18 replies to this topic

[kingsbishop]

Title

[norvegicus]

no

[gstrumol]

It just means that your eye is receiving all the light the scope is giving you, with no light 'wasted'.

[MikeTahtib]

It means you are seeing extended objects as bright as you possibly can in a passive optical (that is, not a camera or night vision device) telescope.  Fun fact:  This is no brighter than the object appears in the sky to the naked eye. In other words, a telescope can not make an extended object brighter than it appears naked eye, it can only make ti dimmer (with increasing magnification and losses within the telescope).  It becomes more visible only because it has been magnified by the telescope, making it easier to see.  Stars can be made brighter, though.

This was one of the most difficult things for me to comprehend, but looking at the bright blue sky through a telescope and then looking at it naked-eye shows this to be true.  I still do not understand why it is true.Goig to a larger exit pupil (lower magnification) doesn't make the object dimmer or brighter, but it does fit more of the object into the field of view if you have a very large telescope.  There may be an issue with going with an exit pupil much larger than your eye pupil, in that if you are using a reflector, the shadow of the secondary may start to appear in the view.  I don't have a lot fo experience with this, but I've seen it happen with my 30mm eyepiece looking at a very bright moon.  On the other hand, people with very large fast dobs have said it isn't a problem for them.

[TOMDEY]

Theoretically - yes; practically - generally not.

 

The limiter is the human eye. "Wide Open" our eye's wavefront quality presented to the retina's centralis is pretty bad. By analogy, nearly all commercial camera lenses present the their best resolution ~stopped down~ a notch or two. Same applies to our eyes. Best visual resolution typically occurs around 1mm or 1.5mm pupil. Some young subjects with especially good eyes (20/10 acuity) max out their demonstrated res around 2.5-3.5mm pupil. This is rare. My busy optometrist said he gets that walk-in performance "only a couple times a year". That's why 20/20 is benchmarked as ~good vision~ --- even though it's far worse than the best attainable. I note that eye lens implants, combined with PRK or Lasik wavefront optimization... often result in ~hyper acuity~ 20/15, 20/12.5, even rarely 20/10. The best font I've seen on the Snellen Chart is 20/8 (?!) which may be possible, but extraordinarily rare. That's where the eye's impulse response is down around the size of the cones. Theoretically possible and occasionally/rarely satisfied.

 

Those with average or deficient vision can nevertheless comfortably achieve the resolution capability of the telescope... by cranking the magnification up... which enlarges the image presented to the retina... and constricts the exit pupil to the good central region of the eye's cornea and lens.    Tom

[siriusandthepup]

Don't forget that the "largest exit pupil" thing only applies when your are totally dark adapted and your pupil in your eye is expanded to it's maximum size.

 

All those calculations go right out the window if you are in daytime or have just looked at the Moon...

 

Look at the Moon in your telescope and immediately your pupil shrinks down to about 1 or 2mm. The exit pupil of the telescope did not change, if you were on your lowest magnification and had say, a 7mm eyepiece exit pupil - that remains the same. Now you have effectively reduced the aperture of your telescope because of all that light coming out the eyepiece is no longer entering your eye.

 

Your eye pupil size and dark adaptation are key factors in observing.

[Inkie]

As others suggest, it's a bit involved.  The reason is that neither the eye nor the scope can stand alone.  They comprise a 'system', with each component interdependently requiring the other to be of any utility. So, the scope and eyepiece selection will provide certain optical utility, but the human observer's eye will impose a constraint of some sort, be it a not-so-widely dilated pupil, or astigmatism, or floaters, etc.

 

You have specified 'resolution' in your question.  In that respect, if the telescope's offered throughput visually is not constrained by the diameter of your pupil (that is to say, your pupil is at least as wide as the exit pupil of the chosen eyepiece), and if the system is in focus (notice that I used the term 'system' again), then the theoretical resolution of the optics should be matched, and should land on, the un-occluded fovea (and that's a whole 'nuther discussion). 

 

Realistically, unless your eyes are perfect, and unless your head is in a vise to keep the center of the pupil centered on the exit pupil, good luck seeing all the optical system can provide.

[treadmarks]

With respect to exit pupil, maximum resolution is theoretically at 1mm but in practice probably a bit smaller than that. This is determined by the diffraction limit, which is the point at which the aperture of the scope causes the airy disc to bloat and break apart into rings, blurring additional detail. It also involves the Dawes limit, which was the result of testing the average person's ability to see separation between stars. The Dawes limit is different from the definition of 20/20 vision: Dawes says ~120 arcseconds is the smallest separation, whereas 20/20 tests for the ability to see a 1 arcminute detail.

 

Yet it is widely seen in practice that going below 1mm exit pupil can be helpful in several cases. The Dawes limit is the limit of human vision, meaning it is difficult and a little magnification can make things easier. Moreover, the Dawes limit is for stars; 20/20 is probably more relevant to astronomical bodies like planets, meaning a human can exceed the Dawes limit by a good margin in those cases. And double star observers feel that sometimes it is helpful to dim a star by overmagnifying it, etc.

Edited by treadmarks, 06 February 2023 - 12:59 PM.

[Tony Flanders]

Almost the opposite. The magnification that yields an exit pupil equal to your entrance pupil is the lowest commonly recommended magnification. In general raising the magnification allows you to resolve finer details; that's the main reason people do it. So of all commonly recommended magnifications, the one where the exit pupil equals your entrance pupil is the one that yields the widest field of view, the most intense possible image, and the least resolution.

 

In practice, the magnification that allows you to see maximum resolution varies greatly depending on the nature of your target and on your eyes. High-contrast targets and bright targets generally do best at very high magnifications, whereas low-contrast targets and faint targets tend to resolve more detail at somewhat lower magnifications. For most objects and most observers the maximum resolution happens somewhere between 1X and 2X per mm of aperture.

[Tony Flanders]

With respect to exit pupil, maximum resolution is theoretically at 1mm but in practice probably a bit smaller than that.

This is actually an empirical observation, not a theoretical rule. The fundamental limiting factor here is the resolution of your eyes, which varies considerably from one person to another.

In general maximum resolution tends to happen somewhere around the point where the eye's resolution is equal to the size of the diffraction disk. Very roughly.

[columbidae]

Fun fact: This is no brighter than the object appears in the sky to the naked eye. In other words, a telescope can not make an extended object brighter than it appears naked eye, it can only make ti dimmer (with increasing magnification and losses within the telescope). It becomes more visible only because it has been magnified by the telescope, making it easier to see.

This is incorrect - the contrast between an extended object and the sky doesn't change, but the brightness (in terms of its photons reaching your eye) definitely does. Assuming the extended object fits in your eyepiece FOV, for it your eye pupil is virtually as big as the telescope's aperture.

If they were never brighter, galaxies with surface brightnesses fainter than 7th magnitude would never be visible in any telescope, no matter how dark the sky. It would also be safe (if painful) to accidentally view the sun through a scope, since your reflexes would be fast enough to save your retinas. In reality, the photons are multiplied by the ratio of effective aperture:entrance pupil and do irreparable damage too fast to react in time.

The contrast not changing is why light polluted skies can't be magnified away when attempting to view extended objects, or similarly with poor transparency. Without that contrast your eye has no way to distinguish between photons from sky glow and photons from your target.

[Keith Rivich]

This is incorrect - the contrast between an extended object and the sky doesn't change, but the brightness (in terms of its photons reaching your eye) definitely does. Assuming the extended object fits in your eyepiece FOV, for it your eye pupil is virtually as big as the telescope's aperture.

If they were never brighter, galaxies with surface brightnesses fainter than 7th magnitude would never be visible in any telescope, no matter how dark the sky. It would also be safe (if painful) to accidentally view the sun through a scope, since your reflexes would be fast enough to save your retinas. In reality, the photons are multiplied by the ratio of effective aperture:entrance pupil and do irreparable damage too fast to react in time.

The contrast not changing is why light polluted skies can't be magnified away when attempting to view extended objects, or similarly with poor transparency. Without that contrast your eye has no way to distinguish between photons from sky glow and photons from your target.

This has always bothered me as well. A few years ago there was a very long and detailed discussion of this very subject. In the end I wondered why can I see 16th magnitude galaxies in my scope? I know I cannot see anything 16th magnitude unaided. Unless a 16th magnitude object large enough to see unaided simply doesn't exist. Or a 7th magnitude for that matter. But then M33 has a integrated magnitude of ~5.5 and a SB of ~14. I can see m33 in dark skies. 

 

I'm missing something...

[TayM57]

This has always bothered me as well. A few years ago there was a very long and detailed discussion of this very subject. In the end I wondered why can I see 16th magnitude galaxies in my scope? I know I cannot see anything 16th magnitude unaided. Unless a 16th magnitude object large enough to see unaided simply doesn't exist. Or a 7th magnitude for that matter. But then M33 has a integrated magnitude of ~5.5 and a SB of ~14. I can see m33 in dark skies. 

 

I'm missing something...

Get a 3x5 map of the United States, or a map of the city of where you live, of similar size. Put it on a wall, and then stand back about 60 feet. Can you read the labels of roads, cities, etc from that distance?

 

Now, stand ~1 feet away from the map. Now can you read the labels?

 

Same concept.

Edited by TayM57, 06 February 2023 - 08:52 PM.

[Tony Flanders]

MikeTahtib said:
 

In other words, a telescope can not make an extended object brighter than it appears naked eye, it can only make ti dimmer (with increasing magnification and losses within the telescope). It becomes more visible only because it has been magnified by the telescope, making it easier to see.

And columbidae responded:
 

This is incorrect - the contrast between an extended object and the sky doesn't change, but the brightness (in terms of its photons reaching your eye) definitely does.

Believe it or not, the two of you are actually saying the same thing. That's why I try never to use the word "brightness" without a qualifier; it has several very different meanings.

An object's surface brightness, or intensity, is the amount of light it emits per unit of area. From the observer's perspective, it's the number of photons per square degree.

An object's total (integrated) brightness is the total amount of light it emits. Total brightness equals surface brightness times area.

A telescope cannot increase an object's surface brightness, but it most definitely does increase an object's apparent total brightness -- just as columbidae says. And as MikeTahtib says, the increase in number of photons is accomplished by leaving the surface brightness unchanged and increasing the apparent size.

[columbidae]

Maybe I should have said something more like "equivalent to 7th magnitude". Surface brightness has units in magnitudes per angular area (typically arcsecond^2) and isn't one-to-one with magnitude as we normally use it.

Rambling approximations aside, I think the point still stands.

[columbidae]

Yeah, I think we somehow all agree on what's happening but then duke it out over the words to describe it. Maybe it's a dialect thing where "brightness" is used to mean either kind, and ends up a tripping hazard.

[Keith Rivich]

Get a 3x5 map of the United States, or a map of the city of where you live, of similar size. Put it on a wall, and then stand back about 60 feet. Can you read the labels of roads, cities, etc from that distance?

 

Now, stand ~1 feet away from the map. Now can you read the labels?

 

Same concept.

The labels aren't all the same brightness...

[dearchichi]

A telescope cannot increase an object's surface brightness

 

Perhaps a better way of stating this is:

 

1. the "intrinsic" average surface brightness of an extended object (it's intensity, Io, per unit angular area, Ao, of the celestial sphere it occupies) is a characteristic property of that object, independent of its distance from the observer or the observer's equipment used to measure it

SBint = Io/Ao

 

2. the "perceived" average surface brightness at the eye of an extended object is proportional to it's intrinsic average surface brightness times the square exit pupil, EP, of the observer's equipment

 

SBper = SBint * EP^2

 

For the naked eye, a dark adapted exit pupil ranges from ~5mm to ~7 mm. Thus, the wider it is, the higher the is "perceived" average surface brightness of the object.

 

SBper-eye = SBint * EPeye^2

For a telescope, with an exit pupil of EPtel, the "perceived" average surface brightness of the object is:

 

SBper-tel = SBint * EPtel^2

 

Thus, the ratio of the perceived average surface brightness of the object as seen through a telescope and the naked eye is:

 

SBper-tel/SBper-eye = (EPtel/EPeye)^2

 

Since EPtel <= EPeye if the eye is to capture all of the light incident on the aperture of the telescope from an object, SBper-tel/SBper-eye <= 1. Thus, SBper-tel can never be greater than SBper-eye.

 

A telescope shows extended objects better than the naked-eye due to it forming a real image of the object that the observer could (theoretically) get arbitrarily close to (using an eyepiece), thereby magnifying it and stimulating more rods and cones of the eye than the naked-eye view would. Telescopes also have apertures larger than that of the naked-eye, potentially causing the image of the object to have the same, or lower, average surface brightness than that perceived by the naked eye. When too low, increased magnification by itself can no longer cause the object to remain visible. This is one reason why the perceived dimensions of objects is sometimes smaller in larger telescopes since they allow higher magnifications to be deployed.

 

Also, the magnification used fixes the intensity of light from an object that egresses the exit pupil, independent of aperture. Therefore, to see the object better at that magnification, one can only widen the field of the light (i.e. the exit pupil) by widening the aperture until it hits the limit of the dark-adapted pupil.

[MikeTahtib]

Believe it or not, the two of you are actually saying the same thing. That's why I try never to use the word "brightness" without a qualifier; it has several very different meanings.

An object's surface brightness, or intensity, is the amount of light it emits per unit of area. From the observer's perspective, it's the number of photons per square degree.

An object's total (integrated) brightness is the total amount of light it emits. Total brightness equals surface brightness times area.

A telescope cannot increase an object's surface brightness, but it most definitely does increase an object's apparent total brightness -- just as columbidae says. And as MikeTahtib says, the increase in number of photons is accomplished by leaving the surface brightness unchanged and increasing the apparent size.

Yes, I agree 100%.  I intended brightness to mean surface brightness, either as seen naked-eye or through a telescope, not total integrated brightness of the entire object.  To me, this seems like the natural meaning of the word brightness in this context, so I often forget to specify which type of brightness I mean.

Edited by MikeTahtib, 07 February 2023 - 11:43 AM.