Introduction

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 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 functions of holo­ graphy were proposed, and a few of those are starting to input the world 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 job within the box is burgeoning. 3 symposia totally dedicated to acoustical holography were held and the papers released in ebook shape. The purposeof this e-book is to assemble the result of examine in acoustical holography, a few of it as but unpublished, lower than one hide in order that staff in holography, nondestructive trying out, scientific imaging, underwater imaging, and seismic exploration can come to a decision even if this new procedure will be invaluable to them.

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19) ([a I2(x, y) This expression is equivalent to Eq. 11). 20) OBJECT WAVf. f3:;:::::-.. OB JECT 2 REFERENCE WAVf. \~ 1111 WAVf. RECORDING PlANE CONJUGATE IMAGE WAVf. TRUE IMAGE (V I RTUALI sin -1 (2 sin 1112 - sin 11111 . / RECONSTRUCTION WAVf. V. z )J1i;:::::,.... 1111 y' Y TRUE IMAGE WAVf. HOLOGRAM WAVE Fig. 7. The physical relationship between object, reference, reconstruction and image waves for Leith-Upatnieks holography is shown here. In this case we are illuminating the hologram so as to obtain the true image.

Rb ............... RECONSTRUCTION SOURCE HOLOGRAM Fig. 15. The image reconstruction from a magnified hologram at a different frequency is shown in this drawing. Chapter 2 42 of the radiation at the true image point becomes where (rl ' - r2')x' denotes that the substitution x = x' Im has been made. 74) Since we wish to find the size of the image point at the image plane, we substitute the image location Eq. 54) into Eq. 78) The Rayleigh resolution criterion states that two points in object space are 43 Holography resolved if the point of maximum intensity of one image falls on the point of zero intensity of the seeond image.

Phys. 4:302 (1965). 5. A. Lohmann, Optical single-sideband transmission applied to the Gabor microscope, Opt. Acta 3:97 (1956). 6. E. N. Leith and J. Upatnieks, Reconstructed wave fronts and communication theory, J. Opt. Soc. Am. 52:1123 (1962). 7. J. B. DeVelis and G. O. , Chapt. 2 (1967). 8. M. Born and E. , New York, p. 382 (1964). 9. M. Born and E. , New York, p. 428 (1964). 10. R. F. van Ligten, Influence of photographic film on wavefront reconstruction I; Plane Wavefronts, J. Opt. Soc. Am.

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