An Introduction to Acoustical Holography by B. P. Hildebrand

By B. P. Hildebrand

Since the 1st papers by means of E. N. Leith and J. Upatnieks just about 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 area of usefulness. one of many purposes that looks to carry nice promise is acoustic imaging via holography. the 1st papers in this topic seemed in 1966, yet already examine job within the box is burgeoning. 3 symposia absolutely dedicated to acoustical holography were held and the papers released in e-book shape. The purposeof this booklet is to collect the result of learn in acoustical holography, a few of it as but unpublished, below one disguise in order that employees in holography, nondestructive trying out, scientific imaging, underwater imaging, and seismic exploration can come to a decision even if this new process may be worthy to them.

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What'happens if we use different wavelengths or propagation media for recording and illuminating the hologram, or if the illuminating beam is not an exact replica of the reference be am ? To answer these questions we must perform a quantitative analysis based upon the very general arrangement shown in Fig. 12. In this analysis we assume that the primary radiation source is a perfect point. 12 shows the general recording arrangement, where for simplicity we have shown only two dimensions. We have three general structures, two of which are identically illuminated by the primary point source.

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.

Another way of obtaining a spatial Fourier transform is to artificially remove the object into the far zone. This is simply done by placing it in the front focal plane of a lens. In this position, the lens transforms each point on the object to a plane wave, which is equivalent to moving it into the far field. Since such a hologram will reconstruct a Fourier transform rather than an image, it is necessary to use a lens in the diffracted field. In asense, one may think ofthe lens as performing an inverse Fourier trans form to recover the image.

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