By B. P. Hildebrand

Since the 1st papers by means of 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 SOO 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 functions that looks to carry nice promise is acoustic imaging by way of holography. the 1st papers in this topic seemed in 1966. yet already study task within the box is burgeoning. Tbree symposia whoUy dedicated to acoustical holography were held and tbe papers released in publication shape. the aim of this ebook is to assemble the result of examine in acoustical holography, a few of it as but unpublished, below one hide in order that employees in holography, nondestructive trying out, scientific imaging, underwater imaging, and seismic exploration can make a decision even if this new approach may be important to them.

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This light source is photographed as it is scanned in synchronism with the receiver. 15) where [, > b - I aaDl(x, y) Imax 2 We see that the only difference between this hologram and the interferometric one [Eq. 6)] is that the bias term is a constant, whereas in the former case it is space variant. Tbe resulting diffraction effects are the same with the exception of the undiffracted term. 3. GABOR HOLOGRAPHY We now consider Gabor's original method which is pictured in Fig. 3 r]. The object is assumed to be rather transparent with the result that the transmitted wave may be considered to be made up of a large plane component and a small scattered component.

This, of course, results in a perfect image with 'b = ± '1' cos ab = ± cos a 1 , and magnification of unity. Another set of conditions yielding a nonaberrated image is m = k 1/k 2 , 'a = '2 = 00, cos aa = ± cos a 2 , which results in an image with the characteristics 'b = ± k 1, dk 2 , cos ab = ± CoS a 1 , and Mn = ± k 1/k 2 , MT = ± k 1 /k 2 . Thus, for this special case, we can obtain undistorted and unaberrated magnification. 9. 8. We could have introduced distortion ofthe image in our discussion of magnification, since that is where it arises.

2. An incremental volume of liquid LlxLlyLlz is used in the derivation of equations describing the propagation of sound in liquids. 17) where i, j, kare unit vectors in the x, y, and z directions, respectively.

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