Re: [ATM] Secondary Spectrum Estimator

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

Richard F.L.R. Snashall wrote:

>
> I welcome comments.  I think it will work to create a good
> secondary spectrum estimates, both in-band (F-e equivalent)
> and out-of-band (g-F equivalent).

Not bad... for being totally wrong.  The derivative estimate
leaves a lot to be desired.

In view of that, I have gone quite the other way.  But I
still use the Buchdahl base.  Basically, this base is now
used as a map from (singularity, infinity) to
(-infinity, infinity).  Given the map from {C,e,F,g} to
{HC,0,HF,Hg} and a given wavelength lambda mapped to
Hlambda.  The values {Hlambda+Hc,Hlambda,Hlambda+HF,Hlambda+Hg}
can be mapped back to four wavelengths that "look like"
but are shifted from C, e, F and g. (Yes, I know that the map
from Hlambda back is to lambda.;-)

The new model uses these mapped values to compute the dispersion,
Abbe number, and partial dispersions.  The only additional
requirement was the definition of a new form of Abbe number --
v = (ne - 1)/(nF - nC).  Basically, this Abbe number differs
from the traditional vd by the partial dispersion Ped,
i.e.: v = vd + Ped; the value of Ped is just under 0.235 for
normal glasses.

In addition, the difference of the partial dispersions from the
normal line is evaluated relative to the new Abbe number:

    PFe = 0.48857884 - 0.00052727 v + dPFe
    PgF = 0.64456089 - 0.00168753 v + dPgF

not a huge amount different from those base upon vd.

In the end, though, I use the refractive indices for the four
wavelengths to compute both in-band ("F"-"C") and out-of-band
("g"-"F") estimates of longitudinal error at the 70% zone.
This new estimate is available in the updated GeeWyld programs:

    http://users.rcn.com/rflrs/GeeWyld1_4_2.jar
    http://users.rcn.com/rflrs/GeeWyld1_5_0.jar
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