Comparing digital and film resolution using MTF (posted 2023-03-29)
I fell down a rabbit hole a while ago trying to come up with the definitive answer to the often-asked question "how can old movies be in HD/4K", which immediately leads to "how does film and digital resolution compare".
The answer to the first question is of course that film as a lot more resolution than standard definition TV, so just scanning the movies at a higher resolution will give you a sharper image than that old DVD or (shudder) VHS tape.
(Actually a good VHS tape on a good player (my last one (at some point I had three) definitely doesn't qualify anymore) can look pretty good as long as the ridiculously low chroma resolution doesn't create problems.)
Film: super high?
For reasons unknown, lots of people quote fairly ridiculous (to me) numbers, such as 20 megapixels for movies on 35 mm film. Between the advent of the 1.85:1 aspect ratio and that of Super35, a movie would effectively be shot at a ~ 22x12 frame size. That is not a lot of film to hold so much resolution.
Film: not so high?
This is where I planned to show damning evidence of film having much lower resolution than 20 megapixel digital using this photo, that I took both on film and digitally:
Nikon F65, Ilford Delta 100 film, camera-scanned with a Nikon Z fc and a 1:2 manual focus macro lens, resulting in a 12.5 megapixel image. Here resized to 3 megapixels, click here to see the original file.
This image certainly seems to make good use of those 12 megapixels. I later did a higher resolution scan of part of the image with a 1:1 reproduction ratio zoom lens, which does bring out a bit of extra detail, but only marginally so.
The problem with reasoning about film grain vs pixels or eyeballing images is that it's very imprecise. But we actually do have a tool that lets us compare digital vs film: the optical transfer function.
This takes the form of a graph that plots the contrast of line pairs against their frequency in line pairs per mm or cycles per mm. It's often called modulation transfer function (MTF), but it's different from the MTF graphs we often see for lenses. Also note "line pairs" vs "lines". In TV/video the number of horizontal lines has always been an important number, but what we care about here is line pairs. So if the P is missing, you never know what people are talking about.
I'll use MTF in the optical transfer function-like meaning.
The nice thing about the MTF is that it lets us compare completely different optical pipelines, such as completely analog film, analog film digitized at some point, and start-to-finish digital images.
Each step, such as lens, sensor and display / print has its own MTF and you simply multiply these. (Which means that a great lens on a mediocre sensor is still better than a mediocre lens on a mediocre sensor!)
Norman Koren has an overview Film MTFs vary of course, with 50% at 40 lp/mm being a reasonable guess for film that doesn't compromise sharpness. Obviously at ISO 3200 all bets are off. So I'm going to assume film with MTF50 at 40 lp/mm for the rest of this discussion.
Koren states MTF curves behave as a Lorentzian function, which means that we should be able to convert between MTF line pair / contrast values easily. Rounded slightly:
- MTF30 = 1.5 x MTF50
- MTF20 = 2 x MTF50
- MTF10 = 3 x MTF50
- MTF06 = 4 x MTF50
The MTF for 80 lp/mm is 20% contrast. This means that with a lens at MTF50 or MTF30 we'll reach the lower limits for film image detail at MTF10 or MTF06. Even if we're generous and go to 120 lp/mm, most 35 mm movie formats top out soon after 4K. And that's only when scanning the original camera negatives. Scanning later copies easily halves your resolution.
Digital (pixel) encoding and display, it looks like the contrast in the MTF stays well above 50% until you closely approach the Nyquist frequency = 2 pixels per line pair.
Use the slider to see what digital resolution you'd need to fully capture different film sizes at a given number of line pairs per mm:
|Type / aspect ratio||Size (mm)||Pixels wide||Megapixels|
|Academy 1930s||22.0 x 16.0|
|Second half 1900s||22.0 x 12.0|
|35 mm anamorphic||22.0 x 18.6|
|Super35 3-perf||24.9 x 13.9|
|Super35 2-perf||24.9 x  9.5|
|65/70 mm||48.5 x 22.1|
|IMAX 70 mm 15-perf||69.6 x 48.5|
|35 mm photos||36.0 x 24.0|
Conclusions: even 70 mm movies don't materially benefit from higher megapixel scans than about 30. For 35 mm photos, it's a struggle for film to hold up beyond12 MPX. (Which phone cameras have reached the better part of a decade ago.)
So it looks like 4k is a very good fit for 35 mm movies, except perhaps ones shot with high quality black and white film. 8k only possibly makes sense for 65/70 mm. But those tend to be old so I doubt there would be much of a difference in practice. And 8k is completely impractical because you need to sit very close to a very big screen to be able to see the extra sharpness anyway.