This is a continuation of a report on new ways to look at depth of field. The series starts here:
Yesterday, we looked at the focus distance that made a minimal impact on the sharpness for objects at infinity, with minimal being defined as a reduction of MTF50 by 10% from the value when the lens is focused at infinity at the same aperture.
Those of you skilled in the art of conventional DOF calculations will recognize the above method as conceptually similar to the derivation of the hyperfocal distance. However, the numbers that I came up with in yesterday’s post are quite different than the ones that you’d find in the DOF card that came with your Leica M3 or Nikon F, and similarly different from what you’d get setting the hyperfocal distance using the DOF ticks on your lens barrel, which assume a circle of confusion (CoC) of about 30 micrometers (um).
That isn’t to say that MTF is MTF and CoC is CoC and never the twain shall meet. MTF50 and CoC are correlated, and with some simplifying assumptions, for any sensor there is a mapping from one to the other. You could get results similar to what I got yesterday by judiciously picking the CoC for each aperture; it would be exceedingly small by conventional DOF standards.
So what do we call the distances that I came up with yesterday. My proposal is the hyper-hyperfocal distances. The “hyperfocal” is a nod to the concept from the conventional DOF canon; the additional prefixing “hyper” is a reference to taking the concept farther than it’s gone before, and maybe a comment on the mentality of those who might use the freshly-minted concept in the future. For concision, I’ll abbreviate the term to HHFD.
I went back and reworked yesterday’s calculations extending the far object distances to increase accuracy. [Thanks to Jerry Fusselman for catching a normalization error that I’ve now fixed.] I’ll put the focal length in mm, and the distance in meters.:
- f/4 — 0.0595 * (focal length)^2
- f/5.6 — 0.0397 * (focal length)^2
- f/8 — 0.0264 * (focal length)^2
- f/11 — 0.0149 * (focal length)^2
- f/16 — 0.0083 * (focal length)^2
- f/22 — 0.0046 * (focal length)^2
For the 55 mm lens that I’ve been using, rounded numbers are:
- f/4 — 180 meters
- f/5.6 — 120 meters
- f/8 — 80 meters
- f/11 — 45 meters
- f/16 — 25 meters
- f/22 — 14 meters
Remember, these are for the Sony a7RII. There is currently no full frame camera with significantly higher resolution. If you have a camera of significantly lower resolution and/or and antialiasing (AA) filter, like an a7S or a7SII, the distances will be somewhat lower. When that great day dawns and we have 200 MP full frame cameras, the HHFDs will — gulp — be even longer.
Eyeballing those numbers, you might see a practical problem: how are you going to set those distances accurately on any lens but a manual focus tele? Well, that’s a problem. Let’s put it aside for now; I can think of at least one workaround.
Would setting lens to the HHFD instead of just saying the heck with it and setting it to infinity provide any useful foreground sharpness in a landscape where most of the subject was at infinity?
Let’s find out. Here are all the whole f-stops from f/4 through f/22, with a 55 mm lens focused at infinity and the HHFD:
If that’s confusing, don’t worry; I’m going to simplify things.
But before I do, Let’s look at the curves normalized to the infinity-focused MTF50 for each f-stop:
That’s rather pretty, at least to me, but it’s too complicated to work with. I’ll show you some subsets with only two f-stops per graph.
If we use the 0.9 line (almost 2000 cy/ph) as our cutoff for the f/4 curves (this is probably unrealistic, as that number is shockingly sharp and unlikely to be actually obtained with the usual field atmospheric conditions), the HHFD setting has given us highly acceptable sharpness at 100 meters instead of at 200 meters for infinity focusing.
Looking at the f/11 curves, we see that the infinity-focused lens resolution at 50 meters is about the same as the HHFD-focused lens at less than 25 meters.
At the f/5.6 curves, we see that the infinity-focused lens resolution at 140 meters is about the same as the HHFD-focused lens at 60 meters. For f/16, the near limit of this high standard of acceptability goes from 25 to 15 meters.
At f/8 and f/22, the pattern of the HHFD having acceptable sharpness at half the near cutoff distance for infinity focusing continues.
I can think of situations in which knowing the HHFD would be useful.