Jump to content

  •  

CNers have asked about a donation box for Cloudy Nights over the years, so here you go. Donation is not required by any means, so please enjoy your stay.

Photo

Binoculars vs telescope objective area and resolution

optics binoculars refractor reflector
  • Please log in to reply
30 replies to this topic

#1 Eliserpens

Eliserpens

    Viking 1

  • -----
  • topic starter
  • Posts: 638
  • Joined: 30 Jan 2020
  • Loc: Near Guelph Ontario

Posted 02 March 2020 - 03:20 PM

I searched for this comparison but, a bit oddly, failed to find anything pertinent.  I'm kinda new here so if it has been covered then please refer me to the source.

 

I think it is generally accepted that resolution depends primarily on aperture, the larger the lens area, the more light.  The question I tried to address is, with respect to viewing only, how big an objective do you need to make a telescope worthwhile over a pair of 50mm binoculars.  The calculation is simple - but the answer was a bit surprising and yet may be consistent with practice.

 

Each of the two binocular-monoculars has an area of pi*625 mm2 , giving a total of pi*1250 mm2.

A single lens with pi*1250 mm2 has a radius of 35 mm, and hence a diameter of 70 mm.  Thus, the calculation predicts that a monocular telescope has to have a larger diameter than 70 mm to actually capture more light than a 50mm binocular.

 

As I see it, eyepieces are irrelevant here since they could be adapted in either case.  The obvious unknown is whether pi*1250 mm2 of captured light gives the same resolution if delivered to one eye (telescope) or split between two.  I don't know the answer to that - maybe someone here can shed some light (oops...).  Its possible that the resolution is greater for two eyes because you are less likely to saturate or vice versa for one eye because the summed light is more likely to be over the threshold for receptor activation.

 

So is this why commercial telescopes generally have an objective (reflector) >70 mm? 



#2 Garyth64

Garyth64

    Fly Me to the Moon

  • *****
  • Posts: 5,935
  • Joined: 07 May 2015
  • Loc: SE Michigan

Posted 02 March 2020 - 03:49 PM

A pair of 50mm binoculars have a 50mm lens for each eye.  There are advantages of using both eyes.

But that does not equate into being a 70mm telescope.

50mm binoculars do not have the resolving power of a 70mm telescope.

The math you did was right, but the assumption of the answer was wrong.


  • Terra Nova and Bean614 like this

#3 carolinaskies

carolinaskies

    Mercury-Atlas

  • *****
  • Posts: 2,811
  • Joined: 12 Dec 2014
  • Loc: Greenville SC

Posted 02 March 2020 - 03:54 PM

OK, lets tackle this from a standpoint of quality comparison first.  A set of cheap Bushnell 10x50 binos are not equivalent to a 50mm finder with a standard mirror diagonal let alone a larger refractor with a glass diagonal.  The prisms in your typical low-mid binocular tend to eat up brightness and have bad edge performance.  You'll find at night time many bargain binoculars underperform because they lose some of the light in the porro-prism Bak7 glass too and even using both eyes it's still not as pleasing as a rock steady telescope.  In this case if you could mount two 50mm spotting scopes side by side you'd have better resolution and brighter objects even using a mirror or prism diagonal because the quality of the glass and the figure is much better. 

Once you move up to the more serious binoculars like Nikon, Celestron, etc.  These are built with both terrestrial and night time in mind and are much better, closer to a telescope's performance.  You'll note that as aperture increases for binoculars the price vs performance increases.  However the weight also becomes a factor so that some type of tripod or parallelogram mount becomes necessary to keep them stable enough to use.  

While you can see a slightly wider field using binoculars, the maximum resolution is still based on the aperture of the lens system, not a combined aperture of both.  What you achieve with binoculars is a wider field of view but at the same resolution as a single optic. 



 



#4 photoracer18

photoracer18

    Skylab

  • *****
  • Posts: 4,280
  • Joined: 02 Sep 2013
  • Loc: Martinsburg, WV

Posted 02 March 2020 - 03:57 PM

Actually in the same light two eyes do see better than one. This is because using both eyes eliminates seeing imperfections in vision of each individual eye. Its one of the keys of why binoviewers see better than one eye even though its just the single light cone split in two. In reality a binoscope would see better than a binoviewer because it would be getting double the light but a binoviewer is still better than one eye due to the human brain and its built in correction of vision differences. Plenty of data on this.

 

Still as noted a larger objective can resolve more detail and a smaller one even a pair of them except for the next statement. On the other hand 2 objectives will resolve detail based on a synthetic aperture equal to the distance between the outer edges of the 2 scopes (separation increases resolution). This is how the interference properties of light work and why major telescopes are usually built in pairs, quads or have multiple objectives in the same housing (Keck telescopes is an example). A technique first used in radio telescopes.


Edited by photoracer18, 02 March 2020 - 04:06 PM.

  • Terra Nova, Eliserpens and Tangerman like this

#5 treadmarks

treadmarks

    Apollo

  • -----
  • Posts: 1,215
  • Joined: 27 Jan 2016
  • Loc: Boston MA

Posted 02 March 2020 - 04:15 PM

The question I tried to address is, with respect to viewing only, how big an objective do you need to make a telescope worthwhile over a pair of 50mm binoculars.

Even a 50mm telescope could be a lot better than 50mm binoculars for a lot of purposes, because it can achieve higher magnifications. Magnification yields resolution at the expense of brightness. If something isn't magnified enough, then all you see is a tiny point of light instead of a galaxy or a planetary nebula. Magnify it way too much, and you might see nothing because it's not bright enough anymore.

 

Now as to your question, or what I think your question is about: the eye-brain system puts together the two images from binoculars through a process referred to as "binocular summation." This has been studied, and most studies conclude the effect is an improvement of approximately 1.25X over monocular viewing of the same aperture. 50*1.25=62.5, so the human brain can use about as much light from 50mm binoculars as it would from a 60mm telescope. Provided of course, the object is big enough to be seen in binoculars...


  • Eddgie likes this

#6 Kunama

Kunama

    Aussie at large

  • *****
  • Posts: 6,026
  • Joined: 22 Oct 2012
  • Loc: Canberra, Australia

Posted 02 March 2020 - 04:47 PM

Actually in the same light two eyes do see better than one. This is because using both eyes eliminates seeing imperfections in vision of each individual eye. Its one of the keys of why binoviewers see better than one eye even though its just the single light cone split in two. In reality a binoscope would see better than a binoviewer because it would be getting double the light but a binoviewer is still better than one eye due to the human brain and its built in correction of vision differences. Plenty of data on this.

 

Still as noted a larger objective can resolve more detail and a smaller one even a pair of them except for the next statement. On the other hand 2 objectives will resolve detail based on a synthetic aperture equal to the distance between the outer edges of the 2 scopes (separation increases resolution). This is how the interference properties of light work and why major telescopes are usually built in pairs, quads or have multiple objectives in the same housing (Keck telescopes is an example). A technique first used in radio telescopes.

The resolving ability of a binocular scope is limited to that of one of the two apertures in visual use as in this use our brain does not act like an interferometer,  Keck and other imaging systems do.


  • Jon Isaacs likes this

#7 Garyth64

Garyth64

    Fly Me to the Moon

  • *****
  • Posts: 5,935
  • Joined: 07 May 2015
  • Loc: SE Michigan

Posted 02 March 2020 - 04:52 PM

Even a 50mm telescope could be a lot better than 50mm binoculars for a lot of purposes, because it can achieve higher magnifications. Magnification yields resolution at the expense of brightness. If something isn't magnified enough, then all you see is a tiny point of light instead of a galaxy or a planetary nebula. Magnify it way too much, and you might see nothing because it's not bright enough anymore.

 

Now as to your question, or what I think your question is about: the eye-brain system puts together the two images from binoculars through a process referred to as "binocular summation." This has been studied, and most studies conclude the effect is an improvement of approximately 1.25X over monocular viewing of the same aperture. 50*1.25=62.5, so the human brain can use about as much light from 50mm binoculars as it would from a 60mm telescope. Provided of course, the object is big enough to be seen in binoculars...

I don't think that is quite right.  In experiments done decades ago, it was found that using binoculars increased seeing by 1.4x over the monocular.  It was explained simply due to the greater probability of detection. "You can account for the improvement simply due to the fact that two independent detectors have a greater probability of detecting faint objects than one detector."  "It may even be due to the probability summation and some physiological mechanism that further enhances binocular vision."

The lecture said nothing that makes it approximate to a larger objective.  It just seems to be eyes being used to their potential.


  • Eddgie likes this

#8 TOMDEY

TOMDEY

    Cosmos

  • *****
  • Posts: 9,968
  • Joined: 10 Feb 2014
  • Loc: Springwater, NY

Posted 02 March 2020 - 05:01 PM

Hi, Elise; excellent research and thoughts up there! We (especially here, on CN!) tend to overthink and overtheorize these things with equations, charts, graphs, and anecdotes. I'm no exception --- so here goes! >>>

 

>Given the choice, two eyes are certainly better than one, most dramatically when each is looking through the same make and model telescope aka True Binocular.

>Brightness, contrast and sharpness all improve dramatically.

>The factor is around root two, provided the metric is aptly defined (information theory, not necessarily the same as more common traditional definitions).

>So, your area of lens(es) is indeed the biggest driver, provided it/they feed the eye(s) optimally.

>Optical Resolution is a somewhat different beast; the larger lens computes to better res in proportion to its diameter; with no binocular benefit --- that's more in the arena of definitions, rather than raw functional performance. And why I chose the word ~sharpness~ up above, to discriminate one's ability to see better detail two-eyed.

>Our eyes-brain system is indeed very good at ringing the best information out of one or both eyes. So, the doubled input (area/info) and unconscious/subconscious processing takes almost full advantage of that. Whether that is equivalent to a diameter-equivalent of 1.25x or 1.41x has always been, and will continue to be a subject of academic debate. I lean in the direction of 1.4, some insist it's closer to 1.0 (aka no improvement)... But, I'll compromise on embracing 1.39, and negotiate from there.

 

Conclusion: Going from mono to true bino helps a lot, is dramatically better. The improvement is most certainly far greater than zero and cannot exceed twice as good. We visual instrument fans will argue the details and nuances... forever!   Tom

 

Full Disclosure: I obsess over and embrace bino --- nearly all of my instruments are true bino, e.g. these sixteen-inch true Night Vision Binoculars!    Tom

 

~click on~ >>>

 

 

Attached Thumbnails

  • 86 Toms JMI RB-16 six-motor electronic controls.jpg

  • Garyth64, vtornado and Binofrac like this

#9 treadmarks

treadmarks

    Apollo

  • -----
  • Posts: 1,215
  • Joined: 27 Jan 2016
  • Loc: Boston MA

Posted 02 March 2020 - 05:21 PM

I don't think that is quite right.  In experiments done decades ago, it was found that using binoculars increased seeing by 1.4x over the monocular.  It was explained simply due to the greater probability of detection. "You can account for the improvement simply due to the fact that two independent detectors have a greater probability of detecting faint objects than one detector."  "It may even be due to the probability summation and some physiological mechanism that further enhances binocular vision."

The lecture said nothing that makes it approximate to a larger objective.  It just seems to be eyes being used to their potential.

The number depends on the study you're quoting. The numbers I've seen range from 1.2 to 1.3, so I choose 1.25 as a happy medium. You have chosen to believe in an extremely optimistic view of what is possible with binoculars. Go with what makes you feel good, I guess.



#10 Sketcher

Sketcher

    Surveyor 1

  • *****
  • Posts: 1,664
  • Joined: 29 Jun 2017
  • Loc: Under Earth's Sky

Posted 02 March 2020 - 05:30 PM

I think it is generally accepted that resolution depends primarily on aperture, the larger the lens area, the more light.  The question I tried to address is, with respect to viewing only, how big an objective do you need to make a telescope worthwhile over a pair of 50mm binoculars.

Aperture isn't the same as area.  Resolution isn't dependent on area.  For example, look at the resolution of the Event-Horizon-Telescope (EHT), and then check out the total area of the energy-gathering components.  Resolution depends on the diameter of circular apertures.  Or, in the case of the EHT; it depends on how long the baselines are between the most widely separated individual apertures.

 

That being said, in order to make good on the resolution of an instrument, one needs to employ sufficient magnification.

 

Lightgrasp, or light-gathering power (which does depend on area), isn't the same thing as resolution.  Light-grasp and resolution are entirely different things.

 

Now to (attempt to) answer your question:

 

Here are some examples of what can be seen with a 1-inch (25.4mm) telescope -- basically a telescope that has half the aperture of one side of a pair of 50mm binoculars:

 

Saturn 1 inch 67x March 30 2019 4
 
Jupiter 1 inch 67x March 30 2019 2
 
Albireo   Gamma Delphini 1 inch aperture 67x Sketcher   text
 
Venus 1 inch aperture 19 Oct 2018 67x Sketcher   Text
 
Arzachel Alphonsus Ptolemaeus 1 inch aperture 18 Oct 2018 67x Sketcher

 

I think you would agree that even a 1-inch telescope has some advantages over a typical pair of 50mm binoculars -- not due to light-grasp, and not even due to having greater resolution (Theoretically, a 1-inch aperture has less resolution than a 50mm aperture.);  but due to the added resolution (amount of detail) one can see due to using higher magnifications.


  • Cali likes this

#11 Jon Isaacs

Jon Isaacs

    ISS

  • *****
  • Posts: 93,579
  • Joined: 16 Jun 2004
  • Loc: San Diego and Boulevard, CA

Posted 02 March 2020 - 05:36 PM

Two sensors reduce the signal noise by a .707. (.51/2) And increase in aperture that accomplishes this same factor is (21/2)1/2 = 1.19

 

This is a noise floor signal processing equation that has been promoted in the binocular forum. It's about light and the human eye.

 

Binoculars do not increase the resolving power because that's based on the size of the Airy disk which is based on aperture. For the eye to resolve the image at the focal plane requires high magnifications, for a 50 mm objective that would be around 100x.. 

 

Jon


  • Eddgie and Terra Nova like this

#12 Barlowbill

Barlowbill

    Apollo

  • *****
  • Posts: 1,351
  • Joined: 05 Apr 2018
  • Loc: Tulsa, Oklahoma

Posted 02 March 2020 - 05:44 PM

Thanks, Sketcher.  Very interesting pictures of views with a 1" scope.  The thing to note, as Sketcher said is, that is at 67X.  If you look at Saturn or Jupiter or whatever at 10X or 15X, you won't see much of anything.  Magnification rules.


  • treadmarks likes this

#13 Kunama

Kunama

    Aussie at large

  • *****
  • Posts: 6,026
  • Joined: 22 Oct 2012
  • Loc: Canberra, Australia

Posted 02 March 2020 - 06:09 PM

We, "TheFacelessMen" and I, put this to the test a couple of years ago...

We set up my Takahashi TSA120 binoscope alongside Phil's TOA150 which we used with the Baader MkV binoviewer and also with a single eyepiece in a 2" diagonal..

 

Using similar eyepiece series and matching the exit pupils as closely as possible we felt that that the apparent image brightness of the TSA binoscope was very close to the TOA150 with single eyepiece and quite noticeably brighter than the TOA/binoviewer combination.

 

However, the ability to resolve fine details on lunar crater rims and very faint stars in NGC4755 was still in favour of the TOA150.  My guess is that the perceived image brightness in a true binoscope is about a 1.3x to 1.35x factor compared to single scope of the same aperture....

Attached Thumbnails

  • MIS_5229 copy.jpg

Edited by Kunama, 02 March 2020 - 06:10 PM.

  • Binofrac and StarAlert like this

#14 Binofrac

Binofrac

    Mariner 2

  • -----
  • Posts: 218
  • Joined: 11 Jul 2019
  • Loc: Kent, UK

Posted 03 March 2020 - 05:37 AM

I'm sure many seasoned astronomers have seen these comparisons many times as it's always a valid question for newcomers to ask and greatly interested me in my earlier days. To my mind it's like the question "What is the best telescope?" It always depends on the individual. It's probably like home sound systems. Many people argue about distortion figures, frequency ranges, the warm sound of valves (tubes), the cold sound of digital, etc. No system is perfect and so it eventually comes down to which sort of distortion do you prefer? There are many people far more experienced than me and I would always bow to their greater knowledge but I have experimented with stereo viewing to find an answer for myself.

 

I have two binoculars, a 10x50 and a 15x70, and a 4" scope. My experiments included these and many tryouts of various instruments at astronomy gatherings. Obviously two eyes are always better than one but it's how this is achieved. I happened to look through a wonderful APM 45 degree 100mm binocular last year which gave very good views. It was on a very stable parallelogram mount which gave that lovely counterbalanced light as air manouverability. The thing was that I didn't think the views were good enough to make the hassle of dealing with such a heavy and expensive setup worthwhile. It would take a fair time and and a few trips to the car (which may be some way off). Some of these setups I haven't been able to use properly due to being unable to merge the images on higher magnifications, although others didn't seem to have any trouble. Although not as bright, I found a good binoviewer on a good scope to be my ideal instrument as it was a lot more user friendly.

 

Currently I keep  the 10x50's in the car as a general purpose instrument, the 15x70's as an astronomy binocular for nice easy widefield views, and my scope for the higher magnifications. I've yet to buy a binoviewer but this will be my next astronomy purchase. As others have said many times in the past, the advantages of stereo over mono viewing are very subjective as they are generally used on different targets. I feel that the normal considerations of cost, size, weight, etc are the prime factors.

 

If money were no object then without question I would have a true binoscope. it would consist of a couple of 6" F8 refractors made by Moonraker in the UK, permanently mounted in some sort of motorised goto mount with a heated chair mounted on the same assembly. I could then cruise around the night sky with ease and comfort.

 

These bino/mono debates are always interesting, not least for the pictures of the beautiful binoscope setups that people post on them so thanks everybody. I can but dream.



#15 Jon Isaacs

Jon Isaacs

    ISS

  • *****
  • Posts: 93,579
  • Joined: 16 Jun 2004
  • Loc: San Diego and Boulevard, CA

Posted 03 March 2020 - 09:57 AM

Thus, to test the specific question of whether a constant focused light input gives more mental resolution when given to one or split between two eyes I suggest a comparison of the following looking at the same, infinite distance, target with a reasonably graded degree of detail (ranging from easy to the theoretical limit).  Both use a standard 50x binocular objectives.  However, both would also have to optimised eyepieces (explanation below)

 

1) Standard binoculars.

2) Standard binocular objectives but a light path, a prism system, that brings both sides to a single eyepiece!

Note, as said, the target would have to be at effective infinity so that there is no parallax (that would introduce blur and give you a head ache with (2). 

Note also that to be fair the scopes should be tested with a range of eyepieces because the increased light in (2) would likely support an increased magnification.

 

 

You really cannot use a prisms to combine the light from two objectives into one eyepiece.

 

But what you can do is the equivalent experiment which is to take the light from one objective and split it two, one half to each eyepiece. 

 

This is what's known as a binoviewer and such comparisons are common. The results depend on the object and the conditions. If one is looking for the most difficult, lowest contrast, dimmest object, then I think one eye is better than two because you're at the noise floor of the visual system and the brighter image is a big plus.

 

Otherwise, results vary.

 

However, in your first post you discussed resolution as a function of one eye versus two and aperture.

 

Resolution is not a matter of light gathering, a larger aperture inherently has greater resolving power. The smallest resolveable detail is inversely proportional to the aperture.

 

As an example, the closest possible split for a pair of binary stars in a 50 mm is 2.30 arc seconds, in a 70 mm, it's 1.65 arc-seconds. This is because a telescope does not produce true points of light, it produces an Airy disk which is a dot surrounded by a series of faint rings. The larger the aperture, the smaller the angular size of the dot.

 

Resolution requires high magnifications... 

 

Jon


  • Garyth64 and Eliserpens like this

#16 Eliserpens

Eliserpens

    Viking 1

  • -----
  • topic starter
  • Posts: 638
  • Joined: 30 Jan 2020
  • Loc: Near Guelph Ontario

Posted 03 March 2020 - 10:15 AM

On further thought, you are right Jon.  I deleted my post, needs some more consideration....



#17 Tamiji Homma

Tamiji Homma

    Skylab

  • *****
  • Posts: 4,430
  • Joined: 24 Feb 2007
  • Loc: California, USA

Posted 03 March 2020 - 10:33 AM

 

I searched for this comparison but, a bit oddly, failed to find anything pertinent.  I'm kinda new here so if it has been covered then please refer me to the source.

 

You probably haven't come across Best of Binocular Forum yet :)

 

I would read up from here and it would take some time to read and comprehend.

https://www.cloudyni...re/#entry285371

 

Happy reading.

 

Tammy


  • Garyth64 and Eliserpens like this

#18 Eliserpens

Eliserpens

    Viking 1

  • -----
  • topic starter
  • Posts: 638
  • Joined: 30 Jan 2020
  • Loc: Near Guelph Ontario

Posted 03 March 2020 - 01:31 PM

Thanks Tammy - great links.  But is there enough time in the universe to read them all!!



#19 helpwanted

helpwanted

    Fly Me to the Moon

  • *****
  • Posts: 5,350
  • Joined: 04 Jul 2007
  • Loc: Phoenix, AZ

Posted 03 March 2020 - 01:59 PM

one of Phil Harrington's books addresses this very question, and includes a chart for comparison... don't remember which book, i can check my bookshelf tonight.



#20 PhilH

PhilH

    Viking 1

  • *****
  • Posts: 669
  • Joined: 27 Jan 2005
  • Loc: Long Island, NY

Posted 09 March 2020 - 04:01 AM

one of Phil Harrington's books addresses this very question, and includes a chart for comparison... don't remember which book, i can check my bookshelf tonight.

I can help.  That's in my book Cosmic Challenge, chapter 1 to be exact.  Let me pull a quote from that discussion:

 

Despite the term, binocular summation does not simply mean adding the apertures of a pair of binoculars together. An 80-mm binocular is not equivalent to a 160-mm telescope. Instead, we must look at the total light-gathering area.To calculate the true advantage of using two eyes over one, plug the binocular’s aperture (A) into the following formula:

Equivalent telescope aperture = √(A^2 × 1.41)

 

Therefore, a pair of 80-mm binoculars is equivalent to a single 95-mm telescope operating at the same magnification. Magnification is key, since different values, and the different exit pupils that result, will affect performance greatly.

 

The book also includes this table (Table 1.1) that summarizes findings for most popular binocular apertures.

 

Cosmic Challenge Table 1.1  Binocular Summation

Edited by PhilH, 09 March 2020 - 04:02 AM.

  • vkhastro1 likes this

#21 Eliserpens

Eliserpens

    Viking 1

  • -----
  • topic starter
  • Posts: 638
  • Joined: 30 Jan 2020
  • Loc: Near Guelph Ontario

Posted 09 March 2020 - 06:36 AM

Hi Phil - I'm a bit confused, does he explain the derivation of his equation?  The example you gave - I don't think anyone suggested that a 80 mm is equivalent to a 160 telescope, obviously the summed objective areas are much greater for the latter.  My calculation was that a 50 mm binocular has the same equivalent objective area as a 70 mm one 2*pi*r2 vs pi*r2, respectively.  Thus, an 80 mm binocular would have the same total objective area as a 113 single objective. 

 

Did Phil Harrington explain the origin of his formula?  I presume he did not also include the brain summation factor - presenting two images instead of only one.



#22 Jon Isaacs

Jon Isaacs

    ISS

  • *****
  • Posts: 93,579
  • Joined: 16 Jun 2004
  • Loc: San Diego and Boulevard, CA

Posted 09 March 2020 - 06:56 AM

My calculation was that a 50 mm binocular has the same equivalent objective area as a 70 mm one 2*pi*r2 vs pi*r2, respectively.  Thus, an 80 mm binocular would have the same total objective area as a 113 single objective.

 

 

Phil is not calculating light gathering area, he is calculating some measure of the effectiveness of binocular summation.  

 

Look through a pair of binoculars and close one eye, how much less do you see?  

 

Jon



#23 Eliserpens

Eliserpens

    Viking 1

  • -----
  • topic starter
  • Posts: 638
  • Joined: 30 Jan 2020
  • Loc: Near Guelph Ontario

Posted 09 March 2020 - 07:00 AM

Ah, you mean a field of view summation!  The above topic was on resolution, not field of view - but that is very interesting.

ee



#24 PhilH

PhilH

    Viking 1

  • *****
  • Posts: 669
  • Joined: 27 Jan 2005
  • Loc: Long Island, NY

Posted 10 March 2020 - 03:43 AM

Ah, you mean a field of view summation!  The above topic was on resolution, not field of view - but that is very interesting.

ee

I misread the original post as asking about binocular summation.  As to resolution, again I'll pull a quote from chapter 1 of my book Cosmic Challenge:

 

While it would appear from the table above [entitled "Rayleigh Criterion and Dawes Limit for Common Apertures"] that a pair of, say 10x50 binoculars (that is, 10 power, 50-mm objective lenses) should be able to resolve binary stars that are separated by only 2.3".  In reality, they don't even come close.  That's because Dawes Limit assumes high magnifications far beyond the values of most common binoculars.  As a result, binoculars will never approach their theoretical Dawes' Limit.  To estimate how tight a pair of stars can still be resolved with binoculars, it's more appropriate to consider magnification than aperture. 


That value, in turn, depends on how close a pair of stars can be resolved with the unaided eye, assuming 20/20 far vision.  In his classic reference Amateur Astronomer's Handbook, author J.B. Sidgwick suggests that 3 arc-minutes is a reasonable value, although he goes on to note that some especially keen observers can better that by nearly a factor of 2.  Other sources state that naked-eye observers can expect to resolve two stars no closer than 5 arc-minutes apart.


For our discussion here, let's draw a happy medium and assume, given 20/20 vision, the human eye can resolve two stars separated by 4 arc-minutes, or 240 arc-seconds.  Using this as our basis, we can now estimate the minimum value for a given binocular by dividing its magnification into 240.  Table 1.4 lists some common values, rounded to the nearest whole number.  Can you do better?  Chapters 3 and 4 will offer you a chance to prove it.


Table 1.4 Binocular Resolving Limits (Binocular magnification --- Resolution threshold (arc-seconds)
6x --- 40"
7x --- 34"
8x --- 30"
9x --- 27"
10x --- 24"
11x --- 22"
12x --- 20"
14x --- 17"
15x --- 16"
16x --- 15"
18x --- 13"
20x --- 12"
25x --- 10"
30x --- 8"


  • Pjxii and Eliserpens like this

#25 Pjxii

Pjxii

    Sputnik

  • *****
  • Posts: 35
  • Joined: 14 Jan 2011
  • Loc: Florida

Posted 14 May 2020 - 08:02 PM

I misread the original post as asking about binocular summation.  As to resolution, again I'll pull a quote from chapter 1 of my book Cosmic Challenge:

 

While it would appear from the table above [entitled "Rayleigh Criterion and Dawes Limit for Common Apertures"] that a pair of, say 10x50 binoculars (that is, 10 power, 50-mm objective lenses) should be able to resolve binary stars that are separated by only 2.3".  In reality, they don't even come close.  That's because Dawes Limit assumes high magnifications far beyond the values of most common binoculars.  As a result, binoculars will never approach their theoretical Dawes' Limit.  To estimate how tight a pair of stars can still be resolved with binoculars, it's more appropriate to consider magnification than aperture. 


That value, in turn, depends on how close a pair of stars can be resolved with the unaided eye, assuming 20/20 far vision.  In his classic reference Amateur Astronomer's Handbook, author J.B. Sidgwick suggests that 3 arc-minutes is a reasonable value, although he goes on to note that some especially keen observers can better that by nearly a factor of 2.  Other sources state that naked-eye observers can expect to resolve two stars no closer than 5 arc-minutes apart.


For our discussion here, let's draw a happy medium and assume, given 20/20 vision, the human eye can resolve two stars separated by 4 arc-minutes, or 240 arc-seconds.  Using this as our basis, we can now estimate the minimum value for a given binocular by dividing its magnification into 240.  Table 1.4 lists some common values, rounded to the nearest whole number.  Can you do better?  Chapters 3 and 4 will offer you a chance to prove it.


Table 1.4 Binocular Resolving Limits (Binocular magnification --- Resolution threshold (arc-seconds)
6x --- 40"
7x --- 34"
8x --- 30"
9x --- 27"
10x --- 24"
11x --- 22"
12x --- 20"
14x --- 17"
15x --- 16"
16x --- 15"
18x --- 13"
20x --- 12"
25x --- 10"
30x --- 8"

 

Phil, after reading your book quotes I am definitely going to get it, but one question I have for now is this-
regarding this table of magnifications, what is the aperture of the binoculars?  I just purchased a pair of 20x80
binoculars and I would think the resolution would be better than a pair of 20x50 assuming the same optics
throughout. Would 30x70 binoculars seperate close stars better, despite the 10mm aperture difference?


Edited by Pjxii, 14 May 2020 - 08:04 PM.



CNers have asked about a donation box for Cloudy Nights over the years, so here you go. Donation is not required by any means, so please enjoy your stay.


Recent Topics





Also tagged with one or more of these keywords: optics, binoculars, refractor, reflector



Cloudy Nights LLC
Cloudy Nights Sponsor: Astronomics