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The lens-grain analogy

The outstanding properties of lenses have been well known since Gallileo Gallilei. In the early nineteenth century, the birth of Fourier optics theory gave a better understanding of optical waves and their behavior with respect to lenses. One of the most important properties is the existence of a focal plane behind the lens where the energy of a normally incident plane wave focuses. A grain can be thought of as a spherical lens whose focus is the center of the grain. From this point, the diffracted wave radiates spherically as shown in Figure (6). The amplitude of this wave is weak and decays with distance as 1/r, whereas the incident plane wave travels without amplitude decay.

 
Foptics
Foptics
Figure 6
The lens-grain analogy. The focus of a thin lens comes closer to the lens when the radii of curvature decrease. At the limit, the focus of a spherical lens is the center of the lens.
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Stanford Exploration Project
11/17/1997