Making effective use of professional photographic ink jet printers is tricky business, especially when the statistics that are commonly used to describe these printers are vague and misleading. Learning how a ink jet printers function, how to properly interpret their capabilities, and make the most effective use of those capabilities, is possible. You may need to deal with a little mathematics to fully understand, but for those brave enough to endure, your answers are below.
In the printing world, there are numerous terms used to describe the various aspects of a printers behavior. Everyone has heard of DPI, many of you have heard of PPI, but not everyone understands the true meaning of these terms and how they relate.
Understanding terms is important, but everything has context, and understanding how these terms relate to each other in the context of ink jet printing is critical to learning how to generate the best quality prints. Every image is composed of pixels, and every pixel in an image represents a single distinct color. The color of a pixel may be produced in a variety of ways, from the blending of RGB light on a computer screen, to a solid mixture of dye in a dye sublimation printer, to the dithered composition of colored dots printed by an ink jet printer. The latter is of interest here.
When an ink jet printer renders an image, it has a limited set of colors to work from, usually cyan, magenta, yellow, and black. Higher-end printers may include a variety of other colors as well, such as blue, orange, red, green, and various shades of gray. To produce the wide range of colors expected of a photo printer, multiple dots of each color must be combined to create a single color as represented by a pixel. A dot may be smaller than a pixel, but should never be larger. The maximum number of dots that an ink jet printer may lay down in a single inch is the measurement of DPI. Since multiple printer dots must be used to represent a single pixel, the PPI of a printer will never be as high as the printers maximum DPI.
Before diving into the details of how to achieve maximum print quality, it is important to understand how the human eye sees a print. The eye is an amazing device, and as photographers, we know that better than most. It can see amazing clarity and dynamic range. It also has a limit on its ability to resolve detail, and that directly affects what resolution you may choose to print at.
The maximum resolving power of the human eye is lower than printer manufacturers would have you believe, which tends to be 720ppi or 600ppi, depending on the manufacturer. It is also lower than most print fanatics would have you believe, as well. Depending on the intended viewing distance, the lowest acceptable PPI may be considerably lower than you might expect. The most general way to describe the resolving power of the human eye is as one arcminute, or 1/60th of a degree, at any distance (for the average eye…those with 20/10 vision see about 30% better, or 1/86th of a degree acuity.) For normal vision, we can use this to approximate the minimum resolvable size of a pixel at a given distance, so assuming a hand-held viewing distance of about 10 inches for a 4×6 inch print:
[tan(A) = opposite / adjacent ]
tan(arcminute) = size_of_pixel / distance_to_image
tan(arcminute) * distance_to_image = size_of_pixel
tan(1/60) * 10″ = 0.0029″ min pixel size
For sanity sake, we can make the tangent of arcminute, or resolving power P, a constant:
P = tan(arcminute) = tan(1/60) = 0.00029
This may be translated into pixels per inch like so:
1″ / 0.0029″ = 343.77 ppi
The minimum resolvable pixel size may be calculated for any distance, and as distance increases, the minimum required PPI will shrink. If we assume an 8×10 print at a viewing distance of around a foot and a half, we would have the following:
1″ / (0.00029 * 18″) = 191.5 ppi
A general formula for this can be created, where D is the viewing distance:
1/(P*D) = PPI
As a simple rule, regardless of how close you may view a photograph, the unaided 20/20 eye is incapable of resolving more than about 500ppi (for those with 20/10 vision, resolving power reaches about 650ppi.) The only reason one may surpass a resolution of 500ppi is when you require more than a standard 300-360ppi, and you need to stay within the limitations of your hardware (i.e. 600ppi for Canon printers.)
While the very vast majority of the time, you will not need more than 300-360ppi, if you do have very fine detail that requires a high PPI, you may wish to base your calculations on a higher visual acuity. For viewers with 20/10 vision, visual acuity is a bit improved, at around 1/86th of a degree (0.7 arcminute). The constant P at this level of acuity is smaller, and therefor necessitates a smaller pixel when printing images with very fine detail.
Given our formula from before, adjusted for improved acuity:
P = tan(arcminute) = tan(1/86) = 0.00020
Taking our 4×6″ print viewed at 10″, and plugging this into our general formula for PPI, we would have a PPI of:
1″ / (0.0002 * 10″) = 1″ / 0.002″ = 500 ppi
Ok, enough math for now. On to the good stuff.
Now that we know the limits of the human eye, we can better determine what resolution to print at for a given paper size and viewing distance. An ink jet printer is not capable of producing ideal results at any PPI, so we must compromise, and choose a resolution that is more appropriate to the hardware. Anyone who has investigated the “best” resolution to print at has likely come across many common terms, such as 240ppi, 300ppi, 360ppi, 720ppi, etc. These numbers are often based in truth, but when to use them, and when you might actually choose a lower resolution, is often left unexplained.
When choosing a resolution to print at, you must make sure it is divisible into the lower bound of the DPI your printer is capable of. In the case of an Epson, this is likely 1440, and in the case of a Canon it is likely to be 2400. Every printer has a native internal pixel resolution that any image printed will be re-sampled to. In the case of Epson, this is usually 720ppi, and in the case of Canon it is usually 600ppi. The PPI of printers is rarely publicized by the respective manufacturers, so it is up to you to figure it out. A handy little tool called PrtD, or Printer Data, can help. Just run, and your printers native PPI will be displayed.
Determining the optimal resolution to print at, now that we have both the printers DPI and native PPI, should be a trivial task: use the native PPI. While this seems logical, there are many reasons why this is less than idea. For one, 720ppi is well beyond the maximum resolving power of the human eye (@500ppi/650ppi). Factoring in viewing distance, it may be possible to get away with less resolution, perhaps significantly less, resulting in smaller image files for print and saving disk space.
If we assume a minimum viewing distance of approximately six inches for a 8×10 print, the theoretical PPI would be about 575ppi. This rounds up to a printer-native 600ppi on Canon, and 720ppi on Epson. A viewing distance of six inches for a person with 20/20 vision (corrected or otherwise) is extremely close, and rather unlikely. If we assume a more realistic minimum viewing distance of ten inches or so, our theoretical PPI drops to about 350.
If we printed our 8×10 photo at a resolution of 350ppi, the results would likely be less than stellar. For one, 350 is not evenly divisible into either 600 or 720, which will cause the printer driver to do some rather unsightly, distorted scaling for us. Any regular, repeating patterns will show up with very undesirable moiré, which can greatly reduce the quality of a print. Choosing a resolution that evenly divides into the native printer resolution, such as 360ppi for Epson, or 300ppi for Canon, will help ensure that any scaling the driver does will produce even results.
Here are some common print resolutions for various DPI’s:
Knowledge is power, as they say, or in the case of photography, knowledge is a better vision envisioned. Despite all the rhetoric about printers on the internet, conflation of distinct terms like DPI and PPI, both from manufacturers and avid consumers, a little math and some logic can provide some useful knowledge. As a general rule of thumb, 300-360ppi for your average professional grade ink jet printer will be sufficient for the vast majority of prints viewed within a few feet. Larger prints framed and hung, viewed at a distance of many feet could do with 200-300ppi, although 300ppi is recommended to maximize detail. Giant prints viewed at more than a five to ten feet, such as wrapped canvas, can do with the bare minimum of 150-180ppi, however as ink jet technology advances, dithering algorithms improve, and more people use corrective lenses, 200ppi can still bring out more detail. For small prints, using the maximum 600-720ppi will bring out the most detail, and is useful for 4×6″, 5×7″, and 8×10″ prints that will be viewed relatively close, within a foot or two.