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 regards to holography seemed in 1961, there was a digital explosion of analysis 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 starting 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 examine job within the box is burgeoning. 3 symposia thoroughly dedicated to acoustical holography were held and the papers released in publication shape. The purposeof this booklet is to compile the result of learn in acoustical holography, a few of it as but unpublished, below one hide in order that staff in holography, nondestructive trying out, clinical imaging, underwater imaging, and seismic exploration can make a decision no matter if this new approach should be necessary to them.

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17) where i, j, kare unit vectors in the x, y, and z directions, respectively. 2. 22) where it is understood that only the real part of the complex expression is used. The wave described by Eq. 23) A where A is the wavelength. The particle displacement in the liquid at a given instant t and position z is denoted by w. The displacement amplitude is denoted by W. 3. Compressibility One of the characteristics of a liquid which relates to the propagation of sound is its compressibility which we shall denote by the symbol ß.

8. This hologram (a) and its reconstructed true image (b) demonstrate the power of the Leith-Upatnieks technique. The image is completely separated from the zero-order light and the out-of-focus conjugate image. 25 Holography and These expressions are the equivalents to Eqs. 14), but are in a form suited to illustrating the separation of the diffracted beams. 20) represents a replica of SI (x, y) propagating at the angle CPI. 22) which for small angles can be written as 2cp2 - CPI. The complete Leith-Upatnieks holography system is shown in Fig.

However, in connection with scanned holography, which we discuss later in this book, we introduce a very important concept that allows one to overcome this type of distortion. Consequently, we fee! this discussion is appropriate to include here. Ifwe consider the magnification equations, we see that radial magnification has, in general, a different magnitude than the lateral magnification. This is true of all imaging systems. 68) where we have used the paraxial approximation. This formula is known as MaxwelI's elongation formula PS].

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