Re: [ATM] stalking the wild achromat - and thoughts on a variable-focus telescope design...

["dave w" <daze39@earthlink.net>]

"Richard F.L.R. Snashall" wrote:
> 
> dave w wrote:
> >
> > There do seem to be a few cases with triplets that will
> > call for a deeper look: a few glass combinations where
> > there's a "sweet spot", where dividing the "compensation"
> > between two negative lenses of different glass types gives
> > a noticeably better result than using a single negative of
> > either type... alas, these effects seem to be much more
> > pronounced with a narrower wavelength range. A combination
> > that seems to have really good consistency over the 480-660
> > nm range is frequently nothing special when calculated over
> > the 350-950 nm range.
> >
> >
> A couple of things I have noted:
> 
>    a) While there are quite of few glasses that go down to the i-line
> (365.0146 nm), few are warranted to go to 350 nm -- especially on the
> flint side.  Your search in flints, especially if you restrict yourself
> to the ECO flints, will be short.

Well, the 350 nm is a bit of an arbitrary value - I can certainly try 
running with 360 or 375 as the starting point and see how the results
change - this is the range where transmission starts to drop off anyway;
no point in trying too hard to match calculated refractive values for 
light that doesn't even get through very much... so far I haven't
done anything with specific UV-cutoff wavelengths for the different
glass type (although these are listed in the Schott spreadsheet, so
I could add some code to limit the match comparison to wavelengths
longer than the UV-edge - e.g., ignore the 350 nm calculation if one
of the glass types only had a passband to 370 or something.)

As far as "ECO" vs. "classical" (lead-bearing types), I'm not 
making a distinction; Schott seems to be making a point of
keeping some of the latter types in the catalog for users who 
want their particular optical parameters and aren't limitated 
to using "ECO" types.

>    b) Imaging will nominally require a flat field; you will have a
> hard time making a flat field with a doublet or triplet.

This is where the "Petzval" designs you've been posting - the 
ones that look like they have an extra set of lenses near the 
image plane - come in?

>    c) You didn't specify any constraints on the lenses.  Does your loop
> check for the ability to actually design a good doublet or just the color
> correction?  Are you allowing for an air-space; how much lateral color
> will you be willing to allow; do the inner radii have to match?

Just primary chromatic correction so far; I haven't got to the point
of setting up ray-trace algorithms and taking a look at the geometric
end of things... I'm figuring on doing a rough comparison on the basis
of a calculated figure of merit to indicate "ability to be fabricated":
combinations with high refractive indices and large ratios of the 
relative dispersions should rate higher; low values on all these 
factors would indicate high individual curvatures for a given net 
lens system power - and I'm assuming that if the lens design starts 
to look like a whiskey-glass chasing a golf-ball, that would tend to 
get in the way of using bending and spacing to tune the geometrical 
corrections (compared to something with more "disk-like" elements).

It will be interesting to do a "scatter plot" with "achromatic
quality" on one axis and "ability to be fabricated" (as thus
calculated) on the other - that might help point up combinations
worth deeper investigation.

>    d) If you need it, the GSUM tool is always available, too. 
> I don't know if someone has put it on a Linux machine yet,
> although there was supposed to be the promise
> with Java that it should be platform independent.

Do you have a link to this?

>    e) Fun stuff!

Bob May wrote:

> The blue end of the spectrum is difficult to get to a goooood
> focus ddue to the N curves varying so much in that region.
> With triplets, you tend to make a split lens with one pair of the
> glasses so that that glass and the third glass make a very nice
> douoblet.

Yes, that's basically how my triplet search is being written - it
looks for cases where splitting the "compensation" between negative
lenses of two different glass types gives a noticeably better result
for a given "primary" lens. (I haven't yet tried the case of a split
"primary" and a single "compensator", so I don't know if there is
anything in that.)

> I am of the opinion that anybody contemplating a refractor really
> not bother unless you reqally want poor performance - this from a
> guy that is finishing up a 6" F8 refractor himself. Leavve the
> refractors to thesmall lens people for camera lenses and so forth
> and let's get some design innovation with reflectors and mixed
> telescopes.  That is where the better performance will be found
> in a telescope.

Interesting point of view, especially since one of the reasons I've
been poking into the whole achromat thing is because of some thoughts
I've had along the line of what might be called a "mixed telescope",
which I might as well go ahead and post:

I was contemplating the fact that if I were to take a negative lens (as 
would be used as a "Barlow" lens) and place it adjacent to a flat mirror,
that this combination would have similar characteristics as the convex 
secondary mirror of a Cassegrain telescope: placed a suitable distance 
inside the focus of a primary objective, it would reflect the beam to a 
more distant focus of greater effective focal length.

I then started wondering what would happen if the spacing between the
lens and the flat mirror were made adjustable...! It turns out that as
that spacing is increased, and the position of the lens/mirror "secondary
assembly" is adjusted to keep the instrument in focus (e.g., at a fixed
eyepiece location behind a perforated primary mirror), the overall 
magnification factor increases rather impressively... 

The idea awaits practical trial, but calculations (at least) 
indicate that this could be a way of building a telescope 
of long, adjustable focal length and compact overall dimensions. 
(Said practical trial would need to address the apparent extreme 
sensitivity of the focus to the distance between the primary mirror 
and the secondary assembly, especially as the magnification is 
increased.) A cam-action mechanism (like that in a zoom camera
lens) that would correlate the adjustment of the secondary
assembly lens/mirror spacing with the position of the sec.
assy. relative to the primary (at least closely enough to 
be within the adjustment of the eyepiece focuser) would be
a useful feature I think.

Since the negative lens would be the only refractive element in the
path between the sky and the eyepiece or CCD chip, its aberrations
will deserve attention... the focus sensitivity will probably also
manifest in a sensitivity to changes in the focal length of this 
lens, but for the most part (especially in the return pass of the
beam) it will operate pretty much on axis, so the optimization 
priorities may be a bit different than they would be for something
like a wide-field objective lens: off-axis coma may be less of an 
issue, really accurate achromatism might be worth struggling for, 
and the overall "bend" of the lens probably should be optimized to 
tune out the spherical aberration of the whole "zoom-Cassegrain" 
optical train.

(First trials would probably use off-the-shelf lenses just to 
see how things work out, but the design of an opitimized one 
seems like it might be worth considering, espeially for a 
larger instrument.)

-dave w

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