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For biological research, I need to print characters so tiny that 2 of them fit in less than 0.5 mm, which I will read under a microscope.

I am currently printing from Excel at font size of 1.5, using a HP LaserJet 400M. The result is slightly larger than what I need it to be, but printing at size 1 produces unreadable results.

How can I print a smaller font size but still get readable results? Are there specialized printers for that? Where could I find one?

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Just curious: Why do you need to be able to read it under a microscope? Labelling? – Anko Jun 7 '14 at 20:24

I don't have hard facts, but I'm still going to wager a guess that what you're trying to do isn't really possible at least with "consumer" equipment. What follows is a back-of-the-envelope style of calculation showing why that is.

You say you want to fit two characters within 0.5 mm. I'll assume we're talking 0.5 mm width (that is the more friendly approach, as characters are usually taller than they are wide) and leave a little bit of spacing between the characters; that gives us a usable width of approximately 0.2 mm per character and something like 0.3 mm character height.

Let's say we need about 10 somehow discrete dots to resolve characters to the point that they are recognizable and readable. That means each dot can be up to 0.03 mm tall. With approximately round pixels (most easily achieved by printers) that gives a print pixel diameter and dot pitch of no more than the same 0.03 mm in both directions.

0.03 mm dot pitch expressed in another way is 0.03/25.4 ~ 847 dpi.

So the printer, and print media (paper) must support an optical resolution in the range 800-900 dpi to meet your stated requirements. That's the number you need to be looking for if you want to purchase equipment to enable you to do this: figure out what exact optical DPI is necessary, then look for hardware (and print media) capable of providing that. Note that this must be non-interpolated numbers. Most printer resolution figures are most likely interpolated values, which doesn't help you; look at the specific dot pitch (distance between individual blobs of color on the page) that the equipment can provide.

You can adjust these figures and come up with different exact numbers, but given that high quality printing is usually on the order of 300 dpi optical resolution (above that you are interpolating, dithering and any number of other techniques to increase the apparent resolution without decreasing the dot pitch), it stands to reason that characters would need to fit within approximately a 2×3 pixel rectangle on average to fit within the resolution limit. Six pixels, even with dithering, is not really enough to make recognizable characters (try for example to tell the difference between a C and an E with such limited resolution). I would imagine you need at a minimum twice that both in terms of height and width for reliably recognizable characters, and even that might be tricky with some combinations.

300 dpi is a dot pitch of about 0.08 mm (let's round that off to 0.1 mm), which agrees well with the above.

Hence, not possible.

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Adding: You can represent text (at least the latin alphabet) relatively well in a 3x5 rectangle. However your printer would have to be very precise if you're pushing its resolution to the maximum; any bleeding / lack of precision may muddle that beyond recognition. The OP might want to seek out a professional printer or anybody else with an ultra high-resolution printer. Or buy one if there's budget; I believe 1200DPI laser printers are in the $500-$1000 range typically (e.g. HP LaserJet M551D, at a cursory search), not prohibitively expensive for medium-sized projects. – Jason C Jun 7 '14 at 20:28
@JasonC A 3×5 rectangle is 15 pixels. Twice in both directions my 2×3 is 4×6 for 24 pixels. Not too far off for a back-of-the-envelope calculation. Without having checked though, I really doubt that 1200 DPI laser printer is 1200 DPI and 1200 LPI optical resolution; that figure is most likely after dithering. And you'd still be pushing the limit on the system, as you say. – Michael Kjörling Jun 7 '14 at 20:30
Paper choice can also make a difference, low quality paper can affect output quality at such tiny sizes. – Jason C Jun 7 '14 at 20:33
Yes, I share your distrust for marketed DPI specifications; I didn't really make any calculations or investigations there, I just arbitrarily picked a number and Googled for prices. – Jason C Jun 7 '14 at 20:34
@JasonC Oh, the marketed DPI spec is probably accurate for what it's supposed to say. There is a value to specifying apparent resolution, it just doesn't help much when you really need those really tiny details. So in a case like this, one needs to be a lot more careful about what numbers one looks at. – Michael Kjörling Jun 7 '14 at 20:35

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