Interesting article on optimum f-stop

[dh003i]

Great article on selecting the optimum f-stop

How to Select the Sharpest Aperture, Considering Depth-of-Field and Diffraction from Ken Rockwell.

[Jeff Conrad]

I dunno ... Although he claims to have solved the problem in 1990, I never heard anything about it until Paul Hansma's article in the March/April 1996 issue of Photo Techniques (available on the LF web site). I'm also puzzled why anyone would bother with a computer program when it's a ten-minute exercise to arrive at the "optimum" from differential calculus, as Hansma did.

I'm not sure there's much theoretical basis for a root-square combination of the defocus blur spot and the blur from diffraction (used by Hansma and presumably by Rockwell), even though this approach has been around for quite some time (H. Lou Gibson of Kodak employed it in the 1970s); perhaps others here could give more authoritative comment. Bob Wheeler has complained that Hansma used the wrong treatment for the diffraction blur spot, giving it undue weight, so his criticism, if correct would apply to Rockwell's result. This issue is discussed in greater detail in QT Luong's article How to select the f-stop on the LF home page.

I looked at this same issue in a paper Depth of Field in Depth, also on the LF home page. I used a more theoretically rigorous calculation of combined defocus and diffraction, using methodology developed in the 1950s by H.H. Hopkins (who did the heavy lifting). My formulas for optimum f-number (I called it "maximum") were empirical fits to the results of the MTF calculations, so they don't have any solid theoretical basis, but they do provide a simple means for calculating the best f-number. Because DoF isn't meaningfully calculated to 6 significant figures, the equations are probably sufficiently accurate. Interestingly, they support the values of Hasma (and Rockwell) more than the values of Wheeler. So perhaps Rockwell's values are OK.

I'm always a bit skeptical when someone presents something not documented elsewhere without explaining how it was obtained, as Rockwell does for tables of the best f-number for hand-camera lenses. I suspect his approach was similar to my Eq. (122), but I cannot be sure. I don't know for sure that Hansma or I got it right, but we did show enough of how we got there for someone reasonably competent to see if there was a major error.

Regardless of who's right or who got there first, there's enough similarity in the results to suggest that they aren't completely off the wall. Significantly, they somewhat refute the concept of a "critical viewing" circle of confusion that's significantly smaller than the standard value for a format. Although the idea sounds good at first glance, one quickly arrives at f-numbers that actually result in less sharpness, even at the DoF limits, and that's assuming motion blur from the longer exposure time would not be a problem. And that the f-number could even physically be set.

Hasma discussed the tradeoff between optimum sharpness and the risk of motion blur (at least for all but completely static subjects), and suggested that a photographer could choose an f-number between that dictated by a traditional CoC and his optimum value. Wheeler and I reached essentially the same conclusion.

So in one sense, what most of us have been doing for years isn't really all that bad.

[aphexafx]

Given that fact that smaller apertures head into a softer definition due to diffraction, does anyone utilize this artifact as an effect? I am dealing with tabletop work mainly so there is no time limitation because of movement, etc.

For instance, if I have a shot that I shoot sharply at say f/16 - can I underexpose the primary (sharp) exposure by some calculated amount, and then trim my aperture down beyond the optimum opening and hit the same film with supplementary diffracted exposures (via strobing, say) to add a softening effect on top of the sharp primary exposure?

It seems to me that this would be similar to the effect obtained in Photoshop where a sharp image is cloned into a new layer, blurred, and then slightly averaged back into the primary layer via the opacity setting. It would be cool to be able to apply this effect in camera.

Is the amount of diffraction at f/64 or f/128 on a LF lens hitting 4x5 too fine to make any difference or would this be applicable? My reasoning is that, going the other way by opening up the aperture for the subsequent hits would only decrease the DOF for the focus extremes and not affect the focus plane, whereas diffraction should affect the entire image, is this correct???

Does anyone do this for controlled studio work?

I think that the answer will be no, because while the diffraction at even f/128 will be enough to affect image sharpness, it probably will not be broad enough to cause this effect when added to a sharp exposure...or would it?

[cjbroadbent]

Given that fact that smaller apertures head into a softer definition due to diffraction, does anyone utilize this artifact as an effect? .....

I have always shot 1/3 or 2/3 below smallest aperture. Nobody complained, because a bit less micro contrast and smoother tones added atmosphere to the LF transparencies. Sometimes an 8x10 can look harsh without some lens diffraction (or a black stocking). Anyway I am always desperately short of DOF .

[Bill_1856]

You're two months early -- this is FEBURARY first.

[cjbroadbent]

You're two months early -- this is FEBURARY first.

You who?

[Alan Davenport]

I always thought that, in the academic world, credit goes to the first to publish, not the guy who comes in later and says, "Well I thought of it first, I just didn't write it down until now."

[aphexafx]

As usual I rambled on about something I could have asked in one sentence:

Do studio photographers ever specifically use aperture diffraction to soften exposures? Yes.

Thanks, Christopher!

[cjbroadbent]

Example of a dirty old sironar 240 on 8x10 stopped all the way down. All the empty space is for headline and copy (i'm an illustrator).

[Dan Fromm]

Oh, come on, Christopher, the brush strokes show.