The effect of on/off-axis sub-apertures

[Paz]

I have been thinking about off axis apertures and the effect they have on f-ratio and aberrations and am not sure what to make of it. I would be interested in any insights and seeing what others think as I may be confusing myself! Here's where I have got to...

I've drawn some pictures below and the commentary refers to them...

 Diagram 1 and 3 - Taking a scope with a 1cm clear aperture and a 5cm focal length as the reference point, 5/1=f5  (diagram 1 being a refractor and diagram 3 being a reflector with a central obstruction and secondary vanes)

Diagram 2 - An on-axis aperture stop in a refactor of half the aperture leads to 5/0.5=f10 (diagram 2).

Diagram 4 - However, what does an off axis aperture of half the aperture do??? In one sense (and this may or may not be faulty thinking) the aperture is still 0.5 so 5/0.5=f10 (diagram 4).

This is what I have been wondering ... The light cone in diagram 2 with the on axis sub-aperture looks like an f10 light cone, with a nice slow angle of rays arriving at the focal point, but the light cone in the off axis sub aperture in diagram 4 just looks like half of an f5 light cone, i.e. the light arriving at the focal point is still a fast/steep cone. I thought if this is the case then the off axis aperture won't provide any benefits driven by improving the f-ratio and therefore any aberrations driven by f-ratio would remain the same.

But if that line of rationale is correct then why bother with off axis apertures? I then thought on any refractor I've seen an aperture stop on it is always central - and this would make sense as that would give the best f-ratio improvement, whereas I've only seen off-axis sub apertures on scopes with central obstructions. I know under a number of conditions/circumstances I get sharper / better views with an off axis sub aperture in my VX14 and had always had f-ratio improvement as one of the reasons but what if the f-ratio is actually no better? I am wondering if it is just because of the elimination of the central obstruction and spider vanes (and maybe sometimes the smaller aperture just works better with the seeing).

Diagram 5 - The last diagram shows how the off axis aperture in a scope with a central obstruction has to be less than half the full aperture in order to not overlap the central obstruction, which leads to a small difference for scopes of this nature. In this case say the actual aperture is 0.4. Then the light cone genuinely is actually slightly slower than the full f5 light cone because it is less than half of the aperture. The simple maths of focal length / aperture leads to f12.5 but in fact is it more a case of an effective focal ratio somewhere close to but slower than f5?

In the end I got to thinking in refractors does an on axis sub aperture just provide the benefits of an improved f-ratio whereas off axis sub apertures on scopes with central obstructions just provide the benefit of having no central obstruction???

[Davey-T]

Not sure if light reacts like that, it's a funny old thing 

Dave

[John]

6 minutes ago, Paz said:

.... I am wondering if it is just because of the elimination of the central obstruction and spider vanes (and maybe sometimes the smaller aperture just works better with the seeing).....

I think these two factors (especially the 2nd one) are quite significant.

I'm being cautious here because my grasp of optical theory is not great but I also think that the light coming from the off axis part of a mirror might be affected by coma ?

[Ben the Ignorant]

35 minutes ago, Paz said:

the light cone in the off axis sub aperture in diagram 4 just looks like half of an f5 light cone, i.e. the light arriving at the focal point is still a fast/steep cone.

No, it's not a steep cone. The angle between edge rays is twice as small. 

[Ben the Ignorant]

1 hour ago, John said:

I also think that the light coming from the off axis part of a mirror might be affected by coma ?

Coma depends on where the light ends up, not where it touches the mirror. At the center of the focal plane there is no coma but light arriving there also touched the mirror's edge. Because that light came in parallel to the mirror's axis.

Coma shows at the edge of the field because light focusing there didn't arrive parallel to the mirror's axis.

[Paz]

21 minutes ago, Ben the Ignorant said:

No, it's not a steep cone. The angle between edge rays is twice as small. 

I see what you mean, the angle between the edge rays is the same but then say in diagram 4 for the off-axis sub-aperture one of the edge rays is on-axis and the other edge ray is further from away from on-axis than with diagram 2 where the edge rays in the on-axis sub aperture are not as far away from on-axis - would that make any difference.

[Ben the Ignorant]

No, the f/ratio is the ratio between diameter and focal length no matter what.

[John]

18 minutes ago, Ben the Ignorant said:

Coma depends on where the light ends up, not where it touches the mirror. At the center of the focal plane there is no coma but light arriving there also touched the mirror's edge. Because that light came in parallel to the mirror's axis.

Coma shows at the edge of the field because light arriving there didn't arrive parallel to the mirror's axis.

So an off-axis aperture used with a newtonian, with the light cone being bought to focus at the original focal plane via the diagonal, would or would not show coma ?

 

[Ben the Ignorant]

8 minutes ago, John said:

So an off-axis aperture used with a newtonian, with the light cone being bought to focus at the original focal plane via the diagonal, would or would not show coma ?

Yes because coma is a consequence of the parabolic surface, even if you use only part of the surface. I'm not sure of the amount of coma, though. Even with coma present, the aberrations in the eyepiece are reduced because of the finer f/beam.

[John]

10 minutes ago, Ben the Ignorant said:

Yes because coma is a consequence of the parabolic surface, even if you use only part of the surface. I'm not sure of the amount of coma, though. Even with coma present, the aberrations in the eyepiece are reduced because of the finer f/beam.

Thats what I thought. Thanks.

 

[Paz]

22 hours ago, Ben the Ignorant said:

No, the f/ratio is the ratio between diameter and focal length no matter what.

The f/ratio is the same but the question is despite the f ratio being the same is the image quality the same. I was thinking not because, taking say spherical abberation the spread of the focal points is a certain amount with full aperture (say "a" in Diagram A below), less with an on axis sub aperture ("b" in diagram B below), but, and this is the key bit, it goes back to being the same length with an off axis sub aperture ("c" in Diagram C below) as it was with full aperture. If this was the case (and that is an if) then you don't get f-ratio related benefits from an off axis sub aperture as you would with an on-axis sub aperture, although you may get other benefits such as eliminating a central obstruction(?).

[Moonshane]

I use off axis masks mainly for doubles and planets when using my big dobs. I have no idea or (to be honest) interest why but can confirm that the image of doubles is refractor like in that it is tight and sharp. The same applies to planets and the moon although I do find that although the image is more stable with the mask, the detail when the seeing stabilises is jaw dropping with full aperture, you just have to wait longer for it. Moons if the outer planets are more easily seen with full aperture.

[Ben the Ignorant]

The main advantage of an off-axis or on-axis mask is steadiness. Many confuse it with resolution because a mask makes some detail easier to see but that's due to the steadiness of smaller aperture. The image from a smaller scope contains less detail but stability makes it easier to see. Simply discerning steadiness from resolution clarifies the thing. In the case of achros an on-axis mask lessens chromatism but also lessens resolution: the steadier and less fringed image passes for more detailed, but that's only lack of discerning different properties of the image.

As you say, Moonshane, full aperture resolves more, and there is no surprise.

In the case of spherical aberration, reducing diameter reduces it but that also reduces resolution. So the benefit of less aberration is offset by less resolution, image quality is globally the same. That was a thought experiment but gross spherical aberration is solved by using a better scope in the real world, not by stopping it down.

And doing away with obstruction is a real benefit because any object (secondary mirror, mirror vanes, dew, massive dirt) in the lightpath disturbs it. When that disturbance happens in the same time as turbulence, they worsen each other. A scope with nothing in the lightpath suffers from turbulence only, best possible case.

I've seen lengthy debates in forums about off-axis masks, all of them fueled by the confusion between steadiness and resolution: things have to be studied separately.