A test to try with your eyepieces

[Wavytone]

There is an optical phenomenon called "the cardboard tube illusion", described thus:

"If you look through a cardboard tube with one eye at a bright wall, the portion of the wall viewed through the tube looks much brighter than the wall seen with the naked eye. It is almost as if it was being illuminated with a flashlight. Colour and texture seem to be similarly enhanced."

This could be significant for eyepieces too, and I'm wondering if some of you might like to try an experiment if you have a mix of eyepieces to select from. The idea is this:

Eyepieces with relatively small fields of view will give you a large area of black (the field stop) around the perimeter, similar to the cardboard tube.

If it does actually enhance your perception of the central field of view (the wall in the case of the cardboard tube) it should do the same in a narrow field eyepiece.

So the question is this:

Suppose you take two eyepieces with similar field stops (so they show the same actual field of view) - one with a narrow field of view (say a 25mm Kellner) and widefield one (say my 13mm LVW) will your visual limiting magnitude be the same ?

It's possible the limiting magnitude may be fainter in the narrow field eyepiece. It's also possible they're much the same.I also can't help wondering whether under light-polluted skies it may be more pronounced.

Now to devise a test...

[erick]

Is the effect because the eye up against the cardboard tube is dilated more that the one exposed to ambient light? Sorry if that is already shown to not be the cause.

If it is, one might not get the same effect through an eyepiece with eyes similarly dark-adapted?

[Robh]

I'm inclined to agree with Eric's explanation. If you hold a tube forward of the eye, the illusion disappears as the dark area around the eye disappears.

Irrespective of the illusion ...
Whether the eyepieces produce the same TFOV or not is irrelevant.
The brightness of the field being viewed is directly related to the size of the exit pupil. An eyepiece with 25mm focal length is roughly twice the 13mm eyepiece but the latter will generate about twice the power.
This means the exit pupil of the 25mm will be about twice the diameter of the 13mm. This equates to 2^2=4 times the brightness or an increase in seeing magnitude of 1.5 (as 2.512^1.5=4, 2.512 being Pogson's ratio).
Therefore, you should be able to see stars 1.5 magnitudes lower in the 25mm eyepiece.

Regards, Rob.

[Wavytone]

Mmm suggest go and try it though this weekend, on a starfield with known magnitudes, I think you are in for a surprise.

I've tried an old 25mm symmetrical eyepiece with a 35 degree AFoV vs my 22 LVW at 65 degrees.

[Paddy]

I suspect the illusion is due to "lateral inhibition" if my memory of retinal physiology is correct. Neighbouring visual receptors mutually inhibit each other when active. When some cells are not stimulated ie are in the dark, they cease to inhibit their stimulated neighbours, thereby increasing the activity/output of the stimulated cells. This accentuates the perception of edges. If you look at a sheet of alternate dark and light bands, you will see that the edges of the bright bands look brighter than their middles and the edges of the dark bands look darker than their middles.When you look throught the tube, the receptor cells receiving the light from the wall are not inhibited by those that are focused on the dark tube, making the wall appear brighter.

What does it mean for eyepieces? I'm not sure, but I imagine the effect would be operating all the time anyway - ie bright bits appear bright against a dark background. But it maybe part of why smaller fov eps seem to give a stronger contrast than wider fields.

[Don Pensack]

I've tried this experiment many times over the years.
I've been able to verify that, whatever the apparent field of view, dimmer stars are seen at higher powers up to a point.
I'll explain:
As magnification is increased, the stars do not get dimmer, being points, but the background sky does, being now spread across a larger apparent field. In fact, a doubling of the magnification reduces the brightness per square millimeter of the background sky by a factor of four.
Accordingly, fainter stars are visible at higher powers.
Once the magnification is high enough the Airy Disc (or spurious disc, if you prefer) becomes visible, increasing the magnification more does not bring in fainter stars.
Also, on any given night, seeing conditions may blur the small points to invisibility if the magnification exceeds the seeing conditions. That is why the very faintest stars in a scope are visible only on the nights of steadiest seeing AND darkest sky.

Now, how does that relate to apparent field of view. Does reducing the field of view open the pupil appreciably alter the faintest star visible?
I, and a few friends, examined that hypothesis. After using several 13mm and 14mm eyepieces of 43 to 100 degree apparent fields, the consensus was that the two eyepieces that showed the smallest star images (indicating good polish on the lenses and good coatings) AND the faintest stars, had fields of view of 70 and 100 degrees. The idea that somehow restricting the field of view would show fainter stars was simply not true.
[We used a known starfield around M57 where we knew the brightness of stars in the field--those two eyepieces were also the only two that consistently showed the central star in M57, as well.]
It seems that coatings and good lens polish mattered more than field of view or number of lens elements.

[Robh]

Don,
I agree with you on nearly every point except that I believe stars must get dimmer at higher magnifications just as everything else does. This is more noticeable in a scope of smaller aperture. The only reason I can think of for fainter stars still being visible at high magnifications is your point about the dimming of the skyglow.
Curiously, in an article on scopecity.net (Optical Terms and Characteristics of Telescopes), it states that the stellar limiting magnitude of an 8" scope is 13.3 at 28x but this increases to 16.1 at 320x.
This I cannot understand. Anyone any clues as to how this can be possible? :shrug:

Regards, Rob.

[Don Pensack]

Stars are essentially mathematical points. It is diffraction caused by the opening of the tube that introduces an apparent disc size (known as the spurious disc) to the image. The fainter the star, the smaller is the spurious disc. In the case of the 8" scope you mention, the magnification enhancement is 11.4X, and the apparent per-square-arc-second brightness of the background sky in the telescope falls by a factor of that magnification increase squared, or to 1/130.6 That's a difference of over 6 magnitudes apparent brightness in the background sky.
A star that has no contrast with the night sky at low power will suddenly have significant contrast with the night sky at the higher power and be quite visible. The star image is still a point at 320X, so it is not dimmed.
Magnification beyond that level will impart both aberrations due to seeing conditions and optical quality and expand the size of the spurious disc, so at some point, any calculator that suggests that higher magnification yields the visibility of fainter stars will fall down due to the conditions of use.
In practice, in the field, higher magnifications generally yield the visibility of fainter stars.
Under ideal conditions, I was able to reach magnitude 15.6 with an 8", though this was not the theoretical limit per the calculator. The reason had to do with the telescope used. A brand new version of the same scope would have gone deeper. At that point, the coatings (standard Al) were 11 years old.
Now it has generally been said that once the spurious disc of the star becomes visible with an apparent size (often quoted as being around 1X/mm of aperture), further increases of magnification subjects the spurious disc to the same dimming due to the square of the area rule. This would account for the reason small scopes could see a dimming of the star image with higher magnifications--the spurious disc is larger in them and lower magnifications make it visible.
In practice, though, the faintest stars visible have exceedingly small spurious discs and higher magnifications than 1X/mm can be used to see fainter stars. This can be due to both the small sizes of the discs and the increased darkening of the background sky with magnification.

One last note: good seeing (steady air) is essential to see the faintest stars. In my 12.5", for instance, I have seen the central star in M57 constantly with direct vision on a couple nights of superb seeing, but on a typical night with mediocre seeing, I am lucky to catch a glimpse 10% of the time with averted vision in skies of near-identical darkness).

Here is a calculator that takes other factors into account when predicting a magnitude limit for a scope:
http://scopecity.com/limiting-magnitude-calculator.cfm
in case you're curious, here are some other calculators you might find useful:
http://scopecity.com/astronomy-calculators.cfm?pn=astronomy+calcul ators
Don

[Wavytone]

Most of the diffraction arises from the aperture stop, which is the primary mirror (reflectors), corrector (Maks and SCT's) or lens (reflectors) - not the tube.

In practice very few astronomical scopes have an aperture stop in front of the first element - about the only one that does is the lensless Schmidt.

Rob - The issue of the limiting magnitude is still bothering me greatly actually as the more I look into it I think its influenced by a combination of two effects - increasing the magnitude pushes the sky background down, and the narrower field of view typical of extreme high power eyepieces (ortho or monocentric eyepieces) reduces the total illumination entering the eye still further.

Over the past few weeks I've been trying to devise a more serious test that I can try when the opportunity arises to get out under some seriously dark skies in steady seeing (I mean 9/10 skies). The weather here unfortunately has been most uncooperative.