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 Author Topic: How DOF scales with increased detail  (Read 3460 times)
BJL
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 « on: January 24, 2006, 06:49:03 PM » Reply

At Ray's suggestion, I would like the raise the topic of how the DOF ones sees in a print (or other final image) changes as one increases the resolution, and then views the image with sufficient enlargement and sufficiently close viewing to see the extra detail revealed by that higher resolution.

I suggest a simple answer: doubling linear resolution (lp/mm) and viewing big enough/close enough to see all the extra available detail gives half the DOF at the same f-stop compared to viewing of the lower resolution image, which means the same DOF as with half the f-stop with the  lower resolution image.

This is because to see that doubled linear detail requires doubling apparent viewing size, such as doubling the degree of enlargement and still viewing from the same distance. This doubles the size of each circle of confusion on the print. Since the perceived DOF is determined by the same upper limit on the size of CoC on the print, this now corresponds to the maximum allowable CoC size on the in-camera image being half as much as before: the relevant CoC value for DOF formulas is halved (just as pixel size has effectively been halved to double resolution). So DOF at equal f-stop is halved, so that it is the same as one previously got with half the f-stop.

For example, f/4 at "double normal resolution" and "double normal viewing size" (say print diagonal length twice as big as viewing distance) gives the same perceived DOF as f/2 with "normal resolution" and "normal viewing size" (print diagonal length equal to viewing distance).

P. S. One consequence is that as one attains higher and higher resolution, proportionately higher f-stops will typically be needed to adequately control OOF blur of subject elements for which one seeks a sharp image.
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Ray
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I suggest a simple answer: doubling linear resolution (lp/mm) and viewing big enough/close enough to see all the extra available detail gives half the DOF at the same f-stop compared to viewing of the lower resolution image, which means the same DOF as with half the f-stop with the  lower resolution image.

P. S. One consequence is that as one attains higher and higher resolution, proportionately higher f-stops will typically be needed to adequately control OOF blur of subject elements for which one seeks a sharp image.
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BJL,
This is certainly a logical conclusion and one that occurred to me a while back when you, Howard and I were discussing DoF and comparing 35mm f8 with 8x10 f64. These two f/stops are supposed to be quivalent for DoF purposes. However, if you consider that no 35mm lenses are truly diffraction limited at f8 and LF lenses are diffraction limited at f64; plus the fact the f64 image at the plane of focus will not be significantly degraded by the film but the f8 image will definitely be significantly degraded by the MTF loss of the film at those high resolutions, then one could easily come to the conclusion that for appropriate size prints, LF f/64 produces less DoF than 35mm f/8.

On the other hand, if we were to ensure that both lenses (35mm and LF) were used at diffraction limited f/stops, which I think would mean using 35mm at f16 and 8x10 at f128, and if were to examine just the image from the lens, say projected on a screen, and ignore sensor and/or film limitations, then the images would have equivalent resolution at the plane of focus as well as equivalent DoF, wouldn't you agree?

I believe I've just rephrased the point you are making, for the sake of clarification (in my own mind, if no-one elses   ).

So, if we start comparing lenses that are diffraction limited in one format with lenses at equivalent f/stops in another format, that are not diffraction limited, we change the balance between maximum resolution and CoC and therefore change the appearance of DoF.

So how significant is this? Is it really an issue in practice? Is anyone going to worry about it?

I recall Jonathan commenting that large prints he made from 1Ds images, that had a fairly shallow DoF, appeared to have a similarly shallow DoF at small 5x7" sizes. Perhaps not quite as shallow, but no dramatic difference. Possibly different sharpening routines had skewed the results. Perhaps the way our eyes pick up detail is not proportional to the distance from the print. Perhaps the 'contrast' of the detail in the print skews the results. Perhaps the degree of OOF changes the degree to which our perception of DoF changes with changing distance from the print.

For example, most shots I've seen taken with the Canon 50/f1 have such an OOF background that the background is unrecognisable. If it's unrecognisable on a small print at close viewing distance, it's certainly going to be unrecognisable on a large print at the same viewing distance, but actually may be 'more' recognisable on the large print from a greater viewing distance. In such situations, the large high resolution print, which might appear to have less DoF than the small, lower resolution print from close up, might appear to have greater DoF than the smaller print, when viewed from a distance.

Perhaps an analogy here is the extremely low resolution jpeg image of say a face on your monitor. From close up, the features are not recognisable. Stand back a few metres and they are.

Are you now going to volunteer to do some practical tests to support your theory, BJL   .
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BJL
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Ray, I turned this on its head, starting with increasing resolution (say doubling), which lumps together effects from sensors, lens aberrations, diffraction and maybe other factors like accuracy of the alignment of the sensor in the focal plane and atmospheric effects. In other words, I do not care whether or not my lens has about the same resolution as an imaginary one with no aberrations ("diffraction limited"), I only care about the bottom line overall system resolution. Once that resolution increase has been increased by whatever means, and is revealed to the viewer by suitable enlargement and viewing, I ask about DOF. Doubling resolution at fixed focal length and aperture might well need more than halving pixel spacing, since diffraction effects are not halved but remain constant. So in fact, such resolution doubling can probably not be done when one is already near the diffraction limit of the lens-sensor system.

Anyway, I was discussing resolution increase with the same format and focal length. I have very little interest in analyzing the potential of 8"x10" format; I greatly doubt I will use it in film, or that anyone will use it in single shot digital sensors (as opposed to scanning backs.)
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Ray
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Anyway, I was discussing resolution increase with the same format and focal length. I have very little interest in analyzing the potential of 8"x10" format; I greatly doubt I will use it in film, or that anyone will use it in single shot digital sensors (as opposed to scanning backs.)
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BJL,
The only reason I ever use 8x10 format in these discussions is to create a significant distance between the formats compared. Exaggerate a point and the principle sometimes becomes clearer. One can also avoid  overlapping considerations such as the fact that 6x4.5 lenses can be as high-resolving as some 35mm lenses, and sometimes even better than their 35mm equivalents.

Whilst we can can't buy cameras of the same format that differ in resolution by a factor of 2 (the closest we could get would be the D30 compared to the 1Ds2, or maybe a 2MP P&S compared with an 8MP P&S), we can make different size prints to simulate the effect. Unfortunately with the 5D, the maximum size print at 240 ppi without interpolation is 12x18", so a print simulating the effect of a same format camera with 1/2 the resolution would be just 6x9.

I think there can be no doubt that such a small print would appear to have greater DoF. If the 5D shot was at taken at f8 and the 12x18 print showed a slight degree of blurring, say in the foreground, then this blurring might not be apparent in the 6x9 print. In order to create an equivalent degree of OOF blurring in the small print we would have to retake the same scene using f4. The 8x12 print would then show significant blurring in the foreground which might ruin the shot, but the small print might show the same degree of blurring as in the first shot at f8.

I think this is a concrete example of the principle you are describing. However, I think the principle needs to be qualified. I would put it this way. There will usually be at least one set of circumstances with regard to print size and viewing distance, such that a doubling of resolution at the plane of focus which is visible on the larger print, will have the effect of halving the appearance of DoF on the larger print, in comparison with the DoF on the smaller print, provided the maximum resolution of the original image is also visible on the smaller print.

My concern is, this is a very narrow set of circumstances. The prints have to be sized exactly in prortion to the resolving power of the camaras used, and both prints have to be viewed from a precisely calculated distance relating in part to one's eyesight capabilities. Change the viewing distance just slightly and the appearance of DoF on both prints will change.

What an inexhaustible topic is this DoF concept   .
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AJSJones
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At Ray's suggestion, I would like the raise the topic of how the DOF ones sees in a print (or other final image) changes as one increases the resolution, and then views the image with sufficient enlargement and sufficiently close viewing to see the extra detail revealed by that higher resolution.

You guys get into some arcane discussions!  Some I can follow, and I think I understand the question here, but maybe not.

I would say you are free to be arbitrary here, given that the "original" definition of DoF was arbitrary but  based on available technology and routine practice (35mm format, ~8x10 in print viewed at ~12", or some closely related version of that).  You should retain the "sharpness/acutance/resolution"  sensitivity value assigned to the average human eye and make up your own viewing distance (or retain 12" and 300ppi!) and degree of enlargement  but you'd probably need to specify print ppi.  If you specify print ppi (using original captured pixels as the first p), you necessarily specify the degree of enlargement of a given sensor array, right?  We are therefore rapidly approaching the question of "Is JW right when he asserts that pixel pitch = CoC?"  Or is that only true for 100% on screen peeping?  How about (pixel pitch) * 3 = CoC if displays now are often at ~100 ppi and prints are at 300?  These are both potentially pragmatic and intuitive limitations, but I suspect you are going for something more based on first principles or theories.

Coupla questions I have for you guys : How often do you use all the pixels you capture in a print, and how often do you crop after the fact? (I know some folks think cropping is "manipulation")  Do you print to a fixed ppi and let the print size fall where it may or vice versa?  How is DoF affected by these decisions?  Are these relevant to the discussion or are you just contemplating the DoF in any part of the image without regard for the absolute image size?  Perhaps all it takes is to specify 300 originalppi and 12" viewing and back-calculate?

PS Is DoF shallower at the corners of an image due to poorer lens performance???
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BJL
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You should retain the "sharpness/acutance/resolution"  sensitivity value assigned to the average human eye and make up your own viewing distance (or retain 12" and 300ppi!) and degree of enlargement  but you'd probably need to specify print ppi.[a href=\"index.php?act=findpost&pid=56920\"][{POST_SNAPBACK}][/a]
With digital, it might be convenient to standardize on some combination of PPI and viewing distance: I would modify you proposal to 300ppi and 10", or in other words, "3000 pixels per viewing distance".  But I was allowing for other factors in resolution too, like lens aberrations and diffraction, so maybe we should settle on something like overall resolution of 5 lp/mm on the print intended for viewing from as close as 10". (I have read figures like 4, 5 or 6 lp/mm for resolution on the print as industry standards.)
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We are therefore rapidly approaching the question of "Is JW right when he asserts that pixel pitch = CoC?"  Or is that only true for 100% on screen peeping?  How about (pixel pitch) * 3 = CoC if displays now are often at ~100 ppi and prints are at 300?  These are both potentially pragmatic and intuitive limitations, but I suspect you are going for something more based on first principles or theories.[a href=\"index.php?act=findpost&pid=56920\"][{POST_SNAPBACK}][/a]
My approach tried to avoid the arbitrariness of declaring one correct CoC for a given pixel size, or for a given print size and viewing distance. All that matters is how the CoC changes as the degree of enlargement changes. When you double the resolution on the sensor and the degree of enlargement, so that the new print is bigger but has the same resolution on the print, it does not change the maximum allowable CoC size on the print for an image to appear in-focus, so to keep within that same CoC limit on the print one must half the maximum allowable CoC size on the sensor.
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BJL
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The only reason I ever use 8x10 format in these discussions is to create a significant distance between the formats compared. Exaggerate a point and the principle sometimes becomes clearer.[a href=\"index.php?act=findpost&pid=56869\"][{POST_SNAPBACK}][/a]
Unfortunately, you then use data relating to specific current lenses in various formats, not necessarily indicative of universal trends. When format- and lens- specific data are used, it is far better for them to relate to actual relevant formats. Do you care to try again with data for lenses designed for a selection from formats like 4/3", DX, 35mm film, 645 film, and maybe sightly larger, like Schneider Digitars? (I omit Canon EF-S format due to a paucity of top quality lenses designed for that format, though the 50mm macro could be considered.)
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Ray
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Unfortunately, you then use data relating to specific current lenses in various formats, not necessarily indicative of universal trends. When format- and lens- specific data are used, it is far better for them to relate to actual relevant formats.
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Unfortunately, there's a great lack of hard information on lenses. Photodo is really my only source for meaningful information on lenses. The rest is just hearsay. I haven't even seen an independent MTF test of Zuiko lenses.

I see a trend for lenses designed for larger formats to have less absolute resolving power but I am never sure at what f/stop any particular lens is diffraction limited because no-one seems to be addressing this issue, and it's quite clear from Photodo tests that the best  MF lenses are as good as many 35mm lenses, although there are few of them that exceed a rating of 4.

To get back to DoF, I'd certainly agree that there is a trend for smaller prints that are unable to display the full resolution at the plane of focus to have greater DoF. However, whilst this is apparent comparing hand-held 6x9 prints with 12x18 prints, it becomes a bit awkward comparing 12x18 with 24x36, in the hand. In this situation we'd have to hang both prints on the wall and view them from the same close distance and whilst that viewing distance might be appropriate for the 12x18 print, to appreciate the scene as a whole, it would then be too close to appreciate the 24x36" print in the same way. You'd have to move your head from side to side in order to appreciate the fact that certain parts of the background in the large print really did appear less sharp than the same areas in the smaller print.

This seems to me a rather artificial comparison. In another thread you actually presented this tendency towards less DoF in large, high resolution prints as some sort of disadvantage, which I don't believe it is.

In practice, if the different sized prints are viewed from proportionally different distances, sufficient for the eye to take in the whole scene, then the larger, higher resolution print will appear to have the same DoF as the smaller print.

If they are both viewed from the same distance, then the viewing distance cannot be ideal for both prints simultaneously. If, as a consequence of this less than ideal viewing distance, the larger print exhibits an apparent shallower DoF, then so what! Step back a bit   .
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AJSJones
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With digital, it might be convenient to standardize on some combination of PPI and viewing distance: I would modify you proposal to 300ppi and 10", or in other words, "3000 pixels per viewing distance".  But I was allowing for other factors in resolution too, like lens aberrations and diffraction, so maybe we should settle on something like overall resolution of 5 lp/mm on the print intended for viewing from as close as 10". (I have read figures like 4, 5 or 6 lp/mm for resolution on the print as industry standards.)

My approach tried to avoid the arbitrariness of declaring one correct CoC for a given pixel size, or for a given print size and viewing distance. All that matters is how the CoC changes as the degree of enlargement changes. When you double the resolution on the sensor and the degree of enlargement, so that the new print is bigger but has the same resolution on the print, it does not change the maximum allowable CoC size on the print for an image to appear in-focus, so to keep within that same CoC limit on the print one must half the maximum allowable CoC size on the sensor.
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I also have heard 5 lp/mm frequently and calculate that 6 lp/mm is ~300 ppi, so these are fine, and so is 10" - IIRC these kinds of values were slightly different between lens manufacturers as they engraved DoF scales, so once the decision is made, we live with it for consistency's sake.

I would agree that to get the new image with double resolution printed at the same ppi as the one from the lower resolution sensor (lower pixel-pitch) the geometric enlargement- i.e.  from original sensor dimensions, is also doubled, so yes the CoC should be halved and therefore the DoF recalculated with the new CoC.

Now, if we take the image from the new sensor and resample down to the same pixel dimensions as the image from the lower res sensor, I think most would agree that the downsampled image benefits (at least at some print ppi and viewinbg distance) from the extra original pixels to make the downsized image "better" than the one captured with the original sensor.  How then to assess DoF?
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Ray
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I would agree that to get the new image with double resolution printed at the same ppi as the one from the lower resolution sensor (lower pixel-pitch) the geometric enlargement- i.e.  from original sensor dimensions, is also doubled, so yes the CoC should be halved and therefore the DoF recalculated with the new CoC.

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Actually, Andy, this little dispute began in another thread where I suggested that it might be technologically easier to manufacture an MF lens that is truly diffraction limited at f8 than a 35mm lens that is diffraction limited at f4. Both lenses, if diffraction limited at those apertures, would theoretically deliver the same 'picture' resolution on both formats if the total pixel count on both sensors is the same and sufficient to resolve the resolution of the lens. The 35mm format sensor would have higher pixel density, but  also a higher resolving lens; a lens in fact with double the resolution of its MF equivalent. The comparison here is between say, 45mm at f4 in 35mm format and 90mm at f8 in MF. The DoF would be equivalent in both cases; that is, the physical aperture is the same diameter for both lenses at those f/stops (45/4 = 90/8), and the CoCs would proportionally be the same size in relation to the sensor size.

Since sensors are not enlarged like film when making a blow-up, the images from both formats would be the same size, according to pixel count and not sensor size.

Provided the two lenses are diffraction limited at those respective apertures (f4 for 35mm and f8 for MF) the prints should be identical in terms of absolute resolution, CoC, percieved DoF and actual depth of definition, whatever the size of the print.

By way of rebuttal, BJL suggested if it were not technologically possible to construct a 35mm lens that is diffraction limited at f4, an MF lens which is  diffraction limited at f8, and therefore higher resolving in terms of 'picture' resolution, would suffer the disadvantage of having less DoF as a consequence of its greater 'picture' resolution.

In other words, in order to actually see that greater detail in the MF print, the print would have to be enlarged to a greater degree. In doing so, one would also be enlarging the CoCs and consequently widening the resolution gap between the parts of the image in sharp focus and the OOF parts. The large MF print would then appear to have a shallower DoF than the smaller 35mm print when viewed from the same distance.

The logical flow-on from this insight is that DoF equivalencies between formats is not just a matter of multiplying the f/stop by the diagonal ratios of the sensors, eg a 50mm lens at f8 on a 20D is only roughly equivalent to an 80mm lens at f13 on a 5D. One has to take into consideration the fact that the 50mm lens at f8 is far from being diffraction limited whereas the 80mm lens at f13 is quite close to being diffraction limited. However, this factor which might appear to give the DoF advantage to the 20D at f8 is partly offset by the greater absolute resolving power of the 20D.

Hope this is now as clear to you as it is to me   .
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Ray
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