<P> The use of achromats was an important step in the development of the optical microscope and in telescopes . </P> <P> An alternative to achromatic doublets is the use of diffractive optical elements . Diffractive optical elements are able to generate arbitrary complex wave fronts from a sample of optical material which is essentially flat . Diffractive optical elements have negative dispersion characteristics, complementary to the positive Abbe numbers of optical glasses and plastics . Specifically, in the visible part of the spectrum diffractives have a negative Abbe number of − 3.5 . Diffractive optical elements can be fabricated using diamond turning techniques . </P> <P> For a doublet consisting of two thin lenses in contact, the Abbe number of the lens materials is used to calculate the correct focal length of the lenses to ensure correction of chromatic aberration . If the focal lengths of the two lenses for light at the yellow Fraunhofer D - line (589.2 nm) are f and f, then best correction occurs for the condition: </P> <Dl> <Dd> f 1 ⋅ V 1 + f 2 ⋅ V 2 = 0 (\ displaystyle f_ (1) \ cdot V_ (1) + f_ (2) \ cdot V_ (2) = 0) </Dd> </Dl>

The focusing of different colors of light at different distances behind a lens