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Questions about optical physics of mirror and eyepiece

Optics Reflector Eyepieces Equipment
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#1 tarvio

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Posted 24 October 2021 - 09:17 PM

Hi. I'm hoping to confirm some assumptions I've made about the physics of reflectors and eyepieces. I'm not a complete beginner but will be buying my first decent telescope, and I'm comparing bigger, faster scopes with smaller, slower ones. 

 

Can anyone help me determine whether the following assumptions are accurate?

 

A reflector observes a fixed field of view in its parabolic main mirror and throws that entire portion of sky onto its secondary mirror, which reflects the image into an eyepiece. For any given aperture, a mirror's FOV is determined by its focal length. A slower telescope (flatter mirror, higher f-ratio) concentrates more resolving power into a narrower FOV than a faster telescope (more concave mirror, lower f-ratio). So a telescope's f-ratio defines its maximum or "natural" FOV.

 

It would be convenient if parabolic mirrors were flexible, and we could adjust their focal length to apply the entire power of the mirror to different fields of view/magnifications. Sadly, this engineering marvel doesn't exist, so magnification is instead achieved by cropping into the full image observed by the mirror and magnifying the result with an eyepiece lens. A higher powered eyepiece means a more aggressive crop of the natural FOV of the mirror. (The eyepiece has its own FOV too, but my understanding is that this describes the size of its image in relation to the eye, not the FOV in terms of degrees of sky.)

 

I assume the diameter of the focuser (whether 1.25" or 2") more or less defines the edges of this natural potential FOV of the main mirror as it projects into the eyepiece. So when we use an eyepiece with a diameter which is substantially less than the diameter of the focuser, we crop into the image observed by the main mirror by the same factor.

 

A slower 6" reflector at f/8 is going to see a narrower FOV than a 10" f/5. The 10" is capable of collecting more light, but due to its fast mirror and corresponding wider FOV, it spreads that power across more of the sky. If the 10" had the same f-ratio as the 6" it would indeed produce a brighter image of the same FOV as the 6", but instead, we must crop into its natural FOV to see a FOV equivalent to the slower 6".

 

Following this logic, for a FOV that the 6" f/8 is capable of observing, its performance is in fact more or less the same as the 10" f/5, because although the 10" mirror is bigger, to achieve the narrower FOV we crop into the main mirror and we're now seeing about 6" of the complete 10" potential of the glass. The only way a 10" f/5 can be said to be more "powerful" than a 6" f/8 is in wider FOVs, which the 6" isn't capable of observing. I understand that these wider FOVs are more suitable for DSOs, but this logic implies that objects preferring a tighter FOV like planets will perform more or less the same in both telescopes.

 

The telescope I'm considering (Skywatcher collapsible 10" dobs) sports a 2" focuser but comes out of the box with eyepieces that are substantially smaller than that: 25mm and 10mm. 25mm is about 1", or half the diameter of the focuser, so with a 25mm eyepiece, if my assumptions about how the optics work are accurate, we're only observing about half the diameter of the 10" mirror. If a 6" reflector also comes with a 2" focuser, then a low power eyepiece approaching the 2" diameter (40mm+) will capture the same light and produce a similar image as the 25mm on the 10" f/5.

 

So in summary, the fast 10" is only a useful upgrade to the 6" f/8 if I also want to buy a low powered eyepiece (perhaps a 42mm) to observe the wide view afforded by the faster mirror, but for planets, it won't perform better than the slow 6".

 

Thanks! I'd really appreciate knowing if these assumptions are accurate or if I've missed something obvious.



#2 KBHornblower

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Posted 24 October 2021 - 09:37 PM

You have a lot to learn about the fundamentals of optics.  That is OK, we all need to start somewhere.  There is more to be corrected in your assumptions than can be handled easily in a single post.  These fundamentals are much easier to explain in person with sketches than with words alone in a forum like this.  Perhaps you could find an astronomy club near your home, where someone could walk you through the fundamentals.  By all means take appropriate pandemic precautions.  They may be able to refer you to books on the subject, and if all goes well someone here in Cloudy Nights can do likewise.


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#3 ngc7319_20

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Posted 24 October 2021 - 09:38 PM

Well I didn't follow all that.  Roughly speaking the FOV in degrees = 57.3 * [eyepiece field stop diameter] / [telescope focal length].   Use inches or mm for both.

 

Obviously a 2" eyepiece (2" focuser) can have a larger field stop than a 1.25" eyepiece (or 1.25" focuser).



#4 Rustler46

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Posted 24 October 2021 - 10:17 PM

The telescope I'm considering (Skywatcher collapsible 10" dobs) sports a 2" focuser but comes out of the box with eyepieces that are substantially smaller than that: 25mm and 10mm. 25mm is about 1", or half the diameter of the focuser, so with a 25mm eyepiece, if my assumptions about how the optics work are accurate, we're only observing about half the diameter of the 10" mirror. If a 6" reflector also comes with a 2" focuser, then a low power eyepiece approaching the 2" diameter (40mm+) will capture the same light and produce a similar image as the 25mm on the 10" f/5.

 

So in summary, the fast 10" is only a useful upgrade to the 6" f/8 if I also want to buy a low powered eyepiece (perhaps a 42mm) to observe the wide view afforded by the faster mirror, but for planets, it won't perform better than the slow 6".

 

You have made a lot of conclusions. If I understand your statement (quoted above), one point deserves to be made. Whatever portion of a telescope's image you choose to examine via different eyepieces (with differing field stop diameters and magnifications) - every point in the image is being formed by the entire mirror. This is true for both the mirror's light gathering power as well as its resolution. You just choose how much of that image you want to examine. But the FOV you have chosen doesn't affect the quality of the image that has been formed by the mirror. Clear 'nuf?

 

Now the above is a general statement, true but subject to specifics.

An example: There can be vignetting on the outer portions of large fields of view, where that portion of the field cannot "see" the entire mirror. This would result in the image being dimmer on the edge of the FOV. Such a situation can be caused by a secondary mirror that is too small. This is a design decision, that affects image quality. But it is not an inherent characteristic of the primary mirror.

 

Another specific is that a reflector (without a coma corrector) makes essentially perfect images only at the center of the field of view. Image will deviate progressively from that away from the optical axis. But even with that in mind the entire mirror contributes to the image all across the field.

 

That's how I see things. As for your other conclusions, I'll leave that to other more skilled and clear-minded ones to comment on.

 

Best Regards,

Russ


Edited by Rustler46, 24 October 2021 - 11:35 PM.

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#5 EJN

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Posted 24 October 2021 - 10:20 PM

I don't know where to begin, but a 6" f/8 and a 10" f/5 will have essentially the same field of view with the same eyepiece. Actually the 6" f/8 would be a hair wider because the focal length is 2" shorter than a 10" f/5.

 

Forget f-ratio. FOV is determined by the focal length of the telescope and the focal length of the eyepiece,

and AFOV (apparent field of view) of the eyepiece. For example, an Ethos has twice the AFOV of a Plossl.

 

The lowest magnification you can get is determined by the exit pupil. Assuming 7mm for a fully dark adapted eye, this corresponds to a magnification of 3.5 * Aperture (in inches). So for a 6" it would be 21x and for a 10" 35x.

 

 

 

25mm and 10mm. 25mm is about 1", or half the diameter of the focuser, so with a 25mm eyepiece, if my assumptions about how the optics work are accurate, we're only observing about half the diameter of the 10" mirror.

 

25mm is the focal length of the eyepiece and has nothing whatsoever to do how much of the mirror diameter is used, on axis it is 100% illuminated by the mirror. The eyepiece focal length determines the magnification, along with the FL of the primary. That is all it does. The only way you can "choke" the aperture is with an undersized secondary. 

 

m = FLt / FLe

 

where m = magnification, FLt is the focal length of the telescope, and FLe is the focal length of the eyepiece

(in the same units, inches or mm).

 

So for a 10" f/5, a 25mm eyepiece gives a magnification of 50x. The same eyepiece in a 6" f/8 gives a magnification of 48x. Interestingly enough, my 3" f/16 refractor with a 25mm eyepiece is 48x, so it would have the same field of view (with the same eyepiece) even though it double the f-ratio. Which is why I said forget f-ratio.

 

There is no such thing as a "natural" field of view for a parabolic mirror, or a lens for that matter.

 

Your assumptions are not accurate, so ditch them and start here:

 

https://www.telescope-optics.net/


Edited by EJN, 24 October 2021 - 10:59 PM.


#6 Star Shooter

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Posted 24 October 2021 - 10:29 PM

Unfortunately, your assumptions have led you astray. To help straighten you out, get the book Telescopes Eyepieces Astrographs by Berry, Ceragioli, Smith. Formerly published by Willman-Bell, Inc. The American Astronomical Society is selling the Willman-Bell titles soon thru their store at www.shopatsky.com. See the announcement at www.aas.org/willbell.

This book covers the optical theory you need and how it affects various types of telescope systems. 

 

What you got right is aperture. A larger objective will collect more light than a smaller one. A larger objective will also allow you to resolve smaller details in the image. The resolution due to diffraction is =1.22x(Lambda) / (Aperture). 

 

The field of view of a telescope is controlled by the Field Stop in the eyepiece. This field stop controls the maximum exit angle of the light exiting the eyepiece. This angle is expressed in degrees and is called the Apparent Field of View. To get the actual Field of View of the telescope / eyepiece system. You divide the Apparent Field of View by the Magnification.

 

The Magnification of the telescope / eyepiece system is the Focal Length of the telescope divided by the Focal Length of the eyepiece. Both focal lengths are expressed in millimeters.



#7 tarvio

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Posted 24 October 2021 - 11:27 PM

Thank you. I suspected my mental model wasn't right. This point in particular was a breakthrough in my understanding so thank you Rustler46 for the highlight:

 

every point in the image is being formed by the entire mirror.

 

I'll choose a first telescope, and in this simple Dobsonian category it seems there are few wrong options. Then I'll school up to make sure I better understand the optics I'm looking through.

Really appreciate your help. Clear skies!

 

T



#8 Rustler46

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Posted 24 October 2021 - 11:42 PM

Thank you. I suspected my mental model wasn't right. This point in particular was a breakthrough in my understanding so thank you Rustler46 for the highlight:

On my part that was a moment of mental clarity, one that so easily fogs over, like a breathed on eyepiece.



#9 Star Shooter

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Posted 25 October 2021 - 12:01 AM

The focuser is the interface between the telescope and any accessories that you use. In this case, eyepieces and cameras. They come in specific sizes. The specific measurement is the diameter of the accessory barrel that will fit into the focuser. The current common sizes are 1.25", 2", 3". For example, a 2" eyepiece will fit a 2" focuser. 1.25" and 3" eyepieces will need an adapter to fit a 2" focuser.

 

Eyepieces come in specific sizes, denoted by the barrel size in inches. The barrel of an eyepiece is the part that fits into the focuser. The barrel is often chrome plated to look attractive. Eyepieces are also denoted by focal length, measured in millimeters. A short focal length eyepiece will give a larger magnification than a long focal length eyepiece for a given telescope. The focal length is usually printed on the eyepiece somewhere. Last, the Apparent Field of View for an eyepiece is generally found in the documentation somewhere. 

 

The 6" f/8 scope has a focal length of about 1200mm. Assuming Plossl eyepieces the AFOV is about 50 degrees.

The 25mm EP has a mag of 48x=1200/25. The FOV is 1 degree = 50/48.

The 10mm EP has a mag of 120x =1200/10. The FOV is .41 degrees = 50/120.

 

The 10" f/5 scope has a focal length of about 1250mm. Assuming Plossl eyepieces the AFOV is about 50 degrees.

The 25mm EP has a mag of 50x=1250/25. The FOV is 1 degree = 50/50.

The 10mm EP has a mag of 125x =1250/10. The FOV is .40 degrees = 50/125.



#10 Jon Isaacs

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Posted 25 October 2021 - 12:02 AM

Thank you. I suspected my mental model wasn't right. This point in particular was a breakthrough in my understanding so thank you Rustler46 for the highlight:

 

 

I'll choose a first telescope, and in this simple Dobsonian category it seems there are few wrong options. Then I'll school up to make sure I better understand the optics I'm looking through.

Really appreciate your help. Clear skies!

 

T

Tarvio:

 

First let me say Hello and :welcome: to Cloudy Nights.  

 

Next:  You have obviously thought a lot about this and you have some sound fundamental understandings but they require some refinement to be entirely correct. Some stuff to think about:

 

-  The field of view of a telescope depends on the particular eyepiece and the focal length of the telescope.  The 6 inch F/8 has a slightly shorter focal length than the 10 inch F/5 so for a given eyepiece, the field of view will be slightly wider in the 6 inch.  

 

-  The maximum possible field of view is determined by the focuser diameter and the focal length of the telescope.  For a 1.25 inch eyepiece, the maximum possible field stop diameter is about 27.5 mm, for a 2 inch eyepiece, the maximum possible field stop diameter is about 46mm.  The field stop is a physical ring at the focal plane of the eyepiece.  It is what we see as the edge of the field. With many eyepieces, looking backwards down the barrel, the field stop can be see.  

 

The equation for calculating the True Field of View of a telescope:

 

TFoV= 180 deg/Pi radian x field stop / focal length telescope.   For a scope with a 1200mm focal length and a maximum field stop 2 inch eyepiece:

 

TFoV = 57.3 x 46mm / 1200mm  = 2.20 degrees.  

 

- The resolving power and light gathering power of a telescope are determined by it's aperture, a 10 inch scope has greater resolving power than a 6 inch and captures more light.

 

Jon


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#11 Rustler46

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Posted 25 October 2021 - 12:52 AM

 

The lowest magnification you can get is determined by the exit pupil. Assuming 7mm for a fully dark adapted eye, this corresponds to a magnification of 3.5 * Aperture (in inches). So for a 6" it would be 21x and for a 10" 35x.

 

 

Lots of good information in your reply. But I must admit to regularly violating the lowest magnification rule. Lock me up - I'm guilty.  I often use a GSO 42mm, 2-inch eyepiece with my 10-inch f/5, providing an 8+ mm exit pupil and 30X. My old eyes' pupil (perhaps 5-6 mm) does considerably stop down the aperture - "wasting aperture". But the waste was worth the bright, expansive (2.2°) FOV. Al Nagler wrote about this on the TV website. Also the following link on the Sky and Telescope website has useful information on this (scroll down to "How Low Can You Go"):

 

Now there are limits to how far one can go in breaking the rule, at least for reflectors. At some point the shadow the secondary mirror will get to be a significant fraction of our eye's pupil. For refractors there isn't such a limit.

 

Just another take on this. 

 

Russ


Edited by Rustler46, 25 October 2021 - 02:16 PM.

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#12 TOMDEY

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Posted 25 October 2021 - 01:23 AM

Howdy, tarvio!

 

Well... you most certainly took a good stab at understanding and explaining how a telescope comprising a primary mirror, folding flat mirror, focuser tube, and eyepiece captures field and resolution. That's commendable and certainly a good exercise prior to then consulting the ~standard model~ one most often finds in books and/or from  novice experts through professionals. I always do that on every subject under the sun.

 

I'd consul it's time to crack the books as recommended by others above. Your opening dissertation is about 10% truth and 90% mumbo-jumbo. No shame in that; that's about average and a good exercise. And, in perspective... most of us here are around 50/50 blend of fact/mumbo. Optics is a rather arcane art, and took several hundred years to "mature". The current state among average professionals is 80/20, and does not exceed 90/10, even among the world-class. --- true of most all sciences and scientists. That means there is still at least 10% to be discovered --- and, historically --- that almost entirely comes from amateurs. When one ~learns too much~, the creativity almost always dries up!   Tom


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#13 spereira

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Posted 25 October 2021 - 08:18 AM

Moving to Reflectors.

 

smp



#14 George N

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Posted 25 October 2021 - 09:20 AM

Lots of good information in your reply. But I must admit to regularly violating the lowest magnification rule. Lock me up - I'm guilty.  I often use a GSO 42mm, 2-inch eyepiece with my 10-inch f/5, providing an 8+ mm exit pupil and 30X. My old eyes pupil (perhaps 5-6 mm) does considerably stop down the aperture - "wasting aperture". But the waste was worth the bright, expansive (2.2°) FOV. Al Nagler wrote about this on the TV website. Also the following link on the Sky and Telescope website has useful information on this (scroll down to "How Low Can You Go"):

 

Now there are limits to how far one can go in breaking the rule, at least for reflectors. At some point the shadow the secondary mirror will get to be a significant fraction of our eye's pupil. For refractors there isn't such a limit.

 

Just another take on this. 

 

Russ

I have used a 40mm 70 degree Brandon Erfle with my 6" and 20" F/5's - with a PII. Years ago I measured my eye at 6.7mm - but at current age it is probably down to 6mm or less. Perhaps because I observe for the most part under dark sky I did not notice the central shadow - except at twilight. I don't use the 40mm much - but at times it helps for observing 'big bright stuff' - or star-hopping to a target.

 

I have two friends with 20" F/3.3, plus Paracoor - who both regularly observe with a 31mm Nagler - TV's eyepiece calculator says exit pupil = 8.2mm!!! However, both report not being bothered by, or even seeing, the central shadow. I've only looked thru one of these scopes with that eyepiece a few times and it looked OK to me. Yes, it is thro'in away a lot of that aperture - but it still provides nice views of big bright stuff, like M-31.

 

I've learned to accept that my reflectors have a minimum power and a largest field of view. That's why I almost always bring along my 10x50 and 20x80 binoculars.



#15 Jon Isaacs

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Posted 25 October 2021 - 02:51 PM

I have used a 40mm 70 degree Brandon Erfle with my 6" and 20" F/5's - with a PII. Years ago I measured my eye at 6.7mm - but at current age it is probably down to 6mm or less. Perhaps because I observe for the most part under dark sky I did not notice the central shadow - except at twilight. I don't use the 40mm much - but at times it helps for observing 'big bright stuff' - or star-hopping to a target.

 

I have two friends with 20" F/3.3, plus Paracoor - who both regularly observe with a 31mm Nagler - TV's eyepiece calculator says exit pupil = 8.2mm!!! However, both report not being bothered by, or even seeing, the central shadow. I've only looked thru one of these scopes with that eyepiece a few times and it looked OK to me. Yes, it is thro'in away a lot of that aperture - but it still provides nice views of big bright stuff, like M-31.

 

I've learned to accept that my reflectors have a minimum power and a largest field of view. That's why I almost always bring along my 10x50 and 20x80 binoculars.

My story:

 

I am 73 years old.. I regularly use exit pupils in excess of 7mm, particularly when using H-beta and O-lll filters.  6 or 7 years ago, I purchased a 41mm Panoptic to use with my 25 inch F/5.. I wanted the maximum possible field of view and I figured I had aperture to burn. 

 

But a funny thing happened. I really never found the wider field of view useful but I noticed that under some circumstances, the 8.2 mm exit pupil of the 41mm Panoptic was brighter than the 7 mm exit pupil of the 35mm Panoptic.  Pretty weird for someone in their late 60's.  I made some measurements and discovered that my dark adapted pupil was closer to 8 mm than to 7mm. 

 

This last new moon, I was observing the Horsehead with my 16 inch and a H-Beta filter.  I tried a variety of combinations, a variety of eyepieces, the emission nebula IC434 behind the Horsehead was clearly the brightest with a 7.7mm exit pupil.  I am still skeptical about just why this is but there is no doubt in my mind that it is brighter.

 

The lesson there is that when push comes to shove, trust your eyes... 

 

A little websearch turned up a study of dark adapted pupil versus age..  The results are interesting.  They tested 30 people in their 60's, the average dark adapted pupil was 5.58 mm but the range was from 3.5mm to 7.5 mm.  You could be that 1 in 30 with the 3.5mm dark adapted pupil or you could be that 1 inch 30 with a a 7.5mm dark adapted pupil.  

 

Another interesting bit is that variation between the age groups is smaller than the variation within the age groups.  For people in their 20s, the average is 7.33mm for people in their 60s, 5.58mm, that's 1.45 mm.. But within each group with 30-50 members, the variation was at least 3mm.

 

https://pubmed.ncbi....h.gov/20506961/

 

So again, the lesson here is trust your eye and if you are wondering where you fit in, measure it.

 

Jon


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