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The equivalent digital resolution of analog film, and at what resolution it should be scanned

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TL;DR: To make absolutely certain beyond any doubt that all the detail from a frame of motion picture film is captured by a digital scan, you need to scan color film at 11495 dpi and black-and-white film at 14369 dpi. Good luck finding a scanner that can do that properly.

I’ve seen so many arguments online about how much detail motion picture film does or does not contain in terms of digital resolution. Never mind all the other factors that go into the look of a piece of film, people only want to argue about megapixels. While the correct answer is going to vary by the exact type of stock used, the exact type of lens used, and the exact contents of the shot itself, I felt like it should surely be possible to calculate an upper limit, a best-case scenario, based on directly quantifiable factors. Yet I haven’t really seen anyone do that in any of the aforementioned discussions. They speak in vague language like “a 6K scan is enough for 35mm film”, without any deeper explanation for how or why.

Film is analog. It doesn’t have pixels. So what does it have? How do you express the smallest resolvable detail in a frame of film? You do so in “line pairs per millimeter” (picture the thinnest possible alternating white and black lines that can be captured by a camera while still being distinct instead of fuzzing into a grey mess). The lp/mm limit for motion picture film, which has a very hard limit to its exposure time (i.e., the 1/48th of a second between the frame before it getting out of the way and the frame after it butting in), seems to lie somewhere between 80 and 100 according to multiple sources written specifically for cinematographers. In particular, after investigating the tech specs of as many different movie film stocks as I could find, the highest lp/mm rating for color film was 80, while for black and white it was 100. By all accounts, those appear to be hard limits. [Please inform me if you find anything higher.]

HOWEVER, the probability of the average subject of a given shot being translated to the negative with that much detail given normal lighting, lenses, etc., then said detail being carried through an interpositive and the various stages of editing, is effectively nil. Reaching these hard limits in a final print would be almost impossible without specifically designing the shot as a boring test pattern, but the point is that it’s technically possible and thus serves as a usable ceiling for our calculations. With this kept in mind, let’s continue.

Alright, so with each of those “lines” (two to a pair) representing the smallest resolvable detail, we would naturally set them equal to a pixel on a given axis. So, the captured detail on film tops out at 160 pixels per millimeter for color and 200 pixels per millimeter for black and white. Since one inch is equal to exactly 25.4 millimeters, you can translate those figures into dots/pixels per inch for film scanner settings, ending up with 4064 dpi for color and 5080 dpi for black and white. So, just plug in the size of a given frame and you have your answer, right?

Well, not exactly. Converting continuous analog detail into discrete digital information isn’t a straightforward process, and doing a simple “one-to-one” conversion often results in aliasing of details. The Nyquist theorem states that capturing that continuous detail in a discrete form requires at least doubling its measured frequency (said frequency in this case being the lp/mm). So just double those dpi settings, then? Close, but not quite. In film, the vertical and horizontal detail are both continuous, as opposed to other analog sources like VHS or LaserDisc, which have discrete vertical detail but continuous horizontal detail. The two axes aren’t a pair of independent lines, they make up a plane. As such, the 45-degree diagonals become pseudo-axes in themselves, and that diagonal detail needs to be doubled as well to get rid of aliasing. Skipping the Pythagorean math, the result is that in order to successfully capture all detail in a continuous 2D plane, the frequency needs to be multiplied by a minimum of 2sqrt(2), or about 2.828. In terms of the dpi on a film scanner, that comes out to minimums of 11495 dpi for color film and 14369 dpi for black and white film before you can be sure that all resolvable detail on the film can be captured properly in a digital format, even though the detail you can actually see could theoretically be found in an image with 1/8th the total resolution.

So… yeah, anyone here have a scanner that goes up to 14500 dpi? No, of course you don’t, because I don’t think such a thing even exists in the industrial sector, much less the commercial side, and I shudder to think what one would cost if it did. But that’s the theoretical limit you’d have to reach in order to say that the film in question was truly “backed up”.

So what does that mean for individual film sizes? Having perused the SMPTE standards for the exact measurements of camera apertures and demarcations for usable film area, I’ve prepared a pair of tables defining in exact terms the “detail resolution” and “scan resolution” for that type of film. The entry format is as follows:

  • [Film size and type]: [resolution of entire exposed frame], scan at min [resolution needed to capture all detail]
  • –[Aspect ratio in readable form] AR [(exact aspect ratio)]: [resolution of picture to be projected], on min scan [resolution of projected picture on aforementioned scan of frame]

A few last notes about the table. In more familiar terms: 8mm Type R is regular 8mm. 8mm Type S is Super 8. 16mm Type W is Super 16. 35mm’s Type A aperture is normal nonanamorphic, Type B aperture is anamorphic, Type C aperture is Super 35, and Type D aperture is three-perf. 65mm 8/70 format is the rarely-seen MagnaVision. 65mm 15/70 is what everyone calls “IMAX”. Some film types and aspect ratios do not have specified projectable areas from the SMPTE, which is why you don’t see them listed. Also, the quotation marks around “2:1 PAR” are used because film has no pixels, but it’s analogous terminology in that any square subset of the final anamorphic picture would have half as much horizontal detail as it does vertical detail. Also also, some of these numbers are hypothetical: For example, I don’t think a MagnaVision project has ever used black and white film, and I don’t know if normal 8mm has ever used stock that was capable of up to 80 or 100 lp/mm. But such film could be custom made using the same material as other stock if you pay through the nose for it, so I included them.

Color

  • 8mm (Type R): 781x589, scan at min 2209x1666
  • –1.324:1 AR (437:330): 700x528, on min scan 1978x1494
  • 8mm (Type S): 927x663, scan at min 2621x1874
  • –1.324:1 AR (531:401): 850x642, on min scan 2404x1815
  • 16mm: 1642x1199, scan at min 4644x3390
  • –1.329:1 AR (190:143): 1545x1163, on min scan 4368x3288
  • 16mm (Type W): 1976x1188, scan at min 5589x3358
  • –1.662:1 AR (118:71): 1888x1136, on min scan 5341x3214
  • –1.85:1 AR (590:319): 1888x1021, on min scan 5341x2888
  • 35mm (Type A aperture): 3520x2560, scan at min 9957x7241
  • –1.371:1 AR (2096:1529): 3354x2447, on min scan 9486x6920
  • –1.661:1 AR (1048:631): 3354x2020, on min scan 9486x5712
  • –1.85:1 AR (2096:1133): 3354x1813, on min scan 9486x5128
  • 35mm (Type B aperture): 3520x2975 w/ “2:1 PAR”, scan at min 9957x8413 w/ 2:1 PAR
  • –2.391:1 AR (4192:1753): 3354x2805 w/ “2:1 PAR”, on min scan 9486x7934 w/ 2:1 PAR
  • 35mm (Type C aperture): 3988x2988, scan at min 11278x8450
  • 35mm (Type D aperture): 3988x2220, scan at min 11278x6277
  • 65mm: 8397x3682, scan at min 23750x10414
  • –2.197:1 AR (2428:1105): 7770x3536, on min scan 21976x10002
  • 65mm (8/70 format): 8421x6036, scan at min 23818x17071
  • –1.349:1 AR (607:450): 7770x5760, on min scan 21976x16292
  • 65mm (15/70 format): 11266x8258, scan at min 31864x23357
  • –1.433:1 AR (870:607): 11136x7770, on min scan 31498x21976

Black and White

  • 8mm (Type R): 976x736, scan at min 2761x2082
    –1.324:1 AR (437:330): 874x660, on min scan 2473x1867
  • 8mm (Type S): 1158x828, scan at min 3276x2342
  • –1.324:1 AR (531:401): 1062x802, on min scan 3004x2269
  • 16mm: 2052x1498, scan at min 5804x4237
  • –1.329:1 AR (190:143): 1931x1453, on min scan 5460x4110
  • 16mm (Type W): 2470x1484, scan at min 6987x4198
  • –1.662:1 AR (118:71): 2360x1420, on min scan 6676x4017
  • –1.85:1 AR (590:319): 2360x1276, on min scan 6676x3610
  • 35mm (Type A aperture): 4400x3200, scan at min 12446x9051
  • –1.371:1 AR (2096:1529): 4192x3058, on min scan 11857x8650
  • –1.661:1 AR (1048:631): 4192x2524, on min scan 11857x7139
  • –1.85:1 AR (2096:1133): 4192x2266, on min scan 11857x6410
  • 35mm (Type B aperture): 4400x3718 w/ “2:1 PAR”, scan at min 12446x10517 w/ 2:1 PAR
  • –2.391:1 AR (4192:1753): 4192x3506 w/ “2:1 PAR”, on min scan 11857x9917 w/ 2:1 PAR
  • 35mm (Type C aperture): 4984x3734, scan at min 14097x10562
  • 35mm (Type D aperture): 4984x2774, scan at min 14097x7847
  • 65mm: 10496x4602, scan at min 29688x13017
  • –2.197:1 AR (2428:1105): 9712x4420, on min scan 27470x12502
  • 65mm (8/70 format): 10526x7544, scan at min 29773x21338
  • –1.349:1 AR (607:450): 9712x7200, on min scan 27470x20365
  • 65mm (15/70 format): 14082x10322, scan at min 39830x29196
  • –1.433:1 AR (870:607): 13920x9712, on min scan 39372x27470