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# Diffraction and Sensor Size

#### MGrayson

##### Subscriber and Workshop Member
Playing around with old lenses got me thinking about diffraction. Why? Because we often need to use f/11. When I was shooting a tech cam with a large sensor, f/11 ws kind of standard. And then there's the whole f/64 thing with large format.

But calculations of diffraction blur show that the size of the Airy disk (blurred image of a point) depends only on wavelength and f-number. For 5µ pixels, pixel level blurring becomes dominant at the same f-number independent of sensor size.

And THIS is why viewing at 100% on a monitor is dangerous. Because what matters is the final image size or, given a sensor size, magnification. Large sensors don't have to be magnified as much to make a final image, so they can afford larger Airy disks. The formula for disk size, BTW, is 1.22*f*w, where f is the f-number and w is the wavelength.

Let's make a 16"x20" print from 8"x10" film using f/64. Pick a wavelength of 6,000 Å, AKA 600nm, AKA 0.6µ, a nice Yellow. This gives us an Airy disk of size 1.22*64*0.6µ = 47µ. That looks like a large number, but when we make our 16"x20" print, that becomes only twice as large, so 94µ = 0.1mm = 1/250". In other words, we get 250ppi resolution.

Let's do the same thing with a 645 digital back at f/11. The disk size is 1.22*11*0.6µ = 8.1µ, and that's like one to two pixels depending on the back. But our sensor is a bit over 2 inches and we need a magnification of at least 9 to make the print, so the spot becomes 75µ. Better, but not hugely better than Ansel Adams at f/64. We could even get away with f/13.

And, as most of us have 44mmx33mm sensors, we get a magnification of 12 and so a disk size of 96µ in the final print. Almost exactly the same as the 8"x10" film at f/64.

Of course, modern lenses are sharp at lower f-numbers, but I wanted to see what corresponded to the historical gold standard. And if you've ever seen a 16"x20" print in person of "Clearing Winter Storm", or "Moonrise, Hernandez", the last thing on your mind is "meh, could have been sharper."

Matt

This, BTW, is George Biddell Airy. He's also the guy who chose Greenwich as the location of the Prime Meridian.

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#### P. Chong

##### Well-known member
Thanks Matt. Best explanation I have ever read on the diffraction and f stops.

#### MGrayson

##### Subscriber and Workshop Member
Thanks Matt. Best explanation I have ever read on the diffraction and f stops.
Many thanks!

The more I look at the realities of different size systems, the more the pure physical size of the lens opening pops up. That aperture is, of course, f-number times focal length, and it shows up everywhere. A 32mm lens at f/8 has the same sized opening (4 mm) as an 8*32mm = 256mm lens at f/64. So while the Airy disk of the larger system is 8 times bigger, that is exactly cancelled out by the 8 times lower necessary magnification.

Three photographers are standing at Tunnel View. Their cameras have perfect optics and infinite resolution. They are only limited by diffraction. One has a sort-of APS-C sensor (17mm x 26mm) with a 17mm lens set at f/2. Another has a FF sensor (24mm x 36mm) and a 24mm lens set at f/2.8, and the third has a 6x9 film camera because she's cool (56mm x 84mm), and a 56mm lens set at f/6.5 (her lens has an f/6.5 setting, ok?) When they make their 24" wide prints, they will all have exactly the same softening due to diffraction, because they all had 17/2 = 24/2.8 = 56/6.5 = 8.5mm physical apertures. When the guy who sets up 20 feet in front of them turns around, he sees three equal size openings in their cameras just before they kill him.

#### Shashin

##### Well-known member
Exactly. This is a relative problem. The interesting thing I see on this discussion is that people stress about sharpness, but they are afraid to optimize depth of field, which ultimately makes more of the image unsharp. For a 33x44 sensor, I have no problem using f/22 if I need the depth of field. Diffraction at that sensor size is not an issue--full image on a 40MP and a 100% crop of the lower right corner.

#### rdeloe

##### Well-known member
I cannot understand people who would spoil a photo by leaving things out of focus that they would prefer to be in focus simply because they want to achieve maximum sharpness at 100% in some other part of the image.

#### MGrayson

##### Subscriber and Workshop Member
Why stop down when you can focus stack?
That's sarcasm, in case it's not obvious. Focus stacking is a great thing, and there are some images that are impossible without it. But the lenses have those higher f-numbers for a reason!

#### rdeloe

##### Well-known member

I'm probably the only person on this site who has convinced themselves that they needed a certain lens and then went to some considerable trouble and expense to research options, choose one, and then buy it... only to almost never use it. Right?

Anyway, I have this very nice Mamiya N 210mm f/8 L that I had converted to work on my digital view camera outfit. And I almost never have it with me. It lives a quiet life in my lens drawer, waiting for the project that I was absolutely certain (at the time of all this researching and buying) I would undertake.

It's not very big or very heavy, unlike the other two lenses in that focal length that preceded it into the lens drawer. Cough. The main reason I don't carry it is because I noticed soon after getting it that cropping and uprezzing an image from my Mamiya N 150mm f/4.5 L was just as good.

Having a bit of time on my hands on the weekend, I decided to revisit that question. Previously I'd tested by using outdoor scenes, where movement and air quality are confounding variables. This time I did it indoors, where a couple coffee makers on my counter provided ideal models.

I shot the images, performed the uprezzing, and this time printed portions of the scene to 19" on the long edge. I had to go back to the computer to figure out whether the image on the left on the print was the uprezzed 150mm, or was it the one on the right. At that point I realized the 150mm is damned good, and I was right that there's really no point in lugging the 210mm along.

So what does this have to do with diffraction? I was judging the lenses based on the ability to resolve scratches on my coffee pots. It's not about the scratches. It's about the whole picture.

Worrying about Ultimate Image Quality (tm) and whether shooting at f/11 makes medium format photography with high quality lenses completely pointless because of diffraction ... that's focusing on the scratches on the coffee pot rather than whether the whole picture works.

#### Shashin

##### Well-known member
Why stop down when you can focus stack?
Seriously. You spend all that money for an f/0.95 lens and then you don't use that stacking software to not only get the sharpness throughout the image, but also the creamy bokeh...

#### Shashin

##### Well-known member
I challenge someone to focus stack with an f/0.95 lens wide open...

#### buildbot

##### Well-known member
And THIS is why viewing at 100% on a monitor is dangerous. Because what matters is the final image size or, given a sensor size, magnification. Large sensors don't have to be magnified as much to make a final image, so they can afford larger Airy disks. The formula for disk size, BTW, is 1.22*f*w, where f is the f-number and w is the wavelength.

Let's make a 16"x20" print from 8"x10" film using f/64. Pick a wavelength of 6,000 Å, AKA 600nm, AKA 0.6µ, a nice Yellow. This gives us an Airy disk of size 1.22*64*0.6µ = 47µ. That looks like a large number, but when we make our 16"x20" print, that becomes only twice as large, so 100µ = 0.1mm = 1/250". In other words, we get 250ppi resolution.
Interesting, I knew that it depended on f-number, I did not know the disk size was dependent on wavelength! That has interesting implications for Achromatic photography with specific bandpass filters. A UV bandpass filter centered at 370nm would have 2.5x the disk size of a 925nm filter!

I challenge someone to focus stack with an f/0.95 lens wide open...
I could try f 1.1 equivalent with my Mamiya f1.9 + focus rail haha

Edit - as @TimoK pointed out, I flipped my sentence and it’s the 925nm filter that has a 2.5x larger disk than a 370nm - this is why you don’t do math right before bed!

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#### dj may

##### Well-known member
Playing around with old lenses got me thinking about diffraction. Why? Because we often need to use f/11. When I was shooting a tech cam with a large sensor, f/11 ws kind of standard. And then there's the whole f/64 thing with large format.

But calculations of diffraction blur show that the size of the Airy disk (blurred image of a point) depends only on wavelength and f-number. For 5µ pixels, pixel level blurring becomes dominant at the same f-number independent of sensor size.

And THIS is why viewing at 100% on a monitor is dangerous. Because what matters is the final image size or, given a sensor size, magnification. Large sensors don't have to be magnified as much to make a final image, so they can afford larger Airy disks. The formula for disk size, BTW, is 1.22*f*w, where f is the f-number and w is the wavelength.

Let's make a 16"x20" print from 8"x10" film using f/64. Pick a wavelength of 6,000 Å, AKA 600nm, AKA 0.6µ, a nice Yellow. This gives us an Airy disk of size 1.22*64*0.6µ = 47µ. That looks like a large number, but when we make our 16"x20" print, that becomes only twice as large, so 100µ = 0.1mm = 1/250". In other words, we get 250ppi resolution.

Let's do the same thing with a 645 digital back at f/11. The disk size is 1.22*11*0.6µ = 8.1µ, and that's like one to two pixels depending on the back. But our sensor is a bit over 2 inches and we need a magnification of at least 9 to make the print, so the spot becomes 75µ. Better, but not hugely than Ansel Adams at f/64. We could even get away with f/13.

And, as most of us have 44mmx33mm sensors, we get a magnification of 12 and so a disk size of 96µ in the final print. Almost exactly the same as the 8"x10" film at f/64.

Of course, modern lenses are sharp at lower f-numbers, but I wanted to see what corresponded to the historical gold standard. And if you've ever seen a 16"x20" print in person of "Clearing Winter Storm", or "Moonrise, Hernandez", the last thing on your mind is "meh, could have been sharper."

Matt

This, BTW, is George Biddell Airy. He's also the guy who chose Greenwich as the location of the Prime Meridian.
View attachment 210958
Great post. I have not seen the effects of diffraction in any of my photos (maybe once squinting at a 100% view of a digital M with 28mm). Certainly never in a print. If I do not require depth of field I tend to shoot at f4.0-5.6 on the Leica S, depending on the lens. I have used f13 and f16 when needed.

#### TimoK

##### Active member
Interesting, I knew that it depended on f-number, I did not know the disk size was dependent on wavelength! That has interesting implications for Achromatic photography with specific bandpass filters. A UV bandpass filter centered at 370nm would have 2.5x the disk size of a 925nm filter!
Isn't it the other way round? A 925nm filter have 2.5x the airy disk size of a 370nm filter.

Or do I some mistake if I count it: 1.22*11*0.375μ = 4,9654μ and 1.22*11*0.925μ = 12,4135μ ,
12,4135μ : 4,9654μ = 2.5

#### MGrayson

##### Subscriber and Workshop Member
Isn't it the other way round? A 925nm filter have 2.5x the airy disk size of a 370nm filter.

Or do I some mistake if I count it: 1.22*11*0.375μ = 4,9654μ and 1.22*11*0.925μ = 12,4135μ ,
12,4135μ : 4,9654μ = 2.5
No, you're correct.

#### MGrayson

##### Subscriber and Workshop Member
Exactly. This is a relative problem. The interesting thing I see on this discussion is that people stress about sharpness, but they are afraid to optimize depth of field, which ultimately makes more of the image unsharp. For a 33x44 sensor, I have no problem using f/22 if I need the depth of field. Diffraction at that sensor size is not an issue--full image on a 40MP and a 100% crop of the lower right corner.

I like this image. It has a great "reality" feel. Almost anything that makes you feel like you could actually *be* there is a good photo IMHO.

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#### buildbot

##### Well-known member
Isn't it the other way round? A 925nm filter have 2.5x the airy disk size of a 370nm filter.

Or do I some mistake if I count it: 1.22*11*0.375μ = 4,9654μ and 1.22*11*0.925μ = 12,4135μ ,
12,4135μ : 4,9654μ = 2.5
Yes I flipped them good catch

#### MGrayson

##### Subscriber and Workshop Member
Interesting, I knew that it depended on f-number, I did not know the disk size was dependent on wavelength! That has interesting implications for Achromatic photography with specific bandpass filters. A UV bandpass filter centered at 370nm would have 2.5x the disk size of a 925nm filter!

I could try f 1.1 equivalent with my Mamiya f1.9 + focus rail haha

Edit - as @TimoK pointed out, I flipped my sentence and it’s the 925nm filter that has a 2.5x larger disk than a 370nm - this is why you don’t do math right before bed!
To be clear, I was laughing at the Mamiya f/1.9 on the rail image, not the typo!

#### buildbot

##### Well-known member
To be clear, I was laughing at the Mamiya f/1.9 on the rail image, not the typo!
I figured but thanks for the clarification
It was a funny typo though too haha.

#### Pieter 12

##### Well-known member
View attachment 210962
I'm probably the only person on this site who has convinced themselves that they needed a certain lens and then went to some considerable trouble and expense to research options, choose one, and then buy it... only to almost never use it. Right?

Anyway, I have this very nice Mamiya N 210mm f/8 L that I had converted to work on my digital view camera outfit. And I almost never have it with me. It lives a quiet life in my lens drawer, waiting for the project that I was absolutely certain (at the time of all this researching and buying) I would undertake.

It's not very big or very heavy, unlike the other two lenses in that focal length that preceded it into the lens drawer. Cough. The main reason I don't carry it is because I noticed soon after getting it that cropping and uprezzing an image from my Mamiya N 150mm f/4.5 L was just as good.

Having a bit of time on my hands on the weekend, I decided to revisit that question. Previously I'd tested by using outdoor scenes, where movement and air quality are confounding variables. This time I did it indoors, where a couple coffee makers on my counter provided ideal models.

I shot the images, performed the uprezzing, and this time printed portions of the scene to 19" on the long edge. I had to go back to the computer to figure out whether the image on the left on the print was the uprezzed 150mm, or was it the one on the right. At that point I realized the 150mm is damned good, and I was right that there's really no point in lugging the 210mm along.

So what does this have to do with diffraction? I was judging the lenses based on the ability to resolve scratches on my coffee pots. It's not about the scratches. It's about the whole picture.

Worrying about Ultimate Image Quality (tm) and whether shooting at f/11 makes medium format photography with high quality lenses completely pointless because of diffraction ... that's focusing on the scratches on the coffee pot rather than whether the whole picture works.
I know this image might have been made just to illustrate focus-stacking (which I don't quite understand), but if one would go to the trouble to make the background bread a bit sharper, time would be better spent with the lighting to bring out the engraving detail in the coffee urn and avoiding the photographers reflection in it.

#### dj may

##### Well-known member
I know this image might have been made just to illustrate focus-stacking (which I don't quite understand), but if one would go to the trouble to make the background bread a bit sharper, time would be better spent with the lighting to bring out the engraving detail in the coffee urn and avoiding the photographers reflection in it.
You missed the point.

#### rdeloe

##### Well-known member
I know this image might have been made just to illustrate focus-stacking (which I don't quite understand), but if one would go to the trouble to make the background bread a bit sharper, time would be better spent with the lighting to bring out the engraving detail in the coffee urn and avoiding the photographers reflection in it.
Hi Pieter. It wasn't made to illustrate focus stacking. Those are just crops from single-frame, quick throw-away test of two lenses. I looked around for something to point the lenses at, and noticed my coffee makers.