A chromatic or color-corrected lenses for use in the visible portion of the electromagnetic spectrum have been addressed in literature, textbooks, and industry journals as early as the 18th Century. Many of these accounts by scientists and optical designers detail a method of selecting two dissimilar materials to form an achromatic pair or doublet with the ability to greatly counter image blurring resulting from the dispersive nature of refractive optical elements. Whether these tried and true optical formulae produce equally successful results in wavelengths beyond the visible range warrants further examination.

Figure 1. Transmission of Schott BK7 optical glass.
Recent efforts have demonstrated considerable promise in producing lenses and optical systems that deliver images captured in the non-visible wavelengths with enhanced resolution and contrast. These unique optical designs are greatly improving the way in which high-quality imaging in the near-infrared/shortwave infrared (NIR/ SWIR) wavelengths is achieved.

Figure 2. Achromatic doublet model of positive crown and negative flint elements.
Unlike the more extreme regions of the infrared, shorter wavelengths are transmitted well by the majority of glass materials used to design visible lenses. Figure 1 indicates the transmittance from 300 nm out to about 2.5 microns for one of these types of glasses, the Schott BK7.

Figure 3. Dispersive properties of optical material.
This seemingly attractive characteristic of optical glass may perhaps be the major contributor to the common misconception that optics designed for visible imaging, since transparent in SWIR light, must also offer comparable imaging performance in the SWIR.

Figure 4. Achromatic doublet now including defocused SWIR energy.
To understand why this is not the case, one must consider how light “bends” or refracts through a transparent medium. The most commonly known effect of dispersion in optics is the separation of white light into the full-color spectrum created by a prism. This phenomenon is scientifically explained by an equation known as Snell’s law, which describes how the angle of refraction for a particular wavelength of light in a prism depends on the refractive index of the prism material. As the refractive index is dependent on wavelength, the angle by which the light is refracted must also be dependent on wavelength, and therefore not constant. Furthermore, since the degree and consistency by which light is refracted in a medium is dependent on wavelength, a material will, for the sake of simplicity, change the way it behaves depending on the band in which it is operating.

The fact that the refractive index of any material is a nonlinear relationship is an added complexity that is not as commonly known. This means that the angle through which light changes with respect to wavelength is better expressed as a polynomial function rather than a linear one.