### Diffraction

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Is the loss of sharpness associated with diffraction an absolute function of the ratio of focal length as related to aperture much the same as is depth of field, or are there other elements associated with this phenomena? if one anticipates shooting at smaller apertures and has a choice of lenses, one faster than the other but otherwise similar, will the slower lens be better at an aperture that might be the minimum setting on the fast lens but in in its mid range? I have always preferred faster lenses for their relative ease of focusing given their brighter image and shallow depth of field in the viewfinder, but am wondering if I should rethink this before making further purchases.

Regards,

DAB.

-- Douglas A. Benson (dab@evcom.net), October 15, 2001

### Answers

Diffraction is purely a function of numerical aperture. That is; a 75mm lens at f/45 will display exactly the same point spread due to diffraction as a 300mm lens at f/45. Depth of field, on the other hand is a function of the physical size of the aperture, and a 75 mm lens at f/16 will have four times the D-o-f of a 300mm lens at that aperture.
Neither diffraction nor depth-of-field are affected by the maximum aperture of a lens.

-- Pete Andrews (p.l.andrews@bham.ac.uk), October 15, 2001.

I'm sure Pete has the math to back his statement up, but it would make sense to me that the physical size of the aperture has something to do with the diffraction effect. Since the circumference - the portion of the aperture that is diffracting light - varies as the diameter, while the area - the undiffracted light that is also exposing the film - varies as the radius squared, it would seem that the smaller the hole, the greater the proportion of diffracted light that is created the image. There use to be a "rule of 4" that said it would be best not to go below the focal length divided by 4 as regards the aperture. Anyone remember that?

-- Chauncey Walden (CLWalden@worldnet.att.net), October 15, 2001.

Sorry! The depth of field goes as the inverse square of the focal length, as well as the physical aperture.
So a 75mm lens will have 16 times the d-o-f of a 300mm lens at the same numerical aperture, not 4 times.

-- Pete Andrews (p.l.andrews@bham.ac.uk), October 15, 2001.

What you say is quite correct Chauncey. The length of the diffracting edge, (the diameter of the aperture) relative to its area, determines the degree of diffraction in absolute terms.
However, diffraction can be thought of as a deviation of light from a normal straight line path, and the longer the path length after passing the edge, the more the light is deviated.
A longer focal length of lens means that light has to travel further after passing through the aperture before it comes to a focus. Therefore, for a given physical hole size, a long focal length lens shows a greater diffraction effect than a short one.
Fortunately, we work in f numbers, which are given by the focal length of the lens divided by the physical diameter of its aperture.
The two effects; of larger hole size, and longer path length; exactly cancel out, and the nett effect is that diffraction is proportional only to the aperture number.

A rough formula for determining the radius of the 'airy disc' (the diffraction blur circle-of-confusion) is .0007 times the f number, in millimetres.

-- Pete Andrews (p.l.andrews@bham.ac.uk), October 15, 2001.

As indicated above, in photography, diffraction is purely a function of f number. Diffraction is related to the physical size of the aperture (and would be defined that way in physics textbooks). However, diffraction are angular apread functions. So a 300mm lens at f/16 may have a larger physical aperture than a 75 mm lens at f/16. However, the distance between the nodal point of the lens and the screen will be longer for the 300mm lens, which gives the diffraction from the larger physical aperture of the 300mm lens a longer travel distance over which the angular spread function can spread. WHn you do macro work, it is very obvious that diifraction is a function of the effective f stop and not the marked f stop. Which sort of proves that it is a combination of the f stop plus the linear distance over which light can spread that contributes to diffraction (which is the definition of the f stop in normal photography).

Strictly speaking, diffraction is also a function of wavelength of light etc. Diffraction patterns looks like concentric rings. The Airy disk referred to above is the central, brightest ring (which is an order of magnitude brighter than the outer rings).

Basically, as you stop down the lens, the central undiffracted AREA (pi*r squared) of the lens reduces much more rapidly than the peripheral, diffracted PERIMETER (2*pi*r). In other words, while the diffracted perimeter formed a negligible part of the image forming light when the lens was wide open, it contributes a significant part of the image forming light when the lens is stopped down. Which is why it is recommended that stopping down be contained to the bare minimum that will accomodate DOF requirements.

Cheers, DJ

-- N Dhananjay (ndhanu@umich.edu), October 15, 2001.

A little light is wished on my ignorance: We know how diffraction affects the sharpness by spreading the light on the shutter edges. But how do you explain that lenses have optimal sharpness at apertures that are not always the same from lens to lens, sometimes even within the same model? (I guess this is a lens positioning issue related to the ammount of light the shutter lets through, and is not directly related to diffraction. Some lenses are optimized at f16 and others are at f32. Would this not be the point when choosing a LF lens that is meant to produce maximum DOF as well as sharpness? For example, a long lens should be built to produce optimal sharpness at f45, and a wide angle at f16-22 (4x5). I would be curious as to how an Apo TeleXenar 400 f5,6 compares to a Fujinon C 450/12 for example. Coming back to diffraction, is there any difference in the way the different shutter sizes behave in this regard (any difference in blades thickness)? Would a Nikkor M450 in Copal 3 be more or less affected than a Fujinon C 450 in Copal 1 ?

-- Paul Schilliger (pschilliger@smile.ch), October 15, 2001.

Diffraction is only one aberration that contributes to lack of sharpness. And this gets worse with increasing stopping down. In contrast, other aberrations tend to be improved by stopping down. In practise, what this means is that most lenses have a sweet spot where other abberations have been reduced but degradation due to diffraction has not yet increased intolerably. So stopping down further does not reduce the other aberrations but increases degradation due to diffraction. This is the idea of a diffraction limited lens i.e., the other aberrations have been corrected to a sufficient degree that the only thing that contributes to image degradation is diffraction, as one stops down further and further.Where this sweet spot is for any lens depends on the design and construction of the lens - in other words, based upon how bad the other aberrations are. Some lenses may need to be stopped down considerably to bring the other aberrations down, while other lenses may be sufficiently well corrected that stopping down a couple of stops will be sufficient. Within a lens line, problems with centering and quality control can provide some variance in the corrections.

I'm not sure I understand what you mean by long lenses should hit optimum at smaller stops. In an ideal world, all lenses would be diffraction limited wide open. Then stopping down is only a function of DOF requirements i.e., when DOF does not dictate, one can operate at wider apertures and still get pictures limited only by the diffraction at that f stop.

I haven't seen any data pertaining to differences as a function of different shutters, due to thickness of the blades etc. I doubt there is much variance there.

Cheers, DJ

-- N Dhananjay (ndhanu@umich.edu), October 15, 2001.

With respect to the shape and thickness of the aperture (not shutter) and it's effect on diffraction: Certainly with pinhole, thinner material and more perfectly round will make improvements in the image quality (f/128 and beyond). The "starburst" pattern on specular highlights is caused by the shape of the aperture blades. This is not an issue with perfectly round aperture plates/pinholes. (maybe those old waterhouse stops were'nt such a bad idea after all.) To what amount this degrades "diffraction limited" resolution I can't say but the effect is easily observed in photographs.

-- Gary Frost (gary.frost@onemain.com), October 15, 2001.

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