Published 17.9.2018

The calibration unit of the ESO SOXS telescope which Incident Angle is developing for FINCA at the time of writing this, operates over a wide spectral range from VIS to NIR. In order to achromatize the collimating lenses, the indices of refraction had to be recalculated.

Achromatization of a pair of lenses is generally straightforward calculation involving indices of refraction and Abbe numbers for the glasses. The well-known formulas for color-correction can be found even in Wikipedia. The formulas are valid for any chosen wavelength pairs, and moving from visual spectral range to others is not a problem, nor is fitting one wavelength from VIS to another in NIR, which was done in the SOXS case.

As you can see, the listed Abbe value is specifically defined to achromatize F and C lines, using indices of refraction at those wavelengths. In order to circumvent this, the indices of refraction must be recalculated using the Sellmeier equation.

where B and C are Sellmeier coefficients, which are listed in glass catalogues. By reclaculating, you can get the indices of refration at specified wavelengths, which in turn you can use to calculate Abbe number for the chromatic correction profile of your choosing.

You can read more about SOXS and our involvement in the project also from SPIE digital library.