of the transducer, while the depth resolution is limited by the pulse length. In addition, for a given aperture diameter, the lateral resolution degrades with depth as given by the Rayleigh criterion. In this paper we discuss a method to increase the effective aperture through aperture synthesis. Waveform data, collected from a scanned transducer focused near the surface of the sample, is coherently processed to yield a synthesized aperture which can be focused to any depth with constant resolution. The synthetic aperture method allows efficient volume inspection by trading off scan time with processing time, the latter of which is constantly decreasing with increasing computing power.

Estimation of Periodic Signals in Noise

Two equivalent methods for the estimation of a periodic signal in additive noise are presented. Both assume that a finite time sample of the signal plus noise is available. Both minimize the mean‐square error between the estimate and the sample. In the first method, estimates for the period of the signal and the complex amplitudes of its harmonics are derived. In the second method, estimates for the period of the signal and the waveform of one period are derived. The estimates for the period are found to be the same by both methods. The estimate is unbiased and has a variance inversely proportional to both the signal‐to‐noise ratio and the cube of the number of periods in the sample. The expected values of the waveform estimates are derived, and the estimates are found to be biased.