Bill D. Cook

Distortion of finite amplitude ultrasound in lossy media

A form of Burgers’ equation is used to derive an algorithm for calculating harmonic generation by a continuous plane wave of ultrasound propagating in a nonlinear, lossy, nondispersive medium. The algorithm accounts for attenuation that is not quadratically related to the frequency of the wave. Attenuation strongly affects the rate of harmonic production. The effect of variations of the relationship between attenuation and frequency is shown. Biological tissue is an example of a highly lossy medium where the attenuation does not increase with the square of the frequency. Calculations for several types of tissue and biological fluids are presented that show, for certain conditions, finite amplitude distortion is possible.

Lens in the nearfield of a circular transducer: Gaussian–Laguerre formulation

The case of a thin lens located in the nearfield of a circular transducer is analyzed assuming circular symmetry for arbitrary transducer size and lens aperture, with or without absorption in the lens medium. Using the Fresnel approximation, the acoustic field is mathematically expressed as a series expansion of Gaussian–Laguerre functions. This technique is applied to the case of a circular‐piston–lens system and an analytical series solution of the field obtained for arbitrary positions of the lens. Numerical results are presented corresponding to several positions of the lens in the nearfield of the circular piston. It is found that the field pattern behind the lens is strongly dependent on the distance between the transducer and the lens, and the ratio of the focal length to the parameter a2/λ. Here a is the radius of the transducer and λ is the acoustic wavelength. It is also shown that the theory presented here can be applied to study the field of finite Gaussian transducers, focused and unfocused, ...

Proposed mapping of ultrasonic fields with conventional light diffraction

A theory is proposed from which a cross-sectional mapping of a beam of progressive ultrasonic waves can be obtained by conventional light-diffraction techniques, i.e., by passing a collimated beam of light through the sound field. To obtain sufficient information, the sound field must be rotated around its major axis for a series of optical measurements. These measurements, along a line perpendicular to the sound-beam axis, are to yield the strength and phase of the effective phase grating. As an extensive amount of data is needed to compute one map by two-dimensional Fourier transformation, a data-acquisition system and digital computer are required. However, in the constraint of linear acoustics, one set of measurements will permit the calculation of the sound field in all space.

Ultrasonic transducer calibration

An acousto-optical method and device for measuring the radiation produced by a transducer is described wherein such radiation is in the range of about 500 KHz to 10 MHz. The method consists of propagating ultrasound frequencies from the transducer through a transparent liquid medium in a cell, said cell having a transparent window or suitable device to provide a clear path for the radiation waves and passing a light through said cell at about a right angle to the direction of said ultrasound wherein the light is modulated in phase with the frequency of the ultrasound. The modulation of the light corresponding to the frequency of the ultrasound can be detected by a photo-cell measured and displayed on various devices. Further, a transducer can be calibrated absolutely using this method and apparatus from known constants and easily measured quantities. Moreover, it is readily adapted to measure the radiation of an unknown source to a known absolute source.

Measurement of high frequency sound fields by optical techniques

This paper summarizes the history of using acousto-optics to investigate ultrasonic fields both continuous and pulsed. There are a variety of methods yielding images of the fields and others yielding quantitative information.

Possible observation of chaos in acoustics

Approximately 20 years ago, I observed an acoustic phenomenon that could have been chaos. Not understanding what I was observing, I found that I could maintain experimental conditions to prevent it from occurring. I did so in order to complete the task at hand. The study involved understanding what conditions subharmonics were generated in an ultrasonic standing wave cavity. Two air‐backed quartz transducers were placed in a Fabry‐Perot configuration with water; one transducer having a resonant frequency of about 1 MHz; the other always being at lower frequency. Their separation was adjustable to be between 5 to 10 cm apart. The 1‐MHz transducer was driven with a variable frequency oscillator. At sufficient power and at some driving frequencies, subharmonics were observed both optically and with a piezoelectric transducer. Upon the onset of subharmonics, an optical diffraction pattern displayed lines in between the lines normally observed. A frequency analyzer connected to the piezoelectric transducer sho...

GENERATION OF UNIPOLAR ULTRASONIC PULSES BY SIGNAL PROCESSING

Synthetic unipolar pulses have been generated, using signal processing, in a pulse/echo ultrasonic system. Analysis reveals that sending-receiving transduction and propagation can each be partially described by the mathematical process of differentiation. Multiple integration of the received signals yield unipolar pulses if the excitation signals applied to the transducer are unipolar.

Alternative procedures for acquiring acousto‐optic data for computerized tomographic evaluation of sound fields

The principles of computerized transverse tomography can be applied to acousto‐optic data for evaluation of local sound pressure. One numerical technique involves building the two‐dimensional Fourier domain associated with the decomposition of the sound field into plane waves. Data acquired in one manner allows building this domain along radial spokes which is not readily convenient for numerical processing by digital FFT algorithms. In this paper we present an alternative data collection procedure which allows building the Fourier domain in a rectangular format which is compatible with two‐dimensional FFT algorithms. Moreover, with this new method, it is possible to evaluate the pressure along a line for a limited set of data using only a one‐dimensional FFT.

Near field of ultrasonic transducers (and how it pertains to acousto-optics)

The acousto-optic methods have given valuable insight to the complicated structure of the near field of ultrasonic transducers. Although the image formed is the result of the change of optical path integrated over essentially a thick grating, the results show interesting details. From the early schlieren photographs made with white light to the signals produced by pulses, surprising results are seen.

An investigation using an optical probe to study ultrasonic pulses

With care and working within well‐defined constraints, it has been previously demonstrated that a laser beam and a fast responding light detector could be made to behave as a linear line receiver of low megahertz sinusoidal ultrasonic waves. It is a sufficiently good line receiver so that the principles of tomography can be used to unfold the sound field. Many of the constraints are frequency dependent and the question arises as to whether a laser beam could be used to investigate a pulse of moderate bandwidth. The studies show that major features of the signal from the line detector can be accounted for when the sound field is produced by a commercial NDE transducer driven with a known Gaussian time pulse.