Calculating the Dragon

A few weeks back I posted a photo that was sublimely sharp. In my novice experience I was accused of "chasing the dragon" as I asked why I was having trouble achieving that level of sharpness again and how I might accomplish it at-will. In a completely separate effort, after doing some tests with my camera, I posted about how I stumbled upon diffraction limits. Since these posts I have been toying with my three lenses to find their sweet spots.

The sublimely sharp photo I mentioned was taken with a aperture of 6.25mm (Panasonic 20mm @ f/3.2). It would seem to me that this would indicate, for an MFT sensor (providing that my photo was truly at the peak of possible sharpness for the gear involved), that 6.25mm is the optimal lens aperture for sharpness. So, were I to use a 60mm focal length, the optimal f-number would be f/9.6.

Intuitively, I don't feel that this is true. Before I do some tests, I want to gather some opinions. Are there other factors involved here that I'm not aware of, yes?

Before you answer, please know that I understand that sharpness isn't everything or that sharpesness won't matter if the circumstances will not also allow for appropriate light, and so on. I'm really asking a physics question regarding the math of lens diffraction shows and its direct relationship between optimal sharpness (a lack of overlap in circles of confusion) and aperture.

The diffraction effect depends on the numerical aperture independent of the focal length. So for all m4/3 lenses diffraction becomes progressively worse after about f/8. For a given lens the sharpest result will usually be somewhere in the f/2.8 to f/5.6 range.

Mark

Hmmm.... good question. If diffraction doesn't have to do with the focal length of the lens, only with the aperture diameter, then you are correct! Trouble is, I have achieved brain lock trying to think about whether diffraction could be affected by focal length. So I can't be sure of that.

Hi,

this may help


tom

Thanks for the link! So it seems focal length is a factor, and therefore it is not the aperture diameter but the actual f number that is the same, for the same diffraction.

j y g said:

j y g wrote:

A few weeks back I posted a photo that was sublimely sharp. In my novice experience I was accused of "chasing the dragon" as I asked why I was having trouble achieving that level of sharpness again and how I might accomplish it at-will. In a completely separate effort, after doing some tests with my camera, I posted about how I stumbled upon diffraction limits. Since these posts I have been toying with my three lenses to find their sweet spots.

The sublimely sharp photo I mentioned was taken with a aperture of 6.25mm (Panasonic 20mm @ f/3.2). It would seem to me that this would indicate, for an MFT sensor (providing that my photo was truly at the peak of possible sharpness for the gear involved), that 6.25mm is the optimal lens aperture for sharpness. So, were I to use a 60mm focal length, the optimal f-number would be f/9.6.

Intuitively, I don't feel that this is true. Before I do some tests, I want to gather some opinions. Are there other factors involved here that I'm not aware of, yes?

Before you answer, please know that I understand that sharpness isn't everything or that sharpesness won't matter if the circumstances will not also allow for appropriate light, and so on. I'm really asking a physics question regarding the math of lens diffraction shows and its direct relationship between optimal sharpness (a lack of overlap in circles of confusion) and aperture.

Click to expand...

Contradictory to some posts I have seen on this forum, peak sharpness with good lenses on the 16MP M43 sensors is achieved at f/4. (You can check this by looking at the resolution numbers for various M43 lenses on Photozone.de ). I see this in my images as well, peak for many lenses (20/1.7, 12-35/2.8, 75/1.8, 45/1.8) is at f/4. f/5.6 is a little worse and f/8 very visibly causes softening through diffraction (resolution is almost cut in half for the 16MP sensors through diffraction softening at f/8).

Lenses which become sharper stopped down past f/4 do so simply because they are still improving then and don't achieve peak performance at a wide enough aperture to give the best possible results on high density M43 sensors.

This is not dependent on focal length, only on aperture f value and pixel size.

It affects M43 at a lower f value than other formats due to the smaller pixels (higher pixel density).

For best results, I shoot raw and sharpen appropriately. With Lightroom sharpening setting of (35,0.7,70,20) I find works quite well with the E-M5 / E-PL5 files.

Focal length!

Everyone is saying, "It's the f-number!" But if f-number is dependent upon focal length and aperture, and we're looking for a constant aperture (designated by the constant construction of the sensor), the variable here is focal length. Am I missing something?

So, I would argue we cannot just say "IT IS f/4.0!" and be done with it. We would take this magic diameter, not magic f-number, of 6.25mm (or whatever it really is) and plug that into our lens' current focal length to get the optimally sharp f-number.

Thanks for the replies so far.

The diffraction blurring of a 25mm lens with an actual aperture of 5mm is exactly the same as a 50mm lens with an actual aperture of 10mm. The constant factors are the blurring and the numerical aperture of f/5.

Mark

(pun intended, sorry!)

I mean, consider all the variables of your set-up. For any lens there is a diffraction softening of the image that is dependent on the physical aperture and the focal length. That means, in the end, the f value. (actually, it also depends on the wavelength of the light, but lets assume the light is uniformly green).

But then, there is also the optical quality of the lens, besides the diffraction effect. This is ideal, but it helps, for our understanding, to consider both independently. In this case, lenses are usually better at higher f values (smaller apertures) and mostly they are at their worst wide open. As you close down a lens, this aspect of its behavior will improve regularly. This optical quality varies wildly from lens to lens, from manufacturer to manufacturer, and the expectations of the users are very different in this respect: some will consider "reasonable" one lens that other will label as "rubbish"!

When considering the actual performance of a lens, both effects have to be considered. You can think of two "performance curves" as you close down a lens. One depends on the optical characteristics, and the performance (however you measure it, for example lets call it "sharpness") increases steadily as f increases. (this is to simple, I know, there is centre sharpness, corner sharpness, contrast, CA, etc). The other depends on diffraction, and goes down as f increases.

The actual result is a convolution of the two curves. It will vary from lens to lens (even if are talking only of MFT lenses). Very good lenses are so good wide open that they show little improvement (optically) by closing down. They can only show small, but increasing softening by closing its aperture. I think I read that this is the behavior of the Olympus 75 f/1.8.

Others, like most kit lenses, are far from the best wide open. Therefore, going to higher f values has a good effect on sharpness at first, until f/5.6, (even f/6.3, may be?). The diffraction softening starts to show then, but it only starts to really affect results above f/8. Most lenses are quite usable at f/11 (without critical pixel peeping).

But it is important to bear in mind that the answer to "At what f/ value do I see diffraction softening?" Depends on the lens, really. There is no general answer. And keep in mind that really diffraction is always present - you may no see its effects!

... as theoretic resolution varies directly with aperture only (not f/, but aperture diameter). A perfect f/1.0 lens of, say, 100mm aperture will resolve the same as an f/10 of 100mm aperture. Any stopping down will reduce the resolution. So our perfect f/1.0 lens with 100mm full aperture will have 10X the resolution of its being stopped to f/10 (a 10mm aperture).

So the less perfect the lens (the more the sum of it aberrations) the more it will need stopping down to improve resolution (minimize aberrations).

The relationship of resolution to f/ stop in the same lens is that theoretic resolution halves for every two stops of numeric f/ increase (while light gathering decreases by 4X).

PB

Others have answered your question, the only point I would add is to recognize the tradeoff between diffraction and DOF. Sometimes, because of the subject, you need a large DOF. In those cases, you may tolerate some softening due to diffraction in order to gain the benefit of a deeper DOF.

Okay, I know this isn't quite exact but think of it this way:

From the aperture to the sensor (focal plane... whatever), you have a cone of light, the opening of your aperture is the diameter of the base of the cone, the height of the cone is the focal length.

What affects diffraction is the incident angle of the light, or in relation to our aforementioned cone, the angle of the sides of the cone.

So, if with the panasonic 20mm at f3.2 you have an aperture of 6.25mm, then you have a cone with a base diameter of 6.25mm and a height of 20mm.

Now we can use geometry and because I'm too lazy to show work, we can find that the incident angle is ~81.1 degrees.

ULTIMATELY, from that if you shorten the focal length then a smaller aperture diameter would result in the same incident angle... Also the ratio would happen to keep the aperture (f) value consistent while keeping the incident angle consistent.

RESULT, it's not about keeping the aperture opening diameter consistent, it's about keeping the incident angle consistent (again, in other words, the f value).

What can you take away from this? Diffraction is a direct result of incident angle and ultimately, the f-value of a lens!

Also sharpness of a lens and diffraction are mostly unrelated because when lenses are wide open, they are less sharp due to the edges of the glass elements being less refined than the centers as well as some minor incident angle issues between elements in the lens. As you stop down you reduce the effects of the elements of the lens but you begin to increase the effects of the incident angle on the microlenses on the photosites. So lens sharpness increases as you stop down, but diffraction issues crop up from the sensor as the incident angle increases.

I could also bring in the effects of circles of confusion and such but that's less of an issue than any of this.

Also what I'd like to point out is that diffraction limiting is more an effect of the sensor rather than the lens.

Spunkweed said:

Spunkweed wrote:

....

ULTIMATELY, from that if you shorten the focal length then a smaller aperture diameter would result in the same incident angle... Also the ratio would happen to keep the aperture (f) value consistent while keeping the incident angle consistent.

RESULT, it's not about keeping the aperture opening diameter consistent, it's about keeping the incident angle consistent (again, in other words, the f value).

What can you take away from this? Diffraction is a direct result of incident angle and ultimately, the f-value of a lens!

Click to expand...

OK, I think this finally got it through to me. After reading your great explanation I also took a look at:

http://en.wikipedia.org/wiki/Numerical_aperture#Numerical_aperture_versus_f-number

So, then, the reason "it" is not simply focal length is because diameter is not the constant. They both will change to achieve the optimal angel of incidence... or f-number.

Thanks!