Focal length, ratio, etc.

[Tim Armes]

Hi,

Coming from a photographic background the optics involved in telescopes are making me a little confused. Things seem similar enough that I should understand them easily, but they're different enough that I'm left scratching my head.

I'm looking for a site that contains above average information about how telescopes work, without delving into heavy maths. Recommendations would be welcome.

I'm fine about things like this:

Big diameter -> very good thing

Magification -> Focal length of scope / Focal length of eyepiece

Diameter of light beam entering eye determines min. useful magnification

However, I'm struggling to understand the importance of the focal ratio for a telescope, probably because of my photography background.

My scope's f/6. This tell's me that it's fast compared to scope's with a higher ratio (but a lot slower than my f/1.4 lenses!!). If this were a camera it would also give me an indication of the depth of field, but that doesn't seem relevant when the objects are so far away.

I've read that higher focal ratios give better resolution for viewing planets, but I just can't see how the focal ratio (I so want to call it the f-number) would have this effect. A higher f-number in a camera results in greater depth of field since the circle of confusion either side of the place of focus stays small for longer. With the subject being so far away however I would expect this to become irrelevant as far as telescope optics are concerned.

I appreciate that this isn't really important as far as actually using the scope is concerned, but I like to understand the equipment that I use.

Tim

[Helen]

You might find this useful Tim Tele Vue Optics: Choosing Your Telescope's Magnification you can also look at the other articles under the 'Advice' tab on that site. Televue optics are amongst the best out there, so they know what they're talking about.

Helen

[acey]

I've read that higher focal ratios give better resolution for viewing planets, but I just can't see how the focal ratio (I so want to call it the f-number) would have this effect.

Forget depth of field and instead think about aberrations. It's more difficult to reduce these in lenses/mirrors with low f-ratio than in ones with larger f-ratio; i.e. a short-focus "achromatic" refractor will show more chromatic aberration than a long-focus one, the latter therefore being better for planets. Similarly, fast newtonians give wide fields but are more prone to coma.

These might help:

http://www.ayton.id.au/gary/Science/Astronomy/Ast_Telescope_Types.htm

http://www.utm.utoronto.ca/~astro/ast110/lectures/aberrations.html

http://www.telescope-optics.net/index.htm#TABLE_OF_CONTENTS

[Ags]

Helen, I read the Televue article again, thanks for pointing it out. Excellent reading and packed with information. It does say though that "Experienced planetary observers use 20x to 30x per inch of aperture to see the most planetary detail.". That really stretches credibility, suggesting as it does that I should stick to 80x to 120x with my Mak. Maybe it is just my eyes, but I can't make out any detail at that microscopic scale. Aside from that, the article is excellent.

[Tim Armes]

You might find this useful Tim Tele Vue Optics: Choosing Your Telescope's Magnification you can also look at the other articles under the 'Advice' tab on that site. Televue optics are amongst the best out there, so they know what they're talking about.

Helen

Thanks for the link.

However, I find that the article makes a lot of statements without explaining the "why".

Tim

[John]

Thanks for the link.

However, I find that the article makes a lot of statements without explaining the "why".

Tim

Could you give some examples Tim - it's always interesting to explore things further on the forum

[Tim Armes]

Could you give some examples Tim - it's always interesting to explore things further on the forum

To be fair, I do think it's a ver good article. Upon second reading most things are explained, although diagrams would really help the understand.

That said, here's an example of a statement that isn't explained:

"F/number is of little importance visually. A "fast" telescope implies a short focal length and a large field. Fast, however, is a term borrowed from photography (an f/5 telescope can take a photograph with one-fourth the exposure time of an f/10 instrument). Visually, well made fast and slow telescopes of the same aperture have no difference in image brightness or resolution."

Why does more light coming in make no difference in image brightness? Isn't that the whole point of a big aperture, to see dimmer things?

This point is actually addressed on this page, which I also found to be very good:

Starizona's Telescope Basics

The explanation being:

"This is because the light from an extended object is being spread out by the fact that the telescope is magnifying the image. So magnification factors into the equation; light is lost in proportion to the square of the magnification. There is a minimum magnification allowed by the limiting size of the pupil as described above. This works out such that the image through a telescope can never be brighter than the image as seen with the unaided eye. This seems counterintuitive. However, with optimum magnification (described below) the image not be significantly dimmer and will be considerably larger and more detailed."

Tim

[Tim Armes]

Forget depth of field and instead think about aberrations. It's more difficult to reduce these in lenses/mirrors with low f-ratio than in ones with larger f-ratio; i.e. a short-focus "achromatic" refractor will show more chromatic aberration than a long-focus one, the latter therefore being better for planets. Similarly, fast newtonians give wide fields but are more prone to coma.

Hi,

That sounds reasonable and makes sense. The article previously linked to on the other hand makes this statement:

"Most large reflectors exhibit better resolution when used with an off-axis aperture mask. This is because you can wait with frustration for those magic, fleeting moments when the atmospheric seeing allows high-resolution glimpses with a large aperture, or you can reduce the aperture and trade off some resolution for much more time when the view is satisfying. Once again, a small aperture gives a sharp image that jumps around in bad seeing, while a large aperture often averages the image into a fuzzy blob."

Why do smaller apertures give sharper images? The above states that you can make a wide aperture telescope into a smaller one, which suggests that the mirror isn't at cause.

There's something I'm missing regarding the effect of focal length and focal length ratios in telescope design.

Tim

[Moonshane]

To be fair, I do think it's a ver good article. Upon second reading most things are explained, although diagrams would really help the understand.

That said, here's an example of a statement that isn't explained:

"F/number is of little importance visually. A "fast" telescope implies a short focal length and a large field. Fast, however, is a term borrowed from photography (an f/5 telescope can take a photograph with one-fourth the exposure time of an f/10 instrument). Visually, well made fast and slow telescopes of the same aperture have no difference in image brightness or resolution."

Why does more light coming in make no difference in image brightness? Isn't that the whole point of a big aperture, to see dimmer things?

This point is actually addressed on this page, which I also found to be very good:

Starizona's Telescope Basics

The explanation being:

"This is because the light from an extended object is being spread out by the fact that the telescope is magnifying the image. So magnification factors into the equation; light is lost in proportion to the square of the magnification. There is a minimum magnification allowed by the limiting size of the pupil as described above. This works out such that the image through a telescope can never be brighter than the image as seen with the unaided eye. This seems counterintuitive. However, with optimum magnification (described below) the image not be significantly dimmer and will be considerably larger and more detailed."

Tim

hi Tim

in relation to fast and slow focal ratios, it's not really like photography at all in my view. with a camera you can adjust the aperture of the diaphragm and this lets in more or less light.

In normal telescope use, this is of course not possible. Therefore the focal ratio is fixed and based on the focal length divided by aperture.

The key thing to understand is that the Televue article specifies the difference between imaging and visual. The latter point regarding there being no difference in image brightness between different focal ratios for the same aperture relates to visual observing. I know almost nothing about imaging so will let others comment on that.

For two 300mm aperture scopes, one f4 and one f8, the fact that light, that has traveled for many light years, has to travel another 1.2m makes absolutely no difference to visual brightness at the same magnification.

You can effectively change the focal ratio of a telescope by using an aperture mask. This is basically a lens cap with a small hole cut in it which creates a smaller aperture and as the focal length is unchanged, the effective focal ratio increases.

Regarding 'best' magnification, this is something which depends on many factors including the type of target, the viewing conditions, whether the scope is at ambient temperature, optical quality, collimation etc.

e.g. for Saturn I find that with my 6" f11 newtonian, I can use between 120x and 225x on average depending on seeing. This equates to 20x and 38x aperture in inches. But with the moon and double stars, I have used up to 533x successfully = 89x inches in aperture.

I think the point they make is that there is a technical optimum maximum where no more detail is viewable but obviously depending on your eyesight and experience (and the above factors) a little more magnification can be useful and usable. My recommendation is keep going up in magnification until the seeing ruins the image, then back off a notch to a better image. This is the reason I have one low power widefield eyepiece (26mm) and higher magnifications of 18mm, 15mm, 13mm, 12.5mm, 11mm, 10mm, 9mm, 8mm, 7mm, 6-3mm zoom. I use them all too, as seeing varies so much especially in the UK.

Hope this makes sense and good luck!

Shane

[acey]

Hi,

That sounds reasonable and makes sense. The article previously linked to on the other hand makes this statement:

"Most large reflectors exhibit better resolution when used with an off-axis aperture mask. This is because you can wait with frustration for those magic, fleeting moments when the atmospheric seeing allows high-resolution glimpses with a large aperture, or you can reduce the aperture and trade off some resolution for much more time when the view is satisfying. Once again, a small aperture gives a sharp image that jumps around in bad seeing, while a large aperture often averages the image into a fuzzy blob."

Why do smaller apertures give sharper images? The above states that you can make a wide aperture telescope into a smaller one, which suggests that the mirror isn't at cause.

There's something I'm missing regarding the effect of focal length and focal length ratios in telescope design.

Tim

The passage you quote relates to a completely separate issue, namely the effect of atmospheric turbulence, which limits the possible resolution. Since the resolving power of a scope is proportional to aperture, it means that for any given sky conditions there is a largest useable aperture, beyond which there can be no further gain in resolution (though there will be a gain in light grasp). In UK, that limit is around 6 inches, though there will be moments of better seeing. But that's got nothing to do with f-ratio, only aperture.

Focal ratio is an issue with respect to planetary viewing for the reasons I stated. In regard to deep-sky viewing, f-ratio plays no role at all: large Newtonians are usually fast because it makes the tube shorter and the scope more manageable. A 12" f8 would be about 8 feet long and you'd need a ladder to use it.

[BlueAstra]

A 12" f8 would be about 8 feet long and you'd need a ladder to use it.

Like this?

[Moonshane]

nothing worse than being woken too early in your hammock after a hard night's observing!

[Tim Armes]

The passage you quote relates to a completely separate issue, namely the effect of atmospheric turbulence, which limits the possible resolution. Since the resolving power of a scope is proportional to aperture, it means that for any given sky conditions there is a largest useable aperture, beyond which there can be no further gain in resolution (though there will be a gain in light grasp). In UK, that limit is around 6 inches, though there will be moments of better seeing. But that's got nothing to do with f-ratio, only aperture.

Focal ratio is an issue with respect to planetary viewing for the reasons I stated. In regard to deep-sky viewing, f-ratio plays no role at all: large Newtonians are usually fast because it makes the tube shorter and the scope more manageable. A 12" f8 would be about 8 feet long and you'd need a ladder to use it.

I'm probably getting far too bogged down in technicalities that aren't really important at all at this stage. I was just interested in the how's and why's.

That said, the book I'm currently reading doesn't agree with you concerning the f-ratio playing no role at all. My current undertanding is that:

A small f-ratio gives greater luminosity but lower resolution. This is ideal for seeing dim things such as DSOs that don't need much magnification.

A large f-ratio gives greater resolution and contrast, but isn't as luminous. This is perfect for viewing planets, since they're bright but need to be magnified more to see them in detail.

The focal ratio of my Dobsonian is targetted towards DSOs, and the f/ratio is therefore based on that rather than the managable size of the scope. Although clearly a 200mm Newton designed for viewing planets would not be practical!

That information was what led me to wonder why the ratio affected the resolution, and start this post

I've since discovered that the "sweet spot" of a telescope, the size of the focal point where the images are sharp and contrasty, depends purely on the f-ratio:

"Surprisingly, the size of the "sweet spot" depends only on the main mirror's focal ratio (the mirror's focal length divided by its diameter) and not its size. For instance, even a perfect f/4.5 mirror, small or large, can provide "diffraction limited" performance only within a 2-millimeter (0.08-inch) circle at the focal plane. An f/10 paraboloid's sweet spot, by contrast, spans 22 mm (0.87 inch). (For the mathematically inclinded, the sweet spot's diameter is proportional to the cube of the f/ratio.)"

(via How To Collimate Your Newtonian Reflector - Do It Yourself - SkyandTelescope.com)

That's probably as much explanation as I'm going to get without delving into maths that are over my head

[GazOC]

Getting tied down to the "large focal ratio= planets, small focal ratio = DSO" ignores the fact that theres also an eyepiece at the other end of the scope. Although there are other aberations such as coma, false colour (in refractors), size of central obstruction (in Newts/ Dobs) to consider, aside from them looking at an object at x150 magnification in a 8" f4 Newt will be very similar to looking at that object at 150 in a 8" f8 Newt.

The main change is the focal length of the eyepiece you've had to use to get to x150 on the two different scopes rather than one design of mirror being suitable or unsuitable for a specific task.

edit: As Acey has said below the brightness of the object is given by the aperture and the magnification. Both of which are the same in the example I've given.

[acey]

Tim - I just wrote a very long reply and lost the lot (aargh!) so I'll summarise.

Image brightness and resolution depend on aperture and are independent of f-ratio. A 200mm f6 Newtonian can be an excellent planetary scope. The sweet spot is indeed smaller for faster scopes, meaning that there's less room for collimation error in these scopes. The pic in this thread shows what looks like a 36" dob of f4 or less - just think what it would look like if it was f8. Commercial large-aperture newts are typically around f4 for manageability, and people buy "coma correctors" to deal with the inevitable aberration that arises. Classical achromats were typically f10 or more, modern short-focus achromats sacrifice image quality for portability.

Regarding brightness, if you look at a galaxy of surface brightness B through a telescope with perfect transmission at lowest power, the image will have the same surface brightness, B. If you look through the same telescope at a magnification of m times lowest useable power, the image brightness will be B/m^2.

Lowest useable power is dictated solely by aperture (and eye pupil diamater). For a 300mm scope and 6mm pupil, lowest power is x50. For a 150mm scope and same eye, it's x25. Point both scopes at the same galaxy at their lowest powers and they will give the same image surface brightness (assuming equal light loss in either scope), but the 300mm scope will have an image area four times larger. That's why big aperture is better - it has nothing to do with f-ratio.

[Bazzaar]

The sweet spot is because the focal plane of a scope isnt a plane, as in a flat two dimensional area, but spherical(er.. elliptical?) The high focal ratio scopes have a larger sphere at focus and seem flatter within the diffraction limits.

Regards

Barry

[vulcan]

If I can just explain something about camera lenses... Most camera lenses give their sharpest images two stops down from full open. So, if you have an f2 lens, you will get optimal sharpness at f4. Stopping down further will increase depth of field but the sharpness lessens as the edge diffraction of the iris kicks-in making it worse.

A large telescope mirror or front lens captures more light than smaller ones. There is more information getting through to the eyepiece so the image is brighter and the detail is in higher definition - like having more pixels in your digital camera.

[Tim Armes]

Image brightness and resolution depend on aperture and are independent of f-ratio.

Ahhgh.

This is an exercise in frustration.

My book states that resolution is higher when the ratio is higher. You say that it's not true - they're independent.

Neither of you explain why, exactly....

Exactly what role does ratio play?

Tim

[ollypenrice]

Just to come in on depth of field (which is governed by f ratio)... Even though the objects we shoot are at infinity, finding critical focus, certainly for imaging, is much much harder on very fast sytems. The number of pixels receiving light from a point source soars as the crtical focal plane is missed even by microns on fast camera lenses, for instance. Last night we were imaging with a 200L lens at f3.5. Using a mechanical micro adjuster it still took about ten minutes to get the optimum FWHM measurement, a measure of the size of a star on the chip. So even though all the objects in the picture are at infinity they still can be devils to get into perfect focus.

In our F7 scope it is all very easy. Small nudges on the slow speed focuser have little effect.

Olly

[vulcan]

Have a look at what Wikipedia says about focal ratio - F-number - Wikipedia, the free encyclopedia

[acey]

My book states that resolution is higher when the ratio is higher.

Which book?

Resolution can be defined in various ways but the basic idea is that a star image in a telescope is really a small pattern of concentric circles (a diffraction pattern). You can then calculate various kinds of resolution limit, and they turn out to depend on aperture - see this link:

the astroscopic labs - article: The Resolution of a Telescope - Dawes, Rayleigh and Sparrow

It gives:

Rayleigh's resolution limit [arc sec] = 140 / Aperture Diameter [mm] (for green light)

Dawes's resolution limit [arc sec] = 116 / Aperture Diameter [mm] (for green light)

Sparrow's resolution limit [arc sec] = 70 / Aperture Diameter [mm] (for green light)

Each limit is inversely proportional to aperture. So assuming equal optical quality, a 6" telescope has better resolving power than a 4", regardless of f-ratio. But in real life, all telescopes are not equal, and nothing is perfect.

F-ratio is obviously important if you want to use a telescope as a camera lens, but for visual use it is theoretically irrelevant, except for the fact that fast scopes offer the potential for lower magnification and wider fields, and offer greater portability, even if it comes at a cost of greater aberration.

[Moonshane]

fast scopes offer the potential for lower magnification and wider fields, and offer greater portability, even if it comes at a cost of greater aberration.

just to be clear, it is surely shorter focal lengths not faster focal ratio that allows low mag, wide fields and portability- a 40" f3.5 is very fast but with a 3.5m focal length won't offer any of these qualities?

[ollypenrice]

Ahhgh.

This is an exercise in frustration.

My book states that resolution is higher when the ratio is higher. You say that it's not true - they're independent.

Neither of you explain why, exactly....

Exactly what role does ratio play?

Tim

Think of prime focus and plate scale, the size of the object in arcseconds on the sky in relation to the size of its image in mm on the chip. This is a measure of resolution.

This is governed by focal length only. Let's keep FL as a constant for a sec.

Now take two apertures, large and small, with that focal length.

Large will out resolve small yet it has a faster f ratio.

Large will have a lower f ratio and will also give more resolution so in this context the statement in your book is clearly wrong, but it may have been made in a different context.

In the context of changing the effective focal ratio of a given telescope from shorter to longer FL by changing the EP then it would be true. A change in f ratio is associated with a change in FL. Longer increases resolution by magnifying.

I think!!

Olly

[acey]

Moonshane - You're right, I typed too fast.

Olly - I think you're right ("large will out resolve small") but if I understand correctly the issue here is visual rather than imaging, so we're dealing with exit pupil rather than plate or chip size.

[rfdesigner]

Ahhgh.

This is an exercise in frustration.

My book states that resolution is higher when the ratio is higher. You say that it's not true - they're independent.

Neither of you explain why, exactly....

Exactly what role does ratio play?

Tim

If you hold aperture constant and increase focal ratio you have just incresaed your focal length so must have added a barlow. So stars on the focal plane are now further apart and easier to resolve. (assuming you weren't already diffraction limited) Frequently if using a CCD your pixels are larger than the airy disk, so increasing focal length increases resolution... you are spreading out what light you have over a wider area with larger focal ratios.

Alternatively...

If you hold your focal length constant and decrease your aperture, then you have just stopped down your lense. Assuming it's a perfect lense then you have just made your image more fuzzy due to diffraction limit and hence lost reslution (pleanty of lense reviews covering this effect). You are throwing away light you don't want at large focal ratios.

In both scenarios the focal ratio has gone up.

Derek