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APO Doublet vs Triplet

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#51 TheFacelessMen

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Posted 18 June 2015 - 07:47 PM

 

 

 

I have to admit to not paying much attention to development of doublets so I am happy to be corrected :-)

My understanding is that current doublets only achieve this for 2 wavelengths in the visible spectrum and third in non visible.

Yep as I mentioned earlier perhaps the specification should be purely performance based and applicable to all configurations.  But for all practical purposes (and still happy to be corrected on the doublet point) my understanding is that this is still only practically achievable in a triplet design.

But from memory the earliest definition of APO came from Triplet Designs which were the only practical way of achieving this.

 

Apparently it is true that the third crossing in not in the visual but it also apparently true that it still helps bring the colors to focus in the visual.  Roland seems comfortable calling a ED or Fluorite doublet an apo, that's good enough for me.. 

 

Let me ask you this:

 

Have you ever looked though a 80mm-120mm ~F/7 FPL-53 doublet at Venus? In my experience, Venus is about the most challenging object in the sky for a refractor.  It is pretty amazing, when all is said and done, apochromat basically means that it has far better color correction than the crown-flint achromat that was the standard for 200 or so years. 

 

In my experience, looking though my various FPL-53 doublets I have owned and still own, the way I can tell that they are not reflectors (besides no Central Obstruction):  On Venus, they show some chromatic aberration out of focus, in focus, I see none. A triplet would also show out of focus color.

 

Jon

 

 

Hi Jon,

 

The last time I used a doublet was many years ago....and yes it was a nice scope and I don't recall noticing any CA on any target with that scope.

 

Now days all I have and use are Triplets ..... my Takahashi TSA120 and TOA150 and i notice absolutely no CA on any targets with these 2 scopes and visuals are exquisite with different spectral classes of stars clearly defined and observed.

 

However not much point in arguing about any scope out of focus. The point is to bring the best possible image to focus :-)

 

Cheers



#52 Jon Isaacs

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Posted 19 June 2015 - 07:42 AM

 

 

Hi Jon,

The last time I used a doublet was many years ago....and yes it was a nice scope and I don't recall noticing any CA on any target with that scope.

Now days all I have and use are Triplets ..... my Takahashi TSA120 and TOA150 and i notice absolutely no CA on any targets with these 2 scopes and visuals are exquisite with different spectral classes of stars clearly defined and observed.

However not much point in arguing about any scope out of focus. The point is to bring the best possible image to focus :-)

Cheers

 

I see no CA in my FPL-53 doublets, even on Venus.. Of course I am 67 and I have undoubtedly lost sensitivity to blue, maybe 15 years ago, I might have seen something. The NP-10 is a Modified Petzval like the 106FSQ is color free even somewhat out of focus. 

 

But the scope that is the subject of this thread.. the Orion 110mm F/6 with the FPL-51 objective, that would be a different story.  Apo/ED glass combinations use the same scaling rules as achromats, the larger the objective, the greater the false color, the faster the focal ratio, the greater the false color.  The reasons for this are simple, the longitudinal color error remains the same in terms of percentage.. 1 part in 2000, 1 part in 12,000.  The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

 

In any event, a 72mm F/6 FPL-51 doublet is nearly free of chromatic aberration, at 110mm, to maintain that same correction, it would have to be F/9.2... So, this is murky ground.. It certainly would have much less CA than a 110mm F/6 achromat but there's enough chromatic aberration that anointing it an apochromat seems dubious.   

 

From Thomas Back's discussion of a practical definition of an apochromat, I would say it is possible for an ED doublet to provide apochromatic performance visually but not all combinations do.  Of course the same can be said of triplets but it is much rarer that a triplet is not an apochromat.. Those who remember the heydays of S.A.A. may remember the thread, An Achromat is an Achromat.. 

 

Jon

 

Jon



#53 GJJim

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Posted 19 June 2015 - 10:45 AM

 

 

The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

The size of the Airy disk depends only on focal ratio. Scopes with the same focal ratio will have the same size Airy disk, regardless of aperture.


Edited by GJJim, 19 June 2015 - 10:46 AM.


#54 Element79

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Posted 19 June 2015 - 10:47 AM

Here is what I think is an interesting addition to this conversation.

 

Jon Isaacs had a post earlier that referenced a partial dispersion graph by Roland Christen in which he detailed several telescopes / glass combinations.  The one glass combination that I truly wanted to see was a FPL-53 / ZKN7 combination which is the preferred mating pair for high performance doublets.  So I went on-line and downloaded a demo version of the optical program (ATMOS) that Roland Christen used to create his graph and I used it to analyze a FPL-53 / ZKN7 doublet myself. 

 

The numbers were: (.45447 - .45389) / (94.93 - 61.16) = .0017175

1 part in 58224!!!

 

No wonder these telescopes perform so well!


Edited by Element79, 19 June 2015 - 11:01 AM.


#55 GJJim

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Posted 19 June 2015 - 10:55 AM

Here is what I think is an interesting addition to this conversation.

 

Jon Isaacs had a post earlier that referenced a partial dispersion graph by Roland Christen in which he detailed several telescopes / glass combinations.  The one glass combination that I truly wanted to see was a FPL-53 / ZKN7 combination which is the preferred mating pair for high performance doublets.  So I went on-line and downloaded a demo version of the optical program (ATMOS) that Roland Christen used to create his graph and I used it to analyze a FPL-53 / ZKN7 doublet myself. 

 

The numbers were: (.45447 - .45389) / (94.93 / 61.16) = .0017175

1 part in 58224!!!

 

No wonder these telescopes perform so well!

There are other factors besides the residual color that have to be balanced in the design. What is the spherochromatism and higher-order aberrations in this doublet?



#56 Element79

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Posted 19 June 2015 - 11:00 AM

I didn't design a telescope.  I only analyzed the partial dispersion of two glass types in the same manner that Roland Christen did in his graph.  And I know for a fact that telescopes with these glass types have been made.  Even by Roland Christen himself...



#57 GJJim

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Posted 19 June 2015 - 11:09 AM

I didn't design a telescope.  I only analyzed the partial dispersion of two glass types in the same manner that Roland Christen did in his graph.  And I know for a fact that telescopes with these glass types have been made.  Even by Roland Christen himself...

Well butter my bread!



#58 BigC

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Posted 19 June 2015 - 11:56 AM

 

 

 

Hi Jon,

The last time I used a doublet was many years ago....and yes it was a nice scope and I don't recall noticing any CA on any target with that scope.

Now days all I have and use are Triplets ..... my Takahashi TSA120 and TOA150 and i notice absolutely no CA on any targets with these 2 scopes and visuals are exquisite with different spectral classes of stars clearly defined and observed.

However not much point in arguing about any scope out of focus. The point is to bring the best possible image to focus :-)

Cheers

 

I see no CA in my FPL-53 doublets, even on Venus.. Of course I am 67 and I have undoubtedly lost sensitivity to blue, maybe 15 years ago, I might have seen something. The NP-10 is a Modified Petzval like the 106FSQ is color free even somewhat out of focus. 

 

But the scope that is the subject of this thread.. the Orion 110mm F/6 with the FPL-51 objective, that would be a different story.  Apo/ED glass combinations use the same scaling rules as achromats, the larger the objective, the greater the false color, the faster the focal ratio, the greater the false color.  The reasons for this are simple, the longitudinal color error remains the same in terms of percentage.. 1 part in 2000, 1 part in 12,000.  The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

 

In any event, a 72mm F/6 FPL-51 doublet is nearly free of chromatic aberration, at 110mm, to maintain that same correction, it would have to be F/9.2... So, this is murky ground.. It certainly would have much less CA than a 110mm F/6 achromat but there's enough chromatic aberration that anointing it an apochromat seems dubious.   

 

From Thomas Back's discussion of a practical definition of an apochromat, I would say it is possible for an ED doublet to provide apochromatic performance visually but not all combinations do.  Of course the same can be said of triplets but it is much rarer that a triplet is not an apochromat.. Those who remember the heydays of S.A.A. may remember the thread, An Achromat is an Achromat.. 

 

Jon

 

Jon

 

I am still able to see blue quite well;perhaps due to the lack of internal lenses(what isn't there anymore can't yellow!) and the  procedures performed more recently which incidentally involved replacement of the eye fluid lost during the operations.

 

The complete lack of blue halos around all but truly blue stars was THE most obvious result of viewing for the first time with the SW120ED versus the Orion 120f8.3 .

For me ,visually, the 120ED is an apo. Others may differ.



#59 Jon_Doh

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Posted 19 June 2015 - 11:56 AM

 

I didn't design a telescope.  I only analyzed the partial dispersion of two glass types in the same manner that Roland Christen did in his graph.  And I know for a fact that telescopes with these glass types have been made.  Even by Roland Christen himself...

Well butter my bread!

 

How about some jam to with it?  ;)



#60 Jon_Doh

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Posted 19 June 2015 - 11:58 AM

 

 

 

 

Hi Jon,

The last time I used a doublet was many years ago....and yes it was a nice scope and I don't recall noticing any CA on any target with that scope.

Now days all I have and use are Triplets ..... my Takahashi TSA120 and TOA150 and i notice absolutely no CA on any targets with these 2 scopes and visuals are exquisite with different spectral classes of stars clearly defined and observed.

However not much point in arguing about any scope out of focus. The point is to bring the best possible image to focus :-)

Cheers

 

I see no CA in my FPL-53 doublets, even on Venus.. Of course I am 67 and I have undoubtedly lost sensitivity to blue, maybe 15 years ago, I might have seen something. The NP-10 is a Modified Petzval like the 106FSQ is color free even somewhat out of focus. 

 

But the scope that is the subject of this thread.. the Orion 110mm F/6 with the FPL-51 objective, that would be a different story.  Apo/ED glass combinations use the same scaling rules as achromats, the larger the objective, the greater the false color, the faster the focal ratio, the greater the false color.  The reasons for this are simple, the longitudinal color error remains the same in terms of percentage.. 1 part in 2000, 1 part in 12,000.  The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

 

In any event, a 72mm F/6 FPL-51 doublet is nearly free of chromatic aberration, at 110mm, to maintain that same correction, it would have to be F/9.2... So, this is murky ground.. It certainly would have much less CA than a 110mm F/6 achromat but there's enough chromatic aberration that anointing it an apochromat seems dubious.   

 

From Thomas Back's discussion of a practical definition of an apochromat, I would say it is possible for an ED doublet to provide apochromatic performance visually but not all combinations do.  Of course the same can be said of triplets but it is much rarer that a triplet is not an apochromat.. Those who remember the heydays of S.A.A. may remember the thread, An Achromat is an Achromat.. 

 

Jon

 

Jon

 

I am still able to see blue quite well;perhaps due to the lack of internal lenses(what isn't there anymore can't yellow!) and the  procedures performed more recently which incidentally involved replacement of the eye fluid lost during the operations.

 

The complete lack of blue halos around all but truly blue stars was THE most obvious result of viewing for the first time with the SW120ED versus the Orion 120f8.3 .

For me ,visually, the 120ED is an apo. Others may differ.

 

I don't know nothing about nothing, but I agree with you fwiw.



#61 junomike

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Posted 19 June 2015 - 12:39 PM


"For me ,visually, the 120ED is an apo. Others may differ."

 

 

I've seen 120 ED's that I would classify an apo and others I would not.  Most however do fall into the apo category.

 

Mike 



#62 Peter Besenbruch

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Posted 19 June 2015 - 01:46 PM

I see no CA in my FPL-53 doublets, even on Venus.. Of course I am 67 and I have undoubtedly lost sensitivity to blue, maybe 15 years ago, I might have seen something. The NP-10 is a Modified Petzval like the 106FSQ is color free even somewhat out of focus.

 

I could see a little blue at high power with the supplied, dielectric diagonal on mine. This as well as mild zones and traces of astigmatism. these went away when I switched to a Takahashi prism. I was rather shocked not to see any color on Venus at 150x.



#63 Peter Besenbruch

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Posted 19 June 2015 - 01:56 PM

 

The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

The size of the Airy disk depends only on focal ratio. Scopes with the same focal ratio will have the same size Airy disk, regardless of aperture.

 

Perhaps, I misunderstand what you are getting at, but I'm going to challenge this. Airy disk size is determined by aperture. Other factors can detract from the theoretical best (smallest) size, but aperture is the main determinant.

 

People sometimes get confused, because in today's world of camera chips overstuffed with pixels, most camera lenses cannot provide the resolution that the chips supply. That is determined largely by f-ratio.

 

Airy disk size, however, is a separate issue. It is fixed by a lens' aperture, and the size can be measured, given sufficient magnification.



#64 GJJim

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Posted 19 June 2015 - 07:50 PM

 

 

The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

The size of the Airy disk depends only on focal ratio. Scopes with the same focal ratio will have the same size Airy disk, regardless of aperture.

 

Perhaps, I misunderstand what you are getting at, but I'm going to challenge this. Airy disk size is determined by aperture. Other factors can detract from the theoretical best (smallest) size, but aperture is the main determinant.

 

People sometimes get confused, because in today's world of camera chips overstuffed with pixels, most camera lenses cannot provide the resolution that the chips supply. That is determined largely by f-ratio.

 

Airy disk size, however, is a separate issue. It is fixed by a lens' aperture, and the size can be measured, given sufficient magnification.

 

You are correct and I stated that wrongly. The Airy disk size is determined by aperture and wavelength, and I was thinking in terms of resolution, the smallest details a lens can define. 

 

Still I'm puzzled because the resolving power can be defined strictly as a function of focal ratio:

 

if R = the the solving power of a lens, it's a commonly stated approximation that:

 

R = L / 2NA, where L is the wavelength, and NA is the numeric aperture of the lens.

 

With a lens focused at infinity, we can also write: f / D = 1 / 2NA, where f / D is the focal ratio.

 

Substituting, I get:

 

R / L = 1 / 2NA = f / D, and

 

R = L(f / D), Apparently resolution equals the wavelength multiplied by the focal ratio.

 

I think the key is your comment above "given sufficient magnification". The limits for visual resolution would depend on our ability to perceive details in the image as magnified by the eyepiece. If the image is too dim, then magnifying it will only make it appear dimmer and will not reveal more detail.



#65 schang

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Posted 19 June 2015 - 08:49 PM

Please see the explanation from the following link...

 

https://en.wikipedia...ular_resolution

 

There is a special case for telescope for point source at infinite distance, where resolution is a function of aperture diameter...



#66 SandyHouTex

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Posted 19 June 2015 - 09:25 PM

 

 

RC's posts on APO's does not dispel the original definition at all, rather it explains the improvements in materials and production that has significantly increase the performance of both triplets and doublets.  

 

What I see being the case is that many of the manufacturers are conveniently calling refractors APO's more as a sales ploy than anything else.

 

I have to disagree.  Roland points out two things:

 

-A doublet can have three color crossings as per the original definition.

 

- Neither doublets nor triplets meet the original definition of an apochromat because they only have one spherical null.

 

- The fact that Roland who does not manufacture doublets is happy to call an ED doublet or a Fluorite doublet, an apochromat, indicates to me that it is more than just marketing, that is what he believes to be the case. 

 

Jon

 

So why if Roland says a doublet is as good an apo as a triplet does he produce triplets?

From a manufacturing aspect it is a lot less cost to produce a doublet and supposidely as good.

 

The refractors Roland has been making are for imaging use.  This places a need to control more wavelengths getting to the CCD or CMOS detectors.  For visual use the criteria are not as strict.  Our eyes are not as sensitive as CCDs or CMOS chips to all of the wavelengths.



#67 Peter Besenbruch

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Posted 20 June 2015 - 01:10 AM

I think the key is your comment above "given sufficient magnification". The limits for visual resolution would depend on our ability to perceive details in the image as magnified by the eyepiece. If the image is too dim, then magnifying it will only make it appear dimmer and will not reveal more detail.

 

Stars, to all practical purposes, are point sources. The Airy disk is the product of a point source hitting a certain aperture. This differs from extended objects, where it's more useful to speak of the ability to resolve subtle differences in contrast. On a camera, a lower f-ratio will do better for a more densely packed CCD than a higher f-ratio. If the f-ratio gets too long, not only do you start losing subtle detail, eventually you lose high contrast resolution. This doesn't directly apply to point sources.

 

For astronomy, when looking at extended objects, we override the f-ratio by using eyepieces to change magnification. Hence, once again, aperture rules. Remember that the f-ratio is the focal length divided by the aperture. You offset the focal length of the objective or primary mirror with the focal length of the eyepiece.



#68 GJJim

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Posted 20 June 2015 - 09:30 AM

Please see the explanation from the following link...

 

https://en.wikipedia...ular_resolution

 

There is a special case for telescope for point source at infinite distance, where resolution is a function of aperture diameter...

Thanks for that link. The article converts from spatial to angular resolution and derives the diameter of the Airy disk as:

 

=(2.44)(lambda)(focal ratio).

 

I suppose the conclusion is that resolvable detail for extended objects is proportional to the focal ratio. For point sources it is proportional to aperture, with both instances limited by seeing conditions. My own experience is that visually, a 14" scope at f/10 shows more planetary detail than a 7" scope at f/7. The eye and brain must be doing some signal processing?



#69 Derek Wong

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Posted 20 June 2015 - 10:09 AM

 

Please see the explanation from the following link...

 

https://en.wikipedia...ular_resolution

 

There is a special case for telescope for point source at infinite distance, where resolution is a function of aperture diameter...

Thanks for that link. The article converts from spatial to angular resolution and derives the diameter of the Airy disk as:

 

=(2.44)(lambda)(focal ratio).

 

I suppose the conclusion is that resolvable detail for extended objects is proportional to the focal ratio. For point sources it is proportional to aperture, with both instances limited by seeing conditions. My own experience is that visually, a 14" scope at f/10 shows more planetary detail than a 7" scope at f/7. The eye and brain must be doing some signal processing?

 

 

I think you are mistaking the ultimate detail you can see with the scope and the physical size of the Airy disc.  

 

Let's say you have a 100mm f/6 and a 100mm f/12.  The image from the f/12 scope will be twice the scale of the image of the f/6 scope in physical terms.  Yes, the Airy disc will be twice the size in microns in the f/12.  However, if you look close enough, you can see all the details in the f/6 scope that you can in the f/12 scope (assuming that the other aberrations are the same, which may not be the case).  With a CCD, you could make pixels half the size in the f/6 vs f/12.  For visual, you can use an eyepiece of half the focal length in the f/6 vs f/12.  In either case, you will end up with the same image.

 

You can blow the image up as large as you want.  However, ultimately there is a limit in the detail of the image, and that is determined by diffraction, which is solely a function of aperture (ignoring central obstruction effects), assuming the optical quality is great.  Your 14" SCT had more light and more resolution than the 7" f/7 due to aperture, not focal ratio.

 

You should download Aberrator 3.0 and play with it to see the images at different apertures.  Better yet, compare a 4" f/15 scope and a 6" f/8 scope.

 

Derek


Edited by Derek Wong, 20 June 2015 - 10:39 AM.


#70 BillP

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Posted 20 June 2015 - 04:44 PM

On a camera, a lower f-ratio will do better for a more densely packed CCD than a higher f-ratio. If the f-ratio gets too long, not only do you start losing subtle detail, eventually you lose high contrast resolution.

 

 

I could be wrong but I am not sure the camera analogy holds.  The f ratio (or f-stop) on the camera lens is not achieved by lengthening the focal length of the lens and keeping the aperture of the lens fixed, but rather the focal length is fixed so the f-stop is reducing the aperture to achieve the f-stop change.  So when you get to f-22 you've lost a lot of aperture (and resolution) and also are past the diffraction limit.  So a 4" f/22 or a 4" f/4 telescope will have the same resolution as any camera lens whose front lens is 4" in diameter and the f-stop is wide open.


Edited by BillP, 20 June 2015 - 04:45 PM.


#71 Peter Besenbruch

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Posted 20 June 2015 - 10:54 PM

 

On a camera, a lower f-ratio will do better for a more densely packed CCD than a higher f-ratio. If the f-ratio gets too long, not only do you start losing subtle detail, eventually you lose high contrast resolution.

 

 

I could be wrong but I am not sure the camera analogy holds.  The f ratio (or f-stop) on the camera lens is not achieved by lengthening the focal length of the lens and keeping the aperture of the lens fixed, but rather the focal length is fixed so the f-stop is reducing the aperture to achieve the f-stop change.  So when you get to f-22 you've lost a lot of aperture (and resolution) and also are past the diffraction limit.  So a 4" f/22 or a 4" f/4 telescope will have the same resolution as any camera lens whose front lens is 4" in diameter and the f-stop is wide open.

 

No, a camera is different, particularly when talking about Airy disks. GJJIM was speaking about f-ratio and detail. As for your example, I wish it was true today. Try getting any compact camera that shoots at anything but full aperture. Even so, the lens lacks the resolving power for the chip inside.

 

Take, for example the case of two zooms. When I was in the market for one, I chose between the Panasonic FZ200 and the Canon SX50HS. Both come with powerful zooms, with the Canon offering twice the range. The Canon's lens ranges from f3.4 at wide angle to f6.5 at full zoom. The Panasonic offers a constant f2.8 over the zoom range. Given the chip size and resolution in both, you start losing subtle detail at f2.4, and it becomes quite noticeable at f3. High contrast detail suffers at f3.6. The Canon offers mostly empty pixel resolution. The Panasonic is a fairly honest 12 mega-pixel camera. When shooting at 12MP in automatic mode, the Panasonic tends to stay at f2.8, and for good reason.



#72 Daniel Mounsey

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Posted 21 June 2015 - 02:53 PM

 

 

 

The reason that larger aperture results in more false color is the Airy disk is smaller and chromatic aberration is measured in relation to the Airy disk.  The focal ratio affects it because it affects the defocused blur size.  

The size of the Airy disk depends only on focal ratio. Scopes with the same focal ratio will have the same size Airy disk, regardless of aperture.

 

 

 

I want to be clear what's being stated about the airy disk because it's easy to get the terms mixed up. Are you referring to the central dot?  Sidgwick covers the topic in great detail. 


Edited by Daniel Mounsey, 21 June 2015 - 03:05 PM.


#73 BillP

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Posted 21 June 2015 - 09:07 PM

 

Thanks for that link. The article converts from spatial to angular resolution and derives the diameter of the Airy disk as:

 

 

=(2.44)(lambda)(focal ratio).

 

 

 

I don't know about that.  But the actual formula Airy derived for the size of the airy disk (i.e., the angle of first minimum in seconds of arc, so more than just the central dot or spurious disk) was and is:

 

s = 2.76 / d

 

s = size of the airy disk in arcseconds

d = aperture of the telescope in inches

Lambda = assumed to be visible wavelengths.

 

More accurately to factor in the specific wavelength of light, the formula becomes...

 

s = 1.22 * Wavelength / d

So focal ratio is not a factor for the airy disk.

-------------------------------------------------------------------------------

For cameras, it works differently...

 

x =  (1.22 * Wavelength) * fn

 

x = the separation of the images of the two objects on the film

fn = f-number of the lens (i.e., f-stop)

 

So basically, as the f-stop gets bigger, while the depth of field is increased the resolution is decreased.


Edited by BillP, 21 June 2015 - 09:08 PM.


#74 GJJim

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Posted 21 June 2015 - 09:23 PM

 

 

Thanks for that link. The article converts from spatial to angular resolution and derives the diameter of the Airy disk as:

 

 

=(2.44)(lambda)(focal ratio).

 

 

 

I don't know about that.  But the actual formula Airy derived for the size of the airy disk (i.e., the angle of first minimum in seconds of arc, so more than just the central dot or spurious disk) was and is:

 

s = 2.76 / d

 

s = size of the airy disk in arcseconds

d = aperture of the telescope in inches

Lambda = assumed to be visible wavelengths.

 

More accurately to factor in the specific wavelength of light, the formula becomes...

 

s = 1.22 * Wavelength / d

So focal ratio is not a factor for the airy disk.

-------------------------------------------------------------------------------

For cameras, it works differently...

 

x =  (1.22 * Wavelength) * fn

 

x = the separation of the images of the two objects on the film

fn = f-number of the lens (i.e., f-stop)

 

So basically, as the f-stop gets bigger, while the depth of field is increased the resolution is decreased.

 

The formula they derived is "2x" as defined in your second case using the focal ratio. To resolve a detail, the separation should be roughly twice the spot size, so it's the same as (1.22 * Wavelength) * fn multiplied by two. There is an odd dichotomy here, and "for cameras it works differently" doesn't explain it. Ghosts of the "focal ratio myth" are swirling about  :shocked:


Edited by GJJim, 21 June 2015 - 09:26 PM.


#75 Derek Wong

Derek Wong

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Posted 22 June 2015 - 01:49 AM

This thread may confuse some people.  I am going to assume we are talking about refractors to avoid central obstructions.  There is a very big difference between the Airy disc angular size, which is a function of the aperture of the scope regardless of f-ratio, and the Airy disc linear size, which is a function of f-ratio regardless of aperture.  Also, the term “resolution” can be used differently and this is the source of the confusion.

 

The Airy disc angular size is often used in visual observations but can apply to images as well.  This size (assuming excellent optics and seeing) determines the double stars you can split and the planetary details that you can see.  This is what the visual observers commonly think of as resolution.  If you have small enough pixels on a CCD, you can resolve the same angular resolution.  This type of resolution is dependent on aperture.

 

The Airy disc linear size is often referred to with cameras, because they have a fixed CCD pixel size.  The important thing is how many pixels across make a desired photo.  If you want more photo resolution, you can increase the scale size by increasing the f-ratio of the scope.  It may be that if you use a large enough f-ratio, you can get 100 pixels for the diameter of the Airy disc.  The resolution the Wikipedia article is talking about is huge in this case, because each pixel represents only a small fraction of an arcsecond.  This resolution is related to how much sky is covered for each pixel.   Such a photo would give you a very large picture of the Airy disc and diffraction rings.  However, pointing this monster 4” f/100 or whatever it was will not give you a better photo than a 4” f/20.  The reason is that the diffraction will limit the actual “resolution”.  You will get a large photo but with a lot of duplicate information, similar to what happens when you use empty magnification of 300x per inch.

 

Please look at the following link, by someone who knows a lot more about optics and observational astronomy than I do:

 

https://groups.googl...KA/Z44fGEv_5a8J

 

If you don’t believe me, ask Roland, Yuri, Vlad, or your favorite optical guru.

 

Derek




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