Diffraction Limits of Lenses and Scanning

[Ken Lee]

According to this article on the LF Forum How to Select the F/stop, diffraction limits resolution as follows:



The chart states that if we take a photo at f/22 with a (hypothetically) perfect lens and film, we can get up to 68 lp/mm (just over 1700 line pairs per inch), but no higher. The article points out that these numbers apply irrespective of focal length.

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

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

Thank you !

[Jim Jones]

The information in the above chart agrees fairly well with much research and many lens tests. It is dependent on several factors such as the wavelength of light used in testing and the ability of the person making the test. Sometimes resolution tests do indicate higher resolution than charts, formulae, and experience suggest. For example, this can be due to spurious lines in images of lens test charts. MTF tests eliminate some human error. We should also consider that the optical resolution of a lens alone may be greater than that of the lens and film combined.

I would prefer a scanner with more than twice the hypothetical resolution when scanning resolution tests. However, in the somewhat mystical world of diffraction limited optics, strange things happen. For example, even some experts have proclaimed that a pinhole camera cannot resolve line pairs smaller than the pinhole diameter. I've repeatedly proven this wrong in tests.

[Taija71A]

Quick Answer:

'In general'... Yes and Yes.
--
Of course, in LF 'Real World' image capture...
One is not going to come 'close' to putting these types of Resolution Numbers on Film and/or Paper
(For numerous different reasons).

Regards, -Tim.

[BetterSense]

The chart is "correct" but as pointed out above, exceptions exist. In particular, in the semiconductor industry we even resolve lines smaller than the wavelength of the light, but use special techniques and huge apertures to do it.

The fact that the chart applies irrespective of focal length is correct but subtle since photographs are routinely enlarged. When normalized for enlargement differences and applying a practical definition of resolution e.g. defined as a fraction of the print diagonal or similar metric, then the result is that if you use a lens of twice the focal length, you only need half the resolution at the film plane. Resolution in lp/mm at the film plane is a good metric for certain things like printing chips or technical photography but may be a confusing metric when comparing camera formats. For pictorial photography resolution should really be formulated in terms of total-system solid angular resolution but I have never seen that done. The closest thing is Zeiss's sharpness criterion of 1/1760 of the final print diameter, which works for all formats. It is typically used for depth of field but is equally valid way to think about resolution and MTF for pictorial photography. When thinking this way you will find the aperture diameter d is the more useful parameter than _camera_ fstop, because the aperture diameter together with the final print+viewer system form basically a "total system numeric aperture". In practice manufacturers quote metrics in terms if the camera system only i.e. in lp/mm on the film. This ignores the total system and end use of the images, but is simple and unambiguous.

[Drew Wiley]

Gosh. Does anyone ever think about this stuff taking a picture? I hope not. Maybe purchasing a lens. Movements complicate it all anyway. I stop down based on
the nature of the subject matter itself - the composition - in relation to my actual experience with a particular lens, the realistic LENGTH of exposure I have in mind, and what I need to do in terms of handling the degree of film plane flatness, which is a far more important variable than nitpicking MTF data. I am perfectly
aware of the point at which diffraction becomes apparent; but this is related to degree of magnification in the print.

[Nodda Duma]

Since this is a technical discussion and not an artistic one..

For anyone wondering how those numbers were derived.

The sampling frequencies listed at the indicated f/#'s correspond to 7.5% contrast (modulation) for a diffraction-limited optic. That's between the two accepted minimum perceivable contrast metrics of 5% and 10% -- depending on the application.

For a square wave input -- ie bar target -- it's a little higher. About 10%. Square-wave mtf values (contrast transfer) always run higher than sinusoidal target MTF (modulation), which is why some testing can indicate better-than-thought-possible performance...rather than human error (except using an incorrect target image to measure MTF).

The best way to measure the MTF of a lens is on an MTF test station such as is available from Optikos. They are pricey, though. When you have access to one, you can easily get spoiled.


By the way: lp/mm (line pairs per millimeter) implies a bar target and contrast transfer function. cyc/mm (cycles per millimeter) implies a sinusoidal target and modulation transfer function (MTF). They are not interchangeable units. Analogous to talking about pixels for film or grains for digital imagers.

[jp]

Ken tends to use smooth lenses rather than hypothetically perfect lenses....

The weak link is the scanner. The Epsons like many of use don't seem to go up linearly in quality as the resolution increases. I think 3200dpi on the scanner is not twice as good as half the DPI.

[Nodda Duma]

Well smooth lenses won't be anywhere near those numbers, and in that case it makes much more sense to talk -- from an optical design point of view -- in terms of ray fans, Seidel aberrations, and spot sizes. Which doesn't help this particular topic, but is much better at describing what the images from a soft lens will look like.

[Ken Lee]

I have some soft lenses and some sharp lenses and appreciate both styles. When both sharpness and softness combine in one image, the results can be very gratifying, since each magnifies the effect of the other.

I ask about optics because it's good to both appreciate and understand, according to our capacity. As with sharpness and softness, the two can often enhance one another. Photography requires a grasp of both technology and aesthetics.

I long wondered why LF lens tests (often performed at f/22) seem to peak at around that limit. Now I know why.

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. As we stop down further to recover depth of field, we lose information due to diffraction (be it square or sinusoidal). I'm fishing around to find the sweet-spot.

[Drew Wiley]

Likewise, I wonder about all the fuss when the bottleneck is often a so-so film plane, or even film that isn't particularly flat in the holder in the first place. Optical
bench testing is one thing, real cameras and holders often, alas, quite another.