Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
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bobn2 Forum Pro • Posts: 41,450
Re: Diffraction Limit Discussion Continuation

Mike Davis wrote:

bobn2 wrote:


No-one is 'right' - so long as someone defines what they say, then they can say what they mean.


I do have an argument over the whole McHugh 'diffraction limit' definition. My arguments are:

i) I can't see anything that would sensibly be called a 'limit'.

ii) A 'limit' that occurs at different magnifications for different cameras doesn't seem much use.

iii) Even if it were well founded and clearly demonstrable, it obviously has not been well articulated, since very many people on reading McHugh's site and discussions arising from it come away with the impression that high MP cameras give worse results than low MP cameras at small apertures, due to this diffraction limit. It is a common confusion, caused in no small part by that site and people who promulgate this bogus 'diffraction limit' idea. For instance, but one example:


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I define the "limit" imposed by diffraction with an equation...

The f-Number at which diffraction begins to inhibit a desired print resolution expressed in lp/mm, at an anticipated enlargement factor, an be calculated as:

(Equation 1)

f-Number "limit" = 1 / desired print resolution / anticipated enlargement factor / 0.00135383


The greater the desired print resolution, the smaller the f-Number one must use to support an anticipated enlargement factor. (Consider the formula - the f-Number must go down when desired print resolution goes up). With all else being equal, the photographer who desires a final print resolution no higher than 2 lp/mm can use larger f-Numbers than a photographer who desires a final print resolution of 4 lp/mm - before diffraction will begin to inhibit their respective desired print resolutions at the same anticipated enlargement factor.

The greater the enlargement factor, the smaller the f-Number one must use to avoid inhibiting a desired print resolution. (Consider the formula - the f-Number must go down when enlargement factor goes up.) With two cameras having the same pixel count but different sensor dimensions, producing like-sized prints, the camera with the smaller sensor requires greater enlargement to achieve the final print dimensions, and thus, the f-Number used with the smaller sensor must be smaller, to make the Airy disk diameters at the sensor plane smaller, before the greater enlargement factor is applied to produce a like-sized print.

It's analogous to CoC diameters: Small sensors (or film formats), suffering greater enlargement factors to achieve a given print size, require smaller CoC diameters for DoF calculations, than do larger sensors (or film formats). Smaller sensors and film formats similarly require smaller Airy disk diameters (use of smaller f-Numbers) to withstand the greater enlargement factors required to achieve a given prints size.

The formula for calculating the maximum CoC diameter one should use for DoF calculations is:

(Equation 2)

CoC (mm) = viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25

Source: http://en.wikipedia.org/wiki/Circle_of_confusion

If we assume that your "desired final-image resolution (lp/mm)" has already incorporated your concerns for viewing distance, we can reduce the CoC calculation to this:

(Equation 3)

CoC (mm) = viewing distance (cm) / desired final-image resolution (lp/mm) / enlargement

Look familiar? (See Equation 1, above.)

Yes, enlargement factor and desired print resolution are the only variables affecting the selection of a CoC diameter for DoF calculations (assuming you have considered viewing distance when specifying your desired print resolution). And they are the only variables affecting the f-Number at which diffraction will begin to inhibit a desired resolution.

Comparing Equations 1 and 3, we can see they differ by just one divisor, the constant 0.0013533, and thus, as long as we are using Equations 2 or 3 for calculating the maximum permissible CoC diameter used for DoF calculations, we can reduce Equation 1 to this:

(Equation 4)

f-Number "limit" = CoC / 0.00135383

Which might beg the question: How is the constant derived? See David Jacobson's Lens Tutorialat http://photo.net/learn/optics/lensTutorial and search for "0.00135383".

With both CoC (defocus) and f-Number "limit" (diffraction) calculations relying on user-specification of a "desired print resolution," further reading is available here: http://www.dpreview.com/forums/post/40100820

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That seems eminently sensible. I note pixel size doesn't come into it.

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