Luneberg lens
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A Luneberg lens is a spherically symmetric, variable-index refracting structure which will form perfect geometrical images of two given concentric spheres onto each other. The Luneberg lens is a spherical lens (usually a ball lens) generally having a gradient of decreasing refractive index n radially out from its center. The focusing properties of the Luneberg lens can be achieved through an infinite number of refractive-index solutions. The simpliest such solution was proposed by R. K. Luneberg in 1944.[1] Luneberg's solution for the refractive-index creates two conjugate foci outside of the lens. The solution takes a simple and explicit form if one focal point lies at infinity, and the other on the opposite surface of the lens. J. Brown and A. S. Gutman subsequently proposed solutions which generate one internal focal point and one external focal point.[2][3] These solutions are not unique; the set of solutions are defined by a set of definite integrals which must be evaluated numerically.[4]
[edit] Luneberg's solution
Each surface point of an ideal Luneberg lens is a focal point for parallel radiation impinging from the opposite side. This kind of lens is usually employed for microwave frequencies, especially to construct efficient microwave antennas and radar calibration standards. The practical implementation is normally a layered structure of concentric shells of differing refractive index. The outermost shell has n=1.0.
[edit] Luneberg lens radar reflector
Radar reflectors can be made with Luneberg lenses. These are usually designed for the X band. As the dielectric has little variation with frequency in the microwave band, the Luneberg radar reflector performs well across a wide band.
[edit] References
- ^ R. K. Luneberg, Mathematical Theory of Optics (Brown University, Providence, Rhode Island, 1944), pp. 189-213.
- ^ J. Brown, Wireless Engineer 30, 250 (1953).
- ^ A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
- ^ S. P. Morgan, "General solution of the Luneberg lens problem," J. Appl. Phys. 29, 1358-1368 (1958).
