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Optical Engineering Science. Stephen RoltЧитать онлайн книгу.

Optical Engineering Science - Stephen Rolt


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of the function of an achromatic doublet."/> equation

      Thus, the two focal lengths are simply given by:

      In the thin lens approximation, therefore, light will be focused at the same point for the red and blue wavelengths. Consequentially, in this approximation, this system will be free from both longitudinal and transverse chromatic aberration. The simplicity of this approach may be illustrated in a straightforward worked example.

      Worked Example 4.6 Simple Achromatic Doublet

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       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.

      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.

      4.7.5 Optimisation of an Achromatic Doublet (Infinite Conjugate)

      Without going through the algebra in detail, it is clear that having determined both t1 and t2, Eqs. (4.30a) and (4.30b) give us two expressions solely in terms of s1 and s2. These expressions for the spherical aberration and coma must be set to zero and can be solved for both s1 and s2. The important point to note about this procedure is that because Eq. 4.30a contains terms that are quadratic in shape factor, this is also reflected in the final solution. Therefore, in general, we might expect to find two solutions to the equation and this, in general, is true.

      Worked Example 4.7 Detailed Design of 200 mm Focal Length Achromatic Doublet

      At this point we illustrate the design of an air spaced achromat by looking more closely at the previous example where we analysed a 200 mm achromat design. We are to design an achromat with a focal length of 200 mm working at the infinite conjugate, using SCHOTT N-BK7 and SCHOTT SF2 as the two glasses, with the less dispersive N-BK7 used as the positive ‘crown’ element. Again, the Abbe numbers for these glasses are 64.17 and 33.85 respectively and the nd values (refractive index at 589.6 nm) 1.5168 and 1.647 69. From the previous example, we know that focal lengths of the two lenses are:

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