Say your thinnest lines are 3/1000 em. Now, I assume some hinting might help keep the them visibile, but how small can it teoretically be printed before they vanish?
Well, of course it depends on printing conditions too...
Way too many variables dude.
You'd need to nail down an exact repro condition.
Way too many variables dude.
What’s the equation? Maybe I can fill in some variables.
Equation too complex. :-) And I'm not good enough to know it anyway.
Mostly I guess paper and ink/toner qualities. But those are pretty
impossible to quantify. You gotta field-test for specific conditions.
Or: compare an existing actual output on a given repro technology
to the font used (if you can get yours hands on it).
But then there's also human acuity, which
might be inferior to the repro's resolution.
Lucas de Groot has a font called The Thinnest, whose stems are 1 UPM (where UPM is 1000 units). So if you print it at 1000 points, the stem will be 1 point width. Since you are talking about a font three times that width, you can go three times smaller than that.
So I think the question is: how thin a line can be printed in any given device? Half point? A quarter?
I habitually use quarter-point rules in my layouts, and 0.15 points strokes to compensate to registration errors. So I think that the visibility threshold is beyond that.
As far as visual limits I read that to detect a white bar between two black bars it needs to be a visual span of one minute (1/60th of a degree,) and that at normal reading distance for printed matter that amounts to .0041 inch, which is a bit over a quarter of a typographic point, and I believe the tolerance that Linotype used in drawing type in the metal days. I would guess that we could see a thinner black line against white than that, but it's starting to get ridiculous around those dimensions. My guess would be that printing technology is more of a limit on thin lines than the eye is.
Frank>Maybe I can fill in some variables.
What are you trying to do? The question, as posed, is not different from "how big should the x height be?" with no other information provided.
David. I'd like to have a caution, e.x: "Be(r)low xxx point size there's a real danger the thinnest lines might disappear ..."
(Mind you — this is top of my head, some figures could be off)
In so called dotless offsetprinting (aka Frequency Modulated) a common size of the smallest pixel is 14 mu, which is 14/1000 of a millimeter.
I do wonder if this is visible to the human eye. Depends of the resokution of the eye, right? : )
Wikipedia: Observing a nearby small object without a magnifying glass or a microscope, the optimal distance is 20–25 cm. At this close range, 0.05 mm can be seen clearly. The accuracy of a measurement ranges from 0.1 to 0.3 mm and depends on the experience of the observer. The latter figure is the usual positional accuracy of faint details in maps and technical plans.