Diffraction vs Resolution

[Rainer SLP]

http://en.wikipedia.org/wiki/Diffraction-limited_system#

[Alan Klein]

Thank you!  Finally, some real world useful perspective.

Diffraction losses are real, but the effect have been way, way overblown.  One should always use the best aperture to get the image.  This includes the optical properties of the lens itself, the properties of the imaging system, the artistic vision trying to be captured, etc.  Hence, if one requires f/11 to get the DOF necessary, then accept the diffraction losses.  Yes, tilts and focus stacking are possible options in SOME situations if you have the equipment and time necessary.

I think of optical quality as a precious resource.  Therefore, I never want to squander it, but spend it wisely.  The very good image you get is better than the great image you didn't!

I figure the f stop I need to get the DOF I want.  Then stop down one stop to make sure.  

[Jim Kasson]

Well stated, Bart. This clears up some of the confusion. Here is a real life demonstration of these principles with an image taken with the Nikon D800e at f/22 using your chart. The Nyquist limit of the sensor is 102 cycles/mm. Optical resolution limits are shown in this table taken from Roger Clark's site. Beyond the Rayleigh limit is there is no useful contrast for practical terrestrial photography and at f/22 the Rayleigh resolution is 75 cy/mm and the camera can resolve approximately 72 cy/mm as shown. At higher frequencies there is no perceptible detail in the image.

Correct me if I'm wrong, but aren't you forgetting the CFA?

Jim

[Bart_van_der_Wolf]

Correct me if I'm wrong, but aren't you forgetting the CFA?

Hi Jim, I don't think it is forgotten, but maybe it complicates matters a bit too much.
 
Each of the R/G/B/G filtered photosites contribute to luminance resolution, although weighted by their contribution to luminance, and even the Green filtered photosites contribute a bit to Red and Blue. Also, demosaicing can limit the loss of effective Luminance resolution to 6 or 7% at most (assuming it is Luminance that we are demosaicing).

If it weren't the case, then Red and Blue channel resolution would be half of G, and it isn't (it's roughly equal). This is because the Luminance signal gets redistributed over all contributors, with a decent algorithm.

So the claim for the 4x multi-shift sensors, that 'true RGB' increases resolution, is true but it is moderate (compared to half photosite offsets or 16x multi-sampling).

But this gets to be a bit off-topic for the OP's question.

Cheers,
Bart

[bjanes]

No, this is why it's confusing. Your 36 MP camera does not become or behave like a 24 MP camera.

All that diffraction does is reduce contrast, increasingly so as it approaches the highest spatial frequencies and the narrower the aperture gets, the micro-detail suffers from reduced contrast. A higher MP camera can sample that micro-detail more finely, and thus may extract more detail out of it (which creates more useful data for post-processing).

There is a physical limit beyond which there will be no contrast left due to diffraction, even for high MP cameras, but for the current 50 MP DSLRs that limit is somewhere near f/14. At that limit even lower MP cameras cannot resolve the detail because they lack the resolution, all they see is a bit of blur, but so does the 50 MP camera, just more accurately.

Diffraction itself is not affected by sensor resolution. It is an optical, lens aperture related, phenomenon. All that the sensor does is either resolve the detail there is, or not, and higher MP sensors are better at that.

Well stated, Bart. This clears up some of the confusion. Here is a real life demonstration of these principles with an image taken with the Nikon D800e at f/22 using your chart. The Nyquist limit of the sensor is 102 cycles/mm and is shown by the black circle on the image. Optical resolution limits are shown in this table taken from Roger Clark's site, and the Rayleigh limit at f/22 is 75 cy/mm . The system resolves approximately to the Rayleigh limit as shown by the extinction of detail in the image at an image diameter of approximately 130 pixels, corresponding to a resolution of 72 cy/mm. It seems as if the Rayleigh limit is the minimal level of contrast that can be made use of by the camera system.

At f/11 the resolution at the Rayleigh limit is 150 cy/mm, and the camera system with a Nyquist of 102 cy/mm could make some use of this level of contrast, especially with deconvolution sharpening.

Cheers,

Bill

[Bart_van_der_Wolf]

Well stated, Bart. This clears up some of the confusion. Here is a real life demonstration of these principles with an image taken with the Nikon D800e at f/22 using your chart. The Nyquist limit of the sensor is 102 cycles/mm and is shown by the black circle on the image. Optical resolution limits are shown in this table taken from Roger Clark's site, and the Rayleigh limit at f/22 is 75 cy/mm . The system resolves approximately to the Rayleigh limit as shown by the extinction of detail in the image at an image diameter of approximately 130 pixels, corresponding to a resolution of 72 cy/mm. It seems as if the Rayleigh limit is the minimal level of contrast that can be made use of by the camera system.

Indeed, although the stated Rayleigh limit is (I assume) based on diffraction alone. The residual lens aberrations PLUS the diffraction blur PLUS photosite aperture PLUS demosaicing equal that theoretical level. Therefore, an even higher sampling density might squeeze a bit more modulation out of the diffracted signal, which the deconvolution can utilize. So in the f/22 example you showed, the Rayleigh limit for diffraction alone happens to be a decent indicator for practical system MTF limits on your (4.88 micron pitch) camera.

At f/11 the resolution at the Rayleigh limit is 150 cy/mm, and the camera system with a Nyquist of 102 cy/mm could make some use of this level of contrast, especially with deconvolution sharpening.

Absolutely, I expect that on the D800/D800E, apertures up to f/16 can deliver images that are almost not resolution limited by diffraction. But even a f/22 a lot of useful signal modulation can be restored to higher SNR levels. Good lenses and perfect focus still have a benefit for that exercise.

Cheers,
Bart

[Jim Kasson]

Hi Jim, I don't think it is forgotten, but maybe it complicates matters a bit too much.

It complicates things a lot, I agree. It complicates them so much that I didn't even try for an analytic solution, I just wrote a simulation. I did find out that Burns'-style slanted edge MTF50 continues to improve as pixel pitch goes down even when analyses that don't consider the CFA say you're done.

I didn't use a sophisticated model for diffraction: just 450 nm for the blue pixels, 550 nm for the green ones, and 650 nm for the red ones. Calculating diffraction patterns every 5 or 10 nm and adding the resulting images up through the simulated passbands of each filter was way too fiddly for me, and the sim takes a long time to run anyway.
 
Jim

[Jack Hogan]

Hi Jim, I don't think it is forgotten, but maybe it complicates matters a bit too much.

Hi Bart, not that much: the way we view MTF curves, it's just multiplication by a cosine.

Jack

[Jack Hogan]

There is a physical limit beyond which there will be no contrast left due to diffraction, even for high MP cameras, but for the current 50 MP DSLRs that limit is somewhere near f/14.

I know most of you here already know this, but for completeness the actual theoretical physical limit imposed by diffraction of monochrome light going through a circular aperture is a resolution of 1/(lambda*N), with lambda the wavelength of light and N the f-number under consideration.  This limit is independent of sensing medium/size.  For instance for pure green light at 550nm and f/14 that would be about 130 lp/mm on the image projected on the sensing plane by a perfect thin lens.  

In order to reconstruct spatial frequencies near theoretical diffraction extinction properly we would need to sample them with a monochrome sensor at least at twice that rate = 260 lw/mm.  For an FF sensor of 24mm height that corresponds to 260*24 =  6240 pixels on the short side, or about 58MP.  For blue light at 400nm and f/8 that would be 337MP.  Pixel pitches in those conditions are about 3.8 and 1.6 microns respectively.

The formula for pitch to capture all frequencies up to diffraction extinction is lambda*N/2, in the same units as lambda.

Jack

[Jim Kasson]

I know most of you here already know this, but for completeness the actual theoretical physical limit imposed by diffraction of monochrome light going through a circular aperture is a resolution of 1/(lambda*N), with lambda the wavelength of light and N the f-number under consideration. 

Let's all raise a glass to CM Sparrow!

http://en.wikipedia.org/wiki/Sparrow%27s_resolution_limit

Jim

[Bart_van_der_Wolf]

I know most of you here already know this, but for completeness the actual theoretical physical limit imposed by diffraction of monochrome light going through a circular aperture is a resolution of 1/(lambda*N), with lambda the wavelength of light and N the f-number under consideration.  This limit is independent of sensing medium/size.  For instance for pure green light at 550nm and f/14 that would be about 130 lp/mm on the image projected on the sensing plane by a perfect thin lens.  

In order to reconstruct spatial frequencies near theoretical diffraction extinction properly we would need to sample them with a monochrome sensor at least at twice that rate = 260 lp/mm.  For an FF sensor of 24mm height that corresponds to 260*24*2 =  12480 pixels on the short side, or about 234MP.  For blue light at 400nm and f/22 that would be 178MP.  Pixel pitches in those conditions are about 1.9 and 2.2 microns respectively.

Hi Jack,

I think you're a factor 2 off (if talking about resolving a single line or point), since 130 cycles/mm is already 260 lines. The 'EOS 5DS/5DS R' has a 4.14 micron pitch (lines) sensor, which is 241.5 lines/mm or 120.8 cycles/mm at the Nyquist limit (which states that it requires more than 2 pixels, or 1 cycle, to unambiguously reconstruct a line), a close match (depending on actual wavelengths) for totally diffraction dominated/limited resolution.

You may have been thinking about being able to separate 2 lines, and that would take a bit of space between them. If we use the Sparrow separation limit (the separation where the lines stop being separable), that would equate to requiring more than 1.79 pixels (with a 4.14 micron pitch) separation between them. To illustrate, I've added a graph that shows the exactly 1.79 pixels separated lines which each have been diffraction blurred.
EDIT: I've also added the same for the Rayleigh separation limit, which would in this case be 2.31 pixels, with plenty of modulation for deconvolution if only diffraction is considered. Of course there is also an influence of residual lens aberrations and defocus, and the unknown characteristics of the OLPF in the 5DS model, so this is the ideal case, assuming a 100% fill-factor due to micro-lenses, and infinity focus.

Cheers,
Bart

[Bart_van_der_Wolf]

And here (see attached) is how the integrated kernel would look. Do note that a Logarithmic representation, instead of the linear ones shown here, is probably closer to how we see the diffraction patterns.

Cheers,
Bart

[Jack Hogan]

Hi Jack,

I think you're a factor 2 off

Yikes!  You are right Bart, I am off by a factor of two (every other time I've done this exercise it was at much lower f-numbers, with the result sub-micron pitches).  Apologies for the error, I'll correct above.

Jack
PS Thanks for the graphs and practical criteria suggested by you and Jim.

[ErikKaffehr]

Hi,

Making errors is human, admitting errors is divine :-)

Best regards
Erik

Yikes!  You are right Bart, I am off by a factor of two (every other time I've done this exercise it was at much lower f-numbers, with the result sub-micron pitches).  Apologies for the error, I'll correct above.

Jack
PS Thanks for the graphs and practical criteria suggested by you and Jim.

[synn]

I work with what aperture works best for the image I am trying to make. Diffraction loses are negligible unless one stand centimeters away from a print.
Saying "I will only work at X aperture" is great for pixel peeing, but is terrible if one has artistic ambitions.

[Bart_van_der_Wolf]

I work with what aperture works best for the image I am trying to make.

But of course. I need mine to be very sharp and rich in detail. That's why I'm often forced to use focus stacking at f/4.0 - f/5.6, depending on the lens.

Diffraction loses are negligible unless one stand centimeters away from a print.

Neglible is subjective. What works for one image may not work for another. There is no single right or wrong approach. It all depends on the goal (artistic intent, if not for straight documentation), and intended end-use.

Saying "I will only work at X aperture" is great for pixel peeing, but is terrible if one has artistic ambitions.

Ah, the high horse posture. How predictable. But you're of course welcome to add your insights to this technical thread about Diffraction and Resolution.

Cheers,
Bart

[synn]

Shot this at f/22. MTF charts tell me that going past f/11 is suicide.
Can't see a damn thing wrong with it. Maybe I should get a technical pony instead of my artistic high horse to see what's wrong.

[Bart_van_der_Wolf]

Shot this at f/22. MTF charts tell me that going past f/11 is suicide.
Can't see a damn thing wrong with it. Maybe I should get a technical pony instead of my artistic high horse to see what's wrong.

Just asking to make sure, you do understand that at this small size almost everything can look sharp enough (if that's what the image needs)?

Some people need sharp images at a larger (e.g. wall) size, or for a different purpose than Web display. I'd e.g. hate to search for forensic evidence in a blurred image if it can be avoided, or not see detail in a Macro shot where the focus (also literally) should be, or an architecture shot of a technical construction, or an urban landscape shot with weathered paint and cracked windows, or ...

Not everybody buys the 'it's a creative choice to have nothing in focus'. It's horses for courses.

Cheers,
Bart

[synn]

I have a 40" print of the same image and still can't see this "Horrendous diffraction problem" when viewed at the intended distance.
You are free to come see it for yourself at your convenience.

[dwswager]

Can a great, and sharp shot be taken at f/22.  Yes!  Will it be as good as one taken on the same senor at f/8?  Well, now that is going to depend on a who host of issues including the performance of the lens at different apertures, the sensor, the need for DOF, proper focus, the lighting, etc.

The attached JPEG shows the onset of diffraction losses for 3 cameras based on some listed general assumptions.  The D7100 I already owned and the D750 and D810 that I was considering buying.  The point of knowing the diffraction limits is not to set a hard and fast rule that you will never shoot at a smaller aperture than X, but to know that at X, I am starting to have to make trades so that one can decide whether the trade is a worth it.  Am I getting something more in return for what I am giving up?

I will usually trade diffraction for DOF.  Meaning, I first determine the aperture necessary for the DOF I want.  Then I worry diffraction.  If I have the opportunity, I usually will take 2 shots.  One at the aperture necessary for DOF and one at the aperture where I feel diffraction is too big a trade.  This also might require rethinking the focus points for each shot based on the main focal point of the image.   Then in post, I compare.  Sometimes, I find I don't prefer the DOF I thought I wanted and use the other shot.  Sometimes, I pick correctly and use the one shot for DOF.  God I love digital!