An Introduction to Acoustical Holography by B. P. Hildebrand

By B. P. Hildebrand

Since the 1st papers by way of E. N. Leith and J. Upatnieks near to holography seemed in 1961, there was a digital explosion of study job 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 commencing 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 thoroughly dedicated to acoustical holography were held and the papers released in booklet shape. The purposeof this booklet is to assemble the result of examine in acoustical holography, a few of it as but unpublished, lower than one conceal in order that staff in holography, nondestructive checking out, scientific imaging, underwater imaging, and seismic exploration can come to a decision even if this new method will be precious to them.

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The first term of Eq. 51) represents the image, the second bracket represents the illumination on the object, the last two terms describe the effect of the reference and reconstruction structures. These last two terms correspond to the amplitude shading expressed in Eq. 12). We have obtained expressions for the true image; the conjugate image is just as easily obtained, and is the complex conjugate of Eq. 51). 53) In the mathematical manipulation described above, we chose not to introduce the additional complexity of allowing for an enlargement or reduction of the hologram itself.

19 Holography SPIf:R,CAA WAVE-' __ . ' a TRANSM ISS I(); OBXCT~ lt1OEVIAlEO __ '"';'<-. ::. ,"I:::=-_ WAVE SCATl'ER[O WAVE R[COROING ;r=== PlANE---- b Fig. 3. Gabor holography is performed as shown here. The photographs show the object, (a) which consists of a small styrofoam letter F, and the resulting hologram. (b) The hologram consists of an intensity scan over a plane; the letter is 1 cm in height and the illumination spherical rather than plane as described in the text. This is the mathematical equivalent of our physical illustration in Fig.

Note that a rather large background obstructs the image; (a) is the true image, (b) the hologram, and (c) the conjugate image. ,(1) "C r+ SI) :r o Holography 21 b Fig. 5. This hologram (a) was made as shown in Fig. 3 with the exception of the object, which now consists of a sheet of styrofoam with the letter F cut out of it. The size of the letter and all other parameters are the same. Note that no image (b) is visible since practically no background penetrates the object. quite good since the true image will be so badly out of focus that it merely contributes to the background.

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