# A (very rare) recommendation for a DPR thread, on fundamental image quality.

#### Bart_van_der_Wolf

##### pro member
Hi folks,

It's a rare occasion that I'll recommend a read of a thread on an other (especially the DPR) forum. However, this thread does currently offer a nice view/development (so far) on a subject, diffraction, that has had my attention for quite a while already.

Diffraction is predominantly caused by our aperture settings. When light is forced down a small physical restraint/aperture, the light will 'diffract' around the edges of the aperture blades (especially noticable if the blades do not provide a perfectly circular edge).

For reasons that will be disclosed in future threads, I've (a while ago already) produced a chart that shows theoretical limitations for several camera sensor pitch dimensions:

The indications from this chart, translate quite well to some of the findings of the referenced article (within that article's margins of visual judgement accuracy), as they do to my personal observations on various sensor/lens/sensor-array combinations.

My basic premise is that when the diffraction blur diameter (first minimum (= zero) of the 'Airy disc' pattern) for the (most important for visual acuity) green wavelengths exceeds 1.5x the sensel pitch, there will be a visually significant impact on resolution. One could quibble if the lower boundary is at 1.5x or 2x the diffraction diameter, but that also depends on the Anti-aliasing filter used in the specific sensor designs at hand.

Bart

#### Emil Martinec

##### New member
Thanks for the chart, Bart.

I was spurred by a related DPR thread

http://forums.dpreview.com/forums/read.asp?forum=1032&message=26504942

to do a few calculations. I haven't yet done the calculation for a round aperture, as our lenses have (approximately, sue to the aperture blades); the math is much easier for a square one. For a square aperture, MTF as a function of spatial frequency linearly decreases with aperture until the size of the diffraction spot equals the spatial wavelength, at which point MTF is zero thereafter. I expect the result for a round aperture will be similar.

So if you want maximum fine detail in the focal plane, even in the "green zone" of your chart, it's best to keep the aperture at the minimum value needed for DOF. I haven't yet done the calculation for the tradeoff between diffraction and DOF for the best MTF near the focal plane. Maybe later.

#### Bart_van_der_Wolf

##### pro member
Thanks for the chart, Bart.

I was spurred by a related DPR thread

http://forums.dpreview.com/forums/read.asp?forum=1032&message=26504942

to do a few calculations. I haven't yet done the calculation for a round aperture, as our lenses have (approximately, sue to the aperture blades); the math is much easier for a square one. For a square aperture, MTF as a function of spatial frequency linearly decreases with aperture until the size of the diffraction spot equals the spatial wavelength, at which point MTF is zero thereafter. I expect the result for a round aperture will be similar.
I haven't gone as far as calculating the MTF, my chart is just based on my empirical judgement that visual degradation seems to set in at approx. 1.5x the sensel pitch. This is also often supported by an observed declining MTF score at higher spatial frequencies when using narrower apertures.

An MTF degradation can be used to calculate a lowest limit of usefulness, and certainly a Sinc function is easier to use than an Airy pattern on an assumed square (sensel) aperture. I don't think we have to draw the line at a zero response, because at 10% MTF we're already pretty much at the practical limiting visual resolution (for average contrast subjects). The ISO also mentions a good correlation between 10% MTF and limiting visual resolution.

So if you want maximum fine detail in the focal plane, even in the "green zone" of your chart, it's best to keep the aperture at the minimum value needed for DOF. I haven't yet done the calculation for the tradeoff between diffraction and DOF for the best MTF near the focal plane. Maybe later.
I could also run a simulation in Mathematica (which I use to calculate a 2-D diffraction pattern PSF kernel), but it would still give a theoretical limit, because of the unknown properties of the AA-filter and residual optical aberrations. That's why I use the rule of thumb of 'sensel widths' which is useful enough to predict the visual on-set of diffraction degradation. Any narrower aperture will degrade the per pixel resolution, and reduce the chance of successful deconvolution to restore the losses.

Bart

#### Emil Martinec

##### New member
I haven't gone as far as calculating the MTF, my chart is just based on my empirical judgement that visual degradation seems to set in at approx. 1.5x the sensel pitch. This is also often supported by an observed declining MTF score at higher spatial frequencies when using narrower apertures.
And that judgment should be pretty accurate. Many demosaicing algorithms use the green channel as an ersatz luminance channel for the purposes of interpolation, and the green pixels are spaced at sqrt2~1.4 times the pixel pitch, so when the diffraction spot exceeds this scale then diagonally nearby green pixels are blurred together.

An MTF degradation can be used to calculate a lowest limit of usefulness, and certainly a Sinc function is easier to use than an Airy pattern on an assumed square (sensel) aperture. I don't think we have to draw the line at a zero response, because at 10% MTF we're already pretty much at the practical limiting visual resolution (for average contrast subjects). The ISO also mentions a good correlation between 10% MTF and limiting visual resolution.
Right. I wasn't using a square sensel aperture, I had in mind a square lens aperture (usual "spherical cow" approximation we physicists use to simplify calculations). Agreed we don't have to draw the line at zero, but I was wanting to calculate how much the finite aperture degrades MTF for any aperture, even above the diffraction limit. I was surprised to find a linear relation, basically for an intensity pattern
I = I_0 cos^2 kx
and diffraction pattern sin^2ax/ax, the output of averaging the intensity pattern against the diffraction pattern is

I_diff = I_0 (1-a/k)
(for a<k), and
I_diff = 0
(for a>k)

I was merely expressing my surprise that the result was linear in the parameter _a_ which is proportional to the f-number. So MTF is decreasing directly with aperture even above the point where pixel-level resolution is diffraction limited (granted, not much for small _k_ but the amount of degradation doubles every time we stop down two stops).

I could also run a simulation in Mathematica (which I use to calculate a 2-D diffraction pattern PSF kernel), but it would still give a theoretical limit, because of the unknown properties of the AA-filter and residual optical aberrations. That's why I use the rule of thumb of 'sensel widths' which is useful enough to predict the visual on-set of diffraction degradation. Any narrower aperture will degrade the per pixel resolution, and reduce the chance of successful deconvolution to restore the losses.

Bart
Yes, doing the full integral against an Airy pattern is probably overkill. But it represents an upper bound on MTF. The MTF due to the AA filter simply multiplies that due to diffraction. Optical aberrations and diffraction effects might not cleanly factorize in this way, I'm not sure, since they arise from the same part of the optical pathway (the lens), in any case can only decrease overall MTF. In any case, these effects are present independent of diffraction and the influence of diffraction is I think reasonably modelled by the simple 1d calculation.

#### Bart_van_der_Wolf

##### pro member
Yes, doing the full integral against an Airy pattern is probably overkill. But it represents an upper bound on MTF.
Agreed, there's not much going to 'contribute' to the image at, or beyond, zero modulation.

The MTF due to the AA filter simply multiplies that due to diffraction. Optical aberrations and diffraction effects might not cleanly factorize in this way, I'm not sure, since they arise from the same part of the optical pathway (the lens), ...
FWIW, I do wonder, when given the point-spread function (PSF) kernel of the total optical chain, if we divide out the diffraction PSF kernel (for a given wavelength pass-band), wouldn't we be left with the lens aberration + AA-filter + sensel geometry effects for the specific aperture? And since the AA-filter and the sensel geometry are constant, and the lens aberrations are aperture dependent, wouldn't it be possible to derive a good model for the different PSFs involved? With a good model it wouldn't be too difficult to synthesize a combined PSF which would allow decent deconvolution (without the need for empirical camera/lens/aperture specific PSF determinations).

In any case, these effects are present independent of diffraction and the influence of diffraction is I think reasonably modelled by the simple 1d calculation.
While I agree it's adequate for general conclusions, it doesn't provide enough guidance for corrective measures, IMHO.

Bart

#### Asher Kelman

##### OPF Owner/Editor-in-Chief
I think this is a thread that is worthy to keep in mind when getting enthusiastic about the increased resolution possible with higher MP counts.

As the sensel pitch decreases the effects of diffraction become more increasingly important at smaller apertures.

This would argue for going to a larger camera format when one seeks to use a higher MP count for the image plane.

Asher