Introduction

The standard by which the technical quality of a photograph is most frequently judged is sharpness or the extent to which detail is faithfully reproduced. That may be unfortunate. While fine detail is, indeed, often important to the successful presentation of a photographic idea it can sometimes be much less important than other factors or even irrelevant, depending upon theme and the intentions of the photographer.

This article is to discuss the subject of image resolution in the context of photo presentation and the capabilities of the human eye with the intention of helping the reader develop a realistic, objective approach to the subject. You can "Google" to find out much more so consider this merely an introduction.

Definitions

Most readers will already know the following but a review can't hurt.

• Dot (same as "pixel") - Digital images are actually composed of small dots or pixels. Each pixel is a sample of the original image's brightness and color at some point within that image. At some distance the eye cannot distinguish the individual dots which then blend together and the impression is obtained of a continuous gradation in tone and color. The pixels of most monitors are large enough to be visible to the unaided eye at comfortable distances although we readily overlook the phenomenon. Camera sensor pixels are microscopic in size. Their center spacing can be 0.005 mm (5 microns ... Nikon D800) or less. There is considerable variation in sensor pixel density depending on the manufaturer's technical and marketing (!) objectives.
• Dot/pixel density - Dots/inch (dpi) or dots/mm (dpm). This tells us how closely the centers of dots or pixels representing an image are spaced. The closer they are (hence smaller) the more detail that can be presented. If they are made too small in an effort to minimize spacing, however, the point of diminishing returns is reached where noise and poor dynamic range begin destroying detail. This is a common problem with many pocket digital cameras where pixel count is used as a sales gimmick to attract customers liable to be less technically aware than buyers of more sophisticated (and expensive) equipment.
• Line pairs/inch (lppi) or Line pairs/mm (lppm) - This concept is derived from classical information/signal theory and the Nyquist Theorem. An example simplifies the idea: If we have a subject comprising 150 alternating black/white line pairs/inch (or more correctly, a pure sinusoidally varying pattern) then to sample that subject in a way that allows us to reconstruct it perfectly (like with a printer) we must evenly sample it at 300 dpi or twice the rate of occurrence of the original pattern. (With images we actually have a two dimensional signal so would have to sample at right angles as well.) If, in this example, we had line pairs small enough that more than 150 of them would fit into an inch, then sampling at 300/inch would produce false patterns commonly called "aliasing" in the reconstructed image. This can prove a serious defect in some digital images where it is also referred to as "moire". It can be especially troublesome in subjects with fine, repeating patterns such as fabrics and some architecture. The way to avoid or, at least, minimize aliasing is to apply a low-pass filter to the image (signal) prior to sampling. The filter attenuates all detail exceeding the Nyquist limit for the sampling density or frequency employed. Most digital cameras have an anti-aliasing filter placed over the sensor. To simplify a bit, this is a piece of slightly blurry glass that limits the amount of detail reaching the sensor.

The Limits of Human Vision

How much detail you can potentially discover in a photograph with the unaided eye is discussed in this Wikipedia article. To summarize, at a distance of 1 meter from the subject the eye (in good condition) can resolve about one line pair (lp) per 0.35 mm or 3 lppm. There is research suggesting ultimate resolution of the eye may be more but it is uncertain what the photographic significance might be or whether such superior capability is even typical. For purposes of discussion here I am going with the above figure. When it comes to photography, most of us are comfortable viewing small to medium size images at a minimum distance of about 0.5 meter (about 18 inches which is what the optometrist tends to recommend as well) which means a resolution of 1 lp/0.175 mm or 6 lppm. That's equivalent to 150 lppi. The latter is a very interesting number as we will see in the next section.

Printer Resolution and the Eye

The inkjet printer is a popular, high quality image presentation device. While many units brag of astronomical dot density (such as 1440 dots/inch), ink spread and other factors limit the effective density to about 360 dpi (Epson printers - for HP and some others a bit less). That translates into a maximum resolution on the print of approximately 180 lppi. This is very close to the 150 lppi resolution of the human eye at our comfortable viewing distance. In short, we can say that inkjet printers have been cleverly (or luckily) designed to produce images capable of representing all the detail most of us can see with the unaided eye at a comfortable viewing distance. Some will quibble with this and should be congratulated upon their good fortune in having exceptional eyesight but for most of us, the inkjet delivers the goods.

In what follows, terms such as "perfect" or "flawless" are derived from the foregoing discussion.

Monitor Resolution and the Eye

Practically all monitors, regardless of size, are built with 100 dpi. Lately 125 dpi has become readily available in some larger units but that's a small difference. The Nyquist theorem informs us these devices can resolve no more than about 50 lppi which is 1/3 the resolution of the human eye at our comfortable viewing distance. That's why you can readily see the individual pixels on a monitor if you make the effort to do so. Apple has recently introduced its "Retina" monitor technology which provides resolution similar to that of the inkjet and, therefore, the eye at comfortable viewing distance. It remains to be discovered if this has been done at the expense of other desireable  image properties such as adequate dynamic range. Apart from the "Retina" technology, monitors are low resolution devices and you must relax your standard for rendition of detail accordingly when viewing their images.

Photographic Implications 

The foregoing analyses and numbers can be used to determine what to expect when printing or when displaying images on a monitor.

Let's consider the Nikon D800 which has a 36 megapixel full-frame sensor (24 X 36 millimeters).  A bit of arithmetic tells us this sensor has a pixel density of 207 ppm (about 5 microns) or 5258 ppi.  We'll assume we are using a lens that can perform at least to this level - that is, it can project onto the sensor an image comprising the equivalent of 5258 distinct ppi.

• To make an 11 X 14 print from this image we must multiply the long dimension by 10 meaning we end up with 526 ppi or 526/2 = 263 lppi - way more than enough for perfect rendition of detail.
• For a 16 X 19 the multiplication factor is almost 14 leaving us with 375 ppi or nearly 190 lppi - still significantly more than we need for perfect rendering of detail on our inkjet/eyeball system.
• At 25 inches on the long side enlargement becomes 18 resulting in 292 ppi or 145 lppi and the D800 image is now at the limit for flawless rendition of detail by any presentation technology whatsoever. Scour the Internet and you will find many reviewers agreeing with this number.

The bottom line is that with top-notch lenses and a good inkjet the D800 is capable of sourcing very large prints approaching poster size. Of course, prints at this size start to get a bit uncomfortable at our regular viewing distance, requiring head motion to take in all the image, so it is reasonable to expect many people would step back a bit more, which reduces resolution requirements. In my experience, the best D800 images hold up well to 32 inches or more at comfortable viewing distances even where sharpness is the primary criterion for evaluation of image quality.

Monitors have about 1/3 the resolution of an inkjet which suggests we could use 3 times the magnification we associate with printers before exhausting the relatively mediocre limitations of these devices. In other words, a camera like the D800 and, indeed, most other digital cameras these days, represent vast over-kill in terms of satisfying criteria for best possible monitor images. For example, when viewed at 100% beyond which monitor resolution would exceed what the image has to offer at that magnification, a best possible D800 image would be almost 6 ft on the long side. 

Printing

I use QImage for most printing. A stand-alone printing package such as this offers far more control and flexibility than something built into an image processing product like Photoshop so if you obsess over print quality you might want to consider this option. Among many other print finishing options, QImage provides an a feature to temporarily sharpen an image "on the fly" prior to printing (you can do this in other ways - but less conveniently - in Photoshop/Paintshop etc.). This recognizes the fact that a droplet of ink fired at the paper by the printer will spread before drying. How much will depend on make of printer, the ink, temperature and type of paper. It could be as much as 25% the diameter of the original droplet. QImage offers 20 sharpening presets intended to offset the visual impact of droplet spread to some degree. Getting the best result will involve some testing but you can always achieve a sharper print image with just a minimum choice. It's important to note that an image prepared to appear optimally sharp on a monitor (which is a low resolution device) is liable to look a bit soft in a print so temporary sharpening is almost always a good idea. Overdo it, however, and you will get a very unpleasant grainy appearance. Similarly, an image optimally sharpened for printing is likely to appear over-sharpened on a monitor.

The author of QImage builds an extensive case on behalf of printing at twice the effective dot density of the printer, that is, 720 dpi rather than 360 dpi in the case of Epson printers.  Quite frankly, I have never been able to see the difference but there is certainly no down-side to following this advice if you want to ensure capturing that last tiny bit of detail for the sharpest eyed of your viewers.

More About Pixels and Dots 

Marketing hype is all about camera pixels these days. The number of pixels a camera sensor has is largely irrelevant without considering also the sensor dimensions so that we can calculate the linear pixel density of the sensor (that is, pixels/mm). From dimensions and density it is then easy to determine how large an image we can make before exhausting capabilities of the eye and/or presentation medium.

Many inexpensive cameras have astonishing pixel density crammed into tiny sensors. These sound great in the promotional literature but in use, the promise of incredible image detail can't be kept because these tiny pixels are unavoidably prone to noise and have poor dynamic range. It is, however, easy to manufacture tiny pixels and, thereby, give the marketing department some nice big numbers with which to bamboozle the unwitting.

Cameras capable of the best images have larger sensors and actually lower pixel density than most point-and-shoot units but ... they aren't crippled by noise and poor dynamic range. These large sensors permit the use of longer focal length lenses to obtain a certain field of view. Less magnification is therefore required (post image taking) to arrive at a particular presentation size and level of detail, resulting in visibly higher image quality.

Conclusion

Lens, camera body, eye and presentation device comprise an imaging system and image quality is determined by all components of this system. The perception of detail in an image is dependent even upon some rather intangible elements such as "comfort" in the context of viewing distance and the highly variable capabilities of human vision. Understandning something about the nature of these factors can be helpful in maximizing image sharpness on monitor and print while conditioning our expectations in regard to the limitations of what is possible at all. Laboratory tests can document the absolute limits of performance in a photographic system and will always find flaws. In the real-world we use our knowledge of what is possible to produce the finest images we can in the face of unavoidable compromises, recognizing that the best way to view a fine photograph may not be with a magnifier.