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Digital Resolution Made Confusing
By Dave Chrestenson, Member of the Fox Valley PC Association, Illinois
Digital Photographer/Hobbyist
There seems to be a plethora of articles on the number of pixels required to create your photos to their full glory. Many of the articles disagree with each other and some are mystifying (to say the least); occasionally a few are wrong. So here I will approach it from a different point of view, I'll give you the knowledge and let you decide what you need. Ready? Here we go!
Let's start with some facts. (I'll reconsider these later, but we have to start somewhere.) First, the average eye, relaxed, focuses at a distance of about fifteen inches. So that's about the distance people view their prints.
Second, the angle of comfortable vision (not acute) is generally agreed to be about fifty to fifty-five degrees. Beyond that is peripheral vision. Now, fifty degrees at fifteen inches subtends a distance of about thirteen inches, just covering the diagonal of an 8x10. Is it any wonder that size is so popular?
 
And third, the typical eye has a resolution of about one minute of angle. This works out, at fifteen inches, to about .004 inches, or approximately 229 dots in an inch. (For purposes of clarity I will use the term pixels when referring to the camera sensor and dots when referring to the print. But in this discussion they can be considered equivalent. (Don't compare this with the resolution (normally also referred to as dots) of printers. They are completely different animals. (Subject for another article?)
For convenience and to assure a tolerance, for now let's round that up to 300 dpi. This means that we need 300 dpi (at 15 inches) on the paper to assure that we won't see individual dots. Now, it's easy enough to work backwards from there. Assume that we wish to print an 8x10. Ten inches across at 300 dpi is 3000 dots. Eight inches down at 300 dpi is 2400 dots. So we need a camera of 3000 x 2400 pixels, or 7.2 meg. (This is assuming a camera with square pixels, not all have that, the Fuji S3 for example has hexagonal pixels, two sizes, no less. (Subject for still another article?) Simple huh? Maybe.
But let's try another example first. Assume you just want to print a picture half that size, 4 x 5 is more com?mon. Then 4 times 300 equals 1200 and 5 times 300 equals 1500, so our camera need only be 1.8 meg. That's not so bad, is it? But before you dash right out to buy a 2 meg camera on sale, let's take a look at some of those original figures.
I said that the average eye views an image at 15 inches. That's an "average" eye. It can vary from that... a lot. Depending on age, it can go from 3 inches (a youngster) to more than 6 feet. (An old timer.) And that's for an eye that's working well. Near-sighted? You'll hold the picture closer. (Assuming you don't wear correction lenses, of course.) Far-sighted? Further away. Have astigmatism? A mess! So, if you hold your picture at 7.5 inches, you will need twice the number of pixels, or 600, per inch. An 8x10 would require a 28.8 meg cam-era. Good grief! Thirty inches viewing distance is a lot easier, a 1.8 meg one will do the job. Also, some eyes can see significantly better than one minute of angle, some can reach ½ minute. That's even worse, you need 600 dpi at 15 inches, which means we're back to a 28.8 meg camera for an 8x10, and a 7.2 meg one for a 4x5. But you can do the math. And do you really need to have the dots as small as theory suggests? Well, to make it more confusing, there are other considerations that affect that. Bright lighting needs higher resolution, dim lighting needs less. Glossy paper? Higher resolution. Matt paper, less. High contrast image, more, low contrast, less. Ad infinitum.

Finally, what if you have taken the definitive photo of Yosemite, the one to equal Ansel Adams, and you want to have it printed at, say, 16x20 and frame it. Do you still need 300 dpi? Probably not. After all, peo?ple don't normally hold a 16x20 in their hands and look at it from 15 inches. Remember the 50 degree vi?sion. So, you'll probably be hanging it on the wall, where they will view it from a distance. Experience shows that people will move backward or forward when viewing a picture until it subtends that 50 degree angle. So you might well get away with 150 dpi.
  
But, getting back to the more normal usage, handheld prints, do you need 300 dpi there? Again, maybe. In many cases you may get away with less. But if you go below 150 dpi you are almost certain to get obvious visual pixilation at that distance. Of course, Photoshop to the rescue, you can resample upwards and in-crease the number of pixels to what works. You're not adding detail, but at least you're getting rid of those annoying jaggies.
Clear? I didn't think so. Remember, I said "Made Confusing." But at least you are now confused on a much higher plane! Good luck.
 
Editor’s comments: Dave has presented several programs over the years that have gone into great detail on various aspects of digital photography. From cameras and lenses and from basic photo software to the flagship of the genre: Adobe Photoshop. His knowledge has always impressed me and we always enjoy his point of view on this topic. He presented a program last month: Pursuing the Path From Pixels to Pic?tures, which could have easily gone late into the afternoon. All present enjoyed his program. Thanks Dave!
Jon Jackman

There is no restriction against any non-profit group using this article as long as it is kept in context with proper credit given the author. The Editorial Committee of the Association of Personal Computer User Groups (APCUG), an international organization of which this group is a member, brings this article to you.