Punchcutters in the 20th century seems to have mostly used 2 kind of loupes for punchcutting: traditional jewellers eyepieces (you can see P. H. Rädisch and M. Carter using them at Enschede in several pictures) or a more sophisticated loupe on a stand like they use at the Imprimerie Nationale (C. Paput, Nelly Gable). Stan Nelson also has a beautiful one.
In his book Paput recommends "a magnifying glass on a stand, with a power of 3X and a diameter of 3,5 cm, which is reduced to 1,5 cm with a mask in order to eliminate distortion."
I tried several jewellers eyepiece but I've found them very uncomfortable and distortion prone, so I started to look of a magnifier similar to the one used by Paput, Gable and Nelson. This double lens magnifier by Bausch & Lomb has an excellent optic with very little distortion:
http://www.bausch.com/our-products/vision-accessories/professional-magnifiers/double-lens-magnifier. It was quite easy to attach it to the articulated arm of an Ikea desktop lamp. It works very well and can be place at any distance from the punch.
Also useful: Entry on Optics/Vision in David MacMillan's txt document:
Optics/Vision
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Loupes. As preferred. I like a 5X loupe; others need less magnification.
Flip-down loupes that attach to your eyeglasses.
The best one is the "Ary" loupe marketed by the
Swiss watch materials firm Bergeon. Not cheap, but nice.
Available from suppliers such as
Otto Frei (watch division, www.ofrei.com)
Esslinger (www.esslinger.com)
Optivisor. The original brand is Donegal. The DX series has
glass lenses (better), the cheaper LX series has plastic lenses.
The number indicates the diopter, not the magnification.
Having bought any number of cheap knockoffs, I now only get
Donegal DX Optivisors.
Note: The "diopter" is a measurement in physical optics
(1/focal length, in meters) and so can always be stated precisely.
"Magnification" is a physiological measurement which depends on
what your own working distance is. Without measuring you, it can
only be stated approximately.
Here is a chart of *approximate* relations between diopters and
magnification:
www.Galleyrack.com/punchcutting/diopter-magnification-and-working-distance.pdf
and a chart of approximate magnification and focal length for
Optivisor lens numbers (diopters):
www.Galleyrack.com/optivisor-lens-numbers.pdf



Comments
One other, completely different, route is to use a stereo inspection microscope. The late Jim Rimmer used one, and I have been told that Richard Årlin (Stigbergets Stamp och Press) uses one today. The working distances of a stereo inspection microscope are very different from those of a loupe, though. I couldn't figure out how to make one bench setup work for both.
In Stan Nelson's 2016 Wells College punchcutting class, most of the workstations had a simple wire holder for their loupe. But he also brought a much nicer one made largely out of standard commercial lamp hardware. He also used a paper iris to stop down the mounted loupe. Here are a couple of snapshots of it (sorry that the second one is fuzzy
So first here is the "Ary" (brand name / model) flip-up eyeglass-mounted loupe marketed by the Swiss watch tools supply wholesaler Bergeon. It's a bit expensive ($80). You can get it in left or right eye versions. You can also get it in different colors, which sounds frivolous until you have two of them of different magnifications. They're available from watch repair supply houses such as Otto Frei (in their ofrei.com division) and Esslinger.
The item that you get for your $80 is just the flip-up loupe itself. In the photos below it is shown attached to a pair of cheap non-prescription reading glasses. If you have to wear glasses anyway, as I do, having a flip-up loupe is very convenient. You might think that the bits of wire which come around the frame of the glasses would be distracting, but they're not.
That's enough for now. Sorry for the deluge of pictures.
Is it just me or do the e, c and a remind one a bit of Adobe Serif? You know, the PDF substitution font one never sees any more, thanks to the ubiquity of reliable font embedding in PDF nowadays.