Max Lyons Forums

[maxlyons]

I have been thinking about diffraction lately, and have updated my photographic calculator page so that the "Lens Equivalence" calculator (at the bottom of the page) now includes diffraction. Here is a little background.

Diffraction, which controls the smallest point to which one can focus a beam of light, limits the maximum resolution of any optical system. No matter how good your camera and lens, or how much you paid for them, the maximum resolution achievable is governed by diffraction. And, the smaller the aperture (i.e. larger "f number"), the more the maximum resolution is limited.

There are a number of calculators on the web that calculate the "diffraction limited aperture" for a lens, i.e. for any given sensor/lens, what is the aperture beyond which the effects of diffraction limit the maximum attainable resolution. The Cambridge in Colour website has a nice calculator to do this as well as some illustrations taken with a 8 megapixel Canon 20D showing the softening effect increasing as the lens is set to F8, F11, F16 and F22.

My calculator works slightly differently. It calculates the "diffraction limited sensor" pixel count for any aperture/sensor size. For example, given a particular aperture (e.g. F8) and a particular sensor size (e.g. 22.3mm x 14.9mm, the size of the sensor in the new Canon T1i and Canon 50D), my calculator computes that 13.4 megapixels is the maximum "useful" number of pixels. Adding more pixels to a 22.3mm x 14.9mm sensor with a lens set to F8 won't produce an image that resolves any more detail. You'll get an image with more pixels, but not with any more detail.

At least, that's the theory. There are a few caveats to mention here. First, the calculation assumes a circular lens aperture, and uses the Rayleigh criterion to determine when the system has become diffraction limited. Second, the precise calculation depends on the wavelength of light that is considered, so one can produce slightly different results using a different wavelength in the calculation (my calculator uses a value of 510nm, which is near the middle of the visible spectrum, and corresponds to green light...the most important color as far as digital imaging is concerned). Lastly, the fact that most consumer level cameras use a color filter array may complicate the calculation as well.

Given the caveats, one can debate about the precision/accuracy of the estimates produced by this (or any) diffraction calculator. But, the general conclusion that I draw is that at some point in the no-too-distant future (if not already), adding more pixels to DSLR cameras may not be too useful for landscape photographers who generally use small apertures to maximize depth of field. For folks who used wider apertures (e.g. F2.8 or F4) we have a long way to go in terms of increasing pixel counts before diffraction becomes an issue. However, my example above shows that the 15 megapixel Canon 50D or Canon T1i is already "diffraction limited" when the lens is stopped down to "only" F8.

One might be tempted to think that a larger sensor camera would produce better results when capturing the same scene, but the answer is no. Here is a specific example that illustrates why. Let's compare the "cropped sensor" 15 megapixel Canon 50D with the "full frame" 21 megapixel Canon 5D II. The 50D has a sensor sized at 22.3mm x 14.9 mm, while the Canon 5D has a sensor sized at 36mm x 24mm. If we want to compare apples to apples, then my view is that we need to compare the cameras when they are using "equivalent" settings so that they produce an image with the same field of view, and the same depth of field. So, to produce the same image as a Canon 50D with a 50mm lens set to F8, the Canon 5D II needs a 80mm lens set to about F13. At these settings, both systems (50D vs 5D II) are diffraction limited at about 13 or 14 megapixels.

Again, one can debate the precise numbers given the caveats above, but it is true that this "lens equivalence" drives the result that larger sensor cameras don't do any better than smaller sensor cameras when it comes to achieving more resolution/detail (image noise is another story, not considered here). If the smaller sensor camera is diffraction limited, so will the larger sensor camera when trying to capture an equivalent image (same field of view, same depth of field). The larger the sensor, the more the lens has to be stopped down to achieve the same depth of field. And, the more the lens is stopped down, the greater the effects of diffraction. If we wanted to compare the two cameras using the same aperture (e.g. F8 on both cameras), then the 5D II will not be diffraction limited. But, the 5D II won't capture the same image as the Canon 50D (the 5D II image will have less depth of field), so we aren't really comparing apples to apples.

Two final thoughts. First, I know from reading internet discussion forums that many people bemoan the increasing pixel count in digital cameras. But, (as far as I can tell), the general objection is that increasing pixel count tends to mean increasing noise. I don't have any such objection (in fact, I welcome the addition), but the effects of diffraction do limit the usefulness of those extra megapixels under some circumstances. Second, there is a relatively easy way to achieve very high resolution photographs with large depth of field, and that is to use focus blending. At least one manufacturer has started offering a camera with an "in-camera HDR" mode that captures a number of images, and then combines them inside the camera. I'm not aware of any manufacturer who has created an "in-camera focus blend", but perhaps it won't be long before we see this feature?

You can use my lens equivalence calculator to compute your own values or change the values used in this example.

Max

[elf]

It's interesting info, but I'm having trouble relating it to stitched images. If I want to make a 100 megapixel image, what sensor size and pixel density will give me the best detail resolution? Or to put it another way: If I have a P65+, Nikon D3x, and an Olympus E3, which of these would capture the most detail in the same stitched image?

An secondary question would be, which one will give the highest resolution per dollar :)

[DJMoore]

Thanks so much Max, this is eloquently put and truly edifying.

[maxlyons]

[Guillermo Luijk]

Hi Max, I find your thoughts highly interesting.

When I first read the CiC article you mentioned time ago, I also started to think about the un-usefulness (no idea if this word exists in English) of high pixel count on very small apertures (I am very interested in arquitecture and indoor photography, where like in landscaping DOF is a critical factor so lenses must be highly stopped down).

I didn't reach so far as you, but still had a feeling DOF had to be someway a limiting factor for effective sensor Mpx given a sensor size, and I agree with your thoughts.


The concept is understood. Now another story are the numbers your math diffraction calculator provides, and I find them highly pesimistic (not meaning they are wrong at all).

I have a 8Mpx 350D which I use with my 10-22 stopped down at f/11 (in real tests, I found f/11 the smallest aperture before really noticing a loss in sharpness over the focused plane because of diffraction), and I use it regularly at 15mm (24mm eq. in FF).

Recently I purchased a 2nd hand 13Mpx 5D (classic), and plan to purchase the new 24mm TS-E II when available.

I used your calculator to simulate the APS-C usage conditions ported to the 5D:

Camera 1 Sensor dimensions (mm): 22.2 x 14.8
Camera 1 Focal Length (mm): 15
Camera 1 Aperture: 11
Camera 2 Sensor dimensions (mm): 36 x 24

Camera 2 Focal Length (mm): 24.3 mm
Camera 2 Aperture: f/17.8
Camera 1 Diffraction Limited Sensor (Megapixels): 7
Camera 2 Diffraction Limited Sensor (Megapixels): 7

The 7 Mpx figure matches well the tests I did on the camera (8Mpx).

And that would mean the 5D stopped at 17.8 would be far diffraction limited since only 7Mpx would be really free of diffraction. Trial/error on your calculator says that reaching and effective 13Mpx diffraction free resolution on the 5D allows as much as f/13, which could be fine for some indoor shooting, but probably not enough in an outdoor application.

Moreover, I find it funny that professional arquitecture photographers (and with 'professional' I don't mean at all their skills or decisions are necessarily right, just that they take pictures for a living), even don't take care of diffraction and stop down their wide angle lenses to the max (typ. f/22) as a general rule. Taking into account that many of them are moving to 20Mpx cameras, and f/22 on a FF sensor on your simulator provides a diffraction free resolution of only 4Mpx!!!, the situation gets even funier.

I guess your math diffraction model considers the worst case, i.e. just when diffraction is about to be detectable for start invading adjacent pixels.

Tell me if you agree with this: in a real application with high DOF requirements, I consider the best tradeoff would be some point (f number) where some loss of sharpness in the focused plane is allowed because of diffraction, but improving thanks to it sharpness in regions far of the focused plane because of DOF.
This could be the reason why values slightly higher (i.e. higher f numbers) than those provided by your simulator could be the right ones to have an overall optimised sharpness in the whole image.

Best regards
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[Guillermo Luijk]

[maxlyons]

Guillermo,

[Terrywoodenpic]

[Guillermo Luijk]

Hi Terry, thanks for your comments. I am going to learn more about sharpness and aperture in this thread than in the last 2 years.

Your distinction between:
- Ultimate sharpness (that could relate to diffraction)
- Overall sharpness (that could relate to DOF)

is interesting. I have made some graphs (f-numbers are just didactical) to try to point that there could be optimum f numbers to maximize overall (uniform) sharpness.

The images plot the blurring effect of DOF and diffraction separately. In a real case the combination of both would give the final sharpness at every distance from the camera.

For arquitecture applications, the last case would be the optimum f number to be used: sharpness is uniform along the overal image but kept to a minimum (a larger f number would increase overall blurring):

The f-number at which diffraction starts to be detectable (Max's simulator value for a given Mpx and sensor size, e.g. f/13 for a 13Mpx 5D), would be represented in these plots as the first time the red graph starts to have >0 values.

Regards
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[Terrywoodenpic]

Guillermo.

Interesting graphs.
Another point to consider, is that in normal use and in photographs that rely on depth of field to extend sharpness, the degree of sharpness is not the same at every distance. The degree of sharpness falls off progressively from the point on which the lens is actually focussed. Using a small aperture only improves the situation, it does not change the fact that a lens can only focus in one plane.

There is some advantage in using diffraction to disguise the fact that only one plane on a building can be the plane of focus.
Selective focus is not usually desirable in architectural photographs, so the more the sharpness is evened out the better.

Extending the depth of field by using a small aperture certainly improves things but looked at closely, there is still a fall off in sharpness away from the plane of focus.

If a lens produces a "useful" degree of diffraction at say f16 i.e the photograph is still adequately sharp, and then the lens is closed down to say f32, there will be an increase in depth of field, but the degree of sharpnes would have become even more limited by diffraction.

Provided the over all sharpness is acceptable, the effect of the difference in sharpness between the plane of focus and the other distances will become reduced. As a result the entire image will appear equally in focus. This might seems to infer that small apertures with comparatively high diffraction are still useful.

This is of course true and has been the normal practice of architectural and product photographers down the ages.

I have used lenses with apertures as small as f128 on large format, and still obtained sharp looking results even on considerable enlargements. On Large format, the superior tonal qualities easily out play any loss in sharpness when using minute apertures.
_________________
Terry

After 60 + years in photography, Now Down sized to Canon G6 Digital and Olympus OM1n film cameras, and accessories. Now up sized/added a Canon 40D and minolta G600

[Guillermo Luijk]

That's fine Terry, and I think is all well explained looking at the qualitative plots I showed.

It's understood then that diffration can be used as a sharpness equalizer, and that's why I pointed the last plot, where diffraction blurring is dominant at all distances, as the optimum for the applications under discussion. What I claim is that, once reached that f-number which makes diffraction dominant, there is no point in increasing further the number.

I.e. there is no point in going from A to B here:

How to calculate that optimum f-number in practice?
I can think of a series of subsequent shots at different apertures, ranging let's say from f/8.0 to max f in the lens (typ. f/22 or whatever), and compare sharpness in the areas far from the focused plane (for example some distant building) in 100% crops.

For some f-number, the sharpness must reach a maximum; a lower f-number will reduce sharpness because of a lack of DOF, and at a higher f-number diffraction will reduce sharpness (it's the above case B).

What do you think of the procedure?

Regards
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[Terrywoodenpic]

Guillermo,
In A, the blue line where it passes through the focused plane will seem more sharp than it does at infinity. At both points it is certainly with in the set criterion of the circle of confusion., but the first will be sharper.
I think that the diffraction acts more like an added softar filter. This reduces sharpness equally from at what ever distance.
I would suppose that the softening effect of the red and blue line would also be additive and produce a third line of softness.

If that is so the lines in "A" would show a greater range of sharpness when added together than the Lines in "B"

Probably the best practical result would be somewhere between the two.

If those are the results from calculations for Digital cameras it is not surprising that Large Format lenses go down to F32 or f64
when serious effects of Diffraction start much later.
_________________
Terry

After 60 + years in photography, Now Down sized to Canon G6 Digital and Olympus OM1n film cameras, and accessories. Now up sized/added a Canon 40D and minolta G600

[Guillermo Luijk]

I wonder how sharpness reduction due to CoC (DOF) and airy disks (diffraction) add in practice. The physical element producing both is the same: the entrance pupil diameter. A basic model could consider that airy disk radius is added to the CoC radius, and then you would be right: A would still be quite un-uniform, lacking of sharpness in the front and back planes.

I will do some real life tests next week, ranging f/8 up to f/22 and comparing 100% crops. Hope something can be clarified because subjectively measuring sharpness is never an easy task.

Any comment about the way to proceed is welcome before I start the work.

BR
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[Terrywoodenpic]

I would be interested to see the results.
I am not sure using a zoom lens would be a good Idea as they are so complex, and the added internal reflections are more likely to degrade the results.

You should have some nice clear air in Madrid, but I suggest the cooler parts of the day will show less aerial perspective through heat haze at infinity.
_________________
Terry

After 60 + years in photography, Now Down sized to Canon G6 Digital and Olympus OM1n film cameras, and accessories. Now up sized/added a Canon 40D and minolta G600

[elf]