4500PW03 - Weierstrass Solid Immersion Lens -...

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Unformatted text preview: Weierstrass Solid Immersion Lens - Magnification and Distortion A Weierstrass solid immersion lens is u‘Sed in a compact disk optical reader. In operation, the compact disk tracks are immediately adjacent to the flat surface of the lens. A Weierstrass solid immersion lens is shown in the figure. The refractive index of the, lens is m. The refractive index of the surrounding medium is m. The radius of cur— vature is R. The Weierstrass solid immersion lens is a truncated sphere with a thickness of (1 + rig/720R. An object on the compact disk is at the flat surface of the lens extending from the axisof the lens to its tip at height h. Two rays from the tip of this object are shown in the diagram. Projecting the refracted rays (right-hand region) back to the left, the image may be visualized. From the exact ray—tracing expression for the magnification, derive, shewing all work, the expression for the paraxial—ray magnification, m0. Simplify your answer to the largest extent possible. Put your final ansWer in the space provided. Paraxial—ray magnification = m0 = The distortion in imaging is defined as Distortion 2 M X 100% me where a positive value corresponds to pincushion distortion and a negative value corre- sponds to barrel distortion. For the case of a lens of radius 1 mm and refractive index 1.5 in air, calculate, without approximations, the distortion for each value of h listed below. Express distortion (with a + or -— sign) as a percentage accurately to three significant figures. h (,um) Distortion (%) 300 250 200 150 ' 100 50 ‘ 10 ...
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4500PW03 - Weierstrass Solid Immersion Lens -...

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