116 replies to this topic

[GlennLeDrew]

When I look into a scope operating at a 1mm exit pupil, I see diffraction subtending some angle. A person suffering a hypothetical condition where the iris is constricted to 0.5mm will see diffraction subtending 2X larger in angle and will enjoy an image 1/4 as bright. A dimmer, softer image with the same scope/eyepiece. The only difference is the stopped down aperture.

 

I would see the very same thing if an objective stop reduced the aperture to 1/2.

 

The afocal instrument before the eye happens to contain optical elements, but the wavefront transiting one's pupil cares not for this. Neglecting any aberrations introduced by those optics (i.e., assuming decent quality--not necessarily perfection), the extent of diffraction scales inversely as the diameter of the pupil at the eye.

 

Whichever is the restricting aperture of the system determines the extent and manifestation of diffraction.

 

For example, if your iris could be made square, and it were smaller than the exit pupil, you would see mutually perpendicular diffraction spikes. Just as would occur if a square mask were placed before the objective. The scope normally produces a clean, circular Fresnel pattern due to its circular entrance pupil, but this is modified if the circular exit pupil is clipped in any way. Our squared-off exit pupil does the same thing as does a square entrance pupil.

 

Again, the light does not care where the aperture limiter lies. As far as the eye is concerned, there is no telescope present before it. Only a view through certain sized pupil in the plane of its iris.

Edited by GlennLeDrew, 12 August 2014 - 01:33 PM.

[drollere]

glenn, jon, i appreciate the clarifications and generous spirit.

 

i tried glenn's pinhole experiment (as jon said, it's difficult to do, i punctured a foil sheet many many times and bobbed my head a little to get star image, exit pupil, foil hole and eye all collimated), and found paradoxical results sighting on vega with a 180mm ƒ/15 mak cass: stopping down a low power eyepiece (EP of around 1.6) the image became quite dim and a small airy disk became visible, which may have been too faint to see completely; but stopping down a high power eyepiece (EP of 0.33) produced very little dimming and no perceptible (clearly different) change in the size of the airy disk. i assume this is because the eyepiece EP and the foil hole were both around 0.33.

 

if the exit pupil, the most variable part of the visual system, is equivalently a criterion for system or image resolution, then why not use it as such? you'd calculate exit pupil directly from ƒ(eyepiece)/N, then calculate resolution as 206265*(lambda/EP) and magnification as D/EP. we would not use aperture (entrance pupil), D, because it is automatically "stopped down" in all situations and therefore the tail end of the system. the resolution on the image plane (aperture diameter) would be superfluous, if we are estimating the *system* resolution. that is probably the crux of my confusion.

 

if that procedure is incorrect, then we're back to my original statement that stopping down the aperture (at the front) is not the same as stopping down the exit pupil (in the back), because as glenn pointed out in the normal range of the human iris, it has no discernable visual effect, other than reducing the image illuminance, which is equally well and factually explained by the simple statement that "you've stopped down the exit pupil". calling in the aperture is to my ear an empty rhetorical gesture. if it doesn't matter where the stopping down occurs, why say it occurs other than where it actually does?

 

don's comments are accurate in my experience with regard to planetary/lunar viewing (and floaters), but double star astronomy is an entirely different visual task. planets are outside the telescope, the airy disk is "inside" the telescope, and is remarkably robust against poor seeing. william herschel regularly observed double stars with exit pupils less than 0.1 mm (!), and herschel's visual reports can be trusted: he measured the airy disk diameter of aldebaran in his 6.2" reflector as 1.77 arcseconds at 460x (EP=0.34), half a century before Airy suggested the calculation that yields 1.76 arcseconds as the correct value (for "green" light, 1.9" for "orange" light). but herschel also found that the disk was 1.2" at 980x (EP=0.16) and the diameter of vega at 6450x (EP=0.02!) was 0.36 arcseconds. he also used the angular gap between the components of eps (5) LYR to document shrinking airy disks down to 2010x. these are exit pupil diameters that (as far as i can tell) should effectively exclude any useable image, yet herschel found them a productive visual tool.

 

there is an explanation that relies on diffraction theory, which is that magnification reduces the image illuminance and contracts the threshold diameter of the disk. but the net effect is that resolution actually *increases* with magnification, making bright but unresolvable stars resolvable, which is (if i understand) directly the opposite effect of the constricted exit pupil, which should (just as would an aperture mask) make the airy disks *larger*.

[GlennLeDrew]

Bruce,

I hadn't extended my thinking to the point of considering the exit pupil as a measure of system resolution. At first blush it seems feasible, although in practice the response of the eye at varying illuminance must rate as a factor which will modify this. But there's nothing really new here; we're merely expressing the relationship in a subtly different way. What I'm stressing is the consideration of the full role played by the sub-exit pupil iris.

[Jon Isaacs]

glenn, jon, i appreciate the clarifications and generous spirit.

 

i tried glenn's pinhole experiment (as jon said, it's difficult to do, i punctured a foil sheet many many times and bobbed my head a little to get star image, exit pupil, foil hole and eye all collimated), and found paradoxical results sighting on vega with a 180mm ƒ/15 mak cass: stopping down a low power eyepiece (EP of around 1.6) the image became quite dim and a small airy disk became visible, which may have been too faint to see completely; but stopping down a high power eyepiece (EP of 0.33) produced very little dimming and no perceptible (clearly different) change in the size of the airy disk. i assume this is because the eyepiece EP and the foil hole were both around 0.33.

 

if the exit pupil, the most variable part of the visual system, is equivalently a criterion for system or image resolution, then why not use it as such? you'd calculate exit pupil directly from ƒ(eyepiece)/N, then calculate resolution as 206265*(lambda/EP) and magnification as D/EP. we would not use aperture (entrance pupil), D, because it is automatically "stopped down" in all situations and therefore the tail end of the system. the resolution on the image plane (aperture diameter) would be superfluous, if we are estimating the *system* resolution. that is probably the crux of my confusion.

 

if that procedure is incorrect, then we're back to my original statement that stopping down the aperture (at the front) is not the same as stopping down the exit pupil (in the back), because as glenn pointed out in the normal range of the human iris, it has no discernable visual effect, other than reducing the image illuminance, which is equally well and factually explained by the simple statement that "you've stopped down the exit pupil". calling in the aperture is to my ear an empty rhetorical gesture. if it doesn't matter where the stopping down occurs, why say it occurs other than where it actually does?

 

 

Bruce:

 

Here's some things to consider:

 

The exit pupil itself is not a measure of the system's angular resolution, the exit pupil multiplied by the magnification is a measure of the system resolution, the exit pupil multiplied by the magnification is equal to the aperture. One can work backwards from the Rayleigh criteria and show that angular resolution ® = 5.45 inch/(Mag x Exit pupil)  

 

The issue here though is somewhat more fundamental. When the exit pupil is larger than the entrance pupil, it means that the entire objective is not seen and that light from the outer portion of the objective does not enter the eye, the aperture is effectively stopped down.  So, the fundamental question here is whether light that is at the focal plane but does not enter the eye can increase the resolution, that it somehow decreases the size of the Airy disk and increases the resolution even though it does not enter the eye.  I think the key here is to realize that light passing through an aperture causes diffraction effects that increases the size of the Airy disk. If the light passes through multiple aperture stops, then the overall size of the disk depends on the both apertures and not just the first one. Thus when the entrance pupil is smaller than the exit pupil, not only does one have to consider the aperture imposed by the objective but also the aperture imposed by the undersized entrance pupil. 

 

One way to see this effect is to calculate Rayleigh criteria (R= (138/D) mm-arcseconds) for the angular resolution of the telescope and the angular resolution of the eye.  Consider the 100mm telescope at 100x,  First I will calculate the angular resolution of the telescope and then the angular size of the Airy disk:

 

Rscope = 138mm/100mm = 1.38 arc-seconds.  Magnify that 100x to produce a 1mm exit pupil and it will be 138 arc-seconds.  That is the angular size of the Airy disk in a 100mm telescope at 100x. 

 

Now consider the resolution of a 1 mm lens, the eye at a 1 mm exit pupil:

 

Reye1mm  = 138mm/1mm = 138 arc-seconds, This is the same as the telescope, the light passes unimpeded because the entrance pupil is at least as large as the exit pupil and the entrance pupil imposes no further diffractive effects.

 

Now consider what happens when the entrance pupil is only 0.5mm even though the exit pupil is 1mm.

 

Reye.5mm = 138mm/.5mm = 276 arc-seconds, the aperture of the eye produces an Airy disk that is twice the diameter of the angular resolution of the telescope, the resolution of the system is now reduced to the resolution of a 50mm telescope rather than a 100mm.

 

I could generalize these calculations and use algebra to show that the size of the Airy disk is determined by the effective aperture of the telescope just as the light gathering is but I think this example should suffice to show that in terms of resolution, stopping down the aperture at the entrance pupil is equivalent to stopping down the aperture .  One only needs to know the effective aperture of the telescope to determine the resolution.

 

Something interesting to understand: The magnified angular size of the Airy disk in a 1mm exit pupil is independent of aperture, larger apertures require proportionally larger magnifications to produce the exit pupil so while the actual resolution and angular size of the airy disk at the focal plane are smaller in the larger scope, they are independent of aperture at a given exit pupil.  A 200mm scope at 200x produces a magnified airy disk that is the same diameter as a 100mm scope at 100x and it's the same angular size as the 1mm exit/entrance pupil at 1x and half the size of a 0.5mm exit/entrance pupil at 1x.

 

All this is not so easy to understand, for those reading it, please take the time to read it and reflect before responding. It took me quite a while to put this into a concise form, there maybe grammatical and mathematical errors but the concepts are solid and the conclusion that the resolution of depends on the effective aperture and it does not matter whether the aperture stop at the objective, the entrance pupil or somewhere else is solid. 

 

I will say I clarified some issues in my mind working this through, I hope others have gained understanding as well.

 

One final thought:  These considerations, while fundamental to understanding what is going optically, have very little importance from a practical point of view. This is because the entrance pupil of the eye is never small enough to mask exit pupils that are small enough for the Airy disk to be seen. One's eye may only be open to 4mm but no one sees Airy disk structures in a 4mm exit pupil, much higher magnifications are needed, something close to 1mm and the entrance pupil of the eye is always larger than 1mm.  At the magnifications where resolution of the telescope is important, the entrance pupil will always be larger than the exit pupil.  At large exit pupils, the resolution/response of the eye is such that masking the aperture so the effective aperture of system is reduced can actually increase the eye's ability to resolve double stars. I once did a test on gamma Arietis, a 8 arc-second double with an 80mm refractor at a constant 17x magnification, a 4.7mm exit pupil.  Keeping the magnification constant and masking the aperture increased the apparent resolution..  There are many factors to consider but a simple focal ratio analysis is useful. the eye has a focal length of about 17mm so a 4.7mm exit pupil means the eye is operating at F/3.6.. ,not likely to be too sharp...

 

'nuff said.

 

Jon Isaacs

[GlennLeDrew]

The diffraction is imparted by that restrictor which clips the beam the most. Let's say we have a scope whose focuser tube protrudes too far up the light cone, thereby reducing aperture. This focuser tube opening then becomes the aperture which induces the visible diffraction. If we then place our smaller iris at the exit pupil so produced, the iris now introduces the diffraction we see.

 

To the retina, the only aperture present is the iris. Neither the objective nor the restricting focuser tube contribute a thing to diffraction.

 

In other words, the objective does not first introduce diffraction, to which is added the contribution from the focuser and then the iris, in turn. Only the iris matters here. If the iris diameter exceeds the exit pupil, then the diffraction-inducing aperture becomes the focuser tube opening--only.

[drollere]

i'm content to leave this at any point that my education appears hopeless, but i feel obliged to answer what is stated.

 

jon provides some basis for me to explain my point because he has stated the position that *both* the entrance and exit pupils are relevant to the system image formation, and this provides the basis for glenn to deny that, it's only *one* pupil, the smallest one in terms of the angular projection of the system, that matters.

 

glenn overrides my earlier calculation, where i suggested that a constricted exit pupil that would produce a 19 arcminute wide airy disk in retinal image space would be overwhelmed by the airy disk on the image plane, as this would appear to be almost one degree wide. if i understand, he is saying that i was wrong to make that comparison because diffraction is not superimposed one on the other the way optical errors are: it's just the image inverse of the smallest pupil.

 

now i go back to the visual evidence: if that is true, then why was my image of vega via a 24mm eyepiece and a 0.33mm foil pinhole *substantially* fainter than my image of vega via a 5mm eyepiece and a 0.33 foil pinhole? the total aperture was the same (180mm), the focal length was the same (2700mm), the magnification was very different (113x vs. 540x), the "true" exit pupil (the pinhole) in both cases was the same, so presumably the same area of aperture utilized should be the same, and therefore the brightness of the airy disk should be the same.

 

(i may have inadvertently viewed through differently sized pinholes, but i repeated the comparison, and made many pinholes in exactly the same way, so i don't feel that is likely. but it bears being repeated to see for yourself.)

 

jon is concerned to define the exit pupil in terms of magnification, but magnification is actually secondary: the principal of the exit pupil is in the focal ratio. take any circular lens and a card with, say, a 3 millimeter hole punched in it. how far away does the object lens have to be until it appears exactly the same naked eye visual size -- "the same image" -- as that 3 mm hole? at whatever distance necessary so that it subtends the same visual angle. what is that angle? "actual size" in vision is at 250mm, so the hole defines an angle of 3/250 radians. this means the corresponding objective producing a 3 mm image will be functioning at a distance of ƒ/83. if it's a 140 mm objective, then its focal length will be 11,667 mm. only then do you get to the magnification, which is 11667/250 = 47x. the situation is complicated in an astronomical telescope because part of the magnification is via the projection of the objective focal length and part of it is via the refraction of the eyepiece, so we observe only a "virtual" 140 mm ƒ/83 objective. but it's the image of that virtual 140mm ƒ/83 objective that you see floating in the eyepiece as the exit pupil. the virtual focal ratio (ƒ/83) is the constant regardless of the aperture size, as jon explained, which is why exit pupil cannot determine the magnification.

 

we can infer that because william herschel was working routinely with 0.08 mm exit pupils he was utilizing an ƒ/3125 virtual focal ratio and was observing airy disks that were (0.00055/0.08)*206265*2.44 = 58 arcminutes in diameter, if i calculate correctly. however in the case of eps 5 LYR he was observing stars that were 2 arcseconds apart in his era and magnified 2010x, and found the airy disk diameters to be 1/2.5 the interval between the stars, or 2"/3.5 = .6"*2010 = 19 arcminutes. this to my point that, even using the exit pupil for the calculation, we don't get a useful handle on the visual optics of the situation.

Edited by drollere, 14 August 2014 - 10:14 PM.

[Jon Isaacs]

 

jon provides some basis for me to explain my point because he has stated the position that *both* the entrance and exit pupils are relevant to the system image formation, and this provides the basis for glenn to deny that, it's only *one* pupil, the smallest one in terms of the angular projection of the system, that matters.

 

Bruce:

 

This discussion is about resolution. We know that because of diffraction, resolution is dependent on the aperture of the system.  You made the statement that masking the exit pupil at the eye does not affect the resolution of the system, it is only based on the aperture of the objective. My point was and is that it is based on the effective aperture of the system.  If the exit pupil is masked by the aperture of the eye, then the effective aperture is calculated:
 

Deff = D x entrance pupil/exit pupil.  

 

This actually determines the diameter of the objective that contributes light that enters the eye.  A 100mm telescope at 100x produces a 1mm exit pupil. If the aperture of the eye is 0.5mm, then the effective system aperture is 50mm. 

 

I think I amply demonstrated in my previous post that the resolution of the system is dependent upon the effective aperture of the system and that it doesn't matter where the aperture stop is. If the iris of the eye is smaller than the exit pupil, not only is less light seen but the resolution is reduced because the eye is also a lens system and the system's resolution is limited by the aperture of the eye, not the aperture of the telescope.  Please think about this.. The eye is an aperture with diffraction... 

 

Exit pupil can be calculated either using the focal ratio or the magnification, these are equivalent expressions and are interchangeable through simple algebra.  Angular field of view does not depend on the exit pupil nor does masking the exit pupil by the eye's iris affect the field of view, it affects the amount of light admitted and the resolution. 

 

Jon Isaacs

 

 

 

 

 

 

[Sarkikos]

Would "vignetting" be more acceptable than "stopping down " to label what is happening when the telescope's exit pupil is met by a smaller eye pupil?  Increasing magnification by substituting a shorter focal length eyepiece is not equivalent or analogous to vignetting by the iris. 

 

Mike

Edited by Sarkikos, 15 August 2014 - 09:12 PM.

[drollere]

This discussion is about resolution. We know that because of diffraction, resolution is dependent on the aperture of the system. You made the statement that masking the exit pupil at the eye does not affect the resolution of the system, it is only based on the aperture of the objective. My point was and is that it is based on the effective aperture of the system. ...

 

Exit pupil can be calculated either using the focal ratio or the magnification, these are equivalent expressions and are interchangeable through simple algebra.  Angular field of view does not depend on the exit pupil nor does masking the exit pupil by the eye's iris affect the field of view, it affects the amount of light admitted and the resolution. 

 

actually, i thought this was a discussion about the claim that stopping down the exit pupil was "the same as" stopping down the aperture. *your* point seems to be to link resolution to aperture, which is fine with me because that is the qualification i introduced in my first post and in my distinction between "ideal" and "real" telescopes.

 

it's useful to take glenn's requirement that "we only see one pupil" as the basis of the exit pupil metric. in that case you certainly can identify the resolution of the system without any reference to aperture, because linear resolution at the image plane is just lambda*N, and the naked eye angular dimension of the resolution at the near point distance of 250mm is therefore 206265*(lambda*N)/250. this will show you, for example with "green" wavelengths and N = 250 (when the exit pupil is 1), that the fresnel interval is 113 arcseconds, which is close enough to the often cited 30 cycles per degree naked eye resolution limit to show both that the normal eye is approximately diffraction limited and that the 1 mm exit pupil is usually the point of complete diffraction visualization.

 

this also concisely shows why the diffraction magnification is entirely independent of anything else about the system, as you showed by enumerated concrete examples in your previous post.

 

if you start with -- and take literally -- the definition that "the exit pupil is the virtual image of the entrance pupil" then you get the resolution of the system and the relative image illumination (ƒ ratio) using only the analysis of the naked eye aspect ratio illustrated in my previous post. this is the fundamental analysis of the exit pupil. as i said before and you have amply demonstrated, as soon as you wave aperture or magnification anywhere near an exit pupil then you immediately get the derivative analysis in terms of a real system: and this was always my point, that you cannot talk about the optics unless it is in terms of a real system.

 

in a real system, the edict that you should not use an exit pupil larger than your eye pupil "because it will stop down the aperture" is guidance without merit, because it is entirely anchored on an ideal telescope. with a real telescope several real factors -- the desirably larger field of view with a larger exit pupil, the fact that the dark adapted eye cannot ever constrict the exit pupil to the point of visibly affecting the diffraction magnification, the fact that stopping the *aperture* does indeed affect the visible diffraction diameter (a fact that WRAK in the double star section uses to measure binary separations), the fact that the exit pupil is not commonly used as the metric of resolution calculation, and the fact that miniscule optical exit pupils exceed the theoretical resolution limit of the telescope due to the compensating effects of mangification (as herschel showed) -- these all illustrate why edicts pronounced from the ideal exit pupil of the ideal telescope only apply to the observation of ideal skies.

[Jon Isaacs]

Would "vignetting" be more acceptable than "stopping down " to label what is happening when the telescope's exit pupil is met by a smaller eye pupil?  Increasing magnification by substituting a shorter focal length eyepiece is not equivalent or analogous to vignetting by the iris. 

 

Mike

 Mike:

 

Vignetting affects the field of view.  An undersized entrance pupil does not cause vignetting, it actually has the same effect as an aperture mask.  The field of view is unaltered but the amount of light entering the eye is reduced and the resolving power  is reduced.  

 

Jon

[Jon Isaacs]

Bruce:

 

My point has always been simple.  If the entrance pupil of the eye masks the exit pupil, then it has the same result as if the aperture were masked in an identical proportion, it affects both the angular resolution at the retina, increasing the size of the Airy disk as well as decreasing the image brightness at the retina.  My analysis demonstrated this was correct and I believe you analysis would yield the same result if you compared the resolving power of a 1 mm entrance pupil with the resolving power of a 0.5 mm entrance pupil. 

 

So in short, do you agree? Yes or no would be sufficient.

 

Jon 

[Sarkikos]

 

Would "vignetting" be more acceptable than "stopping down " to label what is happening when the telescope's exit pupil is met by a smaller eye pupil?  Increasing magnification by substituting a shorter focal length eyepiece is not equivalent or analogous to vignetting by the iris. 

 

Mike

 Mike:

 

Vignetting affects the field of view.  An undersized entrance pupil does not cause vignetting, it actually has the same effect as an aperture mask.  The field of view is unaltered but the amount of light entering the eye is reduced and the resolving power  is reduced.  

 

Jon

 

 

I will accept those labels. Whether the "stopping down" is caused by the iris of the eye or an aperture mask, the result is a loss of aperture, which reduces light grasp and resolving power.  I guess I don't understand optical theory well enough to understand the apparent disagreement on this point in this thread.

 

Mike

Edited by Sarkikos, 16 August 2014 - 12:10 PM.

[GlennLeDrew]

Mike,

To clarify, vignetting is a diminution of illumination with field angle. The image darkens toward the edge. This includes truncation of field, such as occurs for a large field stop behind a small prism aperture.

 

Stopping down a system *could* be accompanied by vignetting if the stopping aperture is located not at a pupil. An example would be a refractor focuser tube which protrudes too far up into the axial light cone.

 

Stopping down at a pupil merely uniformly dims the image.

[great_bear]

if you start with -- and take literally -- the definition that "the exit pupil is the virtual image of the entrance pupil" then you get the resolution of the system and the relative image illumination (ƒ ratio) using only the analysis of the naked eye aspect ratio illustrated in my previous post.

 

No, because "entrance pupil" in that definition means "entrance pupil to the telescope", not "entrance pupil to the eye".

 

One of the problems with this thread is that people haven't been clear about when their use of terms such as "entrance" and "system" are relating to the telescope, the eye, or when both are combined and treated as a single system. Likewise whether "resolution" is pertaining to the image at the telescopes image plane or that which falls on the retina. When someone is convinced that someone else is wrong, they are likely to choose whichever interpretation evidences the other being wrong. It's very frustrating as a reader of this thread - since the subject under discussion is both clearly-understood and not the subject of any scientific debate.

Edited by great_bear, 17 August 2014 - 02:30 AM.

[freestar8n]

A distant planet has no idea what kind of optical system is looking at it.  It just sees a hole out there - in object space.  That hole is an image of a physical thing somewhere in the imaging system - and the image is formed by all the lenses and mirrors "to the left" of that thing.  The physical "thing" that limits the light through the imaging system is called the aperture stop - and the image of that physical thing is called the entrance pupil.  The entrance pupil will subtend some angular size as seen by the planet - and angular frequencies from the surface of the planet either will or will not "fit" into that distant hole.  If the hole subtends a large angle, then higher spatial frequencies from the planet will fit into it - and help it form a higher resolution image by contributing higher spatial frequencies.  The size of the hole is strictly set by the size of the aperture stop and the elements between it and the object, that determine its location and size in object space - which then determines the angular size of the hole seen by the planet.

 

In the case of a large aperture refractor - perhaps 100" diameter - the entrance pupil is the objective itself.

 

If you place a large 10x eyepiece at the end - it is now an afocal system but the limiting aperture in the system is still the objective itself - and it is 100" diameter.  The exit pupil is the image of that aperture stop formed by all elements "to the right" of the aperture stop - and that is just the eyepiece itself, so the exit pupil is 10" diameter and to the right of the eyepiece.

 

But if you now place a human eye behind the eyepiece - the complete optical system includes the eye lens, the iris, and the retina, and the limiting stop is the iris itself.  You now have identified the new aperture stop of the system, and you can systematically determine the size and location of the entrance pupil seen by the object - since that is all it ever knows about the imaging system, and what spatial frequencies will make it through that hole.

 

Glenn's description is largely correct except that there is no strict linkage between "the objective" and the pupils.  Once the iris is the aperture stop - as the eye is moved back and forth or up and down in front of the eyepiece, the size and location of the entrance pupil will change.  At the same time, the exit pupil of the optical system is always the iris itself - and there is no imaging involved in defining the size of the system's exit pupil.  One should never say "the exit pupil is the image of the entrance pupil" or something like that.  It is important to define them in terms of the physical aperture stop - which could be unrelated to the objective.

 

This description ignores details about the exact layout of the iris and eye lens - but those details are trivial compared to the whopping reduction of aperture that results when you place your eye at the location of a 10" exit pupil, and the corresponding loss of resolution that follows directly from this description of the image formation process based on physical diffraction - and not just terminology and semantics.

 

If anyone thinks the resolution and diffraction behavior have not been reduced by the very real reduction of the entrance pupil size - please describe in terms of Abbe diffraction theory - how the high spatial frequencies from the object can reach the retina and contribute to the detail in the image.

 

As for these empirical "tests" - obviously at low power the view is limited by aberration rather than diffraction - and there isn't much of a conclusion to be drawn.

 

Frank

Edited by freestar8n, 17 August 2014 - 05:27 AM.

[freestar8n]

And on the imaging side - the retina just sees a hole out there in image space.  It has no idea where it is or how big it is - it only knows its angular size.  The situation is identical to the view in object space: the angular size of the pupil will limit the spatial frequencies that can be included in the image.  In other words - the physical size of the Airy pattern on the retina only depends on the f-number seen by the retina.  (Here I will ignore the fact that the retina is in liquid with refractive index>1).  If the iris is 5mm and it is 25mm from the retina surface - the retina sees an f/5 system and immediately you know the physical size of the Airy pattern on the retina.  As long as the iris is the aperture stop of the system - it will also be the exit pupil - and the diffraction behavior is known.  No matter what size objective or its focal length - as long as it overfills the iris - the retina sees an f/5 system - and that will determine the spatial frequencies in the image.

 

But in astronomy what matters is the *angular* resolution - and with more power, the spatial frequencies on the retina will correspond to smaller and smaller angles.  So as long as the objective is large enough you can make the focal length arbitrarily long so that the spatial frequencies on the retina correspond to smaller and smaller angular resolution.

 

But in all this, there is one physical aperture limiting the resolution - and that is the iris - if the objective is over-sized.  The iris will then determine the size of the entrance pupil seen by the object - and the limiting spatial frequencies transmitted to the image.  The iris will also determine the size of the exit pupil - and the limiting spatial frequencies transmitted to the retina.

 

It is all symmetric and the imaging system is broken into two halves - for image space and object space.  What matters is the angular size of the pupil seen in each space - and that size is limited by the single restriction in the imaging system that serves as the aperture stop.

 

Frank

[drollere]

the diversity of comment is refreshing and stimulating. i apologize if i miss someone's key point, but i think it's useful to agree on the basics before we proceed to the details.

 

everyone seems to have an anchor of sensibility, so (if it's not already obvious) my anchor is sufficient explanation of the visual image through a real instrument. again, my issue with "exit pupil guidance" as expressed for example in the advice that you shouldn't use an eyepiece that delivers an exit pupil larger than the eye pupil, or that an exit pupil smaller than 0.5mm is "wasted magnification" -- that guidance is purely theoretical only and has no relevance (as theory) to what visual observers should or should not do with real instruments. ultimately i require all optical theoretical arguments to meet that standard of practical relevance.

 

to jon's yes/no question, my answer is no. here is why. if i place an arbitrarily small (estimated 0.33mm) foil pinhole over the exit pupil of a 24mm eyepiece on a ƒ/15 180 mak cass centered on the star vega, i observe a faint, badly degraded image of the star. this is plausibly an enlarged airy disk in the retinal image, but it is so faint that the disk does not even form a distinct border, much less present the first diffraction ring. if i observe through the same (presumably: see description of method above) pinhole the image of vega in a 5mm eyepiece, i see basically no change in the brightness or airy disk details of the image. if i understand jon's analysis, it's the same 0.33 exit pupil in both cases, but the images are drastically, obviously different. my repeated question: why? if the exit pupil determines the image quality, and stars are "point images" that defy magnification, shouldn't the two viewing situations produce an identical image?

 

to jeremy's somewhat scolding comment that it is all very clear and rather frustrating to read, i'd point out that one pivot of the discussion has been that the eye pupil, "projected forward" within the total optical system, in effect stops down the entrance pupil, reducing the aperture. this spawned the secondary discussion about which pupil defines the system resolution, which jon has pressed as a key point. my use of "exit pupil as the image of the entrance pupil" was not intended to derail the discussion but is in fact the definition of exit pupil given in many optical texts and was adopted to show that the exit pupil is fundamentally a *geometrical* concept -- an aspect ratio -- and in those terms would define the system diffraction resolution without any reference to a physical aperture or focal length. you misinterpret my post if you conclude otherwise.

 

i think frank is somehow aiming at me with his jibe at "terminology and semantics", but his claim that (for enormous, 10" exit pupils) it's really the eye pupil that delimits the system resolution, i again have to insist on the practical example of a real observer using a real telescope on a real star. i don't know of any visual system with a 10 inch exit pupil!

 

here is another way to express my discomfort. the standard system resolution formula calcuates the angular resoluton of the system as a diagnostic wavelength divided by the aperture and multiplied by radian arcseconds. so for example a 300mm objective yields a resolution of 0.37". in the retinal image space this is, of course, subject to the system magnification. what happens if we consider the eye pupil as the limiting aperture? the resolution of the system in retinal image space is defined *at the eye pupil" by the same formula, we start with a resolution of 19" for a 6mm eye pupil, and resolution degrades to 8 arcminutes with a 0.25mm pupil. at best we're left with the practical problem of coordinating magnification with eye pupil: for example, if eye pupil is 6mm with a resolution of 19", then a minimum magnification of 50 will be necessary to match this the eye pupil resolution with the angular extent of the aperture resolution on the image plane (and it should probably be much larger, to "bury" the eye pupil airy disk inside the enlarged telescopic airy disk).

 

yet i have never seen this type of "minimum magnification of telescopic resolution in relation to eye pupil resolution" offered anywhere by anybody, and in his post above glenn backs away from my offer that he define system resolution in terms of the exit/eye pupil. i have to conclude that there is something fundamentally wrong with involving the eye pupil *or* the exit pupil in the evaluation, and apart from my conceptual confusion i have repeatedly offered william herschel as an example to show that in practical observation it doesn't seem to matter. if anything, resolution *increases* with tiny exit pupils and their correspondingly high system magnification -- limiting the discussion to stellar images, not to include lunar or planetary images

[GlennLeDrew]

Bruce,

I wonder if the anomalous dimmness you get when interposing the pinhole between eyepiece and eye could result in part from the distance of the pinhole from your iris...

 

I just did a test usng two identical 0.4mm pinholes, without optics. Even when held rather close together and as near to the eye as comfort permits, the differing angular sizes the pinholes subtend at the retina results in the farther one underfilling the nearer, with a resultant overall dimming. But the Fresnel pattern appeared to remain unchanged in angular extent.

 

I think if you could contrive to make your iris as small as your ~0.33mm exit pupil you would find an unchanged Fresnel size/brightness as compared to a larger iris. As long as the exit pupil is not at all offset laterally and hence clipped, of course. There should be *some* tolerance on longitudinal displacement, but I wonder if exceeded might there then result dimming?

 

This is territory I've not wandered into in such detail previously.

[freestar8n]

i think frank is somehow aiming at me with his jibe at "terminology and semantics", but his claim that (for enormous, 10" exit pupils) it's really the eye pupil that delimits the system resolution, i again have to insist on the practical example of a real observer using a real telescope on a real star. i don't know of any visual system with a 10 inch exit pupil!

 

 

I had a sense you were distinguishing irrelevant semantic details from what "really matters" for resolution.  What I am saying is that in this thread people are throwing around terminology and using it in ways that are not consistent with their actual meaning - and confusion results.  There are rigorous diffraction concepts such as "Airy pattern" combined with casually used terms like "pupil" - and nonsensical things like "stopping down at the exit pupil".  This stuff about pupils is in introductory chapters on optics and diffraction theory - and everything hinges on its correct usage.

 

You seem to be quite convinced that the size of the hunk of glass is what matters for resolution - and any changes at the eye and iris do not reduce the amount of glass used in creating the image.   That is why I chose 100" objective and 10" exit pupil.  It is a perfectly realizable example.

 

This stuff was figured out long ago and it is very elegant.  The spatial frequencies in the object radiate angular frequencies that are captured by the entrance pupil.  They are then re-emitted by the exit pupil to form the image.  The relevant angle on both ends is lamba/PD in radians - where PD is the pupil diameter.  A 100" objective will have a limiting angular resolution that goes way out to jupiter - and determines the minimum width of bands seen on the planet.  On the exit pupil side, the angle will be much larger because the pupil is smaller - and the distance to the image plane is shorter - so the spatial size is smaller.  But it is symmetric.

 

In Gaussian image formation you have object space and image space - and an entrance pupil in object space and an exit pupil in image space.  They have well defined sizes and locations relative to the object and the image - but how they were made by the black box optical system doesn't matter - but the pupils should be correct.

 

When you have the pupils defined - you can do diffraction integrals and predict the resolution in the image and so forth.  But you can't do that math if you don't have the pupils defined properly.

 

So - if anyone thinks the entrance pupil won't be directly slaved to the size of the iris, when the iris is smaller than the exit pupil of the telescope alone - they are mistaken.

 

This is not to say there aren't other factors involved such as aberrations and perception.  But the maximum resolution is limited by the entrance pupil diameter - and that is determined by the aperture stop of the system - which in that case is the human iris.

 

I'm not clear on what you are saying or thinking - but if you don't believe this pupil stuff, but you do believe in things like Airy patterns - how exactly does it all work that the full 100" objective make use of all its resolution when the exit pupil is 10" diameter?  For me, if the iris is 5mm diameter and it is at the exit pupil of the telescope itself - then the iris is the aperture stop and the entrance pupil is at the objective - and that entrance pupil is only 50mm diameter.  All the glass outside that diameter does not contribute to the image either photometrically or in terms of resoluiton.  It is completely blocked off from reaching the retina - for an object on-axis.

 

Frank

[great_bear]

The resolution of any optical system is limited by whichever lens is too small to accommodate the bundle of rays passing through it - I'd have thought that this is self-evident.

 

In telescope usage that "limiting lens" is the primary, until the magnification is so low that the combined human iris/lens becomes the limitation. I think we can all agree however that any assertion that light is being "wasted" under these conditions is - from a practical perspective - ridiculous, since the light is no more "wasted" than it is during normal eye use as we go about our day-to-day business.

 

A better assertion would be that the telescope's size is "wasted" at such low magnification.

[freestar8n]

The resolution of any optical system is limited by whichever lens is too small to accommodate the bundle of rays passing through it - I'd have thought that this is self-evident.

 

In telescope usage that "limiting lens" is the primary, until the magnification is so low that the combined human iris/lens becomes the limitation. I think we can all agree however that any assertion that light is being "wasted" under these conditions is - from a practical perspective - ridiculous, since the light is no more "wasted" than it is during normal eye use as we go about our day-to-day business.

 

A better assertion would be that the telescope's size is "wasted" at such low magnification.

 

Well I'm trying to get people to use the precise definitions because they are what actually matter in terms of light collection and resolution.  The resolution is determined by the *image* of the aperture stop that is formed by all lenses/mirrors between it and the object.  That is the entrance pupil.  People often refer to the pupils as "virtual images" of the aperture stop - but they are often not virtual at all.  In a normal telescope, the exit pupil floating behind the eyepiece is a real image - not virtual.  And sometimes it isn't an image at all - as with a refractor.  The entrance pupil is just the lens - and its diameter is the same as the lens.

 

But in a maksutov with an undersized primary, the primary is the aperture stop of the system - and the entrance pupil is *smaller* than the physical size of that mirror - because its size as seen from the object is reduced by the meniscus that is between the aperture stop and the object.  So the primary happens to be the aperture stop, and the entrance pupil is smaller than that.

 

As for "wasting light" - it isn't so much light that is being wasted as money and arm strength - in the case of binoculars.  If you pay extra for binocs that are 10x100 - they will have a 10mm exit pupil - way too big for a human eye.  So the resolution and light gathering will be limited by the iris (which is not a lens).  All that glass you paid for in front and the corresponding weight is a waste of money since it does nothing for resolution or light gathering.  It is useful to have an exit pupil a bit larger than the iris - so the eye can move around a bit without clipping the exit pupil - but when the exit pupil is way too big it is indeed a waste if you only use it at that magnification.

 

For a refractor it is perfectly fine to use it at a range of magnifications, including those that make a giant pupil, because the field is wider and so forth.  But people should be aware that the full aperture is not operating in that mode - both in terms of resolution and light gathering.  If you never use it at a magnification that produces a pupil smaller than the maximum eye pupil size - then it is indeed a waste of money and aperture.

Frank

[drollere]

you guys need to be arguing with my sources. since i am merely the messenger.

 

jacobs, bailey & bullimore (J.OSA, 1992, page 3675); "physical artificial pupil" is a hole in a screen 15 mm in front of the eye, "Maxwellian pupil" is an exit pupil located at the eye pupil:

 

"The results of these experiments show that physical and Maxwellian pupils are essentially equivalent for presenting resolution targets only if the pupil size is 2 mm or larger. For smaller pupil diameters there are significant differences between the two types of artificial pupil. At a diameter of 0.5 mm the physical artificial pupil causes vision to become diffraction limited so that visual acuity becomes reduced. The resolution remains independent of defocus at least over the range of 5-D myopia to 4-D hyperopia.

 

"Even at the smallest pupil size Maxwellian viewing does not cause a comparable diffraction limitation on resolution. Maximum resolution can still be obtained, and also maximum angular resolution and angular blur disk diameter remain dependent on the magnitude of defocus. Thus Maxwellian view systems do not create the same pinhole effect that is shown by the physical artificial pupils.

 

"The progression of the differences between Maxwellian and physical artificial pupils that occur when diameters are < 2 mm is expected because of the coherence properties of light becoming more important to image quality when pupil diameters become smaller. When detailed targets are viewed with a Maxwellian pupil size of 0.5 mm, light may be considered to be essentially coherent, and the plane of the Maxwellian pupil contains the spatial transform of the target being viewed. This diffraction image of a Maxwellian view system occupies an area that is significantly larger than its exit pupil, and provided this diffraction image is not blocked by the eye pupil or media opacities, high-spatial-frequency information may be conveyed to the retinal image. In contrast small physical artificial pupils act to limit resolution by filtering some higher-spatial-frequency content from the image."

 

the data charts in this article show the minimum angular resolution (measured with the RIT resolution target) remains at around 0.63 arcminutes at best focus for the exit pupil from 5 mm diameter all the way down to 0.5 mm. at that smallest aperture the pinhole becomes flat at a minimum angular resolution of around 1.3 arcminutes across all focal positions.

 

physical pupils and exit pupils are not the same thing.

Edited by drollere, 23 August 2014 - 10:37 AM.

[drollere]

In telescope usage that "limiting lens" is the primary, until the magnification is so low that the combined human iris/lens becomes the limitation. I think we can all agree however that any assertion that light is being "wasted" under these conditions is - from a practical perspective - ridiculous, since the light is no more "wasted" than it is during normal eye use as we go about our day-to-day business. A better assertion would be that the telescope's size is "wasted" at such low magnification.

why isn't the better assertion that *nothing* is wasted at low magnification? why is clipping the system light transmission in order to observe an object at high magnification not wasteful, but clipping the system light transmission in order to obtain a very wide field of view so terribly wasteful that we have kind souls wandering into CN and begging to know: "If the exit pupil of an optical system is, for instance, 7mm and the persons eye pupil is 5mm does this mean that the scope etc. is essentially stopped down?"

 

my answer: "after a fashion ... so what?"

 

well ... isn't that, you know, wasteful?

 

"only if you stand looking through your widest of wide field eyepieces at some glorious wide swath of night sky and worry that you are being so terribly wasteful."

 

but isn't it wrong to be wasteful?

 

"agh, nevermind."

[freestar8n]

If you pay a lot for a 4" refractor and only use it at mags that result in a 10mm exit pupil - that is indeed wasteful.  If you are doing it because you have a false impression that extra aperture is helping the image and making it either brighter or sharper - a thread like this is helpful in directing your money to be spent on something cheaper and smaller that will work just as well - for that specific purpose.

 

But if you use it with a range of exit pupils from 0.5mm to 20mm - then it isn't wasteful at all - because in at least some of the use cases you benefit from the full aperture.

 

I have no disagreement at all with any reference that implies the resolution of the eye is not as good as expected based on the expected entrance pupil diameter that I describe.  As with anything there can be other factors that make it worse than the theoretical ideal.  But that is very different from what you have implied - which is that the full aperture of a telescope is still able to contribute to the resolution achieved - which is a case of the eye somehow doing better than ideal diffraction theory.  That I disagree with, but I hope that isn't what your references are implying.

 

Frank

[drollere]

Bruce,

I wonder if the anomalous dimmness you get when interposing the pinhole between eyepiece and eye could result in part from the distance of the pinhole from your iris...

 

I just did a test usng two identical 0.4mm pinholes, without optics. Even when held rather close together and as near to the eye as comfort permits, the differing angular sizes the pinholes subtend at the retina results in the farther one underfilling the nearer, with a resultant overall dimming. But the Fresnel pattern appeared to remain unchanged in angular extent.

 

I think if you could contrive to make your iris as small as your ~0.33mm exit pupil you would find an unchanged Fresnel size/brightness as compared to a larger iris. As long as the exit pupil is not at all offset laterally and hence clipped, of course. There should be *some* tolerance on longitudinal displacement, but I wonder if exceeded might there then result dimming?

 

This is territory I've not wandered into in such detail previously.

when i did my comparison the foil pinholes were stretched over the eye rest of the eyepieces (a meade 24mm SWA and an LVW 5mm) in a 180 mm mak cass, with the head brought as close to normal observing position as possible (head resting against some part of the eyepiece, or against my hands holding the foil against the eyepiece, or hovering just above). at any farther viewing position the collimation tolerances were too severe to manage.

 

try it through a telescope with different eyepieces. (and, glenn, i appreciate that you and i are interested to actually make the observations.)

 

perhaps frank can walk us through an explanation for the differences in *image brightness* perceived in the two conditions. but in the geometric terminology i outlined in a previous example: the 0.33 exit pupil, with an angular extent of 4.5 arcminutes, is "projected forward" onto the diameter of the entrance pupil, per jon's analogy. the 24 mm eyepiece places the entrance pupil at the equivalent of f/113 or 30 arcminutes diameter, but with the 5 mm eyepiece the aperture is at f/540 or 6.4 arcminutes and the censoring is drastically less. with a mask placed in front of the aperture, the difference in eyepieces would produce a dimmer image at higher power.

 

i'm strongly supportive of frank's suggestion that we talk about the same things in the same way, but the issue for me is (and has always been) how optical theoretical statements are used to guide, direct or prohibit (as e.g. "wasteful magnification" or "useless magnification") the visual use of an astronomical instrument.

 

i propose two criteria: is the guidance necessary, and is it accurate? as to accuracy, the study by jacobs et al., and the carefully recorded observations by william herschel (perhaps the greatest visual astronomer in history) to me clearly show that you cannot simply extrapolate optical formulae into the visual case. the theory does not describe what observers actually see. how could it? -- "physics is not psychophysics."

 

separate from its accuracy, "wasteful" and "useless" are such unnecessarily perjorative and condemnatory terms that i have to wonder how the pristine principles of physics have been transformed into a moralizing fiat. it's not helpful to the novices, and the professionals should know better.