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Explanation of an achromat from SPIE Press

Excerpt from Optical Design Fundamentals for Infrared Systems, Second Edition

A thin achromat can be corrected for third-order spherical aberration, coma, and axial chromatic aberration. The combination consists of a positive and a negative element. To eliminate axial chromatic aberration, a simple relation between powers and Abbe numbers of the two elements must be met. This relation is

Equation 3.28.

And, since φ = φA+ φB,

Equation 3.29.

The process of deriving the complete prescription for such a doublet is straightforward but too cumbersome to be included here.1

AchromatThe radii as a factor of an achromat’s focal length are listed in the table below for two objectives: one for the MWIR and one for the LWIR region. For the MWIR lens, silicon and germanium have been the materials chosen, and the combination Amtir-1/zinc sulfide was selected for the LWIR objective. Amtir is an acronym for amorphous material transmitting infrared radiation. The composition of Amtir-1 is 33% Ge, 12% As, and 55% Se.

Radii of lens elements for two selected achromats.

Spectral regionMWIR
(3 – 5 μm)
(8 – 12 μm)
Front elementSiliconAmtir-1
Rear elementGermaniumZinc sulfide

These choices are a sound starting point that lead quickly to good solutions in terms of optimization with the computer after adding thicknesses and spacings.


  1. M. J. Riedl, “The Thin Achromat,” Electro-Optical Systems Design, Cahners Publishing Co. (September 1981), pages 49–52.

M. Riedl, Optical Design Fundamentals for Infrared Systems, Second Edition, SPIE Press, Bellingham, WA (2001).

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