# An Introduction to Acoustical Holography by B. P. Hildebrand

By B. P. Hildebrand

Since the 1st papers via E. N. Leith and J. Upatnieks with reference 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 job within the box is burgeoning. 3 symposia entirely dedicated to acoustical holography were held and the papers released in ebook shape. The purposeof this publication is to collect the result of examine in acoustical holography, a few of it as but unpublished, less than one disguise in order that staff in holography, nondestructive trying out, clinical imaging, underwater imaging, and seismic exploration can make a decision even if this new method could be precious to them.

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39) may be interpreted as a diffraction of SI followed by an inverse diffraction into an image of SI. Of course, the 1/, dependence of the diffraction integral has been neglected under the assumption that it is nearly constant over the domain of integration. By equating Eq. 38) to Eq. 35), we obtain the usual solutions that perfect reconstruction occurs onIy for k 1 = k 2 , 'al = '2 1 in which case Zb = -Zl and Xb = Xl [14]. In other words, the image duplicates the object in position and size. We may expand the distances '11, '2 / , 'al, 'bI about the origin to obtain the solutions for the Gaussian image Iocation [15].

There are certain advantages and disadvantages of side-band Fresnel over side-band Fraunhofer holograms related to the resolution of the recording medium PO]. An example of the improvement offered by this method was shown in Fig. 8. 4. Fourier Transform Holograms A Fourier transform hologram is defined as the interference pattern of a plane wave with the spatial Fourier transform of the object. The spatial Fourier transform ofan object may be obtained in several ways. The simplest way is to move the observation plane into the far zone of the object.

We assume that the complex amplitude of the radiation emanating from the primary source may be written VI(t). The radiation reaching a point P at the hologram plane from the illuminating structure via the object is where Cl is the velocity of propagation, so(xo , zo), SI (Xl' Zl) are the descriptions of the radiation field at the surface of the illumination structure and the object, respectively, and (R o' + ro' + rI')/cl is the transit time of the radiation from the source to the point P via the path indicated in Fig.