Expanding on the previous case for a single lens in Chapter 2, we develop expressions for elements of a multiple lens arrangement, made from the same material and individually bent for minimum spherical aberration.
We then demonstrate the benefit of an aspheric surface. This is especially of interest for elements used in the infrared spectrum because they can be routinely machined with the process of single-point diamond turning.
Coma can be eliminated by properly shaping the single element or by placing the aperture stop at a specific position, which is referred to as the natural stop position. Details will be covered under this Chapter.
3.2 Best Shapes for Minimum Spherical Aberration
To expand on the general case for a single lens with the object located at any position as discussed under Chapter 2, one can develop the following expressions if all elements of a multiple lens arrangement are made from the same material and individually bent for minimum spherical aberration. The surface curvatures of the elements are as follows:
For the first surface (front surface) of element j, curvature is c j1 =n (2n+1) Ï+2 (n+1) v.
In this equation and in the following, j is the element number, and i is the total number of elements in the set.
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