I think the answers so far are right on the money.
The eye relief on a long f/l EP may already be more than adequate, so increasing it might not be an advantage. But, it does save a bit of money to double the f/l of each EP over buying individual f/l EPs.
A good Barlow is pretty transparent, in that you don't notice it in the light path.
The Powermate indeed gives power without changing the eye relief. Not a plus with short f/l EPs but maybe with long f/l EPs. The Powermate is arguably better than a Barlow because of how if works.
This is explained easily with this quote from an article.
One asks about the advantages of the 2.5x Powermate over his "good
ole" 2.5x Tele Vue Barlow, particularly with his 19mm Panoptic and 9mm
Nagler.
There's no significant benefit with those particular eyepieces, except
some possible edge field illumination. There's a much bigger difference
with Plossls, especially longer focal length ones.
You can answer your friend's question regarding what makes a Powermate
different than a Barlow by telling him "it's how the rays exit the two."
The light rays exiting a Barlow are diverging, consequently hitting the
eyepiece lenses at higher than normal heights in their apertures. After
these rays trace through this new path in the eyepiece, they form the
exit pupil at higher than normal position. That is, IF all the rays make
it through the eyepiece at all! The Powermate functions like a Barlow,
but redirects the rays coming out of it, so to the eyepiece it appears as
if everything is "normal."
Then to a more complete explanation, this quote from Televue.
To understand the Powermate, we must first understand the Barlow lens. Barlows amplify the power of a telescope. They can be considered “focal reducers” for eyepieces, or “focal extenders” for objectives. Terence Dickenson, in his Barlow test report in Sky and Telescope, July 1997, says: “Technology has erased the old objections. A modern Barlow will not degrade your telescope’s optics. Anyone telling you otherwise is using outdated information. Moreover, the highly regarded Nagler eyepieces and their clones have built-in Barlows, ample evidence that the lens is not some detrimental intruder.” Thanks, Terence, for laying the myth of the degrading Barlow to rest.
A high quality Barlow must be properly designed and manufactured in order to avoid compromising a telescope’s color and spherical aberration corrections. The “invisibility” of Tele Vue’s 2-element Barlows has been noted in test reports in the astronomy magazines. However, by the nature of its negative power lens, a Barlow will do more than just increase magnification, regardless of the number of elements.
The diverging rays leaving the Barlow result in moving the exit pupil further out, thereby extending the eye relief. In short to medium focal length eyepieces the change is not noticeable. However, in the case of long focal length eyepieces, the increase can be significant and not without performance consequences.
Vignetting can occur due to the altered ray path, when the eyepiece’s lenses are not large enough in diameter to allow all the rays to make it through. Shorter Barlows, or ones with too much magnification, only exacerbate the problem because the ray path entering the eyepiece is steeper.
We had to go beyond the Barlow concept to achieve the goal of a compact, high power, fully corrected image amplifier. The Powermate™ consists of a negative doublet plus a positive “pupil-correcting” doublet. This 4-element system provides the magnifying function of a Barlow without its limitations by restoring the field rays back to their original direction, as if the Powermate™ were not there. The result is a pure magnification increase.
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