A couple of reasons I think diffraction has more of an effect than it first seems it should:
1. Light enters the lens at more angles than just perpendicular to the diaphragm. Entering at an angle, your 1mm hole becomes a smaller slit -- the farther from perpendicular the angle, the smaller the slit becomes.
2. Light travels as a wave, which means light heading near the edge of the 1mm hole will be affected, not just the light headed directly at the edge.
www.craigwphoto.com
Craig;
Interesting! I was thinking along the same lines and was wondering how a very thin waterhouse stop would work. This would minimize light entering from off axis from passing through a slit. I just checked my Melles Griot catalogue and they list precision pinholes up to 1 mm hole dia. Most are drilled in 13 micron stainless which is .0005 inch. The finest pinhole is 1 micron drilled in a .0025 mm disc. Many times thinner than a lens diaphragm. Worth further research at the very least. I will post any worthwhile findings at a later date.
Thanks
Richard
Emmanuel- I'm running across lots of images of Airy discs, so I'm presuming they're a well-documented phenomenon, and they seems pretty fundamental to understanding the mechanics and effects of diffraction. Is there still some debate about there existance or importance?
Non, Mark not at all, we all believe in Airy disks, but the concept is simply outdated in terms of modern photographic optics.
To support this, let me quickly go through some historical notes.
One of the first approach proposed to link the limitation of image quality to diffraction effects was Lord Rayleigh's. www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Rayleigh.html
The problem addressed by the famous physicist was related to the resolving power of prism or grating spectroscopes, but the problem of image resolution is similar, slightly more complex since being two-dimensional. Diffraction limits the width of the image of the entrance slit of any spectroscope to a minimum size diffraction image actually defining the limits of resolving power of the instrument.
The famous physicist proposed to define the limit of resolution for the spectroscope by comparing the distance centre-to-centre (He was British ;-) between two diffraction images ; the so-called Rayleigh's criterion states that the minimum distance between the two diffraction spots cannot be smaller than the full width at half maxium of a single spot. This can be applied to the resolving power of a telescope when you want to separate the images of double stars.
There is another Rayleigh's criterion for the quality assessment of telescope mirrors, this is another story, actually related to what we are considering here but more complex involving aberration theory and their influence on image quality.
In such a problem of diffraction-limited resolving power, either the image of a double star or the image of a fine spectroscope slit, what you actually see is the diffraction image of a single spot or a single line and not the image of an extended object.
Hence the sucess of the Airy disk, image delivered by any diffraction-limited optics for a point-size object like a distant star.. at least when the telescope is located in space, otherwise it might be limite by atmospherric turbulence !
But actually few of us take routinely images from stars, or image of point-source objects. We usually prefer ordinary scenes with extended objects any kind ;-), so the question is the assessment of image quality degraded by aberrations and diffraction is still unclear.
In the forties, electrical engineers developed the theory of electrical signal or image degradation due to the transmission through electrical instruments, say amplifiers. Some time later specialists in optics applied those so-called Fourier concepts to optical systems. In this approach it is considered equivalent to look at the output for a single point input signal, or to consider some filtering effects in the spectrum of the signal.
For optics this approach eventually yielded the MTF approach, and instead of considering an Airy disk, you can consider the spatial frequency filtering function corresponding to the Airy disk. It is a bit more complex in terms of maths (Fourier analysis), but more fruitful, since you can actually synthetise the blurred image when you know the original image and the filtering function, and even more, you can do the reverse, when you know the filtering function, under certain conditions, you can retrieve the un-blurred image.
Unfortunately nobody can retrieve completely an image blurred by diffraction, namely you cannot retrieve details smaller than about the size of the Airy disk. In terms of spatial filtering, every period of the object smaller than N x lambda where N is the effective f-number is definitely lost.
So there is actually no controversy about the Airy disk, simply models have greatly improved since the pioneer work by Lord Rayleigh. But Lord Rayleigh was such a giant in science, that many physicists were paralyzed, unable argue againts His Sacred Criterion.
Now modern computer software are able to compute the MTF of any lens design including diffraction effects with some reasonable assumptions of the wavelengths used. You can do it at home for free with demo-software like Oslo®-edu (limited to 10 surfaces).
You can simulate with a high degree of precision the effect of mixed defocusing and diffraction for the optics. You can choose to represent the image spot of a point source, or you can choose to represent the MTF. My understanding is that for photographic lenses, MTF charts are preferred to the image of a single spot, since it is known that some range of spatial frequencies are most important for a good image quality, e.g. 10, 20 and 40 lp/mm in medium format (see Zeiss charts) or most probably 5, 10 and 20 lp/mm for LF images.
So long life to the Airy disk, no offense against Him, but MTF simulations are mode modern and more efficient !!
Best with some curves. Temporary link valid for 21 days.
I have plotted the theoretical curves for an ideal diffraction-limited lens. Consider the values as realistic at the centre of a top-class lens used at its best f-number or stopped down beyond.
As a comparison I have plotted the theoretical MTF for a pure ideal, geometrical defocus without diffraction fo two circles of confusion, 100 microns and 200 microns.
The diffraction MTF curves have all the same hape and stop at the cut-off frequency of 1/(N*lambda) here I have taken lambda = 0.7 micron, a realistic values fitted to the published manufacturers MTF cruves (e.g. apo-componons at the centre at the best aperture). On the diagram the cut-off frequency is clearly shown.
In order to get a reasonable non-zero contrsta it makes sens to limit the usable part of the curve to 0.8 times the cut-off frequency, eventually we find the same criterion as Rayleigh's but re-visited in terms of a minimum readable period, .8/(N lambda) = 1.2 N lambda.
Defocus MTF curves have the same similar shape and exhibit a first zero at a frequency of 1.2/c where "c" is the coc diameter.
In fact in all photographic situations our MTF is somewhere between the diffraction MTF and the defocus MFT. So we do not want too stop-down too much, since the defocused MTF curves can be considered as our absolute minimum. For me the rule of thumb in large format is that I am always allowed to stop down 1 stop beyond the best recommended f-stop, 2 stops beyond being the maximum. For example in 4x5", N=16 or 22 is often the recommended f-stop, so 32-45 are the absolute limit. In 8x10" those values are approximately shifted by 2 f-stops.
It can also be seen that depth-of-field models in the sense of pure geometrical blur are definitely questionable for example at f/64 in 8x10" where a coc of 200 microns is considered acceptable !!
The other conclusion, is that the Airy disc does not tell us much, whereas the comparison of those MTF curves shows us how the image is degraded and how much contrast we can reasonable expect at 5, 10 20 and 40 lp/mm, the important photographic values.
Well the temporary link is here :
cjoint.com/data/bgswWJ1NYB.htm
Thanks, Emmanuel! This is far more information than is practical for my photography, but I do enjoy learning it, and while it may not always directly influence my shooting decisions, it gives me a better appreciation of the history and physics I'm taking advantage of. I think a fair number of others here are enjoying this too...
(Ansel Adam's story of shooting "Moonrise" would have been soooo much more impressive if, after telling how he calculated the exposure, he had gone on to say something like, "I then calculated the desired CoC resolution of 100 micons by recalling that the Optical Transfer Function can be determined by multiplying the Modulation Transfer Function by the Phase Transfer Function, then quickly plotting graphs of diffraction limitations in the dust on my car hood...")
A very informative post! Note that the results are the same as those in
Jacobson's lens tutorial, except that Jacobson used c = 0.03 mm and N =
f/22 for 35 mm format. Maybe there really is some truth to this stuff ;-)
Although the results indicate that one cannot improve DoF by stopping down
forever, they do seem to suggest that, when you're outdoors, in most cases
the wind will get you before diffraction does. I think, in essence, that
Wheeler reached the same conclusion, though he didn't quite state it in
those terms. This would seem the sort of general conclusion that one,
whether technical or not, could take into the field.
So why are process lenses like my Apo Ronar made to stop down to f/256? Considering they were made for high-resolution copying of a flat subject, it seems the manufacturers went to some trouble to include a feature that wouldn't be used.
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