The View From A Hand-Held Device
If you only view pictures on a cell phone, you only see a few pixels so none of this matters. But if you want to be able to see details in a large picture, perhaps print it, you need to consider just how many pixels the picture should contain.
Sensor Size Matters
This picture shows some common sensor sizes. A Nikon D850 camera has a full frame sensor, an Apple iPhone 5 uses a 1/3.2″ sensor. There are smaller sensors (e.g. a 1/3.6″ sensor is 4.00 x 3.00 mm) and larger sensors (e.g. a Fujifilm GFX 50S camera sensor is 43.8 x 32.9mm).
Larger sensors produce better quality images. For a complete explanation, check out this article on sensor formats.
Inches
The calculations below are done in inches (1″ = 2.54 cm) because printer resolutions are typically quoted in pixels per inch (ppi).
Optimal Viewing Distance
You calculate the required resolution in two steps: first figure out how close the viewer will be to the picture, then figure out the size of pixels a person can see at that viewing distance.
The closer a viewer is to the picture, the higher resolution is required. Pixels that are not visible when you stand far from the picture are very visible when the same pixel size is used on a cell phone.
People hold tiny pictures (e.g. on a cell phone) close to their eyes, but stand further back to view a large picture.
How far away is the viewer? The common rule of thumb is that viewing distance should be 1.5 to 2 times the diagonal length.
Example: A 20″ x 30″ picture has a diagonal of 36″ which gives a viewing distance of 54″ to 72″.
Optimal Viewing Distance of Panoramas
How does this apply to large printed panoramas? Let’s say you are printing a picture to be 120″ long and 17″ high. The standard calculations suggest a minimum viewing distance of 180″, about 15 feet or 5 metres. This is not how people view panoramas. They may stand back to get a general feeling for the picture, but then they move in and look at the story being told by different parts of the picture.
My working theory is that when picture height is much smaller than the width, people move in closer to view a chunk of the panorama whose width is about 1.6 (golden ratio) times the height. If the height is 17″, viewing distance will be 48″, regardless of how wide the panorama is.
Even this is too far. A really wide picture gives an invitation to move from 180″ to 48″. But a picture that is rich in details extends the invitation to move in closer and closer to see the detail.
So you have the odd result that a large detailed panorama may have a very short viewing distance. Our example 120″ x 17″ picture may well have a viewing distance of 24″ (60 cm).
Resolution
For the image to look good at the chosen viewing distance you need the pixels to be small enough to fool the viewer into seeing a smooth, not pixellated, image.
Knowing a bit of biology (the visual acuity angle of human eyes) and applying a bit of math, you can show that the minimum required pixels per inch (ppi) = 3438 / viewing distance.
The minimum pixels per inch (ppi) needed for a print with acceptable quality is calculated by dividing the value 3438 by the viewing distance. Anything above this ppi will look good at the distance chosen.
The crowd of people viewing your picture may force some closer than the optimal viewing distance, or a viewer may just want to look closer at some particular detail. Also, if the image is mounted under glass, the glass blurs things a bit, so a bit more resolution can help clarify the image. So you should definitely print at more than the minimum ppi.
Example: The following table shows some viewing distances, and the corresponding pixels/inch. The doubled ppi numbers give you an extra level of safety for people who want to move in very close.
| Distance | ppi | 2 x ppi |
| 12 | 287 | 573 |
| 24 | 143 | 287 |
| 36 | 96 | 191 |
| 48 | 72 | 143 |
| 60 | 57 | 115 |
At the low end of distance, the high end of pixel count is at the limit of what human eyes can distinguish: around 200 to 300 ppi. High resolution computer displays (Apple calls them Retina Displays) have resolutions in that range.
Conclusion
If your image has enough pixels that you can print at 300 dpi (ppi) or more, you cover all viewing distances. If your image doesn’t have enough pixels to produce the size of image you want, you can reduce the printing resolution based on the expected viewing distance.
Historical Postscript
In laboratory conditions, you can extract about 6K x 4K resolution (24Mpixels) from a 35mm film image. In practice, if you have old film, you can get about half that, perhaps 4K x 3K: family photos were not shot with high quality cameras, and did not have vibration removal technology, so other factors overwhelm the issue of the granularity of silver halide crystals which is the limitation that lab experiments assess.