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Ben R
19-Apr-2007, 06:59
Hi,

I've carefully read the article on choosing the f-stop and I think I understand the Hansma technique even as far as it applies to movements.

On the other hand with a WA like a 90mm the hyperfocal distance will give a sharp picture from just over one meter to infinity.

So which is best for use when the depth of field provided by the hyperfocal distance is sufficient for the composition in question, i.e. anything where focus <1.3m is not important?

Alan Davenport
19-Apr-2007, 10:29
Hyperfocal focusing uses the worst-case to calculate where to focus, i.e., it takes the maximum allowable circle of confusion and and applies that to the limits of focus. If you use hyperfocal focusing, you will have the worst acceptable focus at infinity.

Hansma's system looks at what the photographer needs to have in sharp focus, and chooses an f/stop that will produce the smallest possible circle of confusion over that subject. If the range of subject distances is less than that encompassed by the worst case hyperfocal focusing, then Hansma's formula will always produce superior results.

Once you start using camera movements, the hyperfocal distance is no longer the trivial calculation that is the case with parallel systems. Hansma's system is correctly applied to a scene after the photographer has used movements to optimize the plane of focus, and is a heckuva lot simpler than calculating the hyperfocal distance for a tilted lens.

If the subject falls within the range from 1/2 of the hyperfocal distance out to infinity, then hyperfocal focusing should produce acceptable results. Properly applied, Hansma's will always produce the best possible result, something hyperfocal focusing can't claim.

Leonard Evens
19-Apr-2007, 12:57
The two approaches really deal with two different questions.

What I say below applies to relatively distant subjects. It is a bit more complicated for close-ups.

If you specify a specific f-stop you want to use, fo whatever reason, and you specify a maximal acceptable circle of confusion (which says how sharp you need the image to be), you can calculate a hyeprfocal distance. For example, suppose you chose f/45. For a coc of 0.1 mm, a possible choice for 4 x 5, the hyperfocal distance comes out to 1.8 mm. If you focus at that distance, in principle, everything from 0.9 meters to infinity will be adequately sharp according to that choice of sharpnesss inherent in putting the coc equal to 0.1. In a two times enlargement, viewed closely, (or a larger print viewed proportionately further away) you would in principle be getting 5 lp/mm throughout the DOF region. That is the minimum of what most people would accept.

But all that ignores diffraction. The general rule of thumb is that a diffraction limited lens will deliver 1500 divided by the f-number in lp/mm. 1500/45 ~ 33 lp/mm. Enlarging twice would reduce that to about 16 lp/mm. It can be tricky combining diffraction with defocus (the effect described previously), but the upshot is that you always get something less than the smaller of the two resolutions. So, the image would be degraded by diffraction throughout the nomial DOF region, but its effect would be significant primarily at the limits, 0.9 meters and infinity. so in effect the DOF region would be decreased somewhat in size because of diffraction.

What should you do to deal with this situation? The only plausible thing to consider is stopping down further. That will enlarge the DOF region and thereby yield higher resolution at 0.9 meters and infinity, but diffraction will also play a stronger role. For example a f/64, the diffraction limit would be 1500/64 ~ 23 lp/mm which would reduce to about 11 lp/mm on two times enlargement. It is tricky seeing if this, when combined with defocus, would actually yield an improvement over what you got at f/45.

Hansma's method is designed to answer this question, but it approaches the problem from the near-far point of view, in which you don't decide the f-stop beforehand. Let me first outline that.

You pick a near point and a far point, in this case 1 meter and infinity. You note the positions where these are on the rail and measure the distance in mm between them. That is called the focus spread. You can then choose a f-stop based on on the focus spread.

There are basically two ways to do that. One ignores diffraction and is based simply on a choice of coc. the method is to divide the focus spread by twice the coc. If you now focus halfway between the positions on the rail of the near point and far point, which in this case is at infinity, then you will be focused at the hyperfocal distance for that aperture.

Hansma's method tries to take into consideration diffraction. He uses a formula which supposedly gives you the best resolution you can expect at the limits of the DOF region when defocus and diffraction are both taken into consideration. In some cases, you might get much more resolution than you actually need. (You might be able to enlarge much more than twice and still have at least 5 lp/mm in close viewing.) In other cases, you may not even be able to attain your desired resolution. (For example, if you wanted 5 lp/mm in the final print and you stopped down to f/256, diffraction alone would limit you to about 3 lp/mm, everywhere in a 2 times enlargment.)

People should be aware, however, that Hansma's analysis makes certain pretty rough approximations. ( A really thorough and correct analysis would require using MTF functions and would be much more difficult.) So it should be taken as a guide rather than the last word on the subject.

Here is something one might do in practice. It works for 4 x 5. Find the near and far points and the focus spread between them. Focus halfway between them. (Or course, you may want to depart from that on the basis of what you see on the gg.) Then use the following rule to determine a lower limit for the possible aperture: mulitply the focus spread by 10 and divide the result by 2. Then check Hansma's table to see what he recommends for your focus spread. Finally choose an f-stop somewhere in between based on how slow a shutter speed you can tolerate.

Ben R
19-Apr-2007, 15:45
Thank you, that all made sense, more so than my interpretation of the article! Could you clear up something for me though, there was a table shown at the beginning of the article then several others that seemed to contradict it, could someone point me to a final table of fstop values relative to focusing movement using this method?

Jeff Conrad
19-Apr-2007, 17:52
It's possible to combine the hyperfocal and Hansma techniques.

Hansma's f-number is optimum only for the DoF limits. Once a lens approaches diffraction-limited performance, using any greater f-number will decrease sharpness in the plane of focus, so the optimum f-number at the DoF limits usually is less than optimum at the PoF. Sometimes this is a tradeoff, but uniform sharpness often is preferable to optimum sharpness in the PoF. Of course, as long as the blurring is imperceptible, the loss of sharpness in the PoF is inconsequential.

Exposure time increases with f-number, and in many circumstances motion blur can become a problem when using Hansma's f-number. Hansma recognized this, and suggested a region of acceptable f-numbers, with the minimum determined by the acceptable circle of confusion and the focus spread, and the maximum given by diffraction considerations. There usually is little point in using an f-number greater than Hansma's optimum, because any further increase in f-number actually results in less sharpness, even at the DoF limits.

I agree with Leonard that the Hansma/Peterson method for combining defocus and diffraction is somewhat empirical. I calculated MTFs for combined defocus and diffraction, described in http://www.largeformatphotography.info/articles/DoFinDepth.pdf (http://www.largeformatphotography.info/articles/DoFinDepth.pdf) (PDF), under Diffraction. Interestingly enough, I got maximum f-numbers very similar to Hansma's. It should be noted that although the MTF calculations are rigorous, the formulae for maximum f-number derive from curves fit to the MTF data, so my formulae are empirical rather than derivative of any fundamental principle. Nonetheless, the similarity of my numbers and Hansma's suggests that the approach is not unreasonable. Additional work by Bob Wheeler also supports this approach, though his numbers are slightly different.

Incidentally, the image-side relationships aren't changed by the use of movements, so it's still reasonably easy to use the hyperfocal method with tilts and swings.

Brian Ellis
19-Apr-2007, 22:45
"Could you clear up something for me though, there was a table shown at the beginning of the article then several others that seemed to contradict it, could someone point me to a final table of fstop values relative to focusing movement using this method?"

There's only one table of f stops in the article, that's Table I on p. 56. The other things are labelled "figures" and they're graphs or charts, not tables of f stops. The heading of each explains what each is designed to illustrate but Table I is the only one that you actually use in making photographs.

Jeff Conrad
20-Apr-2007, 18:13
If you wanted to combine Hansma's technique with the traditional method (which is what I assume you meant by "hyperfocal"), you could add a column for minimum f-number to Hansma's Table I. If you are working in 4x5 and use a CoC of 0.1 mm, the table would be something like


Focus Spread/f-Number Range
0.7: (3.5) ~ 16
1.3: 6.5 ~ 22
2.7: 13.5 ~ 32
5.4: 27 ~ 45
11: 55 ~ 64

(I can't figure out how to make a real table). You then could use an f-number anywhere between the minimum and maximum, as other considerations, such as shutter speed, might allow. An f-number less than the maximum would not be optimum at the DoF limits, but the sharpness would meet the criterion dictated by the CoC.

As Leonard mentioned, the values for closeup work would be slightly different. Your original post, however, implied that this isn't an issue.

Alan Davenport
21-Apr-2007, 13:22
Incidentally, the image-side relationships aren't changed by the use of movements, so it's still reasonably easy to use the hyperfocal method with tilts and swings.

Can you expand on that? Do you first focus at the hyperfocal distance, and then not adjust the focus when applying tilts and swings?

Michael Gudzinowicz
21-Apr-2007, 15:40
A number of people have commented on different focusing methods and effects of diffraction, defocus, etc. in the rec.photo newsgroups.

For the past 20+ years I've been using a simple calculator approach which for a given set of circumstances provides the f/stop required to set near/far distances at the edge of acceptable sharpness, to maximize sharpness at those distances, or to provide maximum depth of field. Those formulas have been transposed to a self-documented Excel spreadsheet which a few people use with a PDA. The link is: http://mysite.verizon.net/vzer3mgj/Depth of field & diffraction.xls

Jeff Conrad
22-Apr-2007, 00:29
Alan,

You set the movements and then focus.

When tilt or swing are employed, moving the standard rotates the plane of focus rather than moving it along the lens axis. However, the angular relationships ultimately reduce to the same simple image-side formulae used to determine focus and f-number without movements.

Hyperfocal focusing is just a special case in which the far limit of DoF extends to infinity. With tilt or swing, this is equivalent to the far PoF being inclined at close to 90 degrees to the lens axis, though in practice, I've seldom had to place it that far.

Measuring absolute image distances isn't always easy, especially with tilt or shift (see Leonard Evens's paper Some thoughts on View Camera calculations (http://math.northwestern.edu/~len/photos/pages/dof_essay.pdf) (PDF) for a good description of this), so I find it much easier to determine the far point of focus visually.

As Leonard mentioned, "hyperfocal" focusing often implies that the f-number is chosen first; the focus point and near limit of DoF are then fixed. If that's what is wanted, it's easy enough to rearrange the formula used for determining f-number and solve for focus spread instead:


dv = 2Nc

the standard is then set to


v = v_f + dv/2 = v_f + Nc

Where
dv is the focus spread
v is the final position of the standard (the image-side focus distance)
v_f is the visually-determined position of the standard at "infinity"
N is the f-number
c is the acceptable circle of confusion

For example, for 4x5 with a CoC of 0.1 mm and f/22, the focusing standard would be extended 2.2 mm beyond the position at infinity focus. The procedure would be the same with or without movements, though without movements, you could simply set v_f to the lens focal length if you had an infinity mark on the rail.