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

  1. #1

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

    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..

  2. #2

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

    I know this is not the answer that you want. I have been using LF for 15 years, I stopped trying to use charts more than 10 years ago. No matter how sharp your pencil you can not take all of the variables into account, do the math and make a meaningful photograph. Even if you could figure it all out, accurate measurement is almost impossible in real world situations, at least accurate enough to justify these complicated formula. How many microns off does your film plane need to be to through everything out the window? I would suggest that you read this. I have never found the need to be any more accurate than this article suggests and it works!! Remember, the important thing is to make photos. Have fun!

  3. #3

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

    Bill:

    Read the new section the Q posted on the LF Homepage on "How to select the f-stop" in 8/00.

    This analysis, originally published by Peterson and Hansma in Phototechniques, explicitly includes both diffraction and DOF to obtain an "optimal" f-stop for a given COC. Clearly, one should not pick a COC that the film stock cannot make full use of!

    On the other hand, photography is not just math. One of the main reasons for shooting 8x10 in the first place is that film and diffraction effects can essentially be ignored. You can make a tack sharp 24x30 print with only 15 lp/mm on film! Any film can do that, and you can stop down to nearly f/128 before diffraction becomes an issue. At some point, the light output of the sun becomes the limiting factor!

    Diffraction is not the boogey-man waiting to destroy your images at some magic f-stop. It is a progressive deterioration that, along with all of the other factors that determine image quality, should be considered when selecting exposure settings. If DOF is the overriding factor to produce the image you want to create, select an f-stop that will give you that DOF!

    I dare say that far more disappointment has occurred at the light table due to lack of DOF than softness from diffraction.

  4. #4

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

    Jeff, I do appreciate your attitude in not getting overly tied up in math. I do realize there is a ton of variables. My goal in most photographic math is to just get in the ballpark. Anything more defined than that seems to be futile for all the reasons you mentioned. However, in this scenario, I am looking at two different formulas that are well respected that give answers that are 5x apart!!! Maybe they are even further apart, I made a conservative guess above to even determine this, I think they are closer to 10x apart. This is just too far off, and I want to know what is going wrong here. I did read Q's page, but it did not really get to the bottom of why these two very well accepted formulas conflict each other so bad! May of Q's math never introduced the lens and film potential. But it was an excellent piece...

    Glen... you wrote..

    This analysis, originally published by Peterson and Hansma in Phototechniques, explicitly includes both diffraction and DOF to obtain an "optimal" f-stop for a given COC. Clearly, one should not pick a COC that the film stock cannot make full use of!

    Yes, but I do not see how your last sentence ties in....since it's the lens and the film together that dictactes the system resolving power as per the Fuji formula. You can't just determine a lpmm from all the other variables - and then say, the film must be able to resolve at least this amount. Alhtough that would certainly be nice and would love to see that this is true.

    I understand that one can make a tack sharp print with 3x enlargement with only 15 lpmm to film. That was not my goal, as I stated in my example. As I see how the relationship between film and lens resolving power combine, I do see difraction as a boogey man who is seriously degrading the overall images. It gets worse as the format size goes up, so 8x10 gets hammered!

    Here is a simple example to prove my point. In 8x10 format it is very common to shoot at f45. Lets use f32 to be conservative... so that is 20 lpmm at the point of exact focus. So therefore the moving away from the point of exact focus this 20 lpmm degrades... so at the edges of DOF, assuming non excessive DOF, the lpmm would probably drop to 5 lpmm. So this chrome will allow for a 1x enlargement if your goal is a min. 5 lpmm on the print??

    I just happened to get an email from Chris Perez on this subject. Chris works so hard to help so many of us.... He seems to remember someone discovering the Fuji formula is wrong! He is reasearching this further. Has anyone else heard the formula Fuji posts in their Data Guide is wrong? It sure would be nice if this is true! It would certainly explain the inconsistencies here. Then one could just do as Glen suggested above, be sure your film is capable of acheiving the cc you are entering into your DOF calcs.! This would not be the first time I have seen a major company produce flawed formulas!

  5. #5

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

    I regularly use the maximum f-stop which my shutter allows. My 90/f8 has f64 for the maximum. I don't worry about it being soft due to diffraction at all. I worry about not getting the near/far in focus because of the distances involved. Forget diffraction limits. In LF the 4 or 6 times magnification is really too small to worry about it. James

  6. #6

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

    Bill:

    The Fuji formula is, at best, a worst case scenario. Actual resolutions are much higher than you are calculating. First, you need to use the high contrast resolution, not the low contrast number. I think Provia is over 100 lp/mm at that contrast. Just look at Chris'es test numbers. He gets over 60 lp/mm at f/22 all the time. I shoot lens tests on Velvia at f/22 and clearly get over 50 lp/mm, so even at f/45, you can get over 25 lp/mm, even on color transparency film.

    I can't see where you figure it gets worse with larger format. Essentially its a wash, since all the numbers are linear. Yes you need smaller f-stops, but you can tolerate proportionally lower lp/mm. What you gain is still small grain and better tonality, but not necessarily significantly better on print resolution.

    There are a number of careful analyses online, one I think at Photodo.com, that show that due to DOF and diffraction, essentially all formats are equal... except for film which favors larger formats.

  7. #7

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

    The Fuji formula is a crude reciprocal approximation based on multiplying MTF values of lens and film. Since resolution is NOT REALLY A QUANTITATIVE value, no equation that uses it can be "exact". Resolution is a perceived limit to MTF contrast at a given spatial frequency. Even the diffraction limits we toss around are just approximations using the Rayleigh criterion for resolution of point diffractors. It is not at all clear that that is "exactly" applicable either to arrays of dark and light lines, or worse, to real world spatial frequencies. But, it is a reasonable approximation. So assume Provia can resolve high contrast at about 100 lp/mm (not the 140 at super high contrast) and assume about 22 lp/mm at f/64. Even using the Fuji formula you still get about 18 lp/mm on film which will make a critically crisp 30x40 inch print. Anybody viewing larger prints at this distance is nuts anyway.

  8. #8
    Founder QT Luong's Avatar
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    Is the good ol fashion Hyperfocal distance formula accurate for LF? I think not!

    The optics that I outlined in the article previously mentioned give you the aerial definition r_lens. Applying the 1/R = 1/r_lens + 1/r_film formula would give the actual definition on film. While it seems that this latter would be more relevant, I ignored this point in the article because when r_lens becomes critical, the effect or r_film becomes quite neglectible. In theory, you'd have to convolute MTF's, and what you'd likely find is that the formula 1/R = 1/r_lens + 1/r_film wouldn't be a good approximation. In practice, several people, including Paul Hansma and Chris Perez have measured on-film resolutions pretty similar to aerial resolutions.

  9. #9

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

    Glen..you wrote.. I shoot lens tests on Velvia at f/22 and clearly get over 50 lp/mm, so even at f/45, you can get over 25 lp/mm, even on color transparency film.

    I think this supports what C Perez mentioned, that the Fuji formula is just plain wrong. Q seems to support this also in his response...assuming I understood him correctly.

    YOu mentioned..There are a number of careful analyses online, one I think at Photodo.com, that show that due to DOF and diffraction, essentially all formats are equal...

    I do agree with this, provided the Fuji system formula is false, and as I mentioned I now conclude that it is false... I too have gotten 70 lpmm to Velvia and a SSXL 150 at f22. Even though this was at the focus plane, not at the near and far DOF points. But even so, the Fuji formula says the best on film resolution under this scenario is 48 lpmm. I am convinced I got 70 lpmm. It took a 15x loupe till I saw black and white lines getting fuzzy where they adjoin. So this further supports the fact the Fuji formula must be incorrect!

    Q, you wrote...In practice, several people, including Paul Hansma and Chris Perez have measured on-film resolutions pretty similar to aerial resolutions.

    So what are you concluding in this statement? I don't want to speculate what your intent is...

    It seems that most of the test data supports chris Perez's information that the Fuji formula is not accurate! I wish someone would confirm this. I did speak to Fuji, and they stand by the formula, but I am sure somewhere inside Fuji there would be doubters! This field seems to be filled with bad information. And when it comes from such reliable sources as Fuji, it can really confuse people. Sure glad this forum exist...where else can we bounce these ideas off the best minds in photography!

  10. #10

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

    Bill, if I might add another comment: I've never seen anything definitive on the 1/R = 1/r1 + 1/r2? equation, other than something like "this formula is commonly used".

    In John Williams' book "Image Clarity?", he uses the resolution numbers squared, ie, 1/R^2 = 1/r1^2 + 1/r2^2?etc. I have heard (third hand?) of other powers between 1 and 2 being used; I think it is somewhat empirical.

    FWIW, I believe the book "Basic Photographic Materials and Processes" also uses the same formula for system resolution that you (and Fuji) have, so I wouldn't condemn it so quickly. I think (just guessing) that spread functions of the film (ie, characteristics of how a point of light blurs) might have something to do with the particular formula needed.

    Regarding your large discrepancy, "?and as you can see, these two answers are miles apart! (5x difference)", is this just based on your guess as to resolution at the DOF limits? If so, I would question how legitimate that guess is; res might not fall off near as badly as you might think.

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