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### AuthorTopic: DOF and Micro Four-Thirds Format  (Read 40054 times)

#### Ray

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##### DOF and Micro Four-Thirds Format
« Reply #60 on: May 01, 2009, 07:30:02 am »

Quote from: BJL
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.

Dear me! What confusion!   All the DoF comparisons I've made between FF 35mm and cropped format cameras have involved sensors of approximately the same resolving power. The resolution difference between the 40D and 5D is insignificant. The resolution difference between the 5D and the 50D is also insignificant. However, the resolution difference between the 40D and 50D is probably noticable at 100% on monitor or on very large prints, but such differences between these two sensors of the same format are not of course relevant to these DoF comparisons.

Likewise, most of the MFDB comparisons that have been hotly debated on this forum are between sensors of approximately equal pixel count, the 21mp 1D3 versus the 18mp and 22mp P21 and P25.

If the focal length and F stop number have been adjusted in relation to the differences in sensor dimension, then the diameter of the CoC on the sensor, at a particular distance from the focus point in the image, would presumably automatically be adjusted in proportion so that the DoF differences in the two images will remain constant whatever the size of the print.

To make the point clear with an example, if I shoot a scene using the 5D with 80mm lens at F13, and the circle of confusion is 0.03mm at a certain point in the image, say 2 metres from the point of focus, then the CoC on the 40D sensor at the same place in the image, 2 metres from the point of focus, should be 0.03/1.6=0.019mm, provided I use the appropriate lens (80/1.6=50mm) and appropriate F stop (13/1.6=F8).

If I make an 8x12" print from both images, the CoC in the 5D image becomes 8x0.03=0.24mm. If I make the same size print from the 40D image, the CoC, although smaller in proportion to the smaller sensor, is enlarged to a greater degree (1.6x8=12.8x) and ends up being the same size (12.8x0.019=0.24mm).

Whatever size prints I make, the CoC will be the same size on equal size prints from each camera, even if I examine images at 200% on the monitor. Is this not true?

If in my tests (and other comparisons with MFDBs) the results do not always conform with this F stop and FL multiplier for equal DoF, there must be some factor(s) other than image size going on.
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#### BJL

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« Reply #61 on: May 01, 2009, 01:56:56 pm »

Ray, by my reckoning, the resolution difference between the 40D and 5D leads to about a 1/3 stop change in DOF if "compared at full resolution", shifting the difference from 1 1/3 stops predicted by the traditional formula (which is for conditions where image resolution differences are irrelevant) to 1 2/3 stops.

What are your observed values for the DOF difference between the 40D and 5D, and more important, what is the margin of error in your observed values? Is either 1 1/3 of 1 2/3 stops outside your margin of error? That is, do your observations with a one stop difference between the two cameras give a measured DOF difference that is inconsistent with either 1/3 or 2/3 stops?

Without knowing which MF camera was being compared to which 35mm camera, I can have no comment on the claim of MF revealing relatively less DOF than the formulas predict. And with different approaches to AA filers and different lenses, it is not clear that pixel size alone gives the resolution comparison needed there.

In short, I have not yet seen any quantitative evidence that there is a discrepancy between observation and the standard optical formulas.
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#### BJL

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« Reply #62 on: May 01, 2009, 02:33:10 pm »

Quote from: Ray
To make the point clear with an example ... Whatever size prints I make, the CoC will be the same size on equal size prints from each camera, even if I examine images at 200% on the monitor. Is this not true?

If in my tests ... the results do not always conform with this F stop and FL multiplier for equal DoF, there must be some factor(s) other than image size going on.
Yes, the circles of confusion at corresponding points on the prints will be the same size and so the perceived DOF would be the same when comparing equal sized images small enough that the resolution differences are not perceptible, as with the reference case of 5"x7" prints viewed from 10". But as we agree, and as I have been saying repeatedly, there is something else going on with sufficiently large prints viewed sufficiently closely[/i], like the ones that you say you have to up-sample in order to make. When the equal sized images are large enough that the resolution differences are perceptible, it is likely that certain parts of the scene which are visibly OOF in the higher resolution image (visibly less sharp than the sharpest parts of  the image) may not be visibly OOF on the lower resolution image, because the loss of sharpness due to OOF focus effects is drowned by the overall lower sharpness.

That is, under sufficiently close scrutiny of sufficiently large prints, the perception of being in-focus or out-of-focus is probably influenced by comparing the sharpest at some part of the image to the sharpness of the sharpest part of the image. There, the difference of 1/3 stop between 10MP and 12.7MP is likely to be perceptible when you look closely enough.

Given your enthusiasm for experiment and observation, I  do not think that you should dismiss the resolution differences between these cameras as insignificant without experimenting! Especially since my use of pixel count is only a rough measure of resolution, not accounting for example for lens resolution, which could tend to increase the resolution advantage of the larger format when used with the same zoom lens.
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#### Ray

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« Reply #63 on: May 03, 2009, 06:19:20 pm »

Quote from: BJL
What are your observed values for the DOF difference between the 40D and 5D, and more important, what is the margin of error in your observed values? Is either 1 1/3 of 1 2/3 stops outside your margin of error? That is, do your observations with a one stop difference between the two cameras give a measured DOF difference that is inconsistent with either 1/3 or 2/3 stops?

BJL,
As I showed in post #51, when the 100-400 is focussed at a fairly long distance, a 1 stop difference is sufficient to equalise DoF between the 40D and 5D (comparing 400mm at F11 (5D) with 250mm at F8 (40D). Other shots of the same scene taken on the same occasion show that a difference of 1 1/3 stops is equally satisfactory. I didn't take any shots separated by 1 2/3 stops on that occasion, but I wouldn't be surprised if 1 2/3 stop were also satisfactory and within the range of the margin of error. At print sizes of 30"x45", which a 100% view on the monitor represents, such differences are inconsequential. At smaller print sizes, invisible.

However, when focussing at close distances with a wider lens, such DoF differences seem more noticeable. I've found that a 2 stop difference is required to equalise DoF between the 50D and 5D, comparing 24mm at F4 with 40mm at F8. Do you want to see the images?
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#### Ray

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« Reply #64 on: May 03, 2009, 07:10:55 pm »

Quote from: BJL
Yes, the circles of confusion at corresponding points on the prints will be the same size and so the perceived DOF would be the same when comparing equal sized images small enough that the resolution differences are not perceptible, as with the reference case of 5"x7" prints viewed from 10". But as we agree, and as I have been saying repeatedly, there is something else going on with sufficiently large prints viewed sufficiently closely[/i], like the ones that you say you have to up-sample in order to make. When the equal sized images are large enough that the resolution differences are perceptible, it is likely that certain parts of the scene which are visibly OOF in the higher resolution image (visibly less sharp than the sharpest parts of  the image) may not be visibly OOF on the lower resolution image, because the loss of sharpness due to OOF focus effects is drowned by the overall lower sharpness.

That is, under sufficiently close scrutiny of sufficiently large prints, the perception of being in-focus or out-of-focus is probably influenced by comparing the sharpest at some part of the image to the sharpness of the sharpest part of the image. There, the difference of 1/3 stop between 10MP and 12.7MP is likely to be perceptible when you look closely enough.

Given your enthusiasm for experiment and observation, I  do not think that you should dismiss the resolution differences between these cameras as insignificant without experimenting! Especially since my use of pixel count is only a rough measure of resolution, not accounting for example for lens resolution, which could tend to increase the resolution advantage of the larger format when used with the same zoom lens.

BJL,
I agree. There's not much point in taking into consideration relatively small differences in pixel count without also taking into consideration the sometimes larger differences in lens resolution between the different f stops used to equalise DoF. As you know, lens resolution is typically sharpest at one or two stops down from maximum aperture and then begins to fall off below F8.

If we consider my comparison between the 40D at 250mm and F8, and the 5D at 400mm and F11 & F13, there can be little doubt that the 100-400 zoom is sharper at 250mm and F8 than at 400mm and F11 and F13. The slightly lower resolving power of the 40D, plus it's requirement for a sharper lens due to its higher pixel density, is at least partially met by the greater sharpness of the 250mm lens at F8. The fact is, the images from both cameras in these circumstances appear equally sharp at the plane of focus, so there should be no need to modify the formula.

If we take another example comparing the 50D with the 5D using the Canon 24-105 zoom at 24mm and F4 with the 50D, and at 40mm and F6.3 or F8 with the 5D, the process is reversed to produce a similar effect. The additional resolving power of the 50D is offset by the lower resolving power of the zoom lens at full aperture. Both images are therefore equally sharp at the plane of focus. The multiplier of 1.6 for F stop should therefore hold true, but in these circumstances it doesn't appear to.

On the other hand, there could be some minor difference in focussing responsible for this. The experiment was set up to compare noise between the two cameras, not the accuracy of the 1.6 multiplier. However, I can't detect any misfocussing. Both images appear equally sharp at the plane of focus, and there can be no doubt that the 50D was accurately focussed because I used Live View.
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#### BJL

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« Reply #65 on: May 05, 2009, 01:54:39 pm »

Quote from: Ray
As I showed in post #51, when the 100-400 is focussed at a fairly long distance, a 1 stop difference is sufficient to equalise DoF between the 40D and 5D (comparing 400mm at F11 (5D) with 250mm at F8 (40D). Other shots of the same scene taken on the same occasion show that a difference of 1 1/3 stops is equally satisfactory.
So far so good!: consistent with the traditional reckoning within the experimental margin of error (and the intended precision limits of the formulas).

Quote from: Ray
However, when focussing at close distances with a wider lens, such DoF differences seem more noticeable. I've found that a 2 stop difference is required to equalise DoF between the 50D and 5D, comparing 24mm at F4 with 40mm at F8. Do you want to see the images?
The examples might be interesting. How much closer? The standard basic formulas break down as the magnification become significant, with texts typically limiting their utility to m<1/10 or even m<1/20, meaning subject distance should be at least about ten or twenty times the focal length. At closer range, lens extension means that both the effective focal length and effective aperture diameter shift, and more precise formulas are needed.

Another part of the approximation is that the formulas break down when the aperture is small so that the DOF is very large: large enough to be substantially greater behind the focal plane than in front of it. (The rule of thumb about 1/3 of DOF in front, 2/3 behind has no quantitative scientific basis: DOF is close to equally distributed fore and aft when the DOF is shallow enough, but grows more behind than in front as aperture size is reduced, eventually reaching infinity behind in the hyperfocal case.) The formulas are more oriented to choosing an aperture that ensures enough DOF in situations where DOF is potentially quite limited.

All this "fine print" is why one needs to understand the physics, mathematics, and applicability of the formulas, or otherwise use them cautiously, in the range of conditions for which they were intended. More detailed formulas are available in more advanced optics texts for the harder cases!
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#### Ray

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« Reply #66 on: May 05, 2009, 08:17:06 pm »

Quote from: BJL
The examples might be interesting. How much closer? The standard basic formulas break down as the magnification become significant, with texts typically limiting their utility to m<1/10 or even m<1/20, meaning subject distance should be at least about ten or twenty times the focal length. At closer range, lens extension means that both the effective focal length and effective aperture diameter shift, and more precise formulas are needed.

Another part of the approximation is that the formulas break down when the aperture is small so that the DOF is very large: large enough to be substantially greater behind the focal plane than in front of it. (The rule of thumb about 1/3 of DOF in front, 2/3 behind has no quantitative scientific basis: DOF is close to equally distributed fore and aft when the DOF is shallow enough, but grows more behind than in front as aperture size is reduced, eventually reaching infinity behind in the hyperfocal case.) The formulas are more oriented to choosing an aperture that ensures enough DOF in situations where DOF is potentially quite limited.

BJL,
In the comparisons below, the focussing distances, although close, are significantly greater than 20x the longest focal length used, which was 40mm. The distance to the focus point would have been about 2 metres, or 50x the longest focal length. In order to be pedantic, I've downsampled the 50D image to the 5D size. However, whether the 50D image is downsampled or the 5D image is upsampled makes no difference to the conclusion. In these samples, the 50D still retains a slightly greater DoF edge, even with a 2 stop difference, although I'm prepared to accept that such miniscule differences fall within the margin of experimental error.

As I mentioned before, my purpose in doing these tests, shortly after receiving my brand new 50D, was to check out the noise, comparing it with my 5D at equal shutter speeds and equal DoF, which involved comparing 50D noise at ISO 100 with 5D noise at ISO 320, and ISO 200 with ISO 500 etc. It was as a consequence of such tests that I discovered that the 1 1/3rd stop difference for equal DoF did not seem to apply in those circumstances and that nothing less than a 2 stop difference would produce the desired results.

Here's the over all scene:  [attachment=13510:The_scene.jpg]

The general area of focus at 100%:  [attachment=13511:General_...us_point.jpg]

The specific area of focus at 200% (the pale mauve, artificial flower):  [attachment=13512:precise_..._at_200_.jpg]

The closest points in the foreground:  [attachment=13513:Nearest_points.jpg]

The background, centre right:  [attachment=13514:Centre_right.jpg]

The background centre left:  [attachment=13515:Centre_left.jpg]

You'll notice that I should have used ISO 400 with the 5D instead of ISO 640. However this apparent advantage to the 5D (regarding noise) is at least partly offset by the slightly faster shutter speed (1/15th as opposed to 1/13th for the 50D) and is not as great as it might at first seem. I was simply trying to get a good ETTR. Checking out DXOmark figures later, I discover that at ISO 100, the sensitivies of both cameras is equal at ISO 93. However, at the nominal ISO of 400 the 5D is actually ISO 357, according to DXOmark, but it should be 4x93=372, so it does appear to be slightly understated. Nevertheless, according to EV compensation adjustments in ACR, the 5D has about a 1/3rd stop ISO advantage in these comparisons, that is, it requires -1 EV adjustment whereas the 50D image requires -0.67 EV adjustment.

The noise comparison images below were converted with zero black, zero contrast, linear tone curve, no sharpening, and no noise reduction of either luminance or color. Both images have been lightened to the same degree in 'levels'. The 5D comes out quite well. I was surprised that at ISO 640 the 5D would be on a par with the 50D at ISO 100. One should also bear in mind that the slight ISO advantage I've given the 5D does not translate to more photons per unit area of sensor, but a slightly greater analog amplification of the signal.

Quote
All this "fine print" is why one needs to understand the physics, mathematics, and applicability of the formulas, or otherwise use them cautiously, in the range of conditions for which they were intended. More detailed formulas are available in more advanced optics texts for the harder cases!

The problem here is that, in the field where capturing the moment is often of the essense, we don't have time to engage in complex calculations. Outside of studio conditions, it's also very difficult to get precise measurements of distance to subject, so DoF calculations, however precise theoretically, can be no more precise in practice than the precision with which can one measure distances in the field.
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#### BJL

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« Reply #67 on: May 07, 2009, 10:44:03 am »

Ray,

thanks; I will look at the samples more carefully when I have the time. For now, on high precisision DOF formulas:
Quote from: Ray
The problem here is that, in the field where capturing the moment is often of the essense, we don't have time to engage in complex calculations. Outside of studio conditions, it's also very difficult to get precise measurements of distance to subject, so DoF calculations, however precise theoretically, can be no more precise in practice than the precision with which can one measure distances in the field.
Agreed. My point about understanding the science behind the formulas is only to avoid misusing them, or expecting more precision of them that is justified. The main use for DOF formulas as far as I can tell is to ensure enough DOF in situations when one is facing trade-offs between DOF, shutter speed, diffraction and such. So probably all that is needed in the field is a suitably good approximation, used with sufficient caution. Very careful macro photographers (including the extreme macro case of microscopy) needs more care and have use for more precise formulas.

Then again, with a sufficiently large, sharp, accurate, and bright VF image, one could stop down and verify DOF directly. But no SLR optical VF is up to that task. Live View with zoom might be the coming solution.

But the original question of this thread is much easier, and does not need details of subject distance beyond avoiding the extremes of macro range and hyperfocal distance. Because that question was only about the DOF shift between different choices of format/focal length, under conditions of equal (if unknown!) subject distance and equal display size. I have not yet seen evidence that "equal DOF at equal effective aperture" is insufficiently accurate, but I will keep looking.

P. S. Modest downsampling of Bayer CFA raw data to a RGB format like JPEG or TIFF with about half or more the pixel count might have very little effect on resolution, due to the greater information in one three color RGB pixel than in one single color Bayer CFA pixel.

I would be interested in a careful comparison of 6MP and 12MP conversions from a 12MP raw file, given that
6MP RGB has 6 millions values for each of G, R and B,
12MP Bayer CFA raw has 6 million G values, 3 million each for R and B.
So it could even be that 6MP RGB can hold more detail in some situations than a 12MP Bayer CFA raw provides.
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#### Ray

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« Reply #68 on: May 08, 2009, 11:45:07 pm »

Quote from: BJL
But the original question of this thread is much easier, and does not need details of subject distance beyond avoiding the extremes of macro range and hyperfocal distance. Because that question was only about the DOF shift between different choices of format/focal length, under conditions of equal (if unknown!) subject distance and equal display size. I have not yet seen evidence that "equal DOF at equal effective aperture" is insufficiently accurate, but I will keep looking.

BJL,
I agree completely that taking the ratio of the diagonals of the different size formats as a multiplier for determining appropriate focal length and f stop #, in order to equalise FoV and DoF, is a good starting point. However, when the formats being compared also have a different aspect ratio, as the micro 4/3rds and Canon cropped formats have, then the formula becomes slightly more 'rule-of-thumb'. When one of the formats has a significantly different pixel count, then the formula becomes even more 'rule-of-thumb'. If one of the formats has the benefit of a better lens, then that may also change the rule-of-thumbness to a greater or lesser degree in either direction.

When the subject focussed upon is fairly close to the camera (as in studio conditions rather than macro conditions), that may also affect the rule-of-thumbness to a greater extent than all the other factors mentioned above (in my view; yet to be confirmed.)

As you know, I've often battled with MFDB users on this forum about their slack approach to these matters when comparing their expensive equipment with 35mm format. I was also surprised recently when Michael compared the G10 with a P45 without also taking these matters seriously. He got the focal lengths approximately right, but was miles out with the DoF. As a consequence, when experienced photographers were invited to compare his A3+ size prints from both cameras, they were (eventually) able to identify the P45 because of its shallower DoF.

In the comparison shots of the woods scene, Michael used the G10 at F3.5 and the P45 at F11. The diagonal of the G10 sensor is 9.5mm (info available from Dpreview), and the diagonal of the P45 is 60mm. The multiplier for DoF equivalence is therefore 60/9.5=6.3.  F3.5x6.3=F22. Michael should have used F22 with his P45 in this comparison. By using F11, he gave the game away.

I'm surprised that no-one seems to have pursued this issue and repeated the comparison using images with equal DoF. We are left to speculate on what the results might have been. There's no doubt that the P45 image would be less sharp at F22 (than at F11). How much 'less sharp' and at what print size is the question. Would these experienced photographers whom Michael invited to view his A3+ prints have then confused the greater sharpness of the G10 with the P45? We don't know until someone repeats the comparison.

Out of interest, I downloaded Michael's G10 and P45 images and searched for the out-of-focus areas. They were easy to find. Consider the crop comparisons below, at two different magnifications. In the second image, the G10 crop has been upsampled to the P45 size.

[attachment=13563:G10_v_P45.jpg]  [attachment=13564:G10_upsa...d_to_P45.jpg]

By the way, I understand it is not true that the origins of the expression 'rule of thumb' go back to a barbaric medieval law in England, which permitted a man to discipline his wife with a stick no thicker than his thumb. No record of such a law can be found. Just thought I'd mention it   .
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