By B. P. Hildebrand
Since the 1st papers through E. N. Leith and J. Upatnieks almost about holography seemed in 1961, there was a digital explosion of study task within the box. greater than SOO papers and articles on holo graphy have seemed within the final ten years. Many functions 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. Tbree symposia whoUy dedicated to acoustical holography were held and tbe papers released in ebook shape. the aim of this e-book is to assemble the result of examine in acoustical holography, a few of it as but unpublished, lower than one conceal in order that employees in holography, nondestructive checking out, scientific imaging, underwater imaging, and seismic exploration can come to a decision no matter if this new strategy will be beneficial to them.
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Extra resources for An Introduction to Acoustical Holography
50) 2 and W I , W 2 constant. This can be done in several ways, the simplest of which is to use single point structures. Then r2 , ra , (X2' fXa are constants and together with monochromatic radiation, the problem is solved. For the general ca se of a complex reference structure, the only way imaging can be achieved is if the reconstruction structure is an exact replica of the reference structure, with the scale factor according to Eqs. 50) with suitably chosen constants. The simplest example, of course, is to choose the constants to be zero, in which case k2 ra = "k;r 2 COS fX a = k Ti 2 with the result that COS fX 2 36 Chapter 2 When Eqs.
In this way, the interferogram became a linear grating structure upon which was superimposed a spatial deviation, proportional to the departures from a plane wave that might exist on either or both beams. This situation was simply demonstrated in Fig. 1. We now demonstrate these statements mathematically. 18) where sincf> a=-A,- and we have assumed that the direction of propagation is in the (x, z) plane. We can, therefore, express the amplitudes of beams 1 and 2 in terms of a plane front and a phase deviation from that plane.
55), reveals various conditions under which some or all of the aberrations disappear. All aberrations disappear when k 1 = k 2 , m = 1, = '2' cos aa = ± cos a 2 . 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 .
An Introduction to Acoustical Holography by B. P. Hildebrand