question about chromatic aberration

It appears that chromatic aberration becomes more noticeable as the
magnification goes up, and as the focal ratio shortens. The traditional
definition of "good enough" for an optical system was that if it was 1/8
wave, it was accurate enough. Now, this is an oversimplification, because
it seems that contrast of an image rises with more accurate systems, but in
the same way, it strikes me that there might be a point where an achromat of
long enough focal ratio would be effectively apochromatic. This is the
reason that 17th century astronomers used the great "aerial refractors" of
that period, with extraordinarily long focal ratios to get around not having
even achromats yet.

Traditionally, achromats were made f/15 or even longer. Even these had
significant chromatic aberration, from what I have read.

All of this is just to get around to the ask the question: how long of a
f/ratio would an achromat need to get the color correction of something like
the Televue Ranger? It isn't color-free, but I don't find it terribly
objectionable.

Clayton,
The Ranger's an achromat, and not a terribly good one from the examples I've
seen. Beats the heck out of an f/5 ST80, but is not in the same class as a
good 80mm f/11 achromat. YMMV.
Frank

"Clayton E. Cramer" wrote in message
...
... how long of a
f/ratio would an achromat need to get the color correction of something
like
the Televue Ranger? It isn't color-free, but I don't find it terribly
objectionable.

"Clayton E. Cramer" wrote in message
...

All of this is just to get around to the ask the question: how long of a
f/ratio would an achromat need to get the color correction of something
like
the Televue Ranger? It isn't color-free, but I don't find it terribly
objectionable.

It depends on the aperture. As the aperture increases, you need to increase
the focal ratio. So getting less color from a small aperture isn't really
that big of an accomplishment. For example, a 3" f/15 looks very nice. A 4"
f/15 shows some definite color. A 5" f/15 shows more color and a 6" f/15 is
very nice, but it is definitely an achromat.

When you get down to those overgrown finders, the color can be reduced while
maintaining a faster focal ratio.

Clear Skies

Chuck Taylor
Do you observe the moon?
Try the Lunar Observing Group
http://groups.yahoo.com/group/lunar-observing/

"Clayton E. Cramer" wrote in message ...
It appears that chromatic aberration becomes more noticeable as the
magnification goes up, and as the focal ratio shortens. The traditional
definition of "good enough" for an optical system was that if it was 1/8
wave, it was accurate enough. Now, this is an oversimplification, because
it seems that contrast of an image rises with more accurate systems, but in
the same way, it strikes me that there might be a point where an achromat of
long enough focal ratio would be effectively apochromatic. This is the
reason that 17th century astronomers used the great "aerial refractors" of
that period, with extraordinarily long focal ratios to get around not having
even achromats yet.

Traditionally, achromats were made f/15 or even longer. Even these had
significant chromatic aberration, from what I have read.

All of this is just to get around to the ask the question: how long of a
f/ratio would an achromat need to get the color correction of something like
the Televue Ranger? It isn't color-free, but I don't find it terribly
objectionable.

I don't know about the Ranger specific color error (I wonder how knows
it apart TeleVue) but to work out a reasonable answer here's how I
would tackle it:

An acromatic refractor (fraunhoefer type) for visual use usually
brings the blue and red wavelength to a common focus while it is
designed to give the best perfomance in the green wavelength. The
difference between that focus (R,B) and the focus in green is about
fixed for "normal" optical glasses commonly used and about 1/2500 of
the focal lenght of the instrument itself (that value could be
somewhat different, but not by much).

The focus tollerance (in length units) is proportional to the maximum
error (say 1/4 of green wavelength, or 550/4 nm) you want to have, the
square of the focal ratio and a numerical constant. I'm not sure about
the exact formula here but off the top of my head is: focus tolerance
= 32*FR^2*max.error (FR is the focal ratio) sort of focal length and
focal ratio one has to put up with to have a colour error equal or
less than the focus tolerance (or equal to that of the Ranger).

Let's assume that the color error weighs equally irrespective of the
visual wavelength (it isn't usually so but for sake of semplicity...).
The optimum focus position lies halfaway between the green focus and
the blue/red one. We therefore ask that the focus tolerance is equal
to half of color error between green and red/blue. Given the formula
above (to be checked !!) one gets the answer it needs:

FR = D/(32*max.error*2*Delta.F), where Delta.F is the distance between
green and red/blue focii and D is the diameter of the refractor.

Hope it helps somehow (barring any mistake from my side).

Andrea T.

My Astronomy Pages at:
Http://www.geocities.com/andreatax/index.htm

"Chuck Taylor" wrote in message ...
"Clayton E. Cramer" wrote in message
...

All of this is just to get around to the ask the question: how long of a
f/ratio would an achromat need to get the color correction of something
like
the Televue Ranger? It isn't color-free, but I don't find it terribly
objectionable.

It depends on the aperture. As the aperture increases, you need to increase
the focal ratio. So getting less color from a small aperture isn't really
that big of an accomplishment. For example, a 3" f/15 looks very nice. A 4"
f/15 shows some definite color. A 5" f/15 shows more color and a 6" f/15 is
very nice, but it is definitely an achromat.

When you get down to those overgrown finders, the color can be reduced while
maintaining a faster focal ratio.


Is the original poster any wiser now?

Andrea T.

My Astronomy Pages at:
Http://www.geocities.com/andreatax/index.htm

"andrea tasselli" wrote in message
om...
Is the original poster any wiser now?

Yes, he knows that his question cannot be given a specific answer apart from
stating an aperture, and that as the aperture increases, the focal _ratio_
must increase and not just the focal length.

Clear Skies

Chuck Taylor
Do you observe the moon?
Try the Lunar Observing Group
http://groups.yahoo.com/group/lunar-observing/

"Chuck Taylor" wrote in message ...
"andrea tasselli" wrote in message
om...
Is the original poster any wiser now?

Yes, he knows that his question cannot be given a specific answer apart from
stating an aperture, and that as the aperture increases, the focal _ratio_
must increase and not just the focal length.


All right, yet it doesn't answer his question.

Andrea T.

My Astronomy Pages at:
Http://www.geocities.com/andreatax/index.htm

On 1 Dec 2003 05:45:26 -0800, (andrea tasselli)
wrote:

Let's assume that the color error weighs equally irrespective of the
visual wavelength (it isn't usually so but for sake of semplicity...).
The optimum focus position lies halfaway between the green focus and
the blue/red one. We therefore ask that the focus tolerance is equal
to half of color error between green and red/blue.

The fact that the weighted color error is FAR from equal is why
achromats work as well as they do. Blue and red wavelengths are
only around one tenth the visual weight of yellow-green.
Using your simple example gives the impression that focusing to the
smallest spot size would yield the sharpest focus, which in the case
of virtually any achromat, it wouldn't (although the color would
appear balanced).

Given the formula
above (to be checked !!) one gets the answer it needs:

FR = D/(32*max.error*2*Delta.F), where Delta.F is the distance between
green and red/blue focii and D is the diameter of the refractor.

Conrady's formula F= D(mm)/8.8*delta lambda , where F is focal ratio,
D is dia. in mm, gives f/35 (!) for a 150mm doublet with .5 lambda
from 550nm and is 'a bit' over the top( pun intended:-) At f/18 the
lens would have a delta lambda of ~one wave and such an objective is
quite pleasing on the planets in my experience. My 80mm achromat, at
f/11, has about .7 lambda delta and shows almost no color on anything
in the night sky but Venus and Sirius.
So, the damage done by even as much as 1 wavelength defocus of
blue/red should not be overstated for visual use, with the exception
of Mars and its push towards the red. The abundance of short, cheap
130mm -150mm achromats have exascerbated the seemingly growing
notion of virtually any achromat as a dinosaur less worthy of being a
great visual planetary instrument.

Dan C.

The abundance of short, cheap
130mm -150mm achromats have exascerbated the seemingly growing
notion of virtually any achromat as a dinosaur less worthy of being a
great visual planetary instrument.

Dan C.

It might be the abudance of inexpensive medium sized Newtonians that has caused
the longer focal length Achromat to become something of a dinosaur.

jon

(Dan Chaffee) wrote in message ...
On 1 Dec 2003 05:45:26 -0800, (andrea tasselli)
wrote:

Let's assume that the color error weighs equally irrespective of the
visual wavelength (it isn't usually so but for sake of semplicity...).
The optimum focus position lies halfaway between the green focus and
the blue/red one. We therefore ask that the focus tolerance is equal
to half of color error between green and red/blue.

The fact that the weighted color error is FAR from equal is why
achromats work as well as they do. Blue and red wavelengths are
only around one tenth the visual weight of yellow-green.
Using your simple example gives the impression that focusing to the
smallest spot size would yield the sharpest focus, which in the case
of virtually any achromat, it wouldn't (although the color would
appear balanced).

Well, "work well" is entirely subjective. I find them both amusing and
useless (I mean the big long ones) or entirely worthless, the short
new ones (except maybe as a finder/binocular). My example is far from
trying to give impressions. It is just a procedure to get some more or
less correct value for the original poster to think upon. One thing
can be color-free but not necessarily free of aberrations, that's
granted.


Given the formula
above (to be checked !!) one gets the answer it needs:

FR = D/(32*max.error*2*Delta.F), where Delta.F is the distance between
green and red/blue focii and D is the diameter of the refractor.

Conrady's formula F= D(mm)/8.8*delta lambda , where F is focal ratio,
D is dia. in mm, gives f/35 (!) for a 150mm doublet with .5 lambda
from 550nm and is 'a bit' over the top( pun intended:-) At f/18 the
lens would have a delta lambda of ~one wave and such an objective is
quite pleasing on the planets in my experience. My 80mm achromat, at
f/11, has about .7 lambda delta and shows almost no color on anything
in the night sky but Venus and Sirius.

Entirely subjective statements. If you're old enough you're far less
likely to see blue/violet flashing in achromats. That doesn't make
them a nm more correct than they are.

So, the damage done by even as much as 1 wavelength defocus of
blue/red should not be overstated for visual use, with the exception
of Mars and its push towards the red. The abundance of short, cheap
130mm -150mm achromats have exascerbated the seemingly growing
notion of virtually any achromat as a dinosaur less worthy of being a
great visual planetary instrument.

In fact they are not (great visual planetary instruments) nor they
ever were. The old brass ones are a real treat to look at, however.

Andrea T.