I know this forum has a lot of photographic math wizards, someone should be able to answer this one. I will lay out my question in a logical sequence so it?s easy for you to troubleshoot my thinking?.

1. The Hyperfocal distance formula requires the user to know the lens fl, desire d max. size circle of confusion (cc) and the f stop.

2. The formula will calculate the near (half the hyperfocal distance) and far (i nfinity) in which all parts of film will have a circle of confusion (cc) no larg er than the cc entered in the formula. This assumes that the lens is focused at the hyperfocal distance.

3. Here comes the first part of my question? the formula tells you that all cc o n the film will be no larger than the cc entered in the formula. However, I tru ly doubt this, and will explain why below?.there is more information required to determine the cc size that will end up on film. Lens fl, f stop and desired cc is simply not enough information, specially for LF ?and what?s worse, it deceiv es us into believing the outcome will produce certain results, but in reality it won?t? Here is why I feel this way?. Below is a real world example?.

4. Lets say we are shooting 8x10 format, we use a 360 fl lens, f32 and a desired max. size cc of .02mm (which will accommodate a desired 10x enlargement, or .2m m to print which equals 1/.2 = 5 lpmm to print, (which is the final objective he re). Ok, so the Hyperfocal distance is 664 ft. So we focus at this distance, and have everything from 332 ft to infinity covering the entire gg. So in theor y we should get our ENTIRE final print at 5 lpmm after 10x enlargement, right? No way?here is why, and this is where my real question comes in?where does diffr action and the ?systems resolving power? (film + lens) come into play?

5. At f32, the max. a lens can resolve is diffraction limited at 1500/32 = 46 l pmm. Using the formula in the Fuji handbook of a ?systems resolving power? 1/R = 1/r1 + 1/r2?. Where R = the system resolving power and r1, r2 is the system co mponents, in our case here, r1= lens and r2 = film. So using this formula, and using Provia F film in real world contrast situations (not high contrast lens te st targets) the Fuji film data for Provia F says we will resolve about 55 lpmm. So therefore, using the ?system resolving power? formula, the best case scenari o, which is at the point of exact focus, we should get 25 lpmm to film at the po int of exact focus ONLY. (using 46 lpmm lens and 55 lpmm film). Now as you mov e further from the point of exact focus, 332 ft, the resolution would obviously get worse? so 25 lpmm will be ONLY at the point of exact focus and everything el se in the scene would be much worse, say down to 10 lpmm? (this is just a guess for arguments sake) So if our desired goal was having everything in the print at 5 lpmm, we can only achieve a 2x enlargement, not the desired 10x enlargemen t that the Hyperfocal or DOF formula lead us to believe. This is a real world s cenario, and as you can see, these two answers are miles apart! (5x difference) Yet both seem correct in their own right? I think the problem is a deficiency in the Hyperfocal distance formula. I imagine this time tested formula would w ork well in 35mm world with super high resolving lenses and shooting at f stops f5.6 and below, but it falls way short of the mark for LF!

6. So it seems that just arbitrarily putting a desired cc in the DOF or Hyperfoc al formulas totally ignores, the lens, the film and diffraction. It leaves us w ith answers that are totally misleading as I have shown above. So, is there a f ormula that takes all these variables into account and comes up with the real la rgest cc (worst resolving area) that will end up on film? Even if the formula i s complex, with today?s spreadsheets and programmable calculators, everything is reduced to entering the few changing variables each time.

7. It seems logical to have such a formula because the 1) diffraction limits, 2) the film lpmm and 3) the lens resolving powers can be estimated close enough to get to the PROPER answer. I will not even approach when one shoots at f stops which are not diffraction limited, because it seems from C Perez LF lens tests t hat all modern LF lenses, and most older ones, are always shot at diffraction li mited f stops. (he mentions this in his test summary) Using the Fuji formula a nd estimating the B&W film C Perez used with high contrast targets resolved abou t 180 - 200 lpmm, the backtracking of the math seemed to justify the lenses whic h were shot at f11, 16 and 22 were always producing diffraction limited values. And unless one shoots wider than f11, diffraction is always limiting the LF len ses true capabilities. If you want to backtrack the math, I used the SSXL 110 a s an example at f11= 80 lpmm, f16 = 67 lpmm and f22 = 60 lpmm. The goal is not to make the backtracking perfect, but just to get it close, will prove the poin t?there is many issues that can effect the resolving power outside of this? cons istency of film, camera shake, exposure, etc. Furthermore, considering that LF lens MTF curves show they are optimized to be shot at f16 and higher, LF users are ALWAYS confronted with this scenario! Of course if one used high resolving B&W film the diffraction limiting f stop may move upwards by a one or two stops vs. poor resolving color films. But for arguments sake lets stick to this examp le so we are all comparing the same thing.

Sorry for being so lengthy, but I felt this issue was of importance to all of us who shoot LF since every shot is a battle with DOF and desired cc, and it seems to me, we are quite often confusing ourselves with these formulas that have bee n around forever! Any input would be helpful? Thank you all in advance..

## Bookmarks