A triplet is a system of three lenses. In a straightforward way, one might derive the matrix of a three-lens arrangement by concatenating the matrices of thin lenses and air spacings. Again, it is advantageous for the discussion to reference the spacings that intervene to the focal planes of the lenses. With this prerequisite, we can now state the design approaches for a focusing triplet, an imaging triplet, an afocal triplet, or a collimating triplet. Making reference to the consideration on the matrix entries, we can state the points of departure for the triplet synthesis in these four cases.
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