Aberrations and Plano-convex lenses

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## Aberrations and Plano-convex lenses

Let us look at the effects of using spherical surfaces instead of Cartesian ovals. There are two classes of aberrations, some effects are monochromatic and others are chromatic. Chromatic aberrations rise because the light of different wavelength have different indices of refraction. Because only quasi-chromatic laser light (more or less monochromatic light) will be used in this work only monochromatic aberrations are discussed.

The first approximation made when deriving equation was the series expansion of . Deviations from this first order theory was first studied by Ludwig von Seidel, and are known as Seidel aberrations[17]. To the first order the series expansion of sin gave (equation ) n_1s_1+n_2s_2 & = & n_2 - n_1R, whereas to the third order is found[17] n_1s_1+n_2s_2 & = & n_2 - n_1R+h^2 [n_12s_1( 1s_1+1R)^2+n_22s_2(1R-1s_2)^2].

The effect is that the focal point for light hitting the surface far away from the vertex is focused towards a point closer to the vertex than the light in the paraxial region. The distance between the axial ray focus and the paraxial ray focus () is called the longitudinal spherical aberration. In aberrations the longitudinal spherical aberration is positive, but for a surface with negative curvature the focal point will be further away from , and longitudinal spherical aberration will be negative by sign convention. If a screen is placed at the image appears as a bright spot from the rays in the paraxial region and a symmetrical halo from the marginal rays. For extended objects the effect is reduced contrast and lower resolution.

For light not entering parallel to the optical axis (the normal to the surface in the vertex) there is also a transverse or lateral spherical aberration. It is not treated here because it does not arise in our system. The same holds true for several other types of aberrations.

By choosing the shape of the lens appropriately the aberration effects can be minimized. For instance, with a plano-convex lens the longitudinal spherical aberration depends on the orientation of the lens (see planoconvex.)

An approximation that the lens was infinitely thin () is made in formula . When considering finite width the focal length is changed. This gives rise to different transit times of the light rays depending on where the rays hit the surface. If a dynamic object is imagined the image may have a different time behavior than the object.

Next: Diffraction and finite Up: Some topics in Previous: Some useful formulas

Thomas Walmann
Fri Apr 7 16:34:05 METDST 1995