chapter 5, Design Examples

Excerpt

Having discussed materials, manufacturing methods, and design guidelines in the previous chapters, we now present several design examples. The examples are intended to show several different design considerations, such as using a diffractive surface for color correction, the trade between number of lenses and performance, and the effect of the selection of probability distributions of tolerances. We also consider a more unusual system: a higher-order diffractive.

5.1 Singlet Lens

Probably the simplest example of a plastic optical system is one that uses only a single lens. In this section, we consider the design of a singlet plastic lens and compare its performance to that of a cemented glass doublet. To compare the two systems, we will use a 100-mm EFL f/4 lens, with a full field of 2 deg. This combination of EFL and f/# means that the lens will have an entrance pupil diameter of 25 mm. For the wavelengths, we use the d, f, and c lines (587.6 nm, 486.1 nm, and 656.3 nm, respectively), equally weighted.

We begin the comparison by designing a cemented achromatic glass doublet. We select two glasses, one crown and one flint. For the crown, we select N-SK5, which has a glass code of 589.613. For the flint, we select N-F2, which has a glass code of 620.364. We initially set the thickness of each element equal to 3 mm, about one-tenth of the diameter. We allow all three radii (we assume the cemented radii are equal) to be varied by the optimization algorithm. In reality, we may want the cemented radii to be slightly different so that they do not make contact at the center of the surfaces, but we do not concern ourselves with that now. We use the default (rms wavefront) merit function, with the additional constraint of requiring a 100-mm EFL. We initially set the radius of the first surface to be 100 mm and the second surface to be −100 mm, so that we have a positive-powered doublet as our starting point.

Running the optimization algorithm, we obtain the doublet shown in Fig. 5.1. We can see from the figure that the edge thickness of the front lens (lens 1) is not sufficient. In fact, the front and rear surfaces of the lens have “crossed over.” This is due to the initial thickness that was set as well as the fact that no edge thickness constraint was applied. Some optical design software has default settings that will prevent this from happening, while others do not impose such a constraint. This is mainly a result of the philosophy of the software developers. In order to get a realistic edge thickness, we increase the center thickness of the front lens to 6 mm and rerun the optimization algorithm. With the increased center thickness, the lens 1 surfaces no longer cross over, and a reasonable edge thickness is obtained. The optimized system is shown in Fig. 5.2.