TheSkySearchers

... a historical math approach, not only of interest for our not Fritz Argelander.

From the historical perspective,
there is a downloadable article on the Conrady's Chromatic Condition (in the optical system with the lenses)
in the JRNBS, Vol. 52, No. 1, January 1954, by Donald P. Feder
available as *.pdf
https://www.google.com/url?sa=t&rct=j&q ... P-I2qKx5bw

Happy reading on the rainy days,
JG

I usually look at several factors, such as those in this chart.
I used to own a 4" f/15 doublet refractor, which did not conform to the Conrady standard for absence of CA (f/20+), but did correspond to the Sidgwick standard (f/12+)
I could see no color at all at over 200x.
Many of today's doublets have so much color I call them "Jimi Hendrix" scopes ("Purple Haze").

Hello Don,

and thank you for reminding the Conrady/Sidgwick matrix, which is very popular across The Pond, I mean in the U.S. and Canada.

There is a sort of conceptual problem with what the author(s) are calling the "CA index": f-ratio devided by the objective diameter (in inches).
This "CA index" smells to me like an inverse of truncated étendue. The truncation might have served to the purpose of getting the matrix quasi-diagonal.

Otherwise,
it is comprehensible by means of a trained intuition,
that the high étendue achromats (large aperture and high speed) will deliver more chromatic aberration
than the low étendue achromats (small aperture and low speed).

Another conceptual problem emerges with the "Visual Levels of Chromatic Aberration", on which I will comment later.

Best,
JG

JG,
Yes, it is more of a subjective scale and applies more to the older crown/flint objectives of 100 years ago than it does today in the era of FPL-53 and FCD100 glass.
There is math behind the CA index, however, in determining the amount of defocus at the spectral extremes.
A real examination has to be a lot more nuanced.
A more scholarly approach can be found here:
https://www.telescope-optics.net/refractor.htm
and in the pages that follow.

Hello Don,

I can easily decloak the matrix and put an explanation for the CA index, no problem, and with pleasure.
And I can return the matrix for other glass materials as well.

For the optics calculations, there are more modern (in terms of the mathematics) references than the telescopeѲptics.net.
This should be somehow updated for our forums.

Best,
JG

True.
Vlad's work is a bit dated for the most recent developments in refractor lenses and glass types.
Fortunately, progress never stands still.
When describing CA as visible or invisible, however, that becomes a subjective evaluation.
And it also depends on circumstances.
In night use, I never saw CA in my 102mm f/15 refractor (CA of 3.75), but in the daylight I did.
I presume the activation of the cones in my eyes made me more sensitive to deep violet as well as orange and red, colors essentially invisible at night with scotopic vision.
And there is more than CA Index involved with more complex lenses.
My f/7 triplet is CA-free when in exact focus, but displays color on either side of focus.
In contrast. an f/5.4 quadruplet lens scope I once owned displayed no color when slightly out of focus on either side.
Optical lens configurations on modern scopes are all over the place in terms of their color correction.

Personally, I prefer scopes with mirrors, but, even there, lens assemblies are added to provide coma correction and magnification, so we don't escape from the issue of CA.

I look at that chart as less of a visible color chart and more of a chart describing how picky an observer is

I do agree Bill, some people seem to be of the opinion that if a refractor shows any colour it needs to be condemed as unusable.
I thoroughly enjoy using my various achromats and have even been thinking of a Vixen A105M to add into the mix.