Measurement and Specification of Ultrasonic Lenses

Abstract

Methods approved in optics are applied to the measurement and specification of ultrasonic lenses.T may be confidently expected that ultrasonic lenses will be put into general use very soon. It seems, therefore, to be opportune to suggest a method of measuring and specifying them. This is all the easier as the approved methods used in optics can be likewise applied to ultrasonics.For this simulation, in addition to the radius of curvature and focal length of an ultrasonic lens, their reciprocals, the curvature and focal power, ß have to be introduced. I suggest the adoption of the optical unit of refractive power, the diopter D, and as its appropriate name, when used in ultrasonic work, "diacouster Dac." As the acoustical focal length and focal power of an ultrasonic lens depend on the medium of propagation, a standard liquid must be c. hosen. It is convenient to use water as this standard because its properties are stable and accurately known.The curvature R of an ultrasonic lens expresse. d in reciprocal meters is, of course, the same as in optics, R= 100/r in cm=39.37/r in inches. (1)Then from the fundamental paraxial equation for the refraction at a spherical surface it follows that the acoustical focal power Fac expressed in D• is given bywhere u=v•/v•, v• and v• being the ultrasonic velocities in the solid and liquid respectively. Also an "acoustician's lens measure" can be built, based on the same principle as the widespread "optician's lens measure," and more than this, within a limited range the optician's lens measure itself can be used for ultrasonic lenses, if the values of the divisions are converted. The readings of the optician's instrument are known to be calculated for the refractive index 1.523, therefore F=0.523R. (3) The acoustician's instrument has to show F•c = -(vs/v•-1)R.Consequently, F•= -F(v,/v•-l)/0.523. (5)A table, very easy to calculate, a simple graph, or a sliderfile will help to find corresponding values without any trouble. Since, within the range of frequencies generable at present, no dispersion of ultrasonic velocity occurs either in solids or in liquids, the acoustical focal length and focal power of an ultrasonic lens are independent of the frequency, in other words, even a single ultrasonic lens is "achromatic" or rather, "apochromatic," and the values obtained by means of a lens measure are valid for all frequencies.A very convenient comparison of the concentrating effects of ultrasonic lenses or lens systems is rendered possible by the introduction of the "aperture ratio," a quantity mainly used for the specification of photographic objectives. The aperture ratio is defined as the quotient of the entrance pupil of a lens system by its equivalent focal length or, in the case of a single lens, very nearly the quotient of the diameter of the lens by its posterior focal length. The aperture ratio is denoted as a quotient ..-1'3.5, 1'4.5, 1'6.3, 1: 9 ß ß ß and so on or as a fraction ß ß ß f/2, f/2.8, f/4, f/5.6 ... and so on.The effects produced by ultrasonic lenses under any gi...

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