Fundamentals of Resolution

There's a lot of misconceptions about the idea of resolution...Let's start off by trying to not talk about resolution because it's such an ambiguous word. You might not think that it's a vague word, but it most certainly is.When talking about digital cameras and you talk about resolution you're talking about the sensor's resolution in terms of megapixels. Or if you're really technical it's the X by Y pixel count.Of course when you're talking analog, resolution is going to be measured in line-pairs per mm. It's the resolving power of the optical part of the system. The same measure works for things like lenses as well as film.Then you get to print, and you get other measures of "resolution:" DPI and PPI. Dots per inch and pixels per inch, respectively. Naturally, people confuse those too.Diving in even further you can have other related measures like pixel pitch...The problem is that all of these are correct, and in fact, they are all fundamentally related.Let's figure this all out from start to finish.Modern digital cameras have an incredibly fine pixel pitch. So my 24 megapixel Leica M10, for instance, has a 5952 x 3968-pixel sensor. The pixel pitch is right around 6-micron. (36mm / 5952, expressed in microns). Now, you need to take into account the Bayer filter in front of that for the real correct number, but that's for another day. 6µm is really, really small. The resolving power of that is easily in the 60-100 line-pairs/mm range taking into account demosaicing and whatnot. This is also very close to the resolving power of all but the best lenses as well (which is also expressed in lp/mm). This is also in the same ballpark as low-ISO, fine-grained films. Doing a deep-dive into film is out-of-scope for this, but will most certainly be another post.So, you took a picture and have a file.That file consists of pixels. It has no concept of DPI or anything at all like that. It is quite simply pixels. If you forced it to have a DPI it would have to be the pixel pitch of the sensor itself because the recording medium was the sensor.You can rescale it (note: I say "rescale" not "resample." These are very different things!) to something else, screen or print are the two common forms of output.If you assign the common 72-PPI screen resolution you'd have an image that's nearly 83-inches wide. Alternately, a 300-PPI print (which is excessive, but that's for later), it would be nearly 20-inches wide. The key here is that there is no more information in one than the other. It's quite simply a difference in scale. If you go into photoshop and set the DPI/PPI to 72 or 300 and save it, the files will be the same size, and contain exactly the same information. The only difference is how you, as the artist, is defining the output pixel pitch.Then, if you choose to print it, you'll have to contend with the dichotomy of DPI compared to PPI. The dots per inch is something that is typically controlled by the printer and is normally fixed with the hardware; the printer (assume ink jet for a moment) makes ink droplets of a certain physical size. Regardless of how big a pixel is, the printer's drop size is mostly fixed. The pixels will be stretched to cover whatever area they need to be, and the printer will cover the area of the pixel with as many dots as you need to make the print.In this entire workflow, thus far, we've neither created nor destroyed any information that didn't come from the sensor.Let's go back to the 83-inch-wide 72 PPI image. What would happen if you when into Photoshop (or whatever) and kept the image phyical size the same and simply made it 300 PPI? Photoshop would go in and interpolate the additional pixels and, effectively, manufacture extra pixels (this is the rescaling part I was mentioning earlier). If you were to save that file it would be a lot bigger than the original -- because you made new, mostly imaginary, pixels out of thin air.So, the upshot of all this is that a file that is 1000x1000, for instance, has a fixed information content regardless of the PPI that you're using to represent it. The PPI, when mapped to a physical output medium will be represented as (normally) the fixed DPI of the medium itself (including screens!).