Barlow and eye relief - how does it work?

[vlaiv]

Just wondering what is explanation of increased eye relief when using barlow?

1. Increased focal length

2. Sharper light cone

3. Smaller exit pupil

I know that all above is related, but wondering if I have short eye relief eyepiece in F/5 scope vs F/10 scope (for the sake of argument let it be 4" achro), would F/10 scope offer greater eye relief of the exact same eyepiece?

I've often found in various reviews that people don't agree on "comfort" of eyepiece relief, and sometimes say something along the lines: "Although eyepiece has 10mm eye relief, it feels more than this ..." - could it be due to use in long focal length (or slow) instrument?

 

[Ruud]

Objective lens andv2x Barlow:

Objective lens and 2x Focal extender:

Above are a Barlow compared to an extender. Note that the light cones, after passing the Barlow, diverge. After passing an extender the beams are more or less parallel.

The objective itself causes a weakly divergent set of light cones.
A weak Barlow increases this divergence a little, a strong Barlow increases it greatly.
Below is an example of a 5x Barlow which creates widely divergent light cones:

Exit pupil:

Here is how the exit pupil forms behind an eyepiece. It is actually the projected image of the objective. The projecting lens is the eyepiece.

When the eyepiece receives (near) parallel light cones, it forms an exit pupil at its back-focal distance. 

When an eyepiece receives divergent light cones, as from a Barlow,  it forms an exit pupil at some distance behind its back-focal distance.
This follows from the lens formula: 1/(object distance) + 1/(image distance) = 1/(focal length).
Or, for our interpretation because the exit pupil is the projected image of the objective lens:  1/(objective lens distance) + 1/(exit pupil distance) = 1/(eyepiece focal length)

In the image below you see how
- parallel light cones entering the eyepiece form an exit pupil close to the eyepiece according to the lens formula, and
- diverge cones (after leaving a Barlow) seem to come from much closer by and will, again according to the lens formula, form an exit pupil, this time further from the eyepiece.

Hence the increased eye relief when using a Barlow

Note that stronger Barlows produce strongly divergent light cones. Especially longer focal length eyepieces may vignette with these Barlows, as their lenses may not be wide enough to capture the  the peripheral light cones which can end up very far from the optical axis. Focal extenders will not vignette. They produce parallel light cones. Also, focal ectenders will not extend the eye relief of any eyepiece.

 

 

[vlaiv]

5 minutes ago, Ruud said:

 1/(objective lens distance) + 1/(exit pupil distance) = 1/(eyepiece focal length)

So it is focal length that plays a part - meaning F/10 4" vs F/5 4" and same eyepiece would give longer and shorter eye relief respectively?

[vlaiv]

Ah, it's the other way around - shorter FL scope will have greater eye relief?

Well, I'm confused

Let's rearrange the formula, and see:

1/exit pupil = 1/efl - 1/sfl

exit pupil = efl*sfl / (sfl - efl)

let's see for 25mm eyepiece and 500mm and 1000mm scopes

500mm scope: ~26.315mm

1000mm scope: ~25.641mm

So it looks like longer FL scope will provide shorter eye relief?

That is kind of contrary to using barlow / extending focal length and getting longer eye relief, but my math might be wrong.

 

[vlaiv]

Oh, ignore above post, everything checks out. It is indeed case that shorter FL scopes provide greater eye relief in same eyepiece.

Barlow makes cone looking like it is coming from closer objective although cone it self is more narrow and looking like it has been produced with slower objective.

[Ruud]

Oh, I had already started an answer. Maybe others will benefit from it:

 

Long focal length telescopes produce near parallel light cones. They will give a short eye relief.

Short focal length telescopes produce slightly divergent light cones. They will give a slightly longer eye relief with the same eyepiece.

The light cones after passing a Barlow diverge strongly. The Barlow will noticeably increase the eye relief of the same eyepiece.

A Focal extender may produce an even more parallel set of light cones than the original objective does. In that case, the extender will give the shortest eye relief, again with the same eyepiece.

 

5 minutes ago, vlaiv said:

Barlow makes cone looking like it is coming from closer objective although cone it self is more narrow and looking like it has been produced with slower objective.

Right!

[Louis D]

On a related note, why do some shorty barlows that extend the eye relief also make it very difficult to hold the exit pupil?  Is it something to do with SAEP?

[vlaiv]

15 minutes ago, Louis D said:

On a related note, why do some shorty barlows that extend the eye relief also make it very difficult to hold the exit pupil?  Is it something to do with SAEP?

I think it has more to do with eye centering - further away eye is from eyepiece, there is larger range of eye positions where our brain thinks we are in right place, but in fact part of exit pupil can fall outside our iris aperture.

It has to do with angles, maybe following diagram can explain:

I've marked with green section in which our brain thinks we are "on the mark", but in fact, longer eye relief and further away exit pupil is - creates more "room" for eye positioning - some of them not letting full exit pupil to get into iris.

[Ruud]

With a long 2x Barlow there's a lot of room to increase the original focal plane's  image scale by a factor two.

With a shorty 2x Barlow, the negative lens and the new, up-scaled focal plane must be close together, so the light cones must diverge more.  A shorty 2x will therefore cause a greater increase in eye relief.  This may  make eye placement difficult, as Vlad suggests. Also, most eyepieces are not optimised for wildly divergent light cones and some may not be able to deal with them well. Who knows what could go wrong. Indeed, the slightest trace of spherical aberration of the exit pupil in the original eyepiece design might be amplified to the level of becoming  noticeable. It's also possible that  the shorty itself introduces aberrations. Shorties  need steeply curved lenses and are difficult to produce to the same standard as long Barlows. 

Anyway, shorty Barlows are not recommended unless you are in a situation where you must use a Barlow but cannot use a full sized one.

[martinl]

Ruud, I just have to say that in ~20 years of reading discussions about amateur optics your animations are BY FAR the best and easiest to understand illustrations I’ve seen of those phenomena everyone discusses but no one (including me) seems to fully understand!

Many thanks for your efforts!

[Alfian]

5 hours ago, martinl said:

Ruud, I just have to say that in ~20 years of reading discussions about amateur optics your animations are BY FAR the best and easiest to understand illustrations I’ve seen of those phenomena everyone discusses but no one (including me) seems to fully understand!

Many thanks for your efforts!

Yes indeed,  to be printed off and put in my Astro reference file. It wont capture the animation but I can save the link.

[Ruud]

Thanks guys.

@Alfian - feel free  to right-click the animations and download them. They're GIF files.