Section 2 - Ok, the we use lenses � but why not air spaced ones?

So, returning to our previous topic, the curvature radiuses of the glass surfaces surrounding the oil immersion have to exactly match each other, and the oil immersion is so thin, that it has practically zero effect optically. This is true for two reasons, one of them is that the oil immersion has similar thickness everywhere (as it is between two parallel surfaces with exactly the same curvatures), so we can think of it like an extremely thin lens member with parallel surfaces. A member like this has almost null optical effect, as it does not change the direction of light passing through it. The other reason why it has practically zero optical effect is the fact, that the oil is chosen to closely match the refraction index of the glasses around it (at least in green light). For this reason, green rays go through the oil immersion without even noticing that they crossed borders of different optical materials, as the refraction index does not change within the lens.

Now the above mentioned facts have several results:

As the curvature radiuses surrounding the oil must be exactly the same, and the oil layer has extremely little thickness with no real optical effect of its own, the designer of the lens has less freely variable parameters when designing an oil spaced lens (compared to an air spaced one). An air space gives three free variables to the lens: two possibly different radiuses, and the thickness of the air space. But in the case of an oil space, we can vary only the (common) radius of the surrounding surfaces, nothing else. As the number of free parameters is less in the case of an oil spaced lens, theoretically air spaced lenses can be better corrected for optical aberrations than their oil spaced brothers, as the designer can vary more parameters to achieve excellent correction for every aberration. This is what theory says. But in practice (at least above about F/6 focal ratio) there are still enough free parameters in an oil spaced triplet lens to make it practically as perfectly corrected as a similar air spaced lens. Though, in the case of an oil spaced doublet lens, there would not be enough free parameters to correct it at the same time for spherical aberration, coma and chomatic aberration (this is true at least using optical materials we have ever heard about yet). For this reasion, practically all currently produced doublet lenses are air spaced designs, and we can find oil spaced lenses only with triplet configuration on the market (at least today). If we would allow the lens to produce some off axis coma, then it would be possible to construct a doublet oil spaced lens, but no manufacturer we know about accepts this compromise, as one of the main advantage of refractor lenses compared to mirrors is that they are essentially free of coma.
As oiled triplet lenses offer less degrees of freedom for the designer, to construct a practically perfectly corrected oil spaced triplet lens (matching a similar air spaced lens in every respect), the designer has to use glass materials that have refraction indexes as close to each other as possible. This means, that not every abnormal dispersion (ED or fluoro-crown) glass material can be used to construct an oil spaced lens, only those are usable that have a standard glass pairs (for the mating elements) matching both the refraction index and partian dispersions (e.g. color error) of the ED glass. If we use such glasses, than the oil spaced lens will be similarly well corrected for every aberration as a similar air spaced lens, at least at standard focal ratios. In this range, there is no real difference between an oil spaced and an air spaced lens regarding correction for any optical aberration. Though, under about F/6 focal ratio, the 5th order spherical aberration starts to quickly increase in the case of the oil spaced lens, and from this moment, the maker of the lens has to use aspheric figuring to correct it, which is time consuming and expensive. For this reason, there are hardly any oil spaced lenses at or under F/6 focal ratio, and in this range air spaced lenses are a clearly better (at least using today available optical materials). But above F/6.5, there is practically zero difference between the correction level of an air spaced and oil spaced triplet lens, built with similar optical materials.
The need to use materials with similar refraction indexes in an oil spaced lens have yet another advantage: as all the material inside the lens has the same refraction index (at least in green light), the light crosses the lens without any internal reflections. This reduces the probability of internal ghosting to practically zero, and also the light throughput of the lens will be excellent, as there are only two air to glass surfaces where reflections happen. If we apply multi coatings on these surfaces, the lens will have an excellent transparency and contrast.
And yet another advantage of the similar refractive indexes: an oil spaced lens in green light is practically equivalent to a simple lens with homogenous internal material and only two air to glass surfaces. This means, that even if the figures of the internal lens surfaces would not be perfect, the effect of this problem on the wavefront of the lens in green light would be nearly zero. And theoretically there are NO perfectly figured surfaces on any lens in reality, there is always some little difference of a real optical surface compared to the theoretically perfect surface. We can say, that in the case of air spaced lenses, there are 4 surfaces (in case of doublets) or 6 surfaces (in triplets) to distort the wavefront. In the case of an oil spaced triplet lens, this number is only 2, as the internal surfaces have practically zero effect on the wavefront. For this reason, oil spaced lenses have usually less wavefront error (if the surfaces are polished to similarly accurate figure).

So, after thinking over the above mentioned reasons, we can conclude, that both air spaced or oil spaced designs are usable to achieve an optically highly corrected objective lens, at least in the focal ratio range that we would like to use.

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