By B. P. Hildebrand
Since the 1st papers by means of E. N. Leith and J. Upatnieks with regards to holography seemed in 1961, there was a digital explosion of analysis task 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 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 learn job within the box is burgeoning. 3 symposia entirely dedicated to acoustical holography were held and the papers released in booklet shape. The purposeof this ebook is to assemble the result of learn in acoustical holography, a few of it as but unpublished, less than one hide in order that employees in holography, nondestructive checking out, scientific imaging, underwater imaging, and seismic exploration can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 method should be invaluable to them.
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Additional resources for An Introduction to Acoustical Holography
11. 6. IMAGE LOCATION Up to this point in our discussions we have obtained only qualitative results. What'happens if we use different wavelengths or propagation media for recording and illuminating the hologram, or if the illuminating beam is not an exact replica of the reference be am ? To answer these questions we must perform a quantitative analysis based upon the very general arrangement shown in Fig. 12. In this analysis we assume that the primary radiation source is a perfect point. 12 shows the general recording arrangement, where for simplicity we have shown only two dimensions.
In addition, we have the first term which also propagates in the same direction. We can ignore the space variant portion a 22 (x, y) of the first term since A2 ~ a 2 2 • Thus, if we place a photographic plate at the position of the conjugate image we obtain a picture of the object added to a uniform background due to the true image wave propagated over the equivalent distance 2z1 . If the object consists of a few dense points in a transparent field and if the distance 2z1 is quite large, the result will be TRUE IMAGE lVlRTUAU HOLOGRAM ) I __ ~ b CONJUGA TI IMAGE IREAU 1-- - c Fig.
J Q = mA (~)! 89) A comparison of this expression with Eq. 80) shows that the radial resolution is worse than lateral resolution by a factor 2r1 /A. We now wish to show that the Rayleigh resolution criterion can be related to the change in the interference ring density on the hologram as the object point is moved. We do this by defining aresolution criterion and then using it to obtain the resolution in object space. A comparison of this expression with the one derived previously shows that they are the same.
An Introduction to Acoustical Holography by B. P. Hildebrand