diffraction limits, DX vs 35mm format

It has often been said, including by Thom Hogan, that a larger format like 35mm Film Format (FF) has an advantage in diffraction limitation over a smaller format like DX. I disagree:

• yes, DX format must use an aperture one f-stop lower to limit diffraction to the same degree, maybe f/8 on the D2X instead of f/11 on the 5D, but
• the lower f-stops needed to control diffraction are certainly available with all lenses for DX (we are talking about f/8!)
• the DOF at the lower f-stop like f/8 in DX is the same as at the higher f-stop like f/11 in FF, so there is no more DOF penalty in controlling diffraction
• the extra stop of "lens sped" allows the use of about half the sensor speed (Exposure Index EI, a.k.a. ISO) or twice the shutter speed, neither of which seems to be a disadvantage. In fact the lower Exposure Index usable with the smaller format means that with equal pixel counts, each pixel is receiving the same amount of light, so the shift in both aperture ratio and Exposure Index about equalizes shadow noise along with DOF and diffraction effects.

In other words, this is yet another case where the closest thing to parity between different DSLR formats is given by using the same effective aperture diameter. In more detail, with DX one could

• reduce focal length by 1.5x, to get equal field of view
• reduce aperture ratio by 1.5x or about one stop, to get equal diffraction effects and equal Depth Of Field, and by the way, equal effective aperture diameter
• reduce Exposure Index or "ISO speed" by 1.5 squared or 2.25, so about one stop slower, to get the same shutter speed with the lower f-stop, which is likely to roughly balance out the noise level differences of different photo-site sizes.

If we assume (and it is certainly true in most cases) that a larger sensor or film size corresponds to larger diameter lenses in order to create a large enough image circle, then larger sensors/films have an advantage with regard to diffraction. For example, Ansel and his fellow f/64 club friends actually used these large f/stops sometimes. Can you imagine the image formed by a DX lens stopped down to f/64? Yuck!

Let's consider a given field of view. We all know that larger sensor/film means you need a larger focal length to achieve this field of view. Since f/stop is the ratio of focal length to entrance pupil diameter, if we are using a larger focal length, the physical size of the entrance pupil is also larger to keep the f/stop constant. Since diffraction's significance is inversely proportional to entrance pupil size (it gets worse as entrance pupil size decreases), larger format should have an advantage with regard diffraction and narrow DOF because it's entrance pupil size at a given field of view and f/stop is larger.

In short, larger format means larger hole for the light to pass through, which means all else being equal, diffraction is less significant for larger formats.
--
Dana Paul Franz
[email protected]
http://dfranz.smugmug.com
'You are the master of the unspoken word;
once it is out of your mouth, you are the slave.'

Hi, some thoughts:

Yes, this is a multidimensional problem. One aspect you did not address is lens diffraction vs lens aberrations. For example, a classic rule of thumb (RoT) is to stop down a lens 2 Fstops to reduce lens aberrations. This works well for FF 35, since you rarely get into a diffraction problem with this RoT. However, for a DX size, your window of Fstop options is reduced using the RoT of F8 as the diffraction limit.

Take the new Nikon 18-200 VR DX F3.5-F5.6. You might have to find the sweet spot of trade-offs of diffraction vs lens aberrations at the 200mm position. For the RoT on FF 35, this would not be a problem, since F11 would not be diffraction limited.

BTW, on P&S cameras with the small sensors, it is even worst. You are essentially diffraction limited around F2.8. So in that sense, DX is much better.

Also, I am not sure a F8 RoT is a conservative Fstop for DX. It might be somewhat less. In that case, the above lens would have a very narrow Fstop range for best IQ. Regardless, using your F8 RoT, only one Fstop.

So this is one area I like about FF. The other tradeoffs still positon DX well vs FF for considering today technology/cost.

Well, are you arguing theoretical or practical? Practically, with a D2x I don't find myself overly bound by f/11 (the last aperture where I don't see diffraction effects), though I have sometimes encountered situations where I'd like more DOF than that limit gives me (usually at the telephoto end).

From a theoretical standpoint (future DSLRs with more pixels), I think an f/8 limit would start to be constraining for me, so I can't imagine a 16mp APS sensor body as being something I'd greatly desire over the D2x just from a megapixel standpoint. In my wide angle work I'd probably have to give up infinity focus with such a beast, which seems to defeat the purpose of more pixels. At the telephoto end, f/8 is very constraining in DOF (at 70mm and 10 feet you get a whole 'nother half foot of DOF at f/11 over f/8).

This is an issue that amateurs just don't see (just like they didn't see it with film--my mentor almost always stayed at f/11 and never went past f/16 with his 20mm lens [that gave him 2 feet to infinity as max DOF, but more normally 2.5 feet to infinity]). But pros working for every last pixel of image quality definitely do. Nikon's pushing at the boundaries of what is acceptable.

--
Thom Hogan
author, Nikon Field Guide & Nikon Flash Guide
editor, Nikon DSLR Report
author, Complete Guides: D70, D100, D1 series, D2h, D2x, S2 Pro
http://www.bythom.com

You are correct that at diffraction-limited depths-of-field, format size is irrelevant. So f11 and 20mm on a D2x would be about the same as f16 and 30mm on a 5D.

However, there is an optical penalty for a smaller format. It's actually harder (and more expensive) to control aberrations on a shorter, faster lens than it is on a longer, slower lens. This "difficulty" seems to go approximately inversely with the cube of the f-stop (harder at lower f-numbers).

Presently this doesn't seem to be much of a problem because most lenses are very close to diffraction-limited themselves by the time you stop them down to point at which ideal lenses would be at the diffraction limit for today's sensors.

However, at the other end, this is a problem for a smaller format. A 24/1.4L (Canon full-frame lens) is a very difficult lens to make. A 16/1.0DX would be much, much harder. Note that this condition violates the topic of your post because this will not be a diffraction-limited condition. I just wanted to mention it as it seems related because of that optical penalty I mentioned.

--
Lee Jay
(see profile for equipment)

Lens aberations: If avoiding diffraction limitation were to require f-stops around f/4 or smaller, lens aberrations would start to be an issue, and that likely is the case with trying to take small sensor formats like 2/3" and under beyond 10MP. But for the current smallest DX format pixel spacing of 5.5 microns in the D2X, diffraction only comes in from about f/8 or f/11 and up, high enough that the increasing aberrations at low f-stops are not a problem. Only if DX format reaches about 50MP or beyond would diffraction and aberration limits collide.

Thom: given that the f-stops needed to avoid diffraction in DX format are still well clear of the aberration limits, in what way is it a disadvantage to have to use an aperture ratio one stop lower in DX than in 35mm format a disadvantage, given that you get the same DOF in either format? For example, what is worse about using f/8 with DX versus using f/11 in 35mm format? Is the halving of ISO speed a problem for you?

About 8x10" large format using f/64: yes they could do that while having only the same diffraction limits as f/8 in 35mm, but they also had to do that just to get the same DOF as f/8 gives in 35mm, so where is the advantage to the larger format? The biggest difference I see is that the user of f/64 in 8"x10" format needs to use an exposure time 64 times as long with the same speed of film, (or a film speed 64 times greater to get the same shutter speed.)

It seems that even though most people know that different formats use different but "equivalent" focal lengths to get the same field of view, many still ignore the fact that different but "equivalent" aperture ratios are also needed to get the same DOF and degree diffraction (witness the far higher aperture ratio used in large format). Instead, there is this stubborn insistence that all comparisons between different formats be done at equal f-stop. And the equivalence is so simple: same effective aperture diameter for same DOF, same diffraction, etc.

BJL said:

Lens aberations: If avoiding diffraction limitation were to require
f-stops around f/4 or smaller, lens aberrations would start to be
an issue, and that likely is the case with trying to take small
sensor formats like 2/3" and under beyond 10MP. But for the current
smallest DX format pixel spacing of 5.5 microns in the D2X,
diffraction only comes in from about f/8 or f/11 and up, high
enough that the increasing aberrations at low f-stops are not a
problem. Only if DX format reaches about 50MP or beyond would
diffraction and aberration limits collide.

Click to expand...

Didn't I say that?

--
Lee Jay
(see profile for equipment)

What happens when you shooting for "maximum sharpness" at the sweet spot for the lens. With most "premium" Nikkors that is F4. Use your 58mm Noct Nikkor on the DX format at f4, an 85mm f1.4 Nikkor at f4 on 35mm film and then make identically sized paper prints and the 35mm image will look sharper. I will grant that the 58mm image will have a bit more DOF but the peak sharpness will fall in favor of the 35mm result. I believe that is the point that Thom was making, on the final print, the larger the format, the more "lines" available for making the print. If you assume that either lens will resolve around 60 lp/mm, that means the DX format will have 60x24 (1440) line pairs and the 35mm image will have 60x36 (2160) line pairs.

If you want an extreme example of this, take an 8x10 inch "View Camera" as an example. That will use a 300mm lens at an aperture of around f64 where it will only resolve around 15 lp/mm (which sounds horrible). However, that film is 254mm across so that means that you have a grand total of 254x15 (3810) line pairs for your image. Now "that's what I'm talking about", DETAIL baby! Only problem is that you either need a magnifying glass to see it or a really BIG print, which can be VERY expensive in today's "digital" world.

What it all means is that you both correct and incorrect. For most shooters, your point is correct. However, when you want the absolutely sharpest possible result, the larger the format, the more detail you can capture. It also means that in order to hit the 20 to 24mp resolution that many are currently lusting for, we will need a larger format. Current lenses just can't capture that much detail on the DX format and since it's mainly due to Diffraction limits, it's something that we cannot do anything about. Look at some of the postings from D2x users and you'll see that the practical limit for that camera is somewhere around f4~5.6, use a smaller aperture and you start "losing" megapixels. Shoot at f8 on the D2x and you may as well set the camera to 6mp of resolution because that's about all the detail that the lens can capture.

As for how it effects the FF vs DX debate, my take on this is simple. The reason that I favor the FF side is simple, IT'S THE VIEWFINDERS! That DX "crop" has shrunk viewfinders to the point where they are totally unuseable for critical focus on cameras like the D70 and only very marginally useable on a camera like the D200. Full frame will give us back a "real world" 0.80x magnification and perhaps an old fashioned Ground Glass screen (which are FAR superior for focus than any "Britescreen"). I still shoot occasionally with an F2 that I purchased way back in 1973 and I know how poor the current viewfinders are. To be frank the F5 is mediocre due to the "britescreen" and slightly lower magnification. The D70 is HORRIBLE and all the other DX cameras are only slightly better. Since most of those here have never shot with something like my F2, they have no idea how much has been lost. Since I have, I can tell you it's a LOT. If it weren't for AF, ALL of use would be complaing about soft images because we wouldn't be able to focus that darn cameras.

BTW, my F2 I would have to rate as only GOOD to VERY GOOD. If you want to see great, try using a Mamiya TLR. That coursly ground screen may be a bit dim but it has "snap" you wouldn't believe and a 2.25 inch square frame magnified at 2x is HUGE compared to the F2 using a "normal" prism. I don't think that I have EVER missed the focus with the Mamiya, it's just that good.

Perhaps I should be asking for Nikon to skip Full Frame and go straight to a 36x48mm image size. Only problem is that this would absolutely require that Nikon junk the current F mount and that would have EVERYONE in a rage, myself included. So I'll keep asking for Full Frame simply because it will push Nikon into building "equivalent" viewfinders for the DX format. Once they go Full Frame, the DX useres will see how much better the veiwfinders are on the larger format and really start to demand that Nikon bring the DX viewfinders "up to snuff".

PS, Hey Mamiya, if you have drifted into this, how about a digital back for the good old C-330? Boy would that be a treat, a series of really great lense I already own and no mirror slap from the honking big mirrors that the MF cameras require. That C-330 may be way old tech but it's givem me some of the most detailed images that I have ever taken, on K64 it was flat out amazing.

Shouldn't equal size reproductions be (roughly) identical regardless of the pixel pitch and aperture even if the lens is diffracting?

A 5 billion pixel APS sensor would theoretically diffract at around f0 (heck, they'd probably bring in tunneling effects). But, those pixels, when exposed identically, and at a any consistent f-stop with a D2X, should render an image at least as good as a D2X. Diffraction and airy disk theory is nice, but there are other constraints as well. Like, say:
1_ = ( 1_ + 1 )^1/2
system..........lens rez^2.......film/sensor rez^2

which dictates that any increase in film/sensor resolution will result in better system resolution. That, perhaps, means that we record the airy disk in better detail, but that still renders a sharper final image. Pixel peeping at 100% on-screen is not the same as looking at an 8x12 or 16x24 final print. Even though I have no experience with a D2X, I daresay that a D2X at f16 is equal to film at f16 in sharpness.

I'm not saying that you shouldn't use the best glass and be mindful of diffraction effects, but at around 12+MP, perhaps we should loosen up a bit and just think of the final print effects more than 100% on-screen pixels.

ljfinger said:

BJL said:

Lens aberations: ...

Click to expand...

Didn't I say that?

Click to expand...

Yes you did; the part of my response to you was agreeing about compact cameras possibly being close to limits on resolution due to the squeeze between diffraction at smaller apertures and lens aberrations at larger apertures.

More generally, if aberrations limit best lens performance to f-stops no lower than f/4, then diffraction spot size limits the smallest useful pixels to say 2.5 to 3 microns. If so, diffraction would limit DX format to about 40MP while 35mm format could go to about 90MP.

But other factors like dynamic range will probably stop DSLR pixels from getting that small anyway, so 40MP plus is probably a dream anyway, for DX or 35mm. I am curious how even medium format lenses will handle such high pixel counts with the forthcoming 39MP Kodak and 35MP Dalsa sensors.

I would like to point out that for a larger sensor format (35mm in this case), we are able to provide more pixels (greater number of pixels) for greater resolution, or provide larger pixels (same amount of pixels) with the same amount of resolution. Larger pixels equals less noise, higher usable ISO's, all esle being equal.

The progression to a larger sensor, 35mm, is that in theory and practice, we should be able to get highter resolution, with less noise in our Nikon DSLR.

I believe Nikon will have their 35mm offering in time, and will offer both formats. There are advantages to both.

However, I prefer the angle of view of 35mm over DX. It is more difficult for me, as a portrait photographer, to find quality glass and limit my depth of field. Backing up using my D2X (which increases my depth of field), I am opening up the aperature (difraction not being much of an issue). Offerings in 85mm f/1.4, 105mm f/2 DF, 135mm f/2 DF, 200mm f/2 are pricy indeed.

Cheers,
-
Brooke

D2X, F3, FA, M3

monte12345 said:

What happens when you shooting for "maximum sharpness" at the sweet spot for the lens. With most "premium" Nikkors that is F4.

Click to expand...

As far as diffraction, f/4 will not limit resolution until pixel counts get well past 20-24MP; f/4 gives 50% MTF to about 190lp/mm or about 3000 line pairs per picture height in DX format. With two or three pixels needed per line pair, a DX sensor will only match that resolution limit with about 6000x9000 to 9000x13,500 pixels, about 50MP to 100MP.

(The weaker Rayleigh limit of resolution for f/4 is about 380lp/mm or 6000 line pairs per picture height in DX, which would make it 200MP to 400MP!)

monte12345 said:

If you want an extreme example of this, take an 8x10 inch "View Camera" as an example. That will use a 300mm lens at an aperture of around f64 ... you have a grand total of 254x15 (3810) line pairs for your image.

Click to expand...

That f/64 in the 200x250mm (8"x10") gives about the same diffraction limit on resolution in lines per picture height as DX format with aperture ratio 64*15.7mm/200mm or a quite attainable f/5 (using the short dimensions of each format). In fact I believe that 8"x10" users moved away from f/64 to somewhat larger apertures as film resolutions got higher, and your argument looks better at f/32 or f/22. Then 8x10 can probably give more detail than DX format will ever achieve, but at the cost of a struggle to get adequate DOF.

Brooke A said:

Larger pixels equals less noise, higher usable ISO's, all esle being equal.

Click to expand...

I was only talking about diffraction and resolution, not claiming that 35mm format has no advantages over DX format. However, your claim is only true if by "equal" you mean equal f-stop, and thus with larger aperture diameters with the larger lenses needed to get the same amount of detail on the larger pixels of the larger format. That menas less DOF and bigger, heavier lenses: not at all "equal" for those of us who usually care about getting enough DOF, and about the weight and cost of our gear.

Stop down for equal DOF, or use lenses of equally large front elements, and the larger format must use higher aperture ratios and thus higher ISO speed to get the same shutter speed, so noise comparisons at equal ISO speed become irrelevant.

ljfinger said:

It's actually harder (and more expensive) to control aberrations on a shorter, faster lens than it is on a longer, slower lens. This "difficulty" seems to go approximately inversely with the cube of the f-stop (harder at lower f-numbers).

Click to expand...

I have read this cube law stated before, but can you give me a reference for it?

I suspect that it refers to shorter focal lengths and lower f-stops in the same format , and so with the same sized image circle. Then the shorter focal length designs must cover a wider angular FOV and performance is being measured over that wider FOV. It is a different and easier design situation when the smaller focal length lenses are being designed to give the same FOV but in a smaller format, and thus with aberrations and such corrected and measured only over proportionately smaller image circles.

BJL said:

I have read this cube law stated before, but can you give me a
reference for it?

Click to expand...

Not a great one. A person who posts over in the Canon forum is a real optics expert. His name is Mitch Alsup and he said so. I tend to believe him based on his experience with optics.

--
Lee Jay
(see profile for equipment)

In optical design, ray tracing, you look at the power series for the electric field, more specifically, Snell's law of refraction which involves the sine function, you end up with odd-powered terms x, x^3, x^5...etc. The most commonly spoken of aberrations are third order (5th order aberrations are not very significant in most cases), such as coma, chromatic aberration, astigmatism, spherical aberration, etc. Thus the cubic dependence spoken of here. For reference, see, e.g., Hecht's Optics, or Born & Wolf's Principles of Optics.
--
Dana Paul Franz
[email protected]
http://dfranz.smugmug.com
'You are the master of the unspoken word;
once it is out of your mouth, you are the slave.'

Civengine said:

Shouldn't equal size reproductions be (roughly) identical
regardless of the pixel pitch and aperture even if the lens is
diffracting?

Click to expand...

No. Diffraction affects the capture. Think of it like noise: it's something in the original data that you don't want. And remember that because of the smaller sensor size we're magnifying the capture more than we would with FF.

Civengine said:

Pixel peeping at 100% on-screen is not the
same as looking at an 8x12 or 16x24 final print.

Click to expand...

Absolutely true, a point I make all the time. But a 24" print requires 2x the pixels a D2x produces. At that level I can clearly see the diffraction effects--it's a bit like noise reduction, as it appears as a slightly artifical and "plastic" look in the acuity.

I think we've actually been down this path before. Pinhole cameras (small apertures that produce diffraction) have existed before, and there are such devices the size of a room (increased resolution). You have to get quite a bit of "resolution" and keep a "normal" viewing distance before the diffraction softness isn't perceived, in my experience.

Civengine said:

Even though I
have no experience with a D2X, I daresay that a D2X at f16 is equal
to film at f16 in sharpness.

Click to expand...

I have no experience with a Corvette, but I daresay that it's as good as any Ferrari ; )

I'm an analytical kind of guy (too analytical women tell me ; ). I test everything I get my hands on and compare incessently. I make my statements from observation. I'm quite willing to be corrected when presented with convincing alternative evidence, but the evidence I see is that f/11 is it for my D2x. When I go beyond that I begin to see diffraction impacts I can't completely control, even when printing on my Epson 2200. Now if someone would like to show me how to avoid them, I'd be more than happy to know.

Finally, we need to distinguish between "good enough" and "best." For many amateur photographers, good enough is just that. f/22 on a D2x printed at 36" looks just fine to them (especially compared to anything they've tried before). To a pro, especially a pro that is a control freak like me, we want the best output we can generate. The more garbage (noise, color imbalance, diffraction, chromatic aberration, coma, light falloff, flare, antialiasing, spectrum imbalance, etc.) you put into your original, the more problems you'll find maintaining the highest level of quality in your output. I'd like to think that I've taken or will take pictures that'll someday hang in pride in a museum, gallery, or toilet wallspace (; ), and like Ansel Adams and all the others that have come before me, I'll want to see only what I want to see in those prints...

--
Thom Hogan
author, Nikon Field Guide & Nikon Flash Guide
editor, Nikon DSLR Report
author, Complete Guides: D70, D100, D1 series, D2h, D2x, S2 Pro
http://www.bythom.com

BJL said:

Thom: given that the f-stops needed to avoid diffraction in DX
format are still well clear of the aberration limits, in what way
is it a disadvantage to have to use an aperture ratio one stop
lower in DX than in 35mm format a disadvantage, given that you get
the same DOF in either format? For example, what is worse about
using f/8 with DX versus using f/11 in 35mm format? Is the halving
of ISO speed a problem for you?

Click to expand...

Well, I can't say that I have "a problem." Since realizing that I needed to adjust my diffraction limiting value I've been perfectly pleased with the results my D2x obtains--it tends to force you into the best apertures on the wides, anyway. But every now and then I do encounter a situation where I'm fighting between DOF and diffraction. Usually this occurs with telephoto or macro lenses, not wide angle. I'll have to admit that I haven't "studied" this carefully enough because it doesn't occur often and I'm usually distracted by something more urgent that comes up.

BJL said:

It seems that even though most people know that different formats
use different but "equivalent" focal lengths to get the same field
of view, many still ignore the fact that different but "equivalent"
aperture ratios are also needed to get the same DOF and degree
diffraction (witness the far higher aperture ratio used in large
format).

Click to expand...

Yep.

--
Thom Hogan
author, Nikon Field Guide & Nikon Flash Guide
editor, Nikon DSLR Report
author, Complete Guides: D70, D100, D1 series, D2h, D2x, S2 Pro
http://www.bythom.com

DPFranz said:

In optical design, ray tracing, you look at the power series for
the electric field, more specifically, Snell's law of refraction
which involves the sine function, you end up with odd-powered terms
x, x^3, x^5...etc. The most commonly spoken of aberrations are
third order (5th order aberrations are not very significant in most
cases), such as coma, chromatic aberration, astigmatism, spherical
aberration, etc. Thus the cubic dependence spoken of here. For
reference, see, e.g., Hecht's Optics, or Born & Wolf's Principles
of Optics.

Click to expand...

Cool. Thanks for that.

--
Lee Jay
(see profile for equipment)

I'll accept your criticism with good humor. I won't comment on the D2X any longer. Makes me sound like Ken Rockwell.

I erroneously equated f16 to f16. I should have equated DX f11 to FF f16 due to the depth of field equivalence with same angle of view.

I understand your analytical nature. The engineer in me wants to say too much without sounding long winded in the forums and it gets me in trouble.