DOF and Micro Four-Thirds Format

[Ray]

Ray, this thread was not about the IQ of those entry level Panasonic Micro Four Thirds lenses; it was about DOF comparisons, and the fact for example that equal DOF is achieved at apertures about 2/3 stop lower in 4/3 than with EF-S. The Panasonic lenses are by all accounts the least good of all Four Thirds standard zooms, so not of much interest to me for performance comparisons.

And I do wonder why you choose those atypically small apertures for your comparisons. Remember the lower f-stops typically used with smaller formats: with Four Thirds, the old slogan translates as "f/4 and be there"!

BJL,
Would you rather have endless discussion based upon unreliable and biased subjective opinion from people who are in love with their equipment, or a sound analysis of objective reports? Whether or not the Panasonic lenses designed for their micro-4/3rds system are typical of budget 4/3drs' lenses in general seems a matter of speculation. I've chosen to compare these Panasonic lenses with their EF-S equivalents because I can find no other objective comparisons on the internet. If you are in possession of other tests, on the same level as Photozone's, which allow for a meaningful comparison of equivalent 4/3rds and Canon APS-C systems, then let me know.

I have no particular allegiance to a specific brand of camera. I have an open mind and am always willing to use the best tool for the job, as evidenced by the fact that I bought a D700 because the reported tests and comparisons indicated that the Nikkor 14-24/2.8 zoom was better than, or at least as good as, 14mm primes and certainly better than any Canon wide-angle zoom. However, I would never make such a decision to purchase another system based upon hearsay and rumour. Show me some hard evidence.

[Ray]

And I do wonder why you choose those atypically small apertures for your comparisons. Remember the lower f-stops typically used with smaller formats: with Four Thirds, the old slogan translates as "f/4 and be there"!

F11 with APS-C format and F16 with full frame 35mm are not atypical for me, and I suspect not atypical for many landscape shooters in circumstances where maximum DoF is sought without serious compromise of resolution.

F4 with 4/3rds simply does not get you to F8 with full frame, if we compare the latest prosumer cameras. A 12mp 4/3rds at any aperture can never provide the same resolution as a 21mp 5D2 at F8 (in terms of LW/PH of course. It's understood that resolution per mm has to be greater in 4/3rds lenses).

However, comparing 4/3rds with Canon APS-C is a different matter. We are then comparing F4 with F5. In the Photozone examples I quoted, there are a couple of instances where the Panasonic 14-45 produces sharper results in the centre, at approximately F4, than the EF-S 18-55 at approximately F5, but still not as sharp at the edges however.

I would not deny that there are a few advantages of the 4/3rds' system. It's just a pity we're so hazy about them.

[Er1kksen]

Whether or not the Panasonic lenses designed for their micro-4/3rds system are typical of budget 4/3drs' lenses in general seems a matter of speculation.

Try the SLRGear tests of the Oly kit zooms, perhaps? Excellent performers, both... and they will autofocus on the G1 (a little slower, however) with the 4/3 adapter.

[Ray]

Try the SLRGear tests of the Oly kit zooms, perhaps? Excellent performers, both... and they will autofocus on the G1 (a little slower, however) with the 4/3 adapter.

Since I already have a number of Canon DSLRs, a number of Canon lenses, a D700 and a Nikkor lens, any performance advantage of a 4/3rds' system would have to relate to what I already have, otherwise it wouldn't be reliable or useful for me. The Photozone type of tests seems to lend themselves to direct comparisons of systems, and direct comparisons of lenses if they're tested with the same model of camera. I understand that Zuiko lenses only fit the Panasonic G1 via an adapter and that full functionality is not achieved. That's not an ideal situation. If the Nikkor 14-24 provided full functionality on the 5D, I would not have bought the D700.

SLRGear tests seem to be just standard reviews... the lens is quite sharp wide open...vignetting is quite good... performance drops off towards the long end etc etc. Direct comparisons involving standardised tests, such as MTF at 50% and lines per picture height for a wide range of lenses and equipment, is what's meaningful for me.

If a lens or system is really good, I want to see precisely how good compared with alternative systems. I've always been a bit suspicious of Olympus fanboy claims... 'the camera feels so good in the hands' ... 'the balance is just right'... 'as soon as I picked it up, I knew it was the camera for me'.. etc etc.

But thanks for the SLRGear link   .

[BJL]

BJL,
Would you rather have endless discussion based upon unreliable and biased subjective opinion from people who are in love with their equipment, or a sound analysis of objective reports?

Ray, are you not reading what I said at all? I am not disputing the accuracy of your carefully selected facts about Panasonic's entry level kit lenses for Micro Four Thirds (though as an aside, I am still puzzled by your choice not to quote any comparative data at the larger apertures where lens quality is more typically judged.)

I am disputing the relevance of any such discussion to the subject of this thread, which is DOF comparisons between formats. The discussion is also irrelevant to both your and my equipment choices, since neither of us has much reason to be interested in those lenses. I for example own several f/2.8-3.5 Four Thirds lenses of better quality than those Panasonic entry level models, and you have your far higher level Canon gear. On that topic:

I have no particular allegiance to a specific brand of camera.

No comment!


P. S. On another of your comments: a number of recent FourThirds lenses, the ones designed to work with the CDAF of Live View, apparently give full functionality when used on a Micro Four Thirds body with the adaptor. This is a "smart" adaptor supporting electronic lens-body communication, not merely a mechanical mounting ring that loses AF and aperture control. And no Four Thirds lens suffers the need for stop-down metering that most cross-format lens mount adaptors impose; at worst, AF is impeded.

[BJL]

I would not deny that there are a few advantages of the 4/3rds' system. It's just a pity we're so hazy about them.

You may be hazy, but at least one is blindingly obvious: smaller size and weight of typical lens and body kits, in a trade-off against low-light performance and such, as is routinely the case with kits using smaller, lighter lenses. The size and weight advantage is clear with mainstream options like the E-420, E-450, E-520, E-620, and now the G1 and GH1, combined with standard grade zoom lenses of f/3.5-5.6 or thereabouts. I would even push this advantage to the Olympus 70-300/4-5.6 compared to any lens offering equal telephoto reach on a larger format. When the lower speed is acceptable (which it is more often with IS), some equal FOV comparisons are:
- Olympus 70-300/4-5.6, 620g, US$360
- Canon 100-300/4-5.6, 1380g, US$1429, effectively about 2/3 stop faster on an EF-S body.
- Canon 70-300/4-5.6 IS (630g US$549) with 1.4xTC (220g, US$290) ... but AF then fails on most Canon bodies, and it is still bulkier and more expensive.
- Canon 70-300/4-5.6 IS (630g US$549) and cropping, accepting the lower resolution: surprisingly this is still more expensive, apparently due to the higher cost in doing IS in-lens rather than in-body.

Far less expensive 70-300's area available for Canon mount, but they lack IS, so compare badly to any 4/3 kit with in-body IS, and still give a heaver and more expensive combination once the TC is added.

[Ray]

You may be hazy, but at least one is blindingly obvious: smaller size and weight of typical lens and body kits, in a trade-off against low-light performance and such, as is routinely the case with kits using smaller, lighter lenses. The size and weight advantage is clear with mainstream options like the E-420, E-450, E-520, E-620, and now the G1 and GH1, combined with standard grade zoom lenses of f/3.5-5.6 or thereabouts. I would even push this advantage to the Olympus 70-300/4-5.6 compared to any lens offering equal telephoto reach on a larger format. When the lower speed is acceptable (which it is more often with IS), some equal FOV comparisons are:
- Olympus 70-300/4-5.6, 620g, US$360
- Canon 100-300/4-5.6, 1380g, US$1429, effectively about 2/3 stop faster on an EF-S body.
- Canon 70-300/4-5.6 IS (630g US$549) with 1.4xTC (220g, US$290) ... but AF then fails on most Canon bodies, and it is still bulkier and more expensive.
- Canon 70-300/4-5.6 IS (630g US$549) and cropping, accepting the lower resolution: surprisingly this is still more expensive, apparently due to the higher cost in doing IS in-lens rather than in-body.

Far less expensive 70-300's area available for Canon mount, but they lack IS, so compare badly to any 4/3 kit with in-body IS, and still give a heaver and more expensive combination once the TC is added.

BJL,
Are you a particularly frail person? I think everyone understands that smaller cameras are lighter than larger cameras. The hazy issue is the extent of the trade-off regarding image quality when one moves from a larger format to a smaller format. There's a claim from 4/3rds' enthusiasts that image quality is not compromised, compared with Canon APS-C. I've even seen claims on this forum that the E-3 is sharper than the Canon 5D.

What is very frustrating with this issue is that very few direct system comparisons are available on the internet. I found one comparison on the Photozone site, but it didn't include Zuiko lenses.

This is my point. I'm surprised you did not immediately understand this.

[Ray]

I am disputing the relevance of any such discussion to the subject of this thread, which is DOF comparisons between formats. The discussion is also irrelevant to both your and my equipment choices, since neither of us has much reason to be interested in those lenses. I for example own several f/2.8-3.5 Four Thirds lenses of better quality than those Panasonic entry level models, and you have your far higher level Canon gear. On that topic:

It's very boring if comments on subject topics abide strictly to the original question. There are always ramifications. Anyone who asks questions about DoF differences between two different formats would surely be interested in the ramifications of such differences.

Getting back to the precise point of the topic, you never responded to my comment that your mathematically precise answer is probably wrong in practice. Canon cropped formats have a mathematical 1 & 1/3rd F stop DoF advantage over full frame. My own tests have confirmed that at close distances, this difference in DoF is actually 2 stops, using the same Zoom lens at different focal lengths.

[BJL]

BJL,
Are you a particularly frail person?

No, but I am speaking on behalf of photographers who sometimes wish to carry their camera gear all day while hiking over possibly rough or steep terrain, or wandering in a city with something other than photography and load-bearing exercise as the primary goal.
Remember my goal was to answer your question about the existence of some advantages, not a futile effort to persuade you or anyone that 4/3 is superior in all ways to larger formats! I suggest rereading Michael's essay on street photography and the G1.

But there is really not much point in debating the manifest, widespread preference for lighter gear, or the century long and continuing trend in the direction of lighter kits and increased use of smaller formats when portability is an issue, or that in the telephoto realms of wild-life and macro photography, smaller formats offer a substantial and widely popular weight advantage over larger ones.

[BJL]

... Canon cropped formats have a mathematical 1 & 1/3rd F stop DoF advantage over full frame. My own tests have confirmed that at close distances, this difference in DoF is actually 2 stops, using the same Zoom lens at different focal lengths.

That sounds like what one would see in comparisons at equal PPI (such as in 100% viewing on screen); I am talking instead about comparisons at equal print/display size. The higher pixel count of the larger format means that in an equal PPI comparison, the image from the larger format camera is enlarged more than it would be for an equal print size comparison, increasing the DOF difference.

For eaxmple for the 15MP 50D vs 22MP 5DMkII, the DOF ratio I get is
1.6^2/sqrt(22/15) = 2.1, satisfying close to your "2 stops".


And for the equal print size comparison, it is not just "my theory"; it also follows from the bog-standard DOF formulas as given in numerous texts on photography. All you have to remember is that for equal angle of view and equal print image size, the "circle of confusion" value to use in standard DOF formulas varies in direct proportion to linear format size, as does the focal length.

[Ray]

That sounds like what one would see in comparisons at equal PPI (such as in 100% viewing on screen); I am talking instead about comparisons at equal print/display size. The higher pixel count of the larger format means that in an equal PPI comparison, the image from the larger format camera is enlarged more than it would be for an equal print size comparison, increasing the DOF difference.

For eaxmple for the 15MP 50D vs 22MP 5DMkII, the DOF ratio I get is
1.6^2/sqrt(22/15) = 2.1, satisfying close to your "2 stops".


And for the equal print size comparison, it is not just "my theory"; it also follows from the bog-standard DOF formulas as given in numerous texts on photography. All you have to remember is that for equal angle of view and equal print image size, the "circle of confusion" value to use in standard DOF formulas varies in direct proportion to linear format size, as does the focal length.

BJL,
How does this formula work? I don't have a 5D2. All my DoF comparisons are between the 5D and the 40D or 50D. If I apply this formula to the 40D vs the 5D, I get 2.56/sqrt(12.7/10.1)=2.56/1.12=2.28 stops. Is that right?

I always compare equal size images. Since I have a wide format printer and fairly low-pixel-count cameras, many of my prints require the image to be interpolated beyond its native resolution.

Here are some DoF comparisons between the 40D and 5D using my 100-400 zoom at 250mm and F8 (40D) and 400mm and F11 (5D). As you can see, there's only a 1 stop difference in DoF with this lens at the particular subject distance focussed upon.

[BJL]

First, off, I think my previous formulas was wrong: it should have been DOF ratio 1.6*sqrt(22/15)=1.93, and for your 10MP vs 12.7MP case, 1.6*sqrt(12.7/10)=1.8, a difference of 1/7 stops. But now that I read your procedure involving up-ressing for very large prints, that traditional approach does not apply, so you have inspired me offer a new one. But the formulas comes out the same! So in your test with a one stop difference the ODF ratio is predicted to be 1.3, or 0.73 stops. Is that close enough to what you see?


Why my new calculation:

I always compare equal size images.

Good: with equal size images, ignore my formula, which was for equal PPI (before upressing).

Since I have a wide format printer and fairly low-pixel-count cameras, many of my prints require the image to be interpolated beyond its native resolution.

That probably makes the tradition DOF reckoning not applicable, as it is based on the assumption of the resolution being high enough that it is not a factor in perception of sharp vs OOF. That is, the resolution length scale on the print is assumed to be substantially smaller than the circle of confusion threshold at which OOF effects are noticeable. Remember that the traditional reference for DOF scales was 5"x7" prints viewed from 10". So to check that guideline of "4/3 stops from 35mm to EF-S", it would be better to use a print size not needing any up-ressing, maybe A4.


But the traditional DOF results that I described are giving the right answer to the wrong question for your situation! Instead you have raised an interesting new question:

When images are viewed at sizes so large that the resolution limits of the sensors are visible (roughly, when up-ressing is needed), how is DOF related to format size, focal length, aperture, degree or enlargement and the underlying resolution of the image?


The answer might be one advocated by Jonathan Weinke (sp.?): the parts of the image that are perceived as out of focus are those where the circles of confusion are noticeably larger than the resolution length scale of the sharpest, fully in-focus parts of the image. So in traditional DOF formulas, the CoC threshold value to use would be roughly the pixel spacing, or some suitable fixed multiple of that.

Computational Details
Assume focal length proportional to linear sensor size, for equal FOV, equal focus distance, equal aperture ratio.
Use numerical values LSS for linear sensor size, PC for pixel count.
The pixel spacing is roughly proportional to LSS/sqrt(PC), so we use a value CoC that is proportional to this. The traditional formula says that the DOF is proportional to
CoC/f^2
so in our case this is proportional to
1/(LSS*sqrt(P))

To compare formats that differ in linear sensor size by ratio LSSR and with pixel counts in ratio PCR, the DOF varies inversely with
LSSR*sqrt(PCR)
which is the formula I used above.

If the aperture ratio is also adjusted in ratio NR, the DOF varies in proportion to
NR/(LSSR*sqrt(PCR))

Example
Comparing the 10MP EF-S 40D to the 12.7MP 35mm 5D, we have LSSR=1.6 and PCR=12.7/10=1.27, so the suggested DOF ratio is
1.6*sqrt(1.27) = 1.8
Close enough to a factor or two, or two stops. To be precise, get stops by taking twice the log of this divided by the log of 2, getting 1.7 stops.
With your difference in aperture by a factor NR=1.4, the DOF is less for the 5D by factor
1.4/(1.6*sqrt(1.27)) = 0.77, or 0.73 stops. Doe that match your observation of "only one stop?"

[Ray]

Example
Comparing the 10MP EF-S 40D to the 12.7MP 35mm 5D, we have LSSR=1.6 and PCR=12.7/10=1.27, so the suggested DOF ratio is
1.6*sqrt(1.27) = 1.8
Close enough to a factor or two, or two stops. To be precise, get stops by taking twice the log of this divided by the log of 2, getting 1.7 stops.
With your difference in aperture by a factor NR=1.4, the DOF is less for the 5D by factor
1.4/(1.6*sqrt(1.27)) = 0.77, or 0.73 stops. Doe that match your observation of "only one stop?"

Sounds to me, BJL, that you are massaging the maths to fit the observed results.

The impression I get from the relatively few tests I've made relating to this issue, is that the mathematical DoF calculations are merely a guide, possibly hardly more accurate than the 1/FL(35mm) rule for appropriate shutter speed for hand-held shots.

The 100-400 when focussed at a fair distance (about 30m) produces a 1 stop DoF difference between the 40D and 5D, with same FoV. The 50D when focussed at a close distance (about 2 metres) produces a 2 stop DoF difference compared with the 5D, same FoV, same method of comparison on monitor at 100%, same size images, different lens.

Why this should be, is a bit of a mystery to me. The obvious explanation is that I didn't focus accurately with the 5D. It's a possibility, but I did my best. The experiment with the 50D vs the 5D at close focussing distance was not actually made to observe DoF differences, but to observe noise differences. With all the talk about the 50D being a bit noisy, I wanted to test if I made DoF and shutter speed the reference points, which camera would be noisier. That is, how does 50D noise at ISO 100 and F4 compare with 5D noise at ISO 250 and F6.3.

I took several shots at different ISOs and apertures, working up to ISO 3200. The 50D appeared to be very slightly more noisy, although nothing to worry about. However, as a side effect I noticed that the 50D shots had a sharper background. The background was a bookcase with visible book titles. The 1 & 1/3rd F stop difference was not enough to equalise background blur.

In order to be certain about these results with regard to DoF, I would want to repeat the experiment under different conditions. It's a principle of science that results have to be repeatable, many times. I can't spare the time at the moment to do this. I'm building a house. (To help the Australian economy   ).

However, in general it does seem to me that there are a number of variables that make a nonsense of the maths. It seems a possibility that different lens designs will affect these DoF differences based only upon format size and pixel count differences. We should also look at the accuracy of the F stop markings on lenses. There are certainly discrepancies in focal length marking on lenses, which are easier to see. F stop inaccuracy is perhaps more difficult to determine. I find it strange, for example, that DXOmark ISO ratings are significantly different from Dpreview's.

[BJL]

Sounds to me, BJL, that you are massaging the maths to fit the observed results.

This is puzzling: theory should be tested against the facts, as a protection about errors like inaccurate approximtions or false assumptions, and should be revised when the facts point to an error or limitation of the applicability of the theory, like an unjustified assumption. So why are you so cynical when I revise the assumptions of my calculations to take account of the new facts that you presented me with, about viewing conditions that do not fit the assumptions of traditional DOF calculations?

It almost sounds to me as if you prefer you own experiments and observations over any theory, even theory that has been corroborated by many decades of experiments and experience by many competent photographers, so that the canard "mere theory" does not really apply.


Of course, the usual DOF formulas are not exact, for many reasons. Apart from applying to certain assumptions about adequate image resolution, image size, and viewing distance, they fail at very close distance ("macro"), at very large distances (hyper-focal), and they do not always apply to predicting the degree of blurring in highly out of focus backgrounds. The later is often what people are talking about when they talk of seeking very shallow DOF, but it is not quite the same as DOF.

[Ray]

This is puzzling: theory should be tested against the facts, as a protection about errors like inaccurate approximtions or false assumptions, and should be revised when the facts point to an error or limitation of the applicability of the theory, like an unjustified assumption. So why are you so cynical when I revise the assumptions of my calculations to take account of the new facts that you presented me with, about viewing conditions that do not fit the assumptions of traditional DOF calculations?

It almost sounds to me as if you prefer you own experiments and observations over any theory, even theory that has been corroborated by many decades of experiments and experience by many competent photographers, so that the canard "mere theory" does not really apply.


Of course, the usual DOF formulas are not exact, for many reasons. Apart from applying to certain assumptions about adequate image resolution, image size, and viewing distance, they fail at very close distance ("macro"), at very large distances (hyper-focal), and they do not always apply to predicting the degree of blurring in highly out of focus backgrounds. The later is often what people are talking about when they talk of seeking very shallow DOF, but it is not quite the same as DOF.

I think I probably do prefer my own experiments and observations over a theory that seems less precise than my observations. A theory about DoF relativities amongst different formats should have practical value. I think it's likely that a simple and workable formula that covers all situations doesn't exist. There are probably too many variables to take into consideration. For example, how much variability is there between the accuracy of the F stops on one lens and supposedly the same F stops on another lens on another camera? F5.6 on one lens might actually be F5, and on the other lens F6. Perhaps differences can sometimes be even greater than this.

I imagine that a theory that attempts to predict the DoF differences amongst different formats would be a bit like the theoretical MTF charts of lenses that some manufacturers publish. In practice, the MTF measurements of different copies of the same model of lens can sometimes vary considerably, and none of them might be as good as the manufacturers published charts.

If or when I have the time, I might do some comparisons between the EF-S 10-22 with the 50D and the Nikkor 14-24 with the D700, in preparation for my next photographic trip. I'm curious how centre resolution will compare, although I have no doubt that the Nikkor will have superior edge resolution. Since both cameras have a high resolution Live View screen, there should be no possibility that misfocussing will skew the results.

[BJL]

I think I probably do prefer my own experiments and observations over a theory that seems less precise than my observations.

As far as I can tell, the formula I offered for your case of "highly enlarged" images does fit with your experiment, so no need to defend your experiments, no matter how poorly designed!  By " highly enlarged", I mean enlarged so much that the resolution limits of the camera are visible and even the parts of the image in the plane of critical focus are detectably un-sharp. In particular, situations like 100% pixel peeping, and prints so large that up-sampling ins needed to avoid visible jaggies.

By the way, let me suggest a better experiment, which will give a range of values, or an "error bar" for the result, as all good quantitative experiments should do. Vary the f-stop difference between the two formats and then in image comparisons, judge only whether one image has more DOF, less DOF or about the same DOF. (I.e. do not try to gauge the degree of the DOF difference directly.) This should give a range of f-stop differences over which there is a transition from more DOF to less DOF. Something like "at 2/3 stop difference, the 5D image has less DOF then the 50D image; at 4/3 stop difference it has more DOF, so DOF is equal at an f-stop difference of about one stop, plus or minus 1/3 stop".

[Ray]

As far as I can tell, the formula I offered for your case of "highly enlarged" images does fit with your experiment, so no need to defend your experiments, no matter how poorly designed!  By " highly enlarged", I mean enlarged so much that the resolution limits of the camera are visible and even the parts of the image in the plane of critical focus are detectably un-sharp. In particular, situations like 100% pixel peeping, and prints so large that up-sampling ins needed to avoid visible jaggies.

BJL,
I have assumed that anyone who  enquires specifically about DoF differences between different size formats of cameras would want to know the results in an absolute sense. The fact that print or display size and viewing distance can affect the perception of DoF enormously, is a different issue. Answers relating to camera format DoF differences that assume a particular print or display size and/or viewing distance therefore cause confusion, in my opinion. In other words, at a particular print size and/or viewing distance, there may not any DoF differences at all between formats. You can get any result you want by varying print size and view distance.

It therefore only makes sense to pixel-peep such differences. This is one of the legitimate purposes of pixel peeping. If I want to go to the trouble of testing a number of copies of a particular lens before buying, or test different models of lenses with similar focal lengths in order to get the sharpest and best value lens on offer, it would be plain silly to restrict my self to comparisons at, say, A4 print size. If I were to do that, I might arrive at the conclusion that a $500 lens was as sharp as a $5,000 lens and therefore extremely good value.

The fact is, when comparing DoF issues at 100% on the monitor, the differences in sharpness between a 40D, 50D and 5D at the plane of focus are trivial compared with the differences in sharpness in areas of the image that are OoF to varying degrees.

By the way, let me suggest a better experiment, which will give a range of values, or an "error bar" for the result, as all good quantitative experiments should do. Vary the f-stop difference between the two formats and then in image comparisons, judge only whether one image has more DOF, less DOF or about the same DOF. (I.e. do not try to gauge the degree of the DOF difference directly.) This should give a range of f-stop differences over which there is a transition from more DOF to less DOF. Something like "at 2/3 stop difference, the 5D image has less DOF then the 50D image; at 4/3 stop difference it has more DOF, so DOF is equal at an f-stop difference of about one stop, plus or minus 1/3 stop".

This is more or less the procedure I follow and is what I have done in the limited number of tests I've carried out so far. What I have not done is test the DoF characteristics of the same lens (with different formats) when focussed at different distances. You've mentioned that DoF differences between formats break down with macro shots. I suspect they not only behave differently at very close distances, but also at moderately close distances compared with moderately far distances.

Supposing I outline some specific tests that I shall carry out in the next few days, time permitting, and you advise me beforehand what the DoF differences should be according to your formulas. I shall then be in a position to see just how accurate your formulas are   .

I propose comparing the Canon EF-S 10-22 on the 15mp 50D, with the Nikkor 14-24 on the 12mp Nikon D700. I shall use Live View for absolutely accurate focussing and I shall compare the DoF of images at 100% on monitor taken at focussing distances of 1 metre, 5 metres and 10 metres, and at focal lengths of 16mm, 20mm and 24mm (35mm format equivalent).

Please post your predictions.

By the way, would you also explain what is happening in the following extract from your previous post; that is, the latter part in bold where you arrive at 0.77 stops. Maths is not my forte.  

Example

Comparing the 10MP EF-S 40D to the 12.7MP 35mm 5D, we have LSSR=1.6 and PCR=12.7/10=1.27, so the suggested DOF ratio is
1.6*sqrt(1.27) = 1.8
Close enough to a factor or two, or two stops. To be precise, get stops by taking twice the log of this divided by the log of 2, getting 1.7 stops.
With your difference in aperture by a factor NR=1.4, the DOF is less for the 5D by factor
1.4/(1.6*sqrt(1.27)) = 0.77, or 0.73 stops. Doe that match your observation of "only one stop?"

[BJL]

I have assumed that anyone who  enquires specifically about DoF differences between different size formats of cameras would want to know the results in an absolute sense. ... Answers relating to camera format DoF differences that assume a particular print or display size and/or viewing distance therefore cause confusion, in my opinion.

Firstly, I kindly offered a formula for the different "absolute" terms of comparison that you prefer, and which gives a result that is consistent with your reported observation, so what exactly is your complaint?!

Secondly, it is futile to debate opinions, so I will only point out that your opinion about how people commonly wish to compare DOF is at odds with the opinions of every lens maker that has ever put a DOF scale on a lens, and of every photographic company and author on photography that has published a DOF table, as far as I know. Because more or less universally, those scales are based on describing the DOF at a fixed combination of print size and viewing distance, corresponding roughly to what is sometimes called "normal viewing": a viewing distance equal to print diagonal length. These DOF guides are also easily adaptable to other situations with rules like:
For each doubling of intended print area at equal viewing distance, close down one stop more than the DOF guide suggests, to compensate for the extra 1.4x degree of enlargement. (I believe that Michael discusses some such guideline somewhere on this site.)
or
For a print intended to be viewed at diagonal size greater than viewing distance by an "extra enlargement factor" E, increase the f-stop suggested by the DOF guide by that factor E.

By the way, would you also explain what is happening in the following extract from your previous post; that is, the latter part in bold where you arrive at 0.77 stops. Maths is not my forte.  

Your are referring to

get stops by taking twice the log of this divided by the log of 2 ...
1.4/(1.6*sqrt(1.27)) = 0.77, or 0.73 stops. Does that match your observation of "only one stop?"

so I suppose you are asking how I got from the DOF ratoi of 0.77 to the value in stops of 0.73. That is explained in the previous line, as
each stop is a factor of sqrt(2), about 1.4 in aperture ratio and such. I realize now that a simpler formula is this
log(ratio of DOF values)/log(sqrt(2), and computing this time to four significant digits,
1.4/(1.6*sqrt(1.27)) = 0.7764 is the ratio of DOF, and
log(0.7764)/log(sqrt(2))= -0.7303 is the f-stop change corresponding to this DOF: the f-stop change that would equalize DOF.
(The minus sign means that 0.75 stops less DOF is expected, so the larger format would need to stop down by 3/4 stop.)

And since Maths (along with Optics and most of the science behind photography) is not your forte, let me suggest that rather than asking me, or considering this wrongly as debate between my theory and your experiment, you would benefit from studying some established references on photographic optics, whose conclusions and formulas have been experimentally validated on millions of occasions when they are used to predict the DOF that will be given by a given combination of aperture choice and such and such in technical photography, including much recent digital technical photography.

I suspect that if any solidly established and widely used optical formula were as wrong, inaccurate, or unreliable as you seem to suggest, many professional users of photography would have noticed it, and many would have complained publicly before you!

[Ray]

so I suppose you are asking how I got from the DOF ratoi of 0.77 to the value in stops of 0.73. That is explained in the previous line, as
each stop is a factor of sqrt(2), about 1.4 in aperture ratio and such. I realize now that a simpler formula is this
log(ratio of DOF values)/log(sqrt(2), and computing this time to four significant digits,
1.4/(1.6*sqrt(1.27)) = 0.7764 is the ratio of DOF, and
log(0.7764)/log(sqrt(2))= -0.7303 is the f-stop change corresponding to this DOF: the f-stop change that would equalize DOF.
(The minus sign means that 0.75 stops less DOF is expected, so the larger format would need to stop down by 3/4 stop.)

BJL,
I understand the adjustment that takes into account the different pixel densities and pixel counts of the different formats under consideration, but I don't understand how you got from an initial 2 stop DoF difference to 0.78 or 0.75 DoF difference, which is why I think you are massaging the figures.

Secondly, it is futile to debate opinions, so I will only point out that your opinion about how people commonly wish to compare DOF is at odds with the opinions of every lens maker that has ever put a DOF scale on a lens, and of every photographic company and author on photography that has published a DOF table, as far as I know. Because more or less universally, those scales are based on describing the DOF at a fixed combination of print size and viewing distance, corresponding roughly to what is sometimes called "normal viewing": a viewing distance equal to print diagonal length. These DOF guides are also easily adaptable to other situations with rules like:

These views are now obsolete in relation to the new technology of DSLRs and inkjet printers. The ease and flexibility of producing large prints, or effectively large prints by cropping a small portion of the image and making, say, an A3 print from that small crop, which would effectively be like making a 6x9 Ft print from the whole image, makes a nonsense of the old-fashioned  standard of 8x10". Surely we can move on from that standard.

And since Maths (along with Optics and most of the science behind photography) is not your forte, let me suggest that rather than asking me, or considering this wrongly as debate between my theory and your experiment, you would benefit from studying some established references on photographic optics, whose conclusions and formulas have been experimentally validated on millions of occasions when they are used to predict the DOF that will be given by a given combination of aperture choice and such and such in technical photography, including much recent digital technical photography.

You don't need a knowledge of maths or optical science in order to see the differences in sharpness and DoF at various apertures. I'm into photography for the purpose of taking pictures, not for the purpose of constructing grandiose theories in optical science.

I suspect that if any solidly established and widely used optical formula were as wrong, inaccurate, or unreliable as you seem to suggest, many professional users of photography would have noticed it, and many would have complained publicly before you!

They have. A number of MFDB users have noted on this forum that MFDBs seem to produce a shallower DoF compared with 35mm than the formulas would suggest. Others have suggested that it's impossible to get any precise DoF equivalent between formats, and that it's dependent upon focussing distance and lens design.

[BJL]

... I don't understand how you got from an initial 2 stop DoF difference to 0.78 or 0.75 DoF difference, which is why I think you are massaging the figures.

I never proposed a 2 stop difference for the comparison that your are making between 40D and 5D. Let me summarize my calculations relevant to those cameras.

My first figure in post #3 of this thread was the traditional one relevant to "normal viewing" of images sufficient resolution, and equal aperture ratio, and that was a factor of 1.6 in DOF, or about 1 1/3 stops. That is, using aperture ratios that differ by 1 1/3 f-stop would give about equal DOF under those printing and viewing conditions.

The second calculation in post #52 was instead for equal PPI (better fitting you comparisons of highly enlarged images) and again equal f-stop, and this increased the DOF factor to about 1.8, or about 1.7 stops.

The third calculation also in post #52 was for your experiment with a one stop difference in apertures, which takes a factor of 1.4 off the DOF difference, and subtracts one from the f-stop difference: that is the 0.7764 DOF ratio and 0.73 f-stop difference.

This is simply computing for three different situations from the same well-established scientific basis. Your "massaging the figures" is my "taking account of different situations and data, instead of blindly applying a formula to a situation to which it is not directly applicable, due perhaps to not understanding the science behind the formula, and then declaring that the formula is wrong." A bit like that urban legend, enthusiastically quoted in these forums and many others, that "science has falsely proven that a bee cannot fly", typically used as an excuse for selectively disregarding scientific statements that people wish not to accept.

A number of MFDB users have noted on this forum that MFDBs seem to produce a shallower DoF compared with 35mm than the formulas would suggest.

That is not an error in the traditional formula, but a misunderstanding of when it applies, and of what it does and does not say, as I have already discussed in places like post #58.

To repeat yet again: the standard DOF scales, tables and formulas are for the reference case of comparing prints of equal (and modest) size at equal viewing distance: the traditional reference is 7"x10" prints viewed from 10" I believe. They do not include adjustments for factors like different intended print size, but those can easily be done by someone who makes the modest effort to understand the formula and the science behind it. (Can you tell that I teach science, and hate blind memorization of formulas as a path to misunderstanding and failure?)

When a high resolution image is instead "viewed larger" (larger print size and/or closer scrutiny), the DOF value from the standard formulas needs to be adjusted in inverse proportion to the "extra enlargement". For the case of viewing at enlargement sufficient for resolution differences to be detectable, my formula that allows for pixel count difference is one way to take this into account, and indeed gives lower DOF for higher pixel counts.

So it does not surprise me that when DOF comparisons are made that involve images of higher resolution from larger formats like DMF, the basic DOF formula understates the DOF difference; I doubt that these comparison are done with prints of equal, small size like 7"x10", but would guess that they are instead done at image sizes large enough to reveal the resolution advantage of the larger format.