An Introduction to Acoustical Holography by B. P. Hildebrand

By B. P. Hildebrand

Since the 1st papers through E. N. Leith and J. Upatnieks as regards 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 purposes that looks to carry nice promise is acoustic imaging through holography. the 1st papers in this topic seemed in 1966. yet already learn 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 the aim of this ebook is to collect the result of study in acoustical holography, a few of it as but unpublished, below one hide in order that employees in holography, nondestructive trying out, clinical imaging, underwater imaging, and seismic exploration can make a decision no matter if this new procedure might be necessary to them.

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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 ~I. 22) which for small angles can be written as 2~2 - ~I. The complete Leith-Upatnieks holography system is shown in Fig.

28). The amplitude of the light reaching Q is proportional to Sb(Xb, Zb) = f [/ 1 (x) + A 1A 2* f x r ll [(R 2' X * + r2') - ~o' + ro' + r (Xo, ZO)S2(X 2, Z2)Sa(X a , Za)rll V2( t - R a' + rc:' + r b') dx dX a dZ a Sl(X 1 , Zl)SO(XO, ZO)S2*(S2' z2)six a , Za) dX 1 dZ 1 dxo dz o dX 2 dZ 2 dX a dZ a dx X So X ( + 12(X ) ]sixa , Za) V 2 t - 1')] (t _ Ra' + ::' + rb') V2 + Al*A 2 f Sl *(Xl , Zl) [(Ro'+ ro'+ rn - (R2'+ r2')] Cl R'+r'+r') a c: b dX 1 dZ 1 dx o dzo dX 2 dZ 2 dX a dZ a dx By the Weiner-Kintchine theorem, we may replace the correlation function by apower spectral density pa].

1. The Force Equation Consider the force on a small volume Llx Lly Llz ofliquid such as shown in Fig. 2. Let P(x, y, z) denote the pressure in the liquid at the location (x, y, z). 13) Acoustics 53 Fig. 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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