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### AuthorTopic: DoF, sensor size, and pixel pitch  (Read 13992 times)

#### gkramer

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##### DoF, sensor size, and pixel pitch
« on: January 27, 2007, 11:08:19 PM »

Sidney Johnson's analysis of DoF ("Lens Equivalents") is based on a film-camera era treatment of the topic, and is not valid for digital. The basic problem is that it is implicitly based on the "enlargement factor" as measured by the ratio, in terms of linear dimensions, by which the film negative (or positive) is enlarged to to produce the final print (thus a 35mm negative, which measures 24 x 36mm = 1" x 1.5", when enlarged to produce an 8" x 12" print, has an "enlargement factor" of 8x).

This is inappropriate for digital: the relevant "enalrgement factor" depends only on the pixel count, and is idependent of the physical dimensions of the sensor. A 6MP, 2000 x 3000-pixel image file will produce the 6.7 x 10" print at "native" 300ppi resolution, irrespective of whether it was captured by a 24mm x 36mm full-frame sensor, a 16mm x 24mm APS-C sensor, or a tiny, quarter-inch sensor from a pocket point-n-shoot.

Johnson suggests setting the CoC to (sensor diagonal)/1500, which for a fullframe 24mm x 36mm sensor gives a CoC of 29 microns diameter. For the Canon EOS-1Ds, with a pixel pitch of 8.9 microns, this means the CoC on the sensor is 29/8.9 = 3.25 pixels in diameter; at 300ppi, this would be about .011" on the print.

The Nikon D2X has about the same MP count (12.2MP), on a smaller APS-C sensor, with a much smaller pixel pitch, 5.5 microns; but suppose Nikon decided to produce a full-frame DSLR by simply scaling up the D2X's sensor (it would be an impressive 27MP). Then the CoC on the sensor would be 29/5.5 = 5.27 pixels in diameter, and would produce a blur spot on the print 1.6 times larger, or .017". The difference on the prints (viewed under identical viewing conditions) would be clearly visible.

Of course the print produced by the 27MP Nikon D3Z (let's call it) would be much larger than the 11MP Canon's; at "native" 300-ppi resolution, the "D3Z" image would be 9.5" x 14.3", versus the Canon's 6.8" x 10.3"--roughly the difference between a double-page spread in Audobon magazine, and a shot that would fit comfortably on a single page. But, viewed at the same distance, the blur spot used to define DoF of the D2X image would be visibly larger; or, put differently, the apparent DoF of the D3Z image would be less.

To correctly calculate the DoF for the D3Z, we must use a smaller CoC, of 29/1.6 = 18 microns.

One implication of this is that the DoF scales engraved on lenses are meaningless when the lens is attached to a DSLR, since they do not take account of either sensor size or pixle pitch; and even tables like Johnson's, which do take account of sensor size, are off the mark. I'm working out a corrected one, which I hope to post later.
« Last Edit: January 28, 2007, 08:21:46 AM by gkramer »
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #1 on: January 28, 2007, 11:17:30 AM »

Anyone with a basic understanding of DoF knows CoC is determined by the photogtapher, not the camera (or its maker) or sensor type or size or pixel pitch or kind of film being used, lens, or whatever.  It is simply a number decided on by the photographer when designing a print.

It makes no sense of course to select a CoC smaller than can be resolved by the camera system, be it digital or film.  There is a distinct difference between DoF and maximum DoF.

Sidney Johnson made some assumptions about the size of enlargement and viewing conditions in order to deteremine a CoC, but that CoC is valid only for his set of assumptions.
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#### BJL

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##### DoF, sensor size, and pixel pitch
« Reply #2 on: January 29, 2007, 01:24:35 PM »

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Sidney Johnson made some assumptions about the size of enlargement and viewing conditions in order to deteremine a CoC, but that CoC is valid only for his set of assumptions.
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Give it a rest Howard. The DOF perceived by a viewer of a print depends amongst other things on print size and viewing distance, and so these conditions are a necessary part of any DOF calculation or comparison. These are "assumptions" only in the same sense that reference to a particular focal length, aperture ratio and focus distance are "assumptions": they are all just explicit parts of the statement.

And in fact, so long as one only assumes that different prints from different combinations of focal length, aperture, subject distance etc. are assessed via prints of the same size, viewed from the same distance, by a viewer of the same visual acuity, Johnson's conclusions hold: equal aperture size d=F/N, combined with equal perspective, equal FOV, equal image size and equal viewing distance will give about equal DOF.

Johnson does make some assumptions, mostly rather harmless. Firstly that we are not in the "macro" range, where some of the optical approximations made might become less accurate. Secondly that the sensor resolution is not an issue because it is more than the viewer can make out under the stated viewing conditions, and that lens aberrations are likewise low enough to be ignored.

It might be interesting to rework Johnson's calculations in terms of statements about the effects on angular resolution of various parts of the image from the combination of OOF effects (the various circles of confusion at different parts of the image), Airy disks, pixel sizes, etc. This is more the spirit in which astronomers approach resolution.
« Last Edit: January 29, 2007, 01:34:11 PM by BJL »
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #3 on: January 29, 2007, 02:12:51 PM »

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Give it a rest Howard.   ...

Johnson does make some assumptions, mostly rather harmless. ...

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No.

I didn't say Johnson's assumptions were not harmless or even unusual.  I merely said that assumptions were made and that the reader must understand those assumptions in order to understand Johnson's results.

Not knowing or acknowledging assumptions often leads to results becoming "facts."  Like, DoF is determined by the engraved scales on the lens' barrel, without even caring what the CoC is.  The engraings are true for and only for, prints that are made according to the applicable assumptions.  Canon assumes a print size, viewing dsitance and CoC.  These assumptions do nat have to be made.  Or that the DoF preview in the view finder works (what is the "print size" (maybe 1x1.5"), what is the viewing distance, and isn't the viewfinder dimmer than the print viewing area?).  Or the assumptions for DoF calculators are not provided, but simply provide a CoC value for the camera/lens being used.

Assertions that DoF is dependant on pixel pitch leads me to believe not all the assumptions about DoF and DoF itself are understood.
« Last Edit: January 29, 2007, 03:52:34 PM by howiesmith »
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#### BJL

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##### DoF, sensor size, and pixel pitch
« Reply #4 on: January 29, 2007, 03:54:18 PM »

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I merely said that assumptions were made and that the reader must understand those assumptions in order to understand Johnson's results.
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The viewing conditions and such were clearly stated, and Johnson spent some time explaining the origins of his choice of "CoC diameter of 1/1500 of the diagonal dimension of the image" so your concerns seem to have been addressed. I do not understand your implicit criticism that something important went unstated or unexplained.

I suggest that you read the three paragraphs starting with the words.
"However, there is a caveat. The type of DoF computation depends on the way photographs will be viewed!"
which includes
"There is nothing sacred about this choice of CoC. If very large prints are to be made, perhaps the CoC should be reduced; and vice versa if only 4" by 6" prints are needed one can get away with a larger CoC."

Here is an interesting quote from the first, 1997 issue of Camera Lens News a quarterly newsletter published by Carl Zeiss, interesting in that it mentions 1/1500, not 1/1730:

"According to international standards the degree of blur tolerable is defined as 1/1000th of the camera format diagonal, as the normally satisfactory value. With 35 mm format and its 43 mm diagonal only 1/1500th is deemed tolerable"

I could dig up a citation of Ansel Adams using the 1/1000 figure if you are interested.

I do think that Johnson could have made his explanation clearer at one point. He argues reasonably for CoC of about 1/1500 of the viewing distance, but then shifts to CoC of 1/1500 of the image diagonal, and the two only go together in the case of viewing distance roughly equal to print diagonal size. Johnson says that he is dealing with the case of a viewing distance of 10 to 12 inches, so seems also to be considering prints of about 8"x10" size. It is clear from the quote above that he is explicitly talking about prints of some typical size, not prints of any imaginable size. That is the universal custom, embodied for example in the DOF scales on lenses and such: makers of very larger pritns are expected to know haw to adjust for that situation.

However I would prefer to just saying that the calculations refer to the common case of
viewing distance = image diagonal size
which is often describe as "normal field of view".
One could generalize the result by noting that DOF changes from this value in proportion to the ratio (viewing distance/image diagonal size).
« Last Edit: January 29, 2007, 03:58:31 PM by BJL »
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #5 on: January 29, 2007, 04:07:56 PM »

Quote
I suggest that you read the three paragraphs starting with the words.
"However, there is a caveat.  ..."

[a href=\"index.php?act=findpost&pid=98154\"][{POST_SNAPBACK}][/a]

Thank you, I am familiar with the article and the references you cited.  However, I am not at all sue that everyone is.

"One implication of this is that the DoF scales engraved on lenses are meaningless when the lens is attached to a DSLR, since they do not take account of either sensor size or pixle pitch; and even tables like Johnson's, which do take account of sensor size, are off the mark. I'm working out a corrected one, which I hope to post later."
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#### gkramer

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##### DoF, sensor size, and pixel pitch
« Reply #6 on: January 29, 2007, 04:16:30 PM »

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Assertions that DoF is dependant on pixel pitch leads me to believe not all the assumptions about DoF and DoF itself are understood.
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Since this is a long and somewhat technical discourse, let me try to motivate the potential reader by summarizing the conclusions which I think it demonstates:

-----------
Digital is different. Pixel pitch affects DoF in a serious way, and (except in the exceptional case when pixel pitch is exactly proportional to sensor size), the "M x A rule" and similar rules of thumb, or DoF tables based on film-camera concepts, will be inaccurate and misleading.

Both Nikon and Canon are widely rumored to be contemplating introducing large-MP full-frame "Super DSLR" models. But a "Super DSLR" such as our hypothetical 27MP "D3Z" will have considerably less DoF that existing 10-16MP full-frame DSLRs. As a practical matter, the DoF penalty for such a camera, arising from its necessarily finer pixel pitch, may be so large as to make it effectively impossible to get enough DoF for landscape photography, for example, by simply stopping down. The only recourse would seem to be using lens movements, of the type view-camera users have long been obliged to learn, in a new generation of well-corrected "Tilt & Shift" lenses. Let us hope that Nikon and Canon will attend to this task, as well.
-----------

The mathematics of calculating DoF from the CoC are described in any standard optics text (for example, Chapter 22 of Sidey Ray's Applied Photographic Optics); the basic idea is that if the image of a scene element K units in length can be covered by a "Circle of Confusion" of diameter C on the film, it wiil not be perceived in detail, and will be in the "out-of-focus" zone; while one whose image is too large to be covered by the CoC will be detectable on the print, in the "in-focus" zone. For a camera focused on a subject u meters away, the near and far camera-to-object distances, S < u and and R > u, at which a K-sized element would just span the CoC, define the near and far limits of the "in-focus" field. The Depth of Field T is defined as T = (R-S), and for "normal" (i.e., non-closeup) distances, it can be calculated from the equation

T = (2*u*u*N*C)/(f*f)

where u is the camera-to-subject distance, f is the focal length of the lens, C is the diameter of the CoC, all in meters, and N is the relative aperture, a pure number (2.8, 4, 5.6, etc.). The CoC (value of C) is chosen in view of the intended enlargement, and distance at which the print is to be viewed; a value of 30 microns (millionths of a meter) would be typical for a 35mm negative, enlarged 8x to a 8" x 12" print, to be viewed at 10-12 inches (the 30-micron CoC would thus be enlarged to a 8 x 40 = 240-micron blur spot on the print).

To apply this apparatus to digital, we must re-express the CoC in terms of pixels, not microns, as explained in my previous post.

But let's first apply it to FILM cameras, which have no pixels, to the calculate the DoF's of full-frame vs APS. For concreteness, suppose we're using a full-frame 35mm SLR to photograph an object 10 meters away, using a 100mm lens (f = .1), using a CoC of 40 microns, at an arbitrary aperture N. If we work out the arithmetic (keeping track of all the zeroes) we find that T = .3N, implying a DoF of 1.2 meters at f/4, or 2.4m at f/8, etc., which is in the ballpark with the DoF scales engraved on a typical 100mm SLR lens.

Now suppose we take the same shot from the same vantage point with an an "APS" (16 x 24mm frame) body, using a wider lens (because of the "crop factor") to get the same FoV; the proper lens to use is one of focal length f' = (2/3)f = 68mm. Moreover, because the APS negative is only 2/3 as large, it will have to be enlarged more to yield the same final print size, by a factor of 3/2; hence, in order to end up with the same-sized blur spot on the print, we must take a smaller CoC, C' = (2/3)C. All other factors in the equation are the same, so the DoF for the APS shot, T', is

T' = [2*u*u*N*C']/f'*f' = [2*u*u*N*(2/3)C]/[(2/3)f*(2/3)*f] = (3/2)T = (3/2)*.3N

Thus, at the same aperture, the DoF in the APS image is 3/2 as large; to get the same DOF we would have to open up the aperture to N' = (2/3)N. Or, to put it the other way around, the DoF for a full-frame camera, using a longer lens to give the same FoV, is only 2/3 as deep, compared to the APS camera; and to get the same DoF we would have to stop down the full-frame's longer lens by the "crop factor" of 3/2: if the APS image (using the 68mm lens) were shot at f/4, we would have to stop down the 100mm lens on the full-frame camera to f/6.

This relationship, and the rule "stop down by the crop factor" is a general one, which does not depende on the numerical specifics of our example. This type of ananlysis is the basis for similar "rules", such as Alexander's "CoC =Diag/1500" rule, and Wrotniak's "M x A" rule.

But now let's apply this apparatus to digital, taking account of pixel pitch, specificaly to the issue of DoF on APS-C versus full-frame DSLRs, and using the D2X (an APS-C, 12MP camera with a pixel pitch of 5.5 microns) as a baseline.

The DoF of a 100mm lens focused at 10m, using a CoC = 30 microns, is T = .3N, as shown above (irrespective of the sensor size); so for the D2X, the relevant "CoC" measured in PIXELS--call it the DCoC--is 30/5.5 = 5.5 pixels in diameter. A 300-ppi print has about 12 pixels/mm, so the resulting blur spot would be about 420 microns in diameter, somewhat larger than the film-camera example used above; but this calculation ignores the effects of demosiacing & sharpening, and is close enough for illustrative purposes (suppose we're viewing all the digital prints at a somewhat greater viewing distance.) Thus the DoF for a D2X shot taken with a 100mm lens, focussed on an object 10 meters distant, is also given by T = .3N

Now let's compare the D2X image with one taken by a full-frame DSLR, in which the pixel pitch has been increased (by a factor of 3/2) to make the sensor large enough to fill the full 24 x 36mm frame. The pixel count is the same, so both cameras will yield the same (300-ppi) print size. To get the same-sized blur spot on the print, we must choose a DCoC 5.5 pixels in diameter, which for these larger pixels reqiuires a CoC of C' = (3/2)C. To get the same FoV, because of the "crop factor", we would use a lens of f' = (3/2)f = 150mm; so plugging these into the equation

T' = [2*u*u*N*C']/[f'*f'] = [2*u*u*N*(3/2)C]/[(3/2)f*(3/2)*f] = (2/3)T = (2/3)*.3N

This follows "stop down by the crop factor" rule, as did the film-camera example above.

But now suppose we use a full-frame camera--the "D3Z"--which uses the same pixel pitch as the D2X. Its 27MP image will yield a consdierably larger, 300-ppi print; but suppose we still view it at the same distance, using the same blur-spot size to define the in-focus field. To get the same blur-spot on the print, we must use the same CoC, C' = C = 30 microns, which is still 5.5 pixels in diameter; so, taking account of the longer lens, we have:

T" = [2*u*u*N*C']/[f'*f'] = [2*u*u*N*C]/[(3/2)f*(3/2)*f] = (4/9)T = (4/9)*.3N

There is now less than half the DoF; for the full-frame camera to get the same DoF as in the D2X shot, we must now stop down by the SQUARE of the "crop factor", in this case by (9/4). If the D2X shot were taken at f/4, we would have to stop the D3Z's 150mm lens to f/9--which is approaching the limit (f/11, according to Thom) at which D2X users have found that diffraction-induced blurring effects increase objectioanlly (basically because the diameter of the Airey disk exceeds the 2-pixel Nyquist limit).

There are a couple of morals to this story.

Digital is different. Pixel pitch affects DoF in a serious way, and (except in the exceptional case when pixel pitch is exactly proportional to sensor size), the "stop down by the crop factor" and similar rules of thumb, or DoF tables based on film-camera concepts, will be inaccurate and misleading.

Both Nikon and Canon are widely rumored to be contemplating introducing large-MP full-frame "Super DSLR" models. But a "Super DSLR" such as our hypothetical 27MP "D3Z" will have considerably less DoF that existing 10-16MP full-frame DSLRs. As a practical matter, the DoF penalty for such a camera, arising from its necessarily finer pixel pitch, may be so large as to make it effectively impossible to get enough DoF for landscape photography, for example, by simply stopping down. The only recourse would seem to be using lens movements, of the type view-camera users have long been obliged to learn, in a new generation of well-corrected "Tilt & Shift" lenses. Let us hope that Nikon and Canon will attend to this task, as well.
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#### BJL

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##### DoF, sensor size, and pixel pitch
« Reply #7 on: January 29, 2007, 04:35:35 PM »

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Assertions that DoF is dependant on pixel pitch leads me to believe not all the assumptions about DoF and DoF itself are understood.
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I think those assertions about pixel pitch refer to the case of pushing enlargement and viewing distance to the resolution limits of the sensor. In other words, the minimum DOF that one could perceive with the greatest amount of enlargement and scrutiny. Quite different conditions that the ones usually discussed of viewing with "normal viewing angle" or viewing distance equal to image diagonal.

By "viewing angle", I mean the angle subtended by the longest dimension of the image (its diagonal) from the viewer's eye. Roughly this is the ratio of image diagonal to viewing distance. [To be precise, (image diagonal)/(viewing distance) = 2 * tan (1/2 viewing angle).]

It is often said that about 50º is the viewing angle that best fits the way the human eye perceives a scene, though peripheral vision is far wider and the most detailed image as seen by the fovea is far narrower. 50º gives viewing distance = 107% of image diagonal, close enough to equal.

Every calculation that gives a specific DOF value applies only to one choice of viewing angle; that is, to one particular ratio of viewing distance to image size. So long as the choice of viewing angle is stated, I have no problem: no _unnecessary_ assumptions are being made, only the _necessary_ choice of a viewing angle.
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #8 on: January 29, 2007, 04:38:07 PM »

Quote
One implication of this is that the DoF scales engraved on lenses are meaningless when the lens is attached to a DSLR, One implication of this is that the DoF scales engraved on lenses are meaningless when the lens is attached to a DSLR, since they do not take account of either sensor size or pixle pitch; and even tables like Johnson's, which do take account of sensor size, are off the mark. I'm working out a corrected one, which I hope to post later.
;  ... .

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I agree the DoF scales engraved on lenses are meaningless without the assumptions, but not for the reason you give (they do not take account of either sensor size or pixle pitch).

Let's just agree to disagree.  I doubt any amount or quality of agrument will change anybody's opinion.
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#### gkramer

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##### DoF, sensor size, and pixel pitch
« Reply #9 on: January 29, 2007, 06:04:50 PM »

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Let's just agree to disagree.  I doubt any amount or quality of agrument will change anybody's opinion.
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Your opinion, anyway. Can't you do elemetary math? Consider a Community College.
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #10 on: January 29, 2007, 06:34:19 PM »

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Your opinion, anyway. Can't you do elemetary math? Consider a Community College.
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I was hoping we could just disagree without having to get nasty.  Yes, it is my opinion, but I could provide several references from knowledgible folks.

I can do (and have done) math.  I could provide transcripts to prove I could at least once, but I won't.  I have been to college, just not a community college.
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#### gkramer

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##### DoF, sensor size, and pixel pitch
« Reply #11 on: January 30, 2007, 07:28:58 AM »

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I was hoping we could just disagree without having to get nasty.  Yes, it is my opinion, but I could provide several references from knowledgible folks.
OK, sorry--but the attack on "quality argument" is an attack on the foundations of our civilization, at least since the Enlightenment (and before the Bush42 administration).

You may be right, that mathematical arguments won't convince everyone; so what about some empirical evidence? I took some test shots to try to demonstrate the effect of pixel pitch, using the same lens on my D2X (pp = 5.5 microns) and D70 (pp = 7.9 microns). I thought I could see it pretty clearly; but the shots themselves weren't very good, taken outdoors, in a blustery wind with ever-changing lighting conditions, due to scattered clouds scudding acroos the sky; so I didn't post them.

Why doesn't someone run some more careful tests under controlled studio conditions?

Comparing the DoF results I derived for the "big-pixel FF" and the "D3Z", we see that the latter's DoF T' is related to the former's, T, by

T' = (2/3)T

(at a given aperture N); this is basically because the D3X's pixel pitch is 2/3 as small. The relation is a general one: if pixel pitch of camera A is R times that of camera B, then their DoFs (at any given apeture N) should be related by

T' = R*T

For the D2X vs D70 comparison, R = 5.5/7.9 = .7; another possible pairing would be with one of Canon's large-pixel DSLRs like the 1Ds (8.9 microns) or 1D Mark II (8.2 microns) with one of their small-pixel models. (Sensor size doesn't matter--just crop the image from the larger sensor to the dimensions of that of the smaller, to get the same FoV). The advantage of such same-brand comparisons is that can use exactly the same lens--preferably a longish, sharp prime, like a 300mm f/2.8) on both. The idea would be to set uo a spaced series of targets, well iluminated, and then run two series of shots from a sturdy tipod, starting at the widest aperture, and stopping down to the point where diffraction begins to dominate everything (around f/11, for the D2X).

I'd be interested is seeing the results.
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #12 on: January 30, 2007, 10:18:07 AM »

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OK, sorry--but the attack on "quality argument" is an attack on the foundations of our civilization, at least since the Enlightenment (and before the Bush42 administration).

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I really had no idea I was attacking "quality argument."  I thought I simply said no amount of it was going to change anybody's opinion.  Instead of "anybody," I should have limited it to me.  I apologize.

Nor did I realize I was bashing the "foundations of our civilization."  What do you expect from a Bush Republican newculer engineer who has never been to community college?  And if I had realized that, I would be very surprised that anybody actually cares.

And good luck with your "test."
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#### BJL

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##### DoF, sensor size, and pixel pitch
« Reply #13 on: January 30, 2007, 10:19:29 AM »

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Digital is different. Pixel pitch affects DoF in a serious way ... a "Super DSLR" such as our hypothetical 27MP "D3Z" will have considerably less DoF that existing 10-16MP full-frame DSLRs. [a href=\"index.php?act=findpost&pid=98161\"][{POST_SNAPBACK}][/a]
If sensor (or film resolution) is increased as in these imagined future cameras, and one then views the resulting prints with the same "viewing angle" (e.g. still 11"x14" prints viewed from 15" away), with the resolution of both cameras high enough that sensor resolution is beyond the viewer's visual acuity, the DOF will not change; at least not according to any of the formulas you quote. This is because the threshold print CoC size for being in-focus does not change under these viewing conditions.

If instead the images are printed and viewed in a way that exposes the full resolution capabilities of the new sensor, so that the higher pixel count images are viewed at a larger viewing angle (larger print and/or closer viewing distance), then the extra "enlargement" reduces DOF in the higher pixel count image. (Here I count moving closer to an image as a kind of "enlargement" because it makes the image look larger.)

The mistake to avoid (I am not saying that gkramer made it) is to believe that prints of the same size as one has happily been making will suffer reduced DOF when viewed from the same distance due to the image recorded by the camera having somewhat higher resolution.

Instead, the need for smaller apertures to get adequate DOF comes mainly from the making of larger prints. This is just as true with film when planning to make larger prints that will get close scrutiny, such as when using higher resolution film.

This is not a specifically digital effect; it is an indirect effect of the extra enlargement opportunities offered by using a "light sensitive medium" of higher resolution.
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#### gkramer

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##### DoF, sensor size, and pixel pitch
« Reply #14 on: January 30, 2007, 11:34:03 AM »

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The mistake to avoid (I am not saying that gkramer made it) is to believe that prints of the same size as one has happily been making will suffer reduced DOF when viewed from the same distance due to the image recorded by the camera having somewhat higher resolution.
No, I don't think that's right--or maybe I'm just confused by what you mean by a "camera having somewhat higher resolution," and by the "enlargement" of a digital print.

"Enlargement": For given viewing conditions, the "native" 300-ppi size of a digital print is related to the pixel count, and not to the physical size of the sensor; it is the standard for close-viewed prints. "Enlargement" of a digital print above this size might refer to uprezzing to a larger pixel count, to produce a larger 300-ppi print, for close viewing; or to producing a larger print at lower ppi, for viewing at a greater distance, like a poster on a wall. But neither of these types of "enlargement" is relevant to the issues I was discussing, which is why I studiously avoided using the term, and worked out everything in terms of the 300-ppi "native" standard.

"Higher resolution": If this means a higher pixel count, then the "native" 300-ppi print size also increases, so I don't understand why we should be comparing "prints of the same size."

If, on the other hand, "higher resolution" means the how high a lp/mm value the sensor (& lens) can resolve, as measured from test charts like those used to test lenses & cameras in the photo magazines, then for a well designed digital camera, this is essentually determined by the Nyquist = 2 pixel limit (which is the lp/mm value at which the MTF cuts off) is thus essentially a matter of pixel pitch: finer pixel pitch = higher resolution.

If we decrease the pixel pitch on a sensor of fixed size, then obviously the total pixel count will increase, so we're back situation of the second paragraph: it makes no sense to compare "prints of the same size."

If, on the other hand, we reduce the size of the sensor as we decrease the pixel pitch, so as to keep the total pixel count constant, then we are at essentially the situation described in my post in comparing my hypothetical "big-pixel FF DSLR" with the D2X. In this case, the "higher-resolution" camera with the finer pixel pitch, the D2X, actually has MORE DoF, not less; so I guess that's not what you had in mind.

I'm not necessarily disagreeing with any of your points (which are perfectly sensible for film-camera world), just suggesting that the meanings of terms like "enlargement" and "resolution" are not self-evident in the digital world, and until they have been carefully redefined for digital, it's not clear that a perfectly sound proposition from the film-camera world is also valid, or even meaningful, for the digital-camera world.
« Last Edit: January 30, 2007, 02:16:53 PM by gkramer »
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#### howiesmith

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##### DoF, sensor size, and pixel pitch
« Reply #15 on: January 30, 2007, 12:20:03 PM »

Quote
The mistake to avoid (I am not saying that gkramer made it) is to believe that prints of the same size as one has happily been making will suffer reduced DOF when viewed from the same distance due to the image recorded by the camera having somewhat higher resolution.

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I don't think it is a mistake to believe this.  DoF is a perception of what is considered in-focus enough.  It is easier to see a differences in sharper prints.  A CoC just larger than the edge of an infocus CoC will not appear as much different than a CoC just smaller than in-focus when the image is "fuzzy."  I think this is a perception and not due to pixel pitch.  You can see this efect by "fuzzing" a digital image with a soften filter or blur in photoshop.

Got an image where the subject is slightly out of focus?  (I do.)  Blur the entire print and it won't be as noticible.

The over-all resolution O is:

1/O = 1/S + 1/L

where S and L are the resolution of the sensor (film or digital) and lens respectively.  It seems strange to me that, BD (Before Digital) as lenses and film got sharper (higher resolution), the "laws" of DoF did not need to be changed.  Why didn't DoF calculations change (to include film resolution) when I switched from Tri-X to T-Max 100?  Or I got that new L lens?  It seems only the arrival of digital has made some folks think something else has changed too.

How does one now compsre DoF between a digital camera and a film camera, all else being the same?

To quote a famous digital photographer/educator: "There was a query in October, 2001 on my Discussion Forum as to whether Depth of Field was calculated any differently for digital Vs. film. The answer is, no. There is no difference whosesoever. DOF doesn't care about the recording media type or size, ... "

Bob Atkins at photo.net says: "If you use the same lens on a EOS 10D and a 35mm film body and crop the 35mm image to give the same view as the digital image, the depth of field is IDENTICAL"

"Both Nikon and Canon are widely rumored to be contemplating introducing large-MP full-frame "Super DSLR" models. But a "Super DSLR" such as our hypothetical 27MP "D3Z" will have considerably less DoF that existing 10-16MP full-frame DSLRs."

Have great faith in industry and science, it seems highly unlikely that Nikon and Canon would produce super DSLR models and not notice somewhere along the line that there is little or no DoF, a new bag of lenses is required, there knowledge of DoF is all wrong and they need to rethink the whole mess or hire gkaramer.  I could be wrong but that would rock even my foundation of civilization as I know it.
« Last Edit: January 30, 2007, 04:34:01 PM by howiesmith »
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#### BJL

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##### DoF, sensor size, and pixel pitch
« Reply #16 on: January 30, 2007, 05:42:42 PM »

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I don't think it is a mistake to believe this.  DoF is a perception of what is considered in-focus enough.  It is easier to see a differences in sharper prints.[a href=\"index.php?act=findpost&pid=98325\"][{POST_SNAPBACK}][/a]
Howard, you missed my qualification about comparisons "with the resolution of both cameras high enough that sensor resolution is beyond the viewer's visual acuity". My viewing angle example of 11"x14" prints viewed from 15" away was intended to be within the realm where increasing resolution beyond that of the 1DsMkII would not produce a significant increase in perceived sharpness, and so would not produce a noticeable decrease in perceived DOF.

The situation you are talking about is the other one I discussed, where the prints are large enough to reveal the resolution limitations of the lower pixel count image, making in-focus parts of the image noticeable sharper in the prints from the higher resolution camera.
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#### BJL

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##### DoF, sensor size, and pixel pitch
« Reply #17 on: January 30, 2007, 05:54:06 PM »

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or maybe I'm just confused by what you mean by a "camera having somewhat higher resolution," and by the "enlargement" of a digital print.

"Enlargement": For given viewing conditions, the "native" 300-ppi size of a digital print
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There is nothing "native" about 300PPI; it is a number that has acquired an unwarranted status as "the one and only true PPI choice for printing" And at a quick check, I see nothing in your previous posts stating that all comparisons are done for the case of 300PPI prints. Also, I do not believe that all un-cropped prints from the 1DsMkII are 16.6" by 11" as 300PPI dictates, so I do not see a good basis for an (unstated?) assumption of a fixed 300PPI. This is like assuming that anytime one changes to a higher resolution film, one starts making all ones prints proportionately larger.

But apparently you are assuming comparisons at equal PPI, which is the second case I was talking about, of making larger prints from the camera with more pixels.

I use "enlargement" in the well established photographic meaning of the ratio of the size of the print (or projected image) to the size of the image recorded in the focal plane of the camera. So regardless of film or sensor resolution, prints of the same degree of enlargement from the same format are the same size.

But rather than get into discussion of jargon, let me summarize this way:

1. If one compares prints of equal size, the increased resolution will not increase the OOF effects, and will have no effect on DOF (except a slight effect when the prints are so large that the ones from the camera with a mere 12 or 16MP are noticeably un-sharp everywhere.)

2. If one compares prints made at equal PPI, the larger prints from the camera with more pixels will have less DOF when viewed from the same distance, as larger prints generally do.
« Last Edit: January 30, 2007, 06:02:41 PM by BJL »
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#### Ray

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##### DoF, sensor size, and pixel pitch
« Reply #18 on: January 30, 2007, 06:03:42 PM »

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Bob Atkins at photo.net says: "If you use the same lens on a EOS 10D and a 35mm film body and crop the 35mm image to give the same view as the digital image, the depth of field is IDENTICAL"

Howie,
I think Bob Atkins would have made this statement in the context that both the 10D and 35mm film have approximately the same resolution. He really shouldn't have used the word identical. He probably meant identical with respect to most practical purposes, taking an average quality of film, and ignoring pixel-peeping concerns.

Consider the following example. I use the highest resolution film I can find with my sharpest 35mm lens (say a 50mm lens with a Photodo rating of 4.6, and T-Max 100 B&W film, or Royal Gold 25 color negative). I compare equal size prints from a 4x5" camera using the same film but stopping down 4 stops with the equivalent lens (same vertical FoV) to get the same DoF equivalence. The CoC on the 4x5 negative is 4x larger. However, for the same size prints, the 4x5" film requires 4x less enlargement. I have DoF equivalence on all prints of the same size viewed from the same distance. Right?

However, supposing I'm not too happy with the slow shutter speeds I need to use with the 4x5 format and decide to use a fast, coarse grained ISO 1600 film with the 4x5 so I can freeze a moving subject, but I still use T-Max 100 with the 35mm format. I now find I can use the same shutter speeds with both cameras, in the same lighting conditions.

Have I still got DoF equivalence? I think not. The part of the 4x5 image that's in focus will now be less sharp than it was before, due to the coarse grain obscuring fine detail. At a certain degree of print enlargement, the 4x5 will be perceived as having more DoF than the 35mm format, and probably the over all resolution advantage of the 4x5 format, in large prints, will be lost.
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#### gkramer

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##### DoF, sensor size, and pixel pitch
« Reply #19 on: January 30, 2007, 08:47:30 PM »

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There is nothing "native" about 300PPI; it is a number that has acquired an unwarranted status as "the one and only true PPI choice for printing" ...I do not see a good basis for an (unstated?) assumption of a fixed 300PPI. This is like assuming that anytime one changes to a higher resolution film, one starts making all ones prints proportionately larger.
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I think this as a thoroughly inaccurate and misleading statement: the 300-ppi standard has become the accepted standard for digital prints viewed a close viewing distances (10-12")--just as a 30-micron (give or take a few microns) CoC has become the widely accepted standard for 35mm photography, based on an 8x enlargement factor (to an 8 x 12" print) and the implied 240-micron blur circle on the print, for close-viewing distances of 10-12". That (give or take a few microns) is essentially the standard on manufacturers engrave DoF scales on their 35mm lenses; and I think the 300-ppi standard has acquired essentially the same status in the digital world. By suggesting otherwise, I think you're just trying to confuse the issue; you could equally plausibly (or implausibly) attack the C0C = 30 micron standard for 35mm photography--from which I presume you would conclude that manufacturers shouldn't engrave DoF scales on their lenses.

I think that would be a dumb conclusion. Certainly the 300-ppi standard is not appropriate for producing poster-sized prints to be viewed on a wall--just as one might choose a diferent CoC for film enlargements intended for viewing on a wall. But it's easy to scale up the relevant factors, one we understand the basis on which the standard is based. A well-chosen, fixed standard (CoC = 30 microns, 300ppi), and DoF scales (or tables) based on it are very useful for the photographer who understands them, saving him the hassle of having to recalculate everything from scratch whenever he want to make a different-sized print. I think your implicit claim that "there's no such thing as a standard for digital printing" is misleading at best, if not outright obscurantism.
« Last Edit: January 31, 2007, 09:32:38 AM by gkramer »
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