Diffraction Limits of Lenses and Scanning

[Jim Jones]

Drew brings up valuable practical points in posts #5 & #10. Just the tolerance in film holders make using typical lenses on press cameras wide open a gamble. Lens tests suggest f/22 as a sweet aperture for many 4x5 lenses, but at that aperture diffraction is terribly conspicuous in fine grain 35mm negatives of detailed subjects. The f.64 group were justified in using that aperture for much of their photography. Harold Merklinger and others have written much more on the subject than we can cover here.

[BetterSense]

It's amusing to observe that as we choose larger sized film/sensors for better image quality and less dependence on scanner/enlarger quality, we have to increase focal length, which causes depth of field to decline.

What's really happening as format increases is speed is decreasing, because you are exposing more film. It takes 4 times as many photons to expose a composition on 8x10 than it does 4x5. Photographers often respond to this fact by using larger absolute apertures on the larger format i.e. the same f-number to achieve the same exposure time; that reduces depth of field, but it's because the absolute aperture was opened up. Photographers think longer lenses reduce depth of field because they express aperture casually as a function of focal length without thinking it through. Its nearly circular thinking.

Lens tests suggest f/22 as a sweet aperture for many 4x5 lenses, but at that aperture diffraction is terribly conspicuous in fine grain 35mm negatives of detailed subjects.

That's because f22 on 35mm is not the same as f22 on large format. Fstop is the wrong figure to use for comparing different formats here unless you intend to enlarge the 35mm the same 1-4x enlargement as LF and still view it from the same distance, which nobody does.

You can easily see that absolute aperture is what matters here. With normal- ish lenses, a 10mm aperture may be f/10 on 35mm, f/20 on 4x5, and f/40 on 8x10. Those are not-coincidentally the optimum fstops for each respective format. That's because it is the aperture diameter that matters. Below 10mm diffraction starts to become significant, regardless of what film you put behind it. And of course good results are obtained with apertures down to 5mm and below for non critical work (f/20, f/40, f/80 respectively).

[Ken Lee]

as format increases is speed is decreasing, because you are exposing more film. It takes 4 times as many photons to expose a composition on 8x10 than it does 4x5. Photographers often respond to this fact by using larger absolute apertures on the larger format i.e. the same f-number to achieve the same exposure time;

A 300mm lens at f/10 gives the same amount of light as a 150mm lens at f/10, whether we use it on 4x5 film or 8x10 film. If we had to compensate for focal length, f/stops (and shutter speeds) would not be the convenient and interchangeable measures that they are, no ?

With larger film we choose longer lenses to get equivalent angle of view. At the same distance from the subject, a 300mm lens gives the same angle of view on 8x10 as a 150mm lens on 4x5. However, the 300mm lens gives 1/2 the depth of field, at the same aperture, as the 150mm lens. To get the same depth of field, the 300mm lens needs to be stopped down by 2 more f/stops. A 600mm lens will require 4 more stops, etc.

You can easily see that absolute aperture is what matters here.

Not according to the article quoted in post # 1 (emphasis mine). Is the author confused ?

"Strictly speaking, diffraction is a function of aperture size or the physical size of the hole and that is how it would be defined in a physics textbook. Which means that the larger area aperture in a 300mm lens at f/16 (as compared to a 50mm lens at f/16) should provide lower diffraction. However, diffraction patterns are angular patterns and as such are dependent on how far from the aperture you place the screen used to view it also. In photography, the aperture is at the optical center of the lens and the screen is (for infinity focus) one focal length away. The physical size of the diffraction blur is then the focal length divided by the apparent size of the aperture i.e., the definition of the f stop. Thus, in photography, diffraction is only a function of f stop and not a function of the focal length. In simpler terms, the larger aperture of the 300mm lens does offer lesser diffraction at the diaphragm (i.e., less bending around the diaphragm) but since the light now has a longer distance to travel (as compared to the 50mm lens), the smaller bending still results in a fair bit of blur at the viewing screen. - N Dhananjay"

[BetterSense]

Thus, in photography, diffraction is only a function of f stop and not a function of the focal length

This is 100% correct, when diffraction is expressed in terms of resolution at the film plane, which, perhaps because of lithographic influence, is how it's done for some reason. However, we have seen that is a very awkward measure for pictorial photography because it does not match the photographic use-case. Film-plane resolution must be corrected to account for final magnification differences, and when you do that, the focal length drops back out of the equations. Photographs are routinely enlarged to comfortable sizes, and when they are enlarged to different sizes, they are routinely presented so as to be viewed from different distances depending on the size. So the much better comparison is not lp/mm at the "film plane", but system angular resolution, or if you must avoid angles, "print resolution when final magnification is taken into account"...what other figure of merit than print sharpness? Formulated this way, you will find that it's only absolute aperture that matters both for DOF and diffraction concerns, for any format from minox to ULF. Yes, you can formulate either in terms of f-stop, but to fairly compare different formats you must normalise by magnification which amounts to dividing all the figures by the focal length and then multiplying them all by the focal length again.

To use absolute but artificial nunbers, the quoted passage is saying e.g. that if you use a 3mm aperture on 35mm it may be f/11 and diffraction-limit you to 50lp/mm at the film. Using that same (absolute) aperture on a 10x bigger format (for a much larger fstop) would be f/110 and limit you to 5lp/mm at the film. But after you contact print the larger format, enlarge the 35mm film 10x to match the large format print, and compare them as photographic prints, the print resolutions will be identical, a confirmation of the fact that only the absolute aperture matters when formulated in terms of relative print resolution which is what matters in pictorial photography. You can also do like Ziess and think about it in terms of the image diagonal.

[mdarnton]

In doing art copying and slide duping years ago, and now camera scanning, I have been struck by how much supposedly-good lenses vary in both sharpness and contrast, and how their actual optimum apertures can be all over the place. I really think that if this kind of stuff bothers you, theory can take one only so far, and testing gives the only good answer. In the duping cases above, both times, 40 years apart, I ended up with unlikely lenses doing the jobs the best, perhaps because of the various lenses I had in my hand at the time. In the first case, even though the ungodly-expensive motorized bells-and-whistles Bencher copy setup I was using came with a Componon as stock, I ended up putting that camera aside and using my own OM-1 and 50/3.5 Oly Macro lens. Currently, a 63/2.8N El-Nikkor is doing neg scanning duty at f11 (which previously I had found to be too small with other lenses), having beat out every other option I have, and I'm really blown away by that one.

[ic-racer]

According to this article ...

And according to physical properties of electromagnetic radiation.

1) If we encounter lens tests made at f/22 which report resolution higher than that number, should we be suspicious ?

Lines per millimeters and line-pairs per millimeter can be confused. Also, Modulation Transfer Function is more of an industry standard then lines per millimeter.

[Emmanuel BIGLER]

Coming late to this discussion and since Ken's original question is "diffraction and scanning" it should be added that the original table implies that the f-number is the effective f-number = N(1+M) where N is the engraved f-number as usual, and M the magnification ratio.
Scanner lenses probably do not operate in the infinity-focus position.

Imagine that you use a lens in infinity-focus position, stopped down to f/11 as engraved, when focusing down to the 1:1 magnification ratio, the effective f-number becomes 11x(1+1) = 22, hence the diffraction-limited resolution limit is twice as big with respect to the infinity-focus position, if the aperture ring is unchanged.

See the attached pdf file with official MTF charts for the 240 mm apo-ronar.
The MTF curve at 1:1 ratio for N=22 is plotted above the MTF curve at 1:20 for N=22 and it is obvious if you look at the 20 cy/mm MTF curve that the apo ronar is better at 1:20 than at 1:1, a kind of a paradox for a lens optimized for 1:1 use
The reason is simply that the effective number for N=22 "engraved", is N_eff = 22x(1+1/20) = 23.1 at 1:20 and N_eff = 22 x 2 = 44 (actually = 45) at 1:1.

The MTF charts for the 240 mm apo ronar also show us that the curves are very flat up to 360 mm of image circle at 1/1 and only half this value, 180 mm at 1:20.
On one hand, the minimum detectable optical period at constant N is doubled when changing from infinity-focus to 1:1, because N_eff is doubled; but on the other hand, the image circle is doubled, in consequence the total number of resolved points remains constant !!


2) To effectively scan that (hypothetical) image, would we need a scanner capable of twice that resolution ?

Yes, but in order to avoid to be confused with various factors like 1.2 (in the formula of Rayleigh's criterion for the diffraction limit) or any fudge factor around 1.2 taking into account the minimal acceptable contrast, plus the factor 2x for the number of samples required per one optical / analog period, I prefer to express the diffraction limit in terms of the absolute analogue cut-off period in a diffraction-limited optical image

cut-off period = N_eff λ
cut-off frequency = 1/(N_eff λ) in cycles per mm or mm^-1

where N_eff = N(1+M) as explained above;
λ = wavelength of light

now we can take a safety margin of 80% for the cut-off frequency of 1.2 for the cut-off period in order to maintain a minimum contrast, and with the 1.2 factor we get Rayleigh's resolution criterion = 1.2 N λ

The sampling theorem simply states that you need two samples per analogue period.
imagine that you have a diffraction-limited image behind an optical system with N_eff = 11, the cut-off period for, say, red light λ=0.65 micron is 11x0.65 = 7.2 microns - cut-off frequency = 140 cycles/mm, in principle you should use a sampling rate at 280 cy/mm i.e. about 7100 samples per inch ...

[Drew Wiley]

For film duping work I got addicted to Apo Nikkor 4-element graphics lenses. The only thing better that I'm aware of are the Apo El Nikkors at absurdly higher pricing. A few seconds with a high-quality grain magnifier tells me way more than reading every chart out there.

[Peter De Smidt]

Drew, what about the Printing Nikkors? They're reputably even better.

[onnect17]

Coming late to this discussion and since Ken's original question is "diffraction and scanning" it should be added that the original table implies that the f-number is the effective f-number = N(1+M) where N is the engraved f-number as usual, and M the magnification ratio.
Scanner lenses probably do not operate in the infinity-focus position.

Imagine that you use a lens in infinity-focus position, stopped down to f/11 as engraved, when focusing down to the 1:1 magnification ratio, the effective f-number becomes 11x(1+1) = 22, hence the diffraction-limited resolution limit is twice as big with respect to the infinity-focus position, if the aperture ring is unchanged.

See the attached pdf file with official MTF charts for the 240 mm apo-ronar.
The MTF curve at 1:1 ratio for N=22 is plotted above the MTF curve at 1:20 for N=22 and it is obvious if you look at the 20 cy/mm MTF curve that the apo ronar is better at 1:20 than at 1:1, a kind of a paradox for a lens optimized for 1:1 use
The reason is simply that the effective number for N=22 "engraved", is N_eff = 22x(1+1/20) = 23.1 at 1:20 and N_eff = 22 x 2 = 44 (actually = 45) at 1:1.

The MTF charts for the 240 mm apo ronar also show us that the curves are very flat up to 360 mm of image circle at 1/1 and only half this value, 180 mm at 1:20.
On one hand, the minimum detectable optical period at constant N is doubled when changing from infinity-focus to 1:1, because N_eff is doubled; but on the other hand, the image circle is doubled, in consequence the total number of resolved points remains constant !!


2) To effectively scan that (hypothetical) image, would we need a scanner capable of twice that resolution ?

Yes, but in order to avoid to be confused with various factors like 1.2 (in the formula of Rayleigh's criterion for the diffraction limit) or any fudge factor around 1.2 taking into account the minimal acceptable contrast, plus the factor 2x for the number of samples required per one optical / analog period, I prefer to express the diffraction limit in terms of the absolute analogue cut-off period in a diffraction-limited optical image

cut-off period = N_eff λ
cut-off frequency = 1/(N_eff λ) in cycles per mm or mm^-1

where N_eff = N(1+M) as explained above;
λ = wavelength of light

now we can take a safety margin of 80% for the cut-off frequency of 1.2 for the cut-off period in order to maintain a minimum contrast, and with the 1.2 factor we get Rayleigh's resolution criterion = 1.2 N λ

The sampling theorem simply states that you need two samples per analogue period.
imagine that you have a diffraction-limited image behind an optical system with N_eff = 11, the cut-off period for, say, red light λ=0.65 micron is 11x0.65 = 7.2 microns - cut-off frequency = 140 cycles/mm, in principle you should use a sampling rate at 280 cy/mm i.e. about 7100 samples per inch ...

Allow me a couple of comments.

The Rayleigh's criterion for the diffraction limit applies only to monochrome wavelenghts. Once you compress the spectrum (Apo-chormatic) then the perceived diffraction limits are pushed back a little.

"The sampling theorem simply states that you need two samples per analogue period."
This is a necessary but not sufficient. A "cleaner" rate is at least 4 times.