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By B. P. Hildebrand

Since the 1st papers through E. N. Leith and J. Upatnieks with regards to holography seemed in 1961, there was a digital explosion of analysis task within the box. greater than 500 papers and articles on holo­ graphy have seemed within the final ten years. Many purposes of holo­ graphy were proposed, and a few of those are starting to input the world of usefulness. one of many functions that looks to carry nice promise is acoustic imaging via holography. the 1st papers in this topic seemed in 1966, yet already learn task within the box is burgeoning. 3 symposia completely dedicated to acoustical holography were held and the papers released in e-book shape. The purposeof this publication is to collect the result of learn in acoustical holography, a few of it as but unpublished, below one conceal in order that staff in holography, nondestructive checking out, clinical imaging, underwater imaging, and seismic exploration can come to a decision even if this new method will be worthy to them.

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Born and E. , New York, p. 441 (1964). 21. B. P. Hildebrand and K. A. Haines, Holography by scanning, J. Opt. Soc. Am. 59(1):1 (1969). 1. INTRODUCTION The term acoustics covers a broad range of subjects, many of which need not be considered in this book. Among those subjects not covered are architectural acoustics, communication acoustics, noise and vibration analysis, music, techniques for measuring elastic constants of solid materials, techniques for studying nonisotropic stresses and inhomogeneities, and measurements of molecular structure of organic liquids.

We reeall that in obtaining the image-Ioeation equations we expanded the distanee terms in a binomial series and negleeted eoeffieients of x 2(x - 2Xp )2 and higher. This gave us a first approximation to the loeation of the image point. If we retain eoeffieients of x 2(x - 2Xp )2 and negleet those of higher order, we ean obtain the so-ealled third-order aberrations. 63) Before we introduced the higher order terms in the binomial expansion, we had e free of the variable x. Consequently, we were able to reduce the integral in Eq.

By looking at the expression for Q, we see that it becomes zero when the image location Eq. 54) is satisfied. At the same time, however, Q also approaches zero in such a way that the ratio approaches unity. 87) A plot of this function appears in Fig. 19 . Note that the plot has no zeros since only nonzero positive quantities are involved. It is customary to allow a 20% loss in Intensity from that at the focal plane [20]. From Fig. 0. J Q = mA (~)! 89) A comparison of this expression with Eq. 80) shows that the radial resolution is worse than lateral resolution by a factor 2r1 /A.

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