Pixels on Poster Prints

A few days ago, I got a copy of photos from my sister-in-law's wedding earlier this year. Among those, were a few shots that my mom had specifically requested the photographer for; she wanted a big print of a family portrait. I selected one which seemed the best of the lot and proceeded to make some edits (eliminating the ugly wall and door in the background, moving dad a little closer to the rest of us, adding a different background etc.); thanks GIMP!

Once I was happy with the end result, I showed it to mom, wife and sis (the main stakeholders in the final product) for their suggestions. I was about to order the print from Zno (One of my favourite sites for professional looking photo printing jobs) when I realised I hadn't checked if the resolution was high enough for a poster size print that is supposed to adorn the living room wall. I know, dumb mistake; this should have been one of the first things to check.

I'm used to about 20+ MP photos for big prints (I recently got a 16"x20" print from Shutterfly of a Tulip shot I clicked during a visit to Skagit Valley in April), so when I realised the copy I have is only about 11MP, I was dejected and felt all my effort go to waste. Several follow ups with the photographer revealed that he shoots all weddings on the same mid-resolution setting of his camera (No idea why, it's not the 90's anymore that you have to worry about storage costs). I still wanted to get that poster so I went in research mode to determine what is the biggest print I can get from the limited resolution digital shot I had. That brings us to the topic of this post.

Of course, the higher the resolution in an image, the bigger you can go. More pixels also give you more leeway in post processing, you can play around more with the image to bring your vision to life and you can get away, to some extent, with not so great shots. However, there are some important factors that come into picture (pun intended) when deciding what is the biggest print you can get given an image, or conversely, what is the minimum resoution you need to get the desired print size.

From my research, I realised that the most often overlooked piece of the equation is the viweing distance. The bigger the print, chances are, the further away it will be viewed from. A rule of thumb is 1.5 times the diagonal of the image e.g. if you print a 16"x20" poster, the diagonal will be approx. 25" and the recommended viewing distance will be approx. 38". This will become one of the factors in our calculation.

The second part of the equation is the viewing angle. The human eye cares about the angular size of the object in the field of view (trues for a single eye, with a pair, stereoscopic vision and depth comes into discussion, but that's not the topic here). Every object in the field of view has an angular size and there is a maximum resolution that the eye can perceive. If your pixel density is higher than this, your eye cannot sense individual pixels and the image appears as a smooth curve. This is what Apple famously calls Retina Display.

Based on what I came across, the eye can resolve upto 60 individual elements per degree In pixel terms, this means the eye can identify individual pixels if there are upto 60 in a degree. Any more than that, the human eye won't be able to tell one pixel from another. Rephrasing the same data, an individual pixel should not form an angle of view more than one arc minute or 1/60th of a degree at the viewing angle.

Since 1 arc minute curve is negligible, reasonable approximations will convert the problem of finding the real life size of a pixel to a simple trigonometric problem. Here is an exaggerated view of the problem, since at actual scale, the triangle will pretty much look like a straight line.

Here, V is the viewing distance we calculated earlier by a simple application of Pythagorean Theorm followed by the thumb rule, and P is the physical size of the pixel.

D = sqrt(L^2 + H^2)

V = 1.5*D

P = 2*V*tan(1/120)     [The angle here is in degrees]

For the 16"x20" example we had considered earlier, the size of the pixel computes to approx. 0.0112", or inverting it gives the resolution of approx. 90ppi (Pixels Per Inch). Extrapolating this to the entire image, it means your image should at least be 1440x1800 pixels. Anything smaller than that will give extremely poor results.

That, of course, is the bare minimum resolution you need to fool your eyes under ideal viewing conditions and at proper viewing distances. You wouldn't want to get your print appear pixelated the moment someone walks an inch towards the frame, so you should prefer at least double the resolution given by this formula, i.e. 180ppi for a 16"x20" print, or an image resolution of 2880x3600 pixels which is roughly a 10MP image. Anyhting bigger than that will not make a difference at typical viewing distances. It will improve quality al closer viewing distances, but could also add time and cost to your print. So weigh your options before settling on a print size.

The poster I wanted to print has the final edited image at 3894x2596 pixels and I want to print it at 24"x30". Using the same approach outlined above, for a good 24"x36" print, the viewing distance should be approx. 65" or  5'5" and a maximum pixel size of 0.0188". This translates to 53ppi, or 1272x1908 pixels. Doubling the density gets us 106ppi or 2543x3814 image. Since I have just a little more pixels than that, I should be able to get a decent print.

I used the same approach to calculate the minimum resolution needed for different standard poster sizes listed on Zno

Standard Poster Sizes and Required Image Resolution
Height (Inches)	Length (Inches)	Diagonal (Inches)	Viewing Distance (Inches)	Max Pixel Size (Inches)	Min Pixel Density (PPI)	Min Image Resolution	Recommended Pixel Density (PPI)	Recommended Image Resolution
8	10	12.81	19.21	0.0056	178.96	1432x1790	357.92	2863x3579
11	14	17.80	26.71	0.0078	128.72	1416x1802	257.44	2832x3604
10	24	26.00	39.00	0.0113	88.15	881x2116	176.29	1763x4231
12	12	16.97	25.46	0.0074	135.05	1621x1621	270.09	3241x3241
16	16	22.63	33.94	0.0099	101.29	1621x1621	202.57	3241x3241
16	20	25.61	38.42	0.0112	89.48	1432x1790	178.96	2863x3579
20	30	36.06	54.08	0.0157	63.56	1271x1907	127.13	2543x3814
24	36	43.27	64.90	0.0189	52.97	1271x1907	105.94	2543x3814

I hope this helps out people in a similar situation as myself. Comments and suggestions to make the post better and more useful are always welcome.