J. Eur. Opt. Society-Rapid Publ. 21, 27( 2025) 297
agrees with the estimation resulting from U dC
1; 2
. A detailed look reveals, that for material-combinations that produce a lower minimum than f1 d; 2 > f 1; 2ðkÞ, the estimation may underestimate the numerically correct slope at k C. This miss-estimation could be compensated by changing k d to be closer to k C. However, this may disagree with the actual design wavelength of the stock lens. Furthermore, the underestimation is safer for the actual design, because demand( II) should be maximized. This may compensate the limitations of the applied paraxial estimation.
As the keen reader now probably already found, the just shown results from two positive lenses are harboring an erroneous result for practical systems. In reality, two simple positive spherical lenses made of typical refractive material cannot fulfill the achromatic condition. This is because of the dispersion that appears due to the so far neglected thickness of the lenses. Especially for larger s i, this results in large axial chromatic dispersion. Therefore, here the discriminator is introduced in equation( 12) to judge the confidence about the paraxial estimation result.