Back To Basics: Aperture and DOF?

Okay so I get bigger aperture = less DOF, smaller aperture = greater DOF. I understand hyperfocals and the formula for determining an aperture number. However there is one thing I don't fully understand and that is WHY. Why does a larger aperture give less DOF and a smaller give more? I'm hoping someone might be able to explain the science behind it :o

You really need to look at a diagram to understand this...at least I did. I searched around and found one here...you have to scroll down a little.

http://www.normankoren.com/Tutorials/MTF6.html

This site has lots of details, but you might just need to look at the diagram for a few minutes and think about it. The lower case "a" is the aperture. As "a" gets smaller, "c" gets smaller. The smaller "c" is, the sharper the image.

I really don't know how to explain this in words. I hope the diagram helps.

Paul

That's EXACTLY what I was looking for. Great find Paul! Thanks :D

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Originally Posted by Xia_Ke

That's EXACTLY what I was looking for. Great find Paul! Thanks :D

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Cool. Glad I could help. :)

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Originally Posted by photophorous

Cool. Glad I could help. :)

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I'm glad you could too :D I had an idea in my head that ran along those lines, I just couldn't fully connect the dots. That link filled in the gaps nicely :thumbsup:

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Originally Posted by Xia_Ke

Okay so I get bigger aperture = less DOF, smaller aperture = greater DOF. I understand hyperfocals and the formula for determining an aperture number. However there is one thing I don't fully understand and that is WHY. Why does a larger aperture give less DOF and a smaller give more? I'm hoping someone might be able to explain the science behind it :o

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Not a scientific explanation but one that may work...
The larger the lens opening the more curve of the lens is used to focus with and the smaller amount will be in focus. The smaller the lens opening the less curve is used or flatter the section of lens and more will come out in focus. If you look into a flat mirror at the county fair the image in the mirror looks correct but if you step to the curved mirror the center remains in focus but as more of the mirror is curved the more you look distorted or out of focus, Jeff

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Originally Posted by Grandpaw

Not a scientific explanation but one that may work...
The larger the lens opening the more curve of the lens is used to focus with and the smaller amount will be in focus. The smaller the lens opening the less curve is used or flatter the section of lens and more will come out in focus. If you look into a flat mirror at the county fair the image in the mirror looks correct but if you step to the curved mirror the center remains in focus but as more of the mirror is curved the more you look distorted or out of focus, Jeff

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That is an excellent explanation and comparison :eek: Thank you very much Grandpaw :D :thumbsup: :D

Okay, after reading fully through the link you posted Paul, that wasn't quite exactly what I was looking for. Initially, the diagram at the top looked like the direction my mind was heading. Damn though, there is a lot of good info on that page! :eek: That page had another excellent link listed, http://photo.net/learn/optics/lensTutorial Definitely more than enough to keep my mind pondering for a while :o

Grandpaw, your explanation was basically what I was looking for in the end :)

Thanks again to both of you though for helping me out! I now have a much better comprehension of optics and their variables :thumbsup:

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Originally Posted by photophorous

I really don't know how to explain this in words.

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Same here, not that I really have much of a grasp on it... I didn't read too much on the page but it looks like they cover "Diffraction" and this does make a real-world difference. Basically, once you close a lens down to a certain point the image will start getting soft. In practice there really isn't a magic formula for it, but not using the last stop (or two stops) of a lens unless necessary should take care of it.

One wierd example I had was a 300mm lens that was very nice wide open at f4.5, amazing at 5.6, still just about as good at f8 and then went soft quickly after that - to the point that f32 looked like a handheld shot after seven cups of coffee. OTOH, some lenses will be fine at minimum aperture. Bottom line, don't use more DOF than you need.

Pinhole images will have this diffraction effect, of course - tons of DOF and diffraction due to the very small aperture.

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Originally Posted by another view

... In practice there really isn't a magic formula for it, but not using the last stop (or two stops) of a lens unless necessary should take care of it....

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I thought this was a product of a particular lens' design and not a general rule of thumb up though. Didn't Ansel come to the conclusion that f/64 was the optimum aperture setting for sharpness, henc ethe name behind the group they founded, Group f/64? Maybe that is just for LF lenses which I would think are designed more to be stopped down? I don't know as though I have shot enough with my MF cams to come to a complete conclusion but, my Rolleicord stops down to f/22 and seems to be sharpest at that point. While my Yashica stops down to f/32 but seems best at either f/16 or f/22. I haven't done a real comparison yet with my Canonet but, those are supposed to be, and designed to be, sharpest wide open at f/1.7.

I'm not going to dispute his findings but like I said, some lenses work differently than others - some are fine anywhere and others aren't IME. I don't know the technicalities of it; I just look at the results. I had an 85 f1.4 and there wasn't much reason to have that lens if it wasn't shot at f2 or wider - not sure if I ever tried it past f5.6. The 80-200 f2.8 isn't bad at f22. They're all different. :)

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Originally Posted by another view

...I don't know the technicalities of it; I just look at the results...

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No worries, been following that same line myself :) I dunno, I find myself more and more wanting to know the technicalities and the basic science behind it all. Been interesting so far to say the least.

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Originally Posted by Xia_Ke

No worries, been following that same line myself :) I dunno, I find myself more and more wanting to know the technicalities and the basic science behind it all. Been interesting so far to say the least.

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I don't understand the physics behind diffraction, but in a photographic context, I think I have a pretty good understanding. Someone please correct me if I'm wrong.

The light passing through the middle of the lens is unaffected by diffraction and it's sharp. The light that passes near the edges of the aperture blades is softened by diffraction. As you stop down, the ratio of the Circumference of the aperture opening (where diffraction occurs) to the Area of the aperture opening increases (C/A). This basically means that more of the light (as a percentage) has been affected by diffraction, which will result in an overall softer image. Diffraction exists at all apertures, but at wider apertures, the affected light rays are a much smaller percentage of the overall quantity of light and therefore have less of an effect on the image.

On the other hand, as you open up the aperture, you begin to use the outermost parts of the glass, and this is usually where the glass has more imperfections. Again, you have a situation where the light passing through the middle is passing through the best glass and is sharp, but you have light passing through the outer edges of the lens that is not as sharp, and this combines to create some level of deterioration to the sharpness of the image. The better the quality of the glass, the more you can open up the aperture with out having the glass effect the image. This is good, because it also means you have less diffraction. It's a balancing act.

Fast lenses, like the 85/1.4, are usually more expensive because the glass has to be better out on the edges. One thing I don't understand is how much control the designers have over diffraction. Can they make aperture blades that create less diffraction, or is there a physical limit that prevents lens designers from eliminating diffraction? I don't know, but it certainly seems like some lenses perform better at small apertures than others do. However, some of the most expensive lenses, like Leica lenses, have sweet spots at very wide apertures. You would think if someone is paying $3K for a lens it would have the best diffraction control possible, in addition to great glass. This leads me to believe that there is more a designer can do about glass quality than diffraction. As the quality of the glass increases and the diffraction characteristics of a given aperture design don't improve, the sweet spot occurs at wider apertures.

In terms of large DOF, it's best to experiment to figure out where diffraction begins to outweigh the positive effects of a smaller circle of confusion. It's somewhat subjective, but with my 35mm Voigtlander lens, I find I can get the best overall sharpness over the largest distance range by shooting at f11. I pretty much never use f16 or f22, unless the light levels require it, and I'll shoot at f5.6 if I don't need lots of DOF. This is where a view camera shines, because it allows you to use the sweet spot of the lens, while tilting the film plane to increase DOF.

Paul

Thank you very much Paul :) Now that you guys got me started thinking about the relationship of f-stop to sharpness I did a little more reading to clarify what you touched upon Paul and man, now my head is swimming. If anyone wants to read more on this here's a couple links that will give you more than enough to think about:

Sharpness vs. f/Stop
Diffraction
Diffraction and Depth-Of-field
and if you REALLY want overkill... Modulation Transfer Function

Don't even asked me to summarize those right now...LOL I really need to go back and read them with a clearer head but, this thread has had quite a few views so I thought I would pass them along if anyone was interested.

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Originally Posted by Xia_Ke

If anyone wants to read more on this here's a couple links that will give you more than enough to think about

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I think I'll pass; my head still hurts from that other thread. :p

Paul, that is how I understand diffraction too. I don't know how much control they have either but would imagine it's a matter of compromises - based on the economics of pricing, intended use of the lens, etc. Good post! :thumbsup:

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Originally Posted by Xia_Ke

Thank you very much Paul :) Now that you guys got me started thinking about the relationship of f-stop to sharpness I did a little more reading to clarify what you touched upon Paul and man, now my head is swimming. If anyone wants to read more on this here's a couple links that will give you more than enough to think about:

Sharpness vs. f/Stop
Diffraction
Diffraction and Depth-Of-field
and if you REALLY want overkill... Modulation Transfer Function

Don't even asked me to summarize those right now...LOL I really need to go back and read them with a clearer head but, this thread has had quite a few views so I thought I would pass them along if anyone was interested.

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I'm sure that my circumference to area ratio explanation is neglecting all kinds of details and using the wrong terminology, but it's as close as I'll get to understanding it. I think it's basically correct. :D

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Originally Posted by another view

...my head still hurts from that other thread. :p ...

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You're not alone...LOL That was exhausting.

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Originally Posted by photophorous

I'm sure that my circumfrence to area ratio explanation is neglecting all kinds of details and using the wrong terminology, but it's as close as I'll get to understanding it. I think it's basically correct. :D

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I think you were on the right track. Part of me wants to try and push through those links but, my brain is mush ATM...LOL I really should finally sit down with Ansel's Basics books 1-5. I've had them for a little while now but, don't quite think I was ready to absorb them at the time.

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Originally Posted by Xia_Ke

You're not alone...LOL That was exhausting.



I think you were on the right track. Part of me wants to try and push through those links but, my brain is mush ATM...LOL I really should finally sit down with Ansel's Basics books 1-5. I've had them for a little while now but, don't quite think I was ready to absorb them at the time.

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When it gets too technical, I just have to go out and shoot. :D The best thing you can do is waste some film shooting a brick wall with each lens you care to learn that well. Otherwise, f8 and be there.

Paul

I think the key part is this:
"In practice this implies that at the Nyquist frequency of e.g. an APS-C sensor of 8 Mega pixels, spf ~ 80 lp/mm. Hence one should not stop down much further than N = 8. Stopping down too much, say beyond N = 11, will not improve depth of field, but will wipe out details at the extremes of the depth of field, among which objects near the horizon."

I take every lense I shoot out at dusk and shoot lights. The distortion I see at the edges lets me know how the lense softens. I could be way off base on this but the shot 1/2 lens angel in my gallery is an example of the shot I look for and the f-stop. You can see the difference between the center and the edges quite clearly. Actually I just looked at that shot and you can't see :blush2: . Its way too small :cryin: I'll look for a bigger version so you will understand.:idea:http://forums.photographyreview.com/...1&d=1194083310
This is what I mean by softening. The lights in the center of the photo are slightly distorted as well. The lights just off center are perfect. When I scoped this negative I realized that for me at least, this was a far easier way to understand how sharp my lense was. Numerical values are fine but seeing the sharpness displayed in light was more understandable for me. I went to just in between a full circle and a hexagon. Its a 1/2 stop in the middle of each.

Doh! Lost track of this thread. Sorry :o

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Originally Posted by SmartWombat

I think the key part is this:
"In practice this implies that at the Nyquist frequency of e.g. an APS-C sensor of 8 Mega pixels, spf ~ 80 lp/mm. Hence one should not stop down much further than N = 8. Stopping down too much, say beyond N = 11, will not improve depth of field, but will wipe out details at the extremes of the depth of field, among which objects near the horizon."

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That is a good quote Paul. So basically, the rule of thumb should be when going for maximum DOF you should use the largest aperture that still allows you to obtain the desired depth? Example, say you're shooting a distant landscape. Instead of stopping all the way down, if there's nothing within 30 or 40 feet that falls in frame, to only use f/8 or f/11?

I hope that makes sense. Still getting my morning coffee in me :o

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Originally Posted by reverberation

I take every lense I shoot out at dusk and shoot lights. The distortion I see at the edges lets me know how the lense softens. I could be way off base on this but the shot 1/2 lens angel in my gallery is an example of the shot I look for and the f-stop. You can see the difference between the center and the edges quite clearly. Actually I just looked at that shot and you can't see :blush2: . Its way too small :cryin: I'll look for a bigger version so you will understand.:idea:http://forums.photographyreview.com/...1&d=1194083310
This is what I mean by softening. The lights in the center of the photo are slightly distorted as well. The lights just off center are perfect. When I scoped this negative I realized that for me at least, this was a far easier way to understand how sharp my lense was. Numerical values are fine but seeing the sharpness displayed in light was more understandable for me. I went to just in between a full circle and a hexagon. Its a 1/2 stop in the middle of each.

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That is a great example. Just curious, do you have a full frame shot of this posted anywhere just for comparison to see when the diffraction point falls?

Woops!:blush2: I had thought the link went to the full shot:rolleyes: . I did notice I said the center was distorted as well in my post:eek: . This is incorrect, the center is sharpest:idea: . I was confused, there is an area of distortion just off center, this is what I meant. http://forums.photographyreview.com/...1&d=1194241468

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Originally Posted by photophorous

I don't understand the physics behind diffraction, but in a photographic context, I think I have a pretty good understanding. Someone please correct me if I'm wrong.

The light passing through the middle of the lens is unaffected by diffraction and it's sharp. The light that passes near the edges of the aperture blades is softened by diffraction. As you stop down, the ratio of the Circumference of the aperture opening (where diffraction occurs) to the Area of the aperture opening increases (C/A). This basically means that more of the light (as a percentage) has been affected by diffraction, which will result in an overall softer image. Diffraction exists at all apertures, but at wider apertures, the affected light rays are a much smaller percentage of the overall quantity of light and therefore have less of an effect on the image.

On the other hand, as you open up the aperture, you begin to use the outermost parts of the glass, and this is usually where the glass has more imperfections. Again, you have a situation where the light passing through the middle is passing through the best glass and is sharp, but you have light passing through the outer edges of the lens that is not as sharp, and this combines to create some level of deterioration to the sharpness of the image. The better the quality of the glass, the more you can open up the aperture with out having the glass effect the image. This is good, because it also means you have less diffraction. It's a balancing act.

Fast lenses, like the 85/1.4, are usually more expensive because the glass has to be better out on the edges. One thing I don't understand is how much control the designers have over diffraction. Can they make aperture blades that create less diffraction, or is there a physical limit that prevents lens designers from eliminating diffraction? I don't know, but it certainly seems like some lenses perform better at small apertures than others do. However, some of the most expensive lenses, like Leica lenses, have sweet spots at very wide apertures. You would think if someone is paying $3K for a lens it would have the best diffraction control possible, in addition to great glass. This leads me to believe that there is more a designer can do about glass quality than diffraction. As the quality of the glass increases and the diffraction characteristics of a given aperture design don't improve, the sweet spot occurs at wider apertures.

In terms of large DOF, it's best to experiment to figure out where diffraction begins to outweigh the positive effects of a smaller circle of confusion. It's somewhat subjective, but with my 35mm Voigtlander lens, I find I can get the best overall sharpness over the largest distance range by shooting at f11. I pretty much never use f16 or f22, unless the light levels require it, and I'll shoot at f5.6 if I don't need lots of DOF. This is where a view camera shines, because it allows you to use the sweet spot of the lens, while tilting the film plane to increase DOF.

Paul

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Diffraction is all about how big an opening is compared to the wavelength of light you're using. As a lens is stopped down, the stop aperture starts approaching the critical length over which diffraction is the important factor. First order optics ignores diffraction effects, but if they are considered, then it's quickly realized that diffraction always happens at edges, causing light falloff in the area behind the edge. The nature of that light falloff depends on the geometry of the edge. You are right, in essence, about why diffraction effects become more noticeable when the lens is stopped down. Technically it happens because the area of the image circle over which diffractive light falloff occors is greater in proportion to the entire image circle. Light falloff is a simplistic description, too. There is a distribution of changes in optical path length in the shadow of the edge which cause the blurring. If we were using a really small aperture--on the order of one wavelength--then we'd describe the effect in terms of reduced "visibility", which is a fancy physics/physical optics term for decreased contrast.

Depth of focus........is dependent on the diameter of the exit pupil, which is just the image of the aperture in "image space". The greater the diameter of the exit pupil, the greater the numerical aperture (numerical aperture, NA, is just sin(alpha) where alpha is the angle formed by the optical axis and a ray from the exit pupil edge to the optical axis in the image plane. If it helps, f/#=1/(2*NA).) In simplistic terms, with a large f/#, say f.20, the rate at which the size of the image circle changes as you move away from focus is slower than it would be if you were using f/2. If you consider image blur to be a constant size for a given lens, then the f/2 lens will approach that constant image blur size more quickly.

Someone talked about aberrations. The dominant aberrations in photographic lenses are NOT manufacturing imperfections. The dominant aberrations are the aberrations that result from that the theory does not allow for perfect spherical waves (that would focus at exactly one point) and requires these aberrations, and there 5 of them: spherical aberration, coma, distortion, astigmatism, Petzval curvature. The trick to lens design is designing lenses that balance these aberrations and their higher order forms. When stopping down a lens, what is happening is that you are reducing aperture position dependent aberrations: coma, astigmatism, distortion, and Petzval Curvature.