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Diameter vs CA

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#1 delorehal

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Posted 26 June 2020 - 06:21 AM

I've always wondered the following question :

 

We assume to have several objectives with the same focal length, same materials (ED or not), each one polished with the same optical quality but with different diameters.
For instance f=1200mm and diameters vary from 80mm, 90mm, 100mm up to 250mm.

 

The experimenter is looking at a planet or the moon and swap the different objectives.
Increasing the diameter, increase the resolving power but increase also the chromatic aberration.

Until what diameter (given by the CA ratio) CA become so strong that it reduces the gain in resolving details and the experimenter will see less ?

 

The power (eyepiece) can be chosen at his convenience (and so changed when swaping the objective) to get the best result.

 

If I know that a 4” at f12 will show more planetary details than a 80mm at f15 (so both with a focal length equal to 1200mm), can I still say this for a 6”f8 vs a 5”f9 or for a 8”f6 vs the 6”f8 ?

 

Increasing the diameter will allow an image brighter (at the same magnification) with a greater exit pupil.

 

This theorical experiment is what many owners of big achromatic refractors do by putting an aperture mask when looking at the planets

So the question could also be formulated like this : what aperture mask should I use with my refractor to get the best of it when looking at the planet ? In order to not depend on the lens characteristics (D and f), the answer should be given with the CA ratio.

 

 

The second question I have is this : can I get a perfect apo by reducing the diameter of the objective (example 6”f8 with a 2” aperture mask) ?

 

I only want to understand how optics work, so please do not tell me that using a 6” with a 2” aperture mask has no sense, or a 10” at f5 doesn’t exist (because it does, see the cosmo physics refractor thread smile.gif ).


Edited by delorehal, 26 June 2020 - 07:33 AM.


#2 BillP

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Posted 26 June 2020 - 06:49 AM

A 50mm mask on a 6" f/8 achromat should get the resulting color blur under 1.0 which would then mean fully apochromatic.  Visually though you can probably open it up to 75mm or maybe a little more without any obvious CA being noticeable.

 

For achromats, if you take the focal ratio and divide it my the aperture (in inches), when the resulting number is 5 or greater it is called the Conrady Standard for achieving a relatively CA free view.  So in my example above, masking your 6" f/8 to 75mm (2.95 inches) makes it an f/16 instrument.  The calculation would be 16 / 2.95 = 5.4 which more than 5 so it meets the Conrady Standard for a relatively CA free view from an achromat.

 

Now all of us have different standards for the minimum aperture for serious planetary observing.  Mine is lower than most at 100mm.  However, there is another standard, called the Sidgwick Standard.  Same formula except looking for the result to be at least 3 instead of 5.  With this standard the achromat will still have some CA visible, but will produce a diffraction limited view.  So you could try this and it should get you a good sharp planetary image, with some CA that should not be damaging to the details, just annoying.  For your 6" f/8 you would need to mask it to 100mm.  With this you might find the CA left not annoying, or you could use filters to get rid of the CA like the Baader Constrast Booster or Baader Semi-Apo filter.


Edited by BillP, 26 June 2020 - 07:05 AM.

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#3 junomike

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Posted 26 June 2020 - 07:15 AM

I tried stopping down a 6" F8 to 80mm @ F15. Although a lot better for CA It still wasn't CA free (IMO).

Also, the resolution/detail drop was IMO worse than the CA at full aperture. 

 

Best solution would be to make stop-down masks in sizes from 50mm - 120mm in 10mm increments and see what you prefer.


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#4 t.r.

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Posted 26 June 2020 - 07:30 AM

At 1.3 times the objective diameter for an achromat...at that point the CA is no longer filterable and destroys any contrast advantage when used at medium to high magnification.

Edited by t.r., 26 June 2020 - 07:35 AM.

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#5 Asbytec

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Posted 26 June 2020 - 07:53 AM

Chart from here

 

CA-ratio-chart-achro.jpg


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#6 delorehal

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Posted 26 June 2020 - 07:58 AM

I tried stopping down a 6" F8 to 80mm @ F15. Although a lot better for CA It still wasn't CA free (IMO).

Also, the resolution/detail drop was IMO worse than the CA at full aperture. 

That's interesting.
So u saw more details at full aperture than stopped down to 80mm



#7 Rutilus

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Posted 26 June 2020 - 08:16 AM

I have stopped down my 6 inch f/8 achromat on several occasions to 80mm, and the the full aperture (150mm)

always showed more detail.  Even when stopped down to 100mm, I always go back to 150mm on the planets as I 

see more.

When stopped down to 80mm, the big scope gives very nice views of Venus, however at full aperture I still see more.

With Venus I just use filters when using 150mm.


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#8 BillP

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Posted 26 June 2020 - 02:07 PM

That's interesting.
So u saw more details at full aperture than stopped down to 80mm

That has been my experience as well.  The details are there inside all the CA so makes the view a little nauseating, but the details are there.  When I take my 81mm out I cannot make its aperture larger so no temptation and satisfied with what it gives.  But when you mask a scope it always gnaws at you that unmasked more details show, so hard to resist temptation then you get frustrated because you have to lose details to get a cleaner view without CA.  There are many who are satisfied though with full aperture achromat and they just get past the green views and use a green longpass filter which limits the spectra so they get good clean sharp full aperture views for planets.  Sol Robbins here on CN does that and has some phenomenal sketches using a 6" achromat.


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#9 Echolight

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Posted 26 June 2020 - 02:29 PM

I need to take some snapshots through the barlowed Baader zoom on my C6R of Jupiter and Saturn. Because with full aperture and relatively mild 140x and 190x, respectively, I don't see any unatural color.

 

I'm hoping the African dust will settle before this time next month when the planets are a little higher so I can ramp up the x's a little more. Give it a real test.

 

Now some of the brighter stars look to show some color at high power. But I'm not sure if it is unatural or not.



#10 junomike

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Posted 26 June 2020 - 05:09 PM

That's interesting.
So u saw more details at full aperture than stopped down to 80mm

Yep.  More CA, but more detail as well.


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#11 daquad

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Posted 26 June 2020 - 06:43 PM

My experience with a 4" f/11 Astro-telescope, which does not quite meet the Sidgwick standard, is the same.  I've stopped it down to 75 mm to come close to the Conrady criterion for color correction, but I've always found the full aperture view better at revealing more detail.  

 

Dom Q.


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#12 John Turley

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Posted 27 June 2020 - 04:37 AM

I used to have a pre Starfire 6in f8 Astro Physics Refractor, which still showed quite a bit of false colour, and a 3.5in solar filter in a cell which fitted over the objective. If I removed the filter from the cell it gave me a 3.5in f14 refractor, which showed a lot less false colour, but as others have found, much dimmer images with less detail and contrast.

 

For this reason in particular, I am always very dubious about claims from owners of long focal ratio high end APO's with apertures as small as 76mm or even 60mm, that their scopes provide incredible detailed high contrast views at powers of up to 100x, or even 120x per inch of aperture.

 

John 


Edited by John Turley, 27 June 2020 - 05:31 AM.

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#13 delorehal

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Posted 27 June 2020 - 06:44 AM

 

For this reason in particular, I am always very dubious about claims from owners of long focal ratio high end APO's with apertures as small as 76mm or even 60mm, that their scopes provide incredible detailed high contrast views at powers of up to 100x, or even 120x per inch of aperture.

John,

 

I agree, there seems to be something magic with apo refractors, especially when they have a fluorite lens.

 

I paid only 250 euros for my 6"f8 and one 120 was bought for 150 euros including a motorised EQ5.

For me who began astronomy with a 60mm in the seventies, when the biggest refractors in the catalogs didn't exceed 115mm, buying a 6" refractor at this price still appear to me insane.

I think that used achros are a very good bargain, you can use them and then sale for the same price they have been bought.


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#14 Asbytec

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Posted 27 June 2020 - 09:35 AM

"...that their scopes provide incredible detailed high contrast views at powers of up to 100x, or even 120x per inch of aperture."

I've seen Jupiter's bright low contrast detail at very high magnification. It's been my experience Jupiter begins to be less detailed around 60x per inch and increasingly so at higher magnification. There is still detail to be seen up that high, but increasingly only the larger higher contrast detail such as the main belts, GRS, polar regions, barges, maybe a strong festoon, and the like. Soft low contrast detail is gone. Not from the telescopic image, but on the eye.

Interestingly, it's the same highly detailed image we are viewing at 40x to 50x per inch, so it's probably not the scope "breaking down". It's us. The limb is still "sharp", so it's probably not the optics or obstruction. At 50x per inch, we're well beyond the point aberration and obstruction effects become visible. Still some of the lower contrast detail starts to become more difficult, if not impossible, to see with increasingly diminished exit pupils and image brightness. Saturn's rings, on the other hand and being brighter with higher contrast, can survive a little higher magnification and still show detail.

I'd imagine the slightly improved contrast of an unobstructed refractor, particularly an APO, with improved throughput can survive a bit more magnification. But, at some point even the most acute observer will fall prey to lower image surface brightness at smaller exit pupils. It's just a matter of how small. Having seen Jupiter's detail fall off with increased magnification, I often wonder what folks see at 100x per inch, too. I know what I see, and it's disappointing compared to half that magnification.

Even the moon is dim up that high with nothing more to see. We can still see high contrast craters and similar, it's just the entire scene is dimmer.

Edited by Asbytec, 27 June 2020 - 09:38 AM.


#15 Jon Isaacs

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Posted 27 June 2020 - 09:49 AM

Increasing the diameter will allow an image brighter (at the same magnification) with a greater exit pupil.

 

 

Moderator note; at Jon's request, we pass on the following important correction on his behaf:

 

 

"When I wrote this, I was mistakenly thinking another situation and what I have written is just plain wrong. Read it as an example of how someone can be so sure of themselves and yet be wrong.  Don't trust anything.

 

 

 

 

The important thing increasing the aperture does is increase the resolution and, at least if reasonably color free, increase the fine scale contrast.

 

It's a complicated equation. But one fact is often overlooked:

 

The way color correction is thought of is relative to the size of the Airy disk. The Sidgwick standard (f/D = 3) means the out of focus chromatic blur is about 3.3 times the Airy disk, the Conrady standard (f/D = 5) means the chromatic blur is about 2x the Airy disk.  This really quite color free.

 

But I think this is something often not realized:

 

When you increase the aperture for a given focal length, say an 3 inch F/16 to a 6 inch F/8, the angular diameter of the chromatic blur stays the same, the diameter of the Airy disk is now 1/2 the diameter.

 

The ability to resolve color has not decreased, the blur is just not being hidden behind the Airy disk to the same extent.

 

This is why masking reduces the visible color.  The size of the defocused chromtic blur is unchanged, you are just increasing the size of the Airy disk to hide the chromatic blur, as well as dimming the image.

 

When I think about it this way, I can see that with a larger aperture of the same focal length, I will see more chromatic aberration but probably more detail as well.

 

Jon


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#16 daquad

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Posted 29 June 2020 - 10:06 AM

The chromatic blur in a 6" f/8 achromatic refractor is ~7.35X that of its Airy disc, measured to the first minimum.  The chromatic blur in a 3" f/16 achromatic refractor is ~1.84X its Airy disc.  The angular size of the Airy disc in the 3" is 2X larger than that of the 6", which means that the actual size (angular or linear) of the color blur in the 6" is 2X greater than that of the 3". 

 

So, although the color blurs are not equal, the conclusion is the same; we see more out of focus blue/red in the 6" f/8 because the color blur is so large relative to its Airy disc.  To use Jon's terminology, I would say that the  increased size of the Airy disc in the 3" f/16  "hides" a greater portion of its yet smaller color blur.

 

Dom Q.


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#17 Jon Isaacs

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Posted 30 June 2020 - 09:26 AM

The chromatic blur in a 6" f/8 achromatic refractor is ~7.35X that of its Airy disc, measured to the first minimum.  The chromatic blur in a 3" f/16 achromatic refractor is ~1.84X its Airy disc.  The angular size of the Airy disc in the 3" is 2X larger than that of the 6", which means that the actual size (angular or linear) of the color blur in the 6" is 2X greater than that of the 3". 

 

So, although the color blurs are not equal, the conclusion is the same; we see more out of focus blue/red in the 6" f/8 because the color blur is so large relative to its Airy disc.  To use Jon's terminology, I would say that the  increased size of the Airy disc in the 3" f/16  "hides" a greater portion of its yet smaller color blur.

 

Dom Q.

:waytogo:

 

Dom:

 

Thank you for catching my error.  What I had written is wrong.  I was thinking of the case where the focal ratio is constant but the aperture is changed.  

 

Good job. 

 

Jon


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#18 TareqPhoto

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Posted 30 June 2020 - 09:53 AM

Post images or examples please.



#19 daquad

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Posted 30 June 2020 - 06:25 PM

Post images or examples please.

Of what?



#20 daquad

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Posted 30 June 2020 - 06:32 PM

waytogo.gif

 

Dom:

 

Thank you for catching my error.  What I had written is wrong.  I was thinking of the case where the focal ratio is constant but the aperture is changed.  

 

Good job. 

 

Jon

Yeah, well I had to think about it a while before I was sure that what I wrote was correct.  I'm sure many of us here make similar errors, including, yours truly.  I enjoy your posts, so keep them coming.  You have very valuable info on this and other forums.

 

Dom Q.


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#21 TareqPhoto

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Posted 30 June 2020 - 06:45 PM

Of what?

Of Diameter vs. CA as the title of thread says, and the posts here.



#22 delorehal

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Posted Today, 06:30 AM

The chromatic blur in a 6" f/8 achromatic refractor is ~7.35X that of its Airy disc, measured to the first minimum.  The chromatic blur in a 3" f/16 achromatic refractor is ~1.84X its Airy disc.  The angular size of the Airy disc in the 3" is 2X larger than that of the 6", which means that the actual size (angular or linear) of the color blur in the 6" is 2X greater than that of the 3". 

What I would like also to understand is how an achromatic refractor which meet the Conrady standard, like the 3"f16 can be "CA free" if the colour blur is bigger than the airy disk ?

 

And why a fast achro, like a 6" f7 is described in the char above to have unacceptable level of CA that can't be filtered (in the red zone), despite being an achro (so 2 colors having the same fl) and furthermore by using a narrow band filter it should be color free.



#23 delorehal

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Posted Today, 09:16 AM

waytogo.gif

 

Dom:

 

Thank you for catching my error.  What I had written is wrong.  I was thinking of the case where the focal ratio is constant but the aperture is changed.  

 

Good job. 

 

Jon

I would like to tanks Jon for PMed me about this.

 

it would be nice if someone could put some drawing pictures showing the color blur between 2 refractors w/ the same fl but with different diameters


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#24 Jon Isaacs

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Posted Today, 09:26 AM

I would like to tanks Jon for PMed me about this.

 

it would be nice if someone could put some drawing pictures showing the color blur between 2 refractors w/ the same fl but with different diameters

Louis:

 

Thank you for the suggestion.  I have drawn a simple image depicting the 3 inch F/16 and the 6 inch F/8, both with 48 inch focal lengths.   I have drawn the Airy disk as yellow since there is a yellowing of the disk since the purple (red and violet) is absent.  

 

CA drawings two refractors.jpg

 

Hopefully this will help alleviate any confusion my previous post caused.  

 

Jon

 

 


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#25 daquad

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Posted Today, 12:54 PM

Jon, those drawings illustrate the situation perfectly.  Shows the relative sizes of the CB's with respect to each other and to their respective Airy discs.  

Dom Q.




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