I have been thinking about resolution. As we all know, the benchmark resolution for photographs in publishing is 300 ppi (pixels per inch).

A problem is that things get so darned confusing when we are discussing other matters using metric sizes (centimeters, millimeters, micrometers, what have you) and also referring to resolution using the inch/pound system.

So the thought occurred to me to convert 300 ppi to pixels per centimeter (let’s call it px/cm). That’s easy to do: divide 25.4 into 300, and you get a bit more than 118.1. Well, that’s not even an integer, but even if it were, the number 118 is not convenient to use, so let’s change that to the nearest round number, which is 120.

Thus, 120 px/cm is very close to 300 ppi, just slightly higher resolution. And that’s fine. After all, there’s nothing magical about 300 ppi. At some time in the past it was determined to use the standard for publication to be approximately 300 ppi, so it was decided to use exactly 300 ppi. But if instead the number used were, let’s say 301, or 305, or 298, any such number like that would be indistinguishable from 300.

In the same way, there’s scant difference between 118.1 and 120 (120 px/cm is exactly equivalent to 304.8 ppi).

So there we have it: Using metric notation, the standard resolution for publishing should be 120 px/cm.

But wait – there’s more.

Easy arithmetic shows that 120 px/cm equals 12 px/mm (that is, pixels per millimeter).

And we can go one step further, noting that 12 pixels per millimeter equals 12 pixels per 1000 micrometers. (For those who may not know it, a micrometer is the formal name for a micron, and its symbol is μm. The diameter of a strand of human hair may be as narrow as 10 micrometers, and if so, you could lie 100 such strands next to each other in a millimeter).

OK, let’s do one more division and see that 12 pixels per 1000 micrometers equals 3 pixels per 250 micrometers.

Now, 250 micrometers – in other words, one quarter of a millimeter – is a very special number. I will quote from a magnificently excellent web site devoted to measurement. First, here is the link to that web site:

http://www.unc.edu/~rowlett/units/

This site refers to a Q (just the capital letter), and defines a Q as “a metric unit of distance equal to exactly 0.25 millimeter ... used by typographers and page designers in Japan, in Germany, and in other countries in preference to the traditional point … This unit is also spelled

**kyu**.”

A Q is a most useful measurement. It is very fine, yet sufficiently coarse as to make rough calculations on small objects.

So, let’s recapitulate what we have. Working in the metric system, we have the following equations serving as a benchmark for publishing-quality resolution:

120 px/cm = 12 px/mm = 3 px/Q

Stanley