Is the good ol fashion Hyperfocal distance formula accurate for LF? I think not!

[Bill Glickman]

Bill, thanks for the input... you may have just rekindled the Fuji formula... to answer your question about the 5x discrepancy, see item #5 in the original post, it clearly esplains who I derived at it.. the only estimating I did was how much less resolution is at the near and far points of DOF vs. the plane of sharp focus which is what the formula calculates at.

BTW, all those A's eith the rounded top hats in my original post are a result of cutting and pasting the text from Microsoft Word into this forum. I was not aware this happened until after I did it...sorry about that...

[Glenn Kroeger]

Bill: The Fuji formula isn't really wrong, it is just an approximation. The derivation depends on convolving the response of the film and optical system. The approximation is most valid when both the film and lens are being used at spatial frequencies with very low contrast, ie. near their resolution limits. Thus the formula is pretty good for 35mm work where lenses and films are operating near their limits. In LF work, we are usually interested in frequencies (lp/mm) where the film is not near its limit. This is particularly true with 8x10 where 20 lp/mm is way short of the films limits. This is where Q is correct, that you can essentially neglect the film, and consider only the lens limits. In this situation, the Fuji formula is a poor approximation. As to whether the frequencies need to be squared or not, it depends on assumptions about the shape of the response curves of film and lens, but again, in the case of 8x10 it is a poor approximation in either case.

[Bill Glickman]

Glen, this is very well stated and more clear than before. Maybe the Fuji formula is a good fit for 35mm only, all other formats stay clear of it!

It seems the best approach is to use the standard DOf formulas, but be sure to select a desired cc which is less than what the film is capable of recording at a given contrast level. Then one should be safe.

BTW, I do like the article, View camera focussing by Hansma referenced on Q's page. It offers a simple approach to DOF...I will have to test it out...

[Sean Billy Bob Boy yates]

I am not one to get into all the theory here, but the number of posts caught my eye. Wasn't there a website that demonstrated a format comparison with unaltered scans of Velvia in 3 formats at varying apertures? I can't recall where I found the link. Could've been a year ago.

Anyone know/remember what I'm talking about? Granted viewing results on the net is NOT what one would call a final arbiter but it was interesting, nonetheless.

[Glenn Kroeger]

Bill: Even in 6x9 cm, color film is being used near its limit for enlargements >16x20. Most color emulsions really don't have much contrast above 50 lp/mm. From my experience, the film's MTF (or resolution) stops being a significant factor in 4x5 and larger formats.

[Struan Gray]

In applications like photogrammetry and machine vision where you really do need to know the resolution of your system, lens manufacturers often supply a graph which shows how the MTF at some high spatial frequency dies away as you move from the point of best focus. It almost always forms a peak which is narrower than the spread between the usual depth of focus points. Edmund Scientific sell a suitable target if you want to estimate this at home.

Diffraction is one cause, as explained by Bob Atkins here:

http://bobatkins.com/photography/technical/dofdiff.html

Another cause is residual aberrations. The usual derivation of the DOF draws a diagram in which two rays from the outer edge of the lens' aperture (ok, exit pupil) cross at the focal plane. Aberrations turn this into a spray of lines with an outer envelope of sharpness which looks a bit like those 70's string and nail pictures. This can not only shift the point of best focus (the waist of the ray bundle isn't necessarily the classical focus point) but can also change how the light spot looks and spreads as you move away from the focal plane.

This can be, and is, handled mathematically with the use of optical transfer functions (a slightly more involved version of the MTF), and the blur on the resulting image treated like a convolution of errors. Quantifying the amount of blur at each individual stage and using a formula to find the total is conceptually simpler but because the blur from lenses and film follows non-gaussian statistics, the familiar root-mean-square combination is incorrect (though it'll usually get yu in the ballpark). Empirical and theoretical considerations of how film and lenses blur a point source leads to the 1/Rtot = 1/Rlens + 1/Rfilm formula. For more about this, try the following thread at Deja news, particularly Michael Gudzinowicz's contributions:

http://x72.deja.com/[ST_rn=ps]/viewthread.xp?AN=665426227

So it *can* be done, but in practical photographic use it usually turns out that the common trick of conservatively using the front and back hyperfocal distances for the next f-number more than covers the errors.

[Bill Glickman]

Struan you wrote... So it *can* be done, but in practical photographic use it usually turns out that the common trick of conservatively using the front and back hyperfocal distances for the next f-number more than covers the errors.

What exactly does this mean? What is the front and back hyperfocal distances?

[Struan Gray]

"What exactly does this mean?"

I'm not sure myself - probably that I'd drunk too much Sk?nerost coffee before writing :-)

In smaller formats, where the lenses are usually mounted in a focussing helicoid and kind manufacturers put DOF markings on the barrel, it's quite common for people to use the markings for, say, f11 when photographing at f8. Other common tricks (in all formats) are to focus beyond the true hyperfocal distance to ensure that infinity is sharper than just 'acceptably blurred', and to stop down a bit more than a formal calculation suggests.

All of these things essentially hide the excess errors introduced by diffraction and finite film resolution, especially for large format film printed at normal sizes, where both effects are much less of a worry than accurate focussing and placement of your depth of field.

[Bill Glickman]

Thank you all for your contributions.... rethinking this, I have done more research.... I now beleive there is much more credence to 1/R formula...here is a Mamiya 7 lens tested by Chris Perez. His results track 1/R perfectly...

I hope this post correctly..

Editor: if you want to make sure that the line breaks are preserved (such as in tabular data like below), enclose the section which you don't want reformated between the tags [pre] and [/pre]

[pre] to film lens 1/R vs. actual f stop lpmm Difr Estimate 1/R % difference

4 76 375 180 95 20% 5.6 95 268 180 95 0% 8 95 188 180 95 0% 11 85 136 136 81 -5% 16 67 94 94 64 -5% [/pre]

As you can see above, 1/R tracks Chris's findings perfectly! This assumes about 200 lpmm for the Tmax film used. (I backtracked into this value) At f4 it makes sense that the lens is not shooting at its best, so therefore it is slightly off vs. 1/R, the rest are right on the money.

This is just one example, however, I now do beleive that in more than 95% of the tests I looked at, 1/R is the max. the system can resolve. So Glen, when you suggest just pick a cc that the film can resolve, I would now suggest it makes much better sense to pick a cc that 1/R is capable of resolving. When a film like Provia F is displaced by the above, and LF f stops are used, the figures change to this...

[pre] f stop diff film max. 1/R

16 94 60 36 22 68 60 32 32 47 60 27 45 33 60 21 64 23 60 16 [/pre]

I now beleive that shooting at f32 and hoping for 47 lpmm to film would not be practical - the best I will be able to resolve is 27 lpmm to film. This is off by almost 100%, this is why I now suggest using 1/R as the ceiling, not the films resolving power.

This 1/R would have been almost perfect after applying it to all C Perez's tests, however there was a few super lenses, like SSXL 110mm, and Fuji A series in which they defied the 1/R a bit. But since these represented less than 5% of the lenses tested I think the 95% is more compelling evidence that 1/R is the max that can be resolved to film.

Does anyone see any holes in this theory? I am starting to think the lack of providing 1/R as a ceiling for cc selection in DOF calc. has been long fooling people into beleiving they are getting more enlargement potential than actualy exist! Also this effect shortens the DOF...whereas had one chosen the ceiling value of 1/R, it would have provided much greater DOF in the shot. LF shooters beg for more DOF, that is why I see this as such great importance.

[QT Luong]

The "hole in this theory" was already pointed out to by Glenn and myself. What your first table (experimental) indicates, is that the 1/r_final = 1/r_lens + 1/r_film works well for *high frequencies and small f-numbers*. Glenn and myself don't disagree on that. However, what we were saying about low frequencies, implies that your second table (calculated) might not be that accurate.

Also, a "super lens" cannot do better than the diffraction limit.