Читать книгу Optical Engineering Science - Stephen Rolt - Страница 92

We wish to construct and achromatic doublet with a focal length of 200 mm. The two glasses to be used are: SCHOTT N-BK7 for the positive crown lens and SCHOTT SF2 for the negative lens. Both these glasses feature on the Abbe diagram in Figure 4.24 and the Abbe number for these glasses are 64.17 and 33.85 respectively. The individual focal lengths may be calculated using Eq. (4.52):

Therefore, the focal length of the first ‘crown lens’ should be 94.5 mm and the focal length of the second diverging lens should be −179 mm.

Thus far, the analysis design of an achromatic doublet has been fairly elementary. In the previous worked example, we have constrained the focal lengths of the two lens elements to specific values. However, we are still free to choose the shape of each lens. That is to say, there are two further independent variables that can be adjusted. Achromatic doublets can either be cemented or air spaced. In the case of the cemented doublet, as presented in Figure 4.25, the second surface of the first lens must have the same radius as the first surface of the second lens. This provides an additional constraint; thus, for the cemented doublet, there is only one additional free variable to adjust. However, introduction of an air space between the two lenses removes this constraint and gives the designer an extra degree of freedom to play with. That said, the cemented doublet does offer greater robustness and reliability with respect to changes in alignment and finds very wide application as a standard optical component.

As a ‘stock component’ achromatic doublets are designed, generally, for the infinite conjugate. For cemented doublets, with the single additional degree of design freedom, these components are optimised to have zero spherical aberration at the central wavelength. This is an extremely important consideration, for not only are these doublets free of chromatic aberration, but they are also well optimised for other aberrations. Commercial doublets are thus extremely powerful optical components.