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Apochromatic
Unlike other articles, this one has a more pedagogical purpose.
In the next post we will review the fundamentals of an apochromatician and show five different apochromaticians.
Figure 1 shows the three conditions that an apochromatic must meet. The first condition is about power, the second about the primary color and the third about the secondary color.
Looking briefly at Figure 1 we see that we have a system of three equations with three unknowns. We can clear the power of the three elements to later calculate the curvatures. In Figure 2 I leave the equations already cleared, where "P" is the partial dispersion, while "v" is the Abbe number.
Figure 1. Conditions of an apochromatic crystal.
Figure 2. Power calculation for an achromatic triplet
The selection of crystals in this case is fundamental. The rules are:
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The first and second crystals must have a similar dispersion and refractive index.
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The third crystal will have a lower index and a greater dispersion.
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All three will have a very similar partial dispersion.
In Joseph M. Geary's book he gives as examples the SSKN5-BAK1-FPL53 crystals (in that order). The technical characteristics of the crystals can be easily consulted through the web https://refractiveindex.info/
Several examples are shown below. All triplets with a focal length of 400 mm and span 5º of field with a f-number is 10.
Figure 2. Apochromatic version 1
Figura 3. Cálculo de potencias, radios y separación de las lentes de la parte anterior.
Figure 3. Apochromatic version 2
Figure 4. Apochromatic version 3
Figure 5. Apochromatic version 4
In all cases we see how the Chromatic Focal Shift passes at least four times the zero value.
Before closing the article, I would like to point out that acromaticity can also be achieved only with a doublet as shown in Figure 6.
Figure 6. Apochromatic doublet.