Re: [ATM] Littrow Solutions

["Richard F.L.R. Snashall" <rflrs@rcn.com>]

Richard F.L.R. Snashall wrote:
> This lens generally has coma. However, by choosing the refractive
> indices, spherical aberration can be removed.  Again, to a first
> approximation, the G-Sum must be null.  If the crown refractive
> index is known, this results in a quartic in the flint refractive
> index.  Using the crown index as the initial guess of the flint
> index for Newton-Raeffson iteration gives the following table:
>
>    Crown      Flint
>
>    1.45     1.546776
>    1.50     1.598978
>    1.55     1.652089
>    1.60     1.706211
>    1.65     1.761396
>    1.70     1.817666
>    1.75     1.875025
>
> A cubic fits this within about 2e-5:
>
>     0.056558x^3 - 0.063360x^2 + 0.861277x + 0.258722
However, if one wanted to solve for nulling the coma G-Sum, instead,
the results would be:

    Crown       Flint


    1.45      1.393162
    1.50      1.457427
    1.55      1.524025
    1.60      1.592755
    1.65      1.663443
    1.70      1.735932
    1.75      1.810081

The fitting cubic is:

    -0.223093x^3 + 1.465059x^2 - 1.580081x + 1.284117

I suppose the next question is "Can it have both?".  The answer
appears to be yes and no.  When the crown refractive index is
1.933863 and the flint refractive index is 2.095067 (with the
same 1:2 ratio of dispersions), the Littrow doublet nulls both
spherical aberration and coma.


Oh well...
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