Diffraction and MTF

We often hear the question posed, "For such-and-such a situation, how large an f-number can we use before diffraction has a significant degrading effect on system resolution?"

Of course that question has no simple answer, in part because there is no obvious meaning to "a significant effect on system resolution."

And in fact, we cannot even tell from any "measurements" of a system what its resolution is.

We might try and make that matter (arbitrarily) definitive by saying, for example, we will consider the resolution of the system to be the spatial frequency at which the MTF drops to 50%.

Now, what effect on the overall MTF would the diffraction from the use of a certain f-number have to have before we would consider the diffraction to have "significant effect"?

I will not propose any answer for that, as it would not likely be of any real use in "shot planning".

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Of course the phenomenon of diffraction can itself be characterized in terms of an MTF. Suppose that we said, "an interesting metric of the diffraction caused by the use of some f-number is the spatial frequency where the MTF of the diffraction phenomenon itself is 50%.".

It can be shown that that spatial frequency is:

where n is the f-number.

Thus, for an aperture of f/11, the value of the MTF reflecting the phenomenon of diffraction alone will be 50% at a spatial frequency of about 67 cy/mm.

Will that be "intrusive"? Well, suppose that the spatial frequency at which the MTF of the lens and sensor (not considering any diffraction) is 50% is about 60 cy/mm (about true for the Canon EOS 6D with a "pretty good" lens aboard).

Then we might intuitively imagine that the effect of diffraction at f/11 would be "intrusive".

Best regards,

Doug

Doug,

You use the word, "intrusion". Intrusion has the sense of unwanted entry into some defined space. Is this the right metaphor?

May I propose we talk, instead of "loss of expected resolution". If then, (assuming we're talking about the same loss of "quality" effects, it's will be dependent on 3 factors: f stop, sensel size and format, (4/3, APS-C, "Full Frame 35nm" or MF). Small pixels and large real estate makes quality more resistant to loss of quality found on aperture reduction. So we get short-changed as we defy the diffraction-limiting barriers and go to progressively smaller apertures.

So, for example, the Canon 6D with 6.55 micro square sensels, suffers a loss of effective expected resolution. At f11, one cannot get effectively more than 12 MP sensor, no matter what else one does!

If one needs that 20MP at f 11, a 20 MP MF camera with those size sensels will deliver all that quality with applomb! So I commend everyone to use Bart van Der Wolf's look up table for DOF and experiment with scenarios and your available cameras.

Asher

Doug Kerr said:

Then we might intuitively imagine that the effect of diffraction at f/11 would be "intrusive".

Click to expand...

In actual photographic practice, f/11 shows no "intrusive" effect on DSLRs. On very detailed subjects, one will note a slight lowering of contrast, sometimes as early as f/8 with DSLRs with very tiny sensels, but f/11 stays perfectly usable.

The experiment is easy to design: just take a series of pictures of a detailed subject at various apertures.

Hi, Asher,

Asher Kelman said:

Doug,

You use the word, "intrusion". Intrusion has the sense of unwanted entry into some defined space. Is this the right metaphor?

Click to expand...

I like it. Note that my intent is to describe where the effect of diffraction has a significant subjective impact of degradation.

May I propose we talk, instead of "loss of expected resolution".

Click to expand...

Fair enough. Would you care to recommend a definition of "resolution"? Perhaps where the overall system MTF drops to 0.50? Or do you have something more subjective in mind? Or do you denominate it in (mega)pixels?

I assume that by "expected resolution" you mean essentially the resolution obtained with an aperture for which the effect of diffraction is inconsequential. But of course for most lenses, diffraction aside, the attainable resolution varies with aperture (typically becoming "worse" at larger apertures. So perhaps what is meant is the best resolution available over the available range of apertures - at the "aperture sweet spot".

I know. "Kerr, why do you make this so complicated?"

Best regards,

Doug

I refer to Jerome's helpful impressions, LOL. I'm not creating a defendable definition!

Asher

Hi, Asher,

Asher Kelman said:

I refer to Jerome's helpful impressions, LOL.

Click to expand...

Myself. [You see, even though I have escaped from Texas, I can still speak the language.]

Best regards,

Doug

Hi, Asher,

Asher Kelman said:

Small pixels and large real estate makes quality more resistant to loss of quality found on aperture reduction.

Click to expand...

Why does a larger format (for a given sensel pitch) make the process more resistant to the loss of resolution from diffraction at some f-number? I don't understand the mechanism here.

Is it because we have higher resolution (relative to image size) to begin with and thus a certain fraction of decline in the resolution is less "bothersome"?

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Oh, I get it.

By going to a larger format size, we do not diminish the decline in resolution (at that format size) from the use of a certain f-number. Rather we increase the potential ("expected") resolution so that, after a certain decline due to the use of a small aperture, we still have "plenty".

Fair enough.

Best regards,

Doug

Hi, Jerome,

Jerome Marot said:

In actual photographic practice, f/11 shows no "intrusive" effect on DSLRs. On very detailed subjects, one will note a slight lowering of contrast, sometimes as early as f/8 with DSLRs with very tiny sensels, but f/11 stays perfectly usable.

Click to expand...

Sure. And "usable" is the key word here.

Best regards,

Doug