Depth of Field and the Small-Sensor Digital Cameras

I'm glad somebody put this in to words. Too many numbers and calculations for me to do it, I'm just a student and have better things to do. But well done and hopefully we can just refer people here when they start arguing again.

Maybe someone that knows more about optics than me can clarify this to me; I always thought it was like this.
Isn't DOF related only to subject magnification? (i mean how large is the image of the subject projected by the lens; this will include the factors image size and lens field of view). Isn't the DOF the same if you do a 1:1 macro with a 35mm camera or with a LF camera, regardless of the lens on either case? (I say ONLY depth of field, of course you'll get different image sizes).

Depth of field in the macro range is approximated by:

DOF = 2*COF*fstop*(m+1)*(m*m)

where COF is the circle of confusion value and m is magnification of the object onto the film (or digital sensor). Obviously this breaks down at the hyperfocal distance since DOF becomes infinite (infinity minus the near point in focus distance is still infinity!) so it's not a universal formula but it's a good approximation in the macro range (from larger than life size to maybe 1/20 to 1/50 life size depending on a few other factors).

The full equation relating DOF to magnification includes a term with the focal length of the lens in it. For macro work this turns out to be a negligable correction, but for non-macro work it does make a difference and so DOF is not JUST a function of magnification.

Equally obviously at 1:1 imaging every different format size has a different field of view. To compare equal fields of view you have to calculate the magnification in each case (which will be proportional to the film or sensor size). You'll end up with the same conclusions as in the article of course!

I should add here (and probably in the article) that all the calculations here are based on a geometric optics model, i.e. they don't include any diffraction terms. In reality diffraction matters, especially when using small f-stops to try to get large DOF, but that's a matter for another article. I touch on it very briefly in an article on my own website (http://bobatkins.com/photography/technical/dofdiff.html).

This is a tremendous piece of work. Thank you Bob. I have alternately heard blanket statements on DOF (35mm FF vs. DSLR with crop) from intelligent sources claiming; 1) it's the same 2) it's greater and 3) it's less.

It took me an hour to compose a response on another board explaining a fraction of what you have done (breezed over Circle of Confusion) and providing one lousy example. Now I can just reply "it depends" and link to this article.

Kudos, kudos, kudos. Thanks for effort I know it required to put this article together. Now, perhaps we could get a "lite" version for the left brain impaired.:)

Great Article.

This is the sum and substance of why I prefer medium format and am having to wait impatiently before diving in to the digital camera world. The lack of creative control found in consumer digital cameras just kills it for me. Losing the ability to isolate your subject from the background in-camera, is something I choose not to live with. I cant wait for fullframe DSLR's to hit about $2K.

JOE

Thank you Bob!

Nice work summing up this topic - this seems to be one of the most confusing things in photography. Only thing that is missing, is the situation of "real" lenses: they can't produce a COC of 0mm. This is obviously mostly because of spherical aberration. The equations, on the other hand, assume that the COCs from focus distance is 0mm. Well, the actual difference between theoretical situation and real life is so small that maybe there is no point confusing this matter more. I hope the folks at www.dpreview.com also find this.

Severi - that's quite correct. The geometric optics model isn't very good for precicting sharpness at the point of focus since it assumes an infinity small spot size. In fact the minumum spot size is given by the Airy disk diamter, which at f8 is about 10 microns.

The geometric optics model isn't that bad once you get a reasonable distance from focus though, so it's not bad for DOF at reasonably wide apertures. The real problem comes when you try to do something like calculate the DOF of a lens operating at f16 on a 10D and use the circle of confusion value of 18.45 microns as given above. The diffraction limited spot size at f16 is about 20 microns, which is larger than the circle of confusion you are using. Clearly, though you can do the math, the result has little, if any, physical meaning. If you've defined your sharpness limit as corresponding to a CoC value of 18.45 microns, NONE of your image will be acceptably sharp at f16, so it has zero depth of field.

People should (but usually don't) realise that Depth of Field is an artifical construct, full of subjective parameters, and that the geometric optics approach to calculating DOF has parameter limits outside of which it's pretty meaningless. However presenting the full wave optics solution would be overkill since it's an exact way of calculating a very "nebulous" concept, plus it would be impossible for the average photographer to follow or duplicate the math!

You run into diffraction limitation of sharpness at larger and larger apertures as the format gets smaller and smaller. This is one reason why many consumer digicams (with very small sensors) don't let you stop down past f8, while 8x10 large format lenses are often stopped down to f64 for a shot.

"<em>... Losing the ability to isolate your subject from the background in-camera, is something I choose not to live with...</em>" <p> You don't really have to, the effect isn't huge for DLSRs (though it can be huge for consumer digicams with really small sensors). The DOF of an EOS 10D is about the same as the DOF on a 35mm full frame camera stopped if you open up an extra stop and a third. <p> So for example to get about the same depth of field as a 50mm lens on a full frame camera at f2.8 a 31.25mm lens on a 10D needs to be opened up to f1.8 <p> Distant background blur is proportional to format size (assuming equal size prints). So a 10D image will have 1.6x less far distant background blur than a 35mm full frame camera when using equivalent lenses at the same aperture. Again not a huge factor for an EOS 10D, but a significant factor for a digicam with a sensor 4x smaller than full frame 35mm. As before, if the EOS 10D lens is opened up by a stop and a third, background blur will equal that of a full frame image. <p> In practice it's pretty easy to use selective focus with a 10D and blurring the distant backgound is also quite possible with the right lens.

"# 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" <p> Nope. Once some image is taken, it will retain its inherent DoF however you crop it.<br> Doesn't your statement show confusion about the CONCEPT of "circle of confusion"?

Nope. Once some image is taken, it will retain its inherent DoF however you crop it. Doesn't your statement show confusion about the CONCEPT of "circle of confusion"?

Indeed it does show confusion about the CONCEPT of "circle of confusion" Michael, but it's your confusion that it shows!

The circle of confusion value is NOT an inherent property of the image recored on film. Neither is DoF. As I carefully explained above DoF depends on the circle of confusion value, which in turn depends on how much you enlarge the image. The more you enlarge it, the smaller the circle of confusion which you must use. If you crop a 35mm frame, YOU CHANGE THE REQUIRED CIRCLE OF CONFUSION VALUE because you have to enlarge the cropped sction more in order to get the final print size, so you have to start out with a sharper image (smaller circle of confuision value) to get an equally sharp print.

I know this is confusing, but if it still doesn't make sense to you, carefully read the section of the article on circle of confusion again. The math is very simple.

"... the circle of confusion value, which in turn depends on how much you enlarge the image".
"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"
=================================

So, let's say 10D in your approximation has 1.6 MORE DoF compared to the 35mm camera. To end up cropping the shot to include the same field of view as the 10D, one has to be much, much farther from the object (i.e. one's field of view from point B (35mm camera) must include even more than the wider-view from a closer point A for 10D.) If that is the idea of your comparison, you may be correct about DoF - but that is a meaningless comparison.

In calculating CoC two values are given: the (constant) spherical angle value of the eye resolution, and the spherical angle value of the image as it is going to be viewed.
In copying/retyping other people's writings on DoF you change the viewing conditions (i.e. the angle at which the resulting image is going to be viewed) at will to produce conclusions/comparisons.
If the viewing conditions remain the same (as calculated for the full image), DoF for any crop will remain the same.

Yes, it's a very nice overview and I especially like the direct comparisons between different formats, so it has a practical useful point. Just one comment: it's soooooo annoying to follow a text which talks about 24X36mm film and 8X10" enlargements! Can't we all agree on one bloody length unit at least within one single article? I know, it's not your duty, Bob, to change the US/UK unit system to the SI, as it's not mine to change the (continental) european units to the imperial feet-and-pound stuff, but still, mixing millimeters, microns and inches, feet, in one paragraph, just makes things really confusing. This is nothing personal; you easily see on official sheets (e.g.lens specifications)the same - the focal length in millimeters and the closest focussing distance in inches. Or, feet, to make it even worse. Why?

With respect,

(a) sorry, my understanding of comparison above is incorrect; my understanding of comparison as based on the viewing angle of the resulting image is correct;
Your approximations are approximations, and look correct only for a certain range of distances: see the "ratio" plot and note that Dof(digital)/DoF(35mm) is not a constant. You also base reasoning on the premise that the resolution of film is infinite.

It is refreshing to see a discussion of depth of field which is actually correct.

Let me expand on the confusion about magnification. First of all the magnification, as it is usually meant, only applies to the plane of exact focus. It is true, for subjects which are relatively close to the lens (not necessarily in the macro range), that if you keep the format the same (and hence the degree of enlargerment) and you vary the distance to the plane of exact focus so that the magnification is kept constant, then the depth of field in front and in back of the plane of exact focus is essentially independent of focal length. (This follows from formulas given in Jacobson's Lens Tutorial.) So if your primary interest is portraiture in a specific format, you are only interested in focusing on a subject's face, and you keep the relative size of the head in the frame constant, then you are not going gain any depth of field by using a short focal length lens (and getting appropriately closer). Unfortunately, some people have generalized this to all aspects of photography. As you have pointed out, it is patently false in other common photographic situations. You have done an excellent job of explaining it, but in the end it comes down to interpreting mathematics. Often people don't want to give mathematics its due, so they oversimplify what it says in an attempt to avoid the full complexity caught in the formulas.

Anyway, you have done a great job.

"... Losing the ability to isolate your subject from the background in-camera, is something I choose not to live with..."

You don't really have to, the effect isn't huge for DLSRs (though it can be huge for consumer digicams with really small sensors).

It certainly is a huge issue with consumer digicams, even the semi-pro ones. For example, my DC4800 has a 6-18mm zoom lens. This won't help you in the background blurring dept., no matter what you do with the aperture.

The main reason I bring this up is that many photographers new to digial look for aperture control when buying a new camera, and pay a lot extra for it. IMO, it's not worth worrying about (in these consumer-type cameras).

The only time I've found aperture control useful (with the DC4800) is in stopping down, to increase depth of field for macro work -- especially with there being no way to focus precisely. However, with more light, almost any camera will do this automatically anyway.

Depth of field issues are indeed important for some consumer digicams. People don't realize just how small the sensors are in some of these cameras. They can be as small as 3mm x 4mm, that's 1/8 the size of 35mm, which is about same ratio as 35mm to an 8x10 large format negative! Such tiny sensors have a huge depth of field, even with fast lenses.

Even relatively high end digicams, like the Sony F717 only use an 8.8mm x 6.6mm sensor

DSLRs are somewhat different as even the smallest current sensors are about 15mm x 22mm, so you can still blur backgrounds and use selective focus, just not quite as much as you can with 35mm.

Here's a picture to derive hyperfocal distance... f is the focal length and g is the distance to the film. g = f*d/(d-f) where d = distance to the subject. So for a focus position, focal length, and apperture size you can work out circle of confusion. Then you can rearrange ...

I can appreciate this, because I just wrote a similar article and had to derive the same equations. I had to draw ray diagrams [see image link below] showing how the lens brought rays from the edge to a focus and how making the apperture smaller made the circle of confusion smaller - because the rays at the edge of the circle didn't get through. It's worth pointing out to the F stops are focal length / apperture diameter hence written correctly as f/8 not f8. The progression is for exposure convenience (the area of the hole doubles or halves, the diameter goes up or down by the square root of 2). When a simple lens is focused on infinity the distance to the film is equal to the focal length, its quite easy to stop worrying about the apperture size in equations and work in terms of the f stop. I had to work all this out because I have a Pentax Optio 430 RS - 4M Pixel resolution, and lots of control, but the zoom lens moves in steps, and there are only two apperture sizes (so the f stop changes at each focal length). Someone said something about assuming resolution was infinite - actually with digital once the circle of confusion is smaller than one pixel the image doesn't get any sharper. This has some interesting effects for fixed focus consumer cameras (may disc cameras rot in hell !) - since people want as much as poss to be in focus, build a camera with a small film (or digital sensor), wide angle lens (38mm equiv on 35mm seems typical) set a smallish apperture - say 5.6, focus on hyperfocal distance and you have an image which is sharp from arm's length to infinity. If you remember the "F/64" club, they were all working with 10x8 or 5x4 cameras, you need to go to F/64 for 10/8 to get an image as sharp as you would get at more 'normal' apperture on 35mm.

Bob, it would be great, if you added a section describing how to actually determine the permissible COC of final print. Then one could use DOF calculators and equations efficiently (provided the photographer understands how the COC value must be altered as print or medium size is changed).

Basically this would mean taking a shot of a ruler (should not be at macro region though) pointing away from the camera. Then enlarging to the desired size. On could then determine the DOF by viewing the print at the desired distance and resolve c from the next 2nd degree equation. It should be right, but I didn't double check it. The below equation is derived from DOF equation from Canon website. Have to see if Bob's equation gives same result.

c2 + (2*F2/df)*c - F4/(f2*u2) = 0

Where c = COC, F = Focal legth, d = DOF, f = aperture, u = focus distance.

Severi,

I think a quick way to do what you want would be as follows. Take a picture of a tape measure at some moderate distance D (like 6 - 10) feet, set the f-number N to some convenient setting, enlarge the image to a print of the desired size, and view it at your normal distance. Say the amount in focus under these circumstances is X. Then use the formula

X = D^2/(H^2 - D^2)

to solve for the hyperfocal distance H. In fact

H = sqrt(D^2/X + D^2) = D sqrt(1/X + 1).

Once you know the hyperfocal distance, you can use the formula

H = f^2/(Nc)

where f is the focal length and c is the coc. In fact,

c = f^2/(H N)

One should probably do this for several different lenses, distances from the camera, and f-numbers, and then take an average of the values of c so obtained. However, the degree of enlargement and viewing conditions of the print should be kept fixed. Once you have it for one degree of enlargement, you should be able to determine it for others by dividing or mulitplying by the appropriate ratio.

Nice page; just wanted to point out that these results have been available for more than a year on:

http://www.wrotniak.net/photo/dof/

to which I contributed by correcting the formula. BTW, there is no need for any number crunching nor assumptions on what's sharp and what isn't. Since you are comparing, all the factors cancel out except for a term involving the focussing distance; a limit when it goes to infinity will give you that exact result.

Three things:

(1) I've added an addendum to the article describing how you can use the DOF scales on a lens when a full frame lens is used on a small format digital camera.

(2) Since DOF is, at best, a fuzzy concept, and you get what you get no matter what value you pick for the circle of confusion, there's really no need to try to measure it exactly. For 35mm if you're picky, use 25 microns, if you're average use 30 microns, if your eyesight isn't that great use 35 microns. Divide these numbers by 1.6 for a 10D. Beware of using a CoC value smaller than the diffraction limited spot size at any aperture or any DOF calculations will be pretty meaningless!

(3) None of this is new. I imagine it's been in the optics textbooks since the invention of photography. Image sharpness, depth of field, circle of confusion and how they change with format are all things that have been around and been discussed from the earliest days of photography. The ancient Greeks could have done the math!

I'm still arguing with my friend. He sent me a webpage, http://www.luminous-landscape.com/tutorials/understanding-series/dof.shtml

Below is one of the sentance from the page.

"Now, the camera industry figures for the purposes of calculating depth of field (and therefore Circle of Confusion) that an image is typically enlarged 5X from the negative to a print."

This does not agree with what is said in this article. So, which is the real case?

thx

"Now, the camera industry figures for the purposes of calculating depth of field (and therefore Circle of Confusion) that an image is typically enlarged 5X from the negative to a print."

Why do you think it doesn't agree with the article?? It just means that DOF scales and charts made by lens manufacturers have an assumption that the negative is usually enlarged 5x and COC value was selected accordingly. If you enlarge more (or use digital camera with smaller sensor etc.) you have to use different COC for DOF calculations. I don't think this is at all in contradiction with this article.

With regard to DOF scales the only thing that matters is what COF you pick. You could assume a 5x enlargement viewed from 1ft or a 10x enlargement viewed from 2ft and you'd get the same number. Similarly you could assume a 5x enlargement and a requirement of 10 lp/mm resolution in the print or a 10x enlargement and a requirement of 5 lp/mm in the print. Again you'd get the same number for the COC value.

You need to specify enlargement factor AND viewing distance AND your resolution criterion before you can calculate COC. Just specifying an enlargement factor tells you nothing.

So I don't know what "manufacturers" use as their assumptions. In fact they don't all use the same assumptions since DOF scales do differ slightly from manufacturer to manufacturer for the same focal length lens.

Whatever assumptions they make about enlargement size, viewing distance and visial accuity, most lens manufacturers use a COC value between 30 and 35 microns for 35mm lenses. It's just a guess, an estimate, just as DOF is an approximation of what an average viewer looking at an averge print from an average distance will consider to be acceptably sharp.

James, I have to agree with you on the disc camera comment. My first camera was a disc camera. Also, I assume you are using the term "sharp" very loosely :)

Hehe, now I understand why my recent pictures were so blurry. I tried to use the dof scales the same way I used them on my analog system; and I got blurry images. It's simply because I focused wrong since the scales actually move with the focal lenght multiplier.<br><br> Thank you very much Bob! Now I'll go outside and try again.

Two remarks:

In the above article, the nomenclature “circle of confusion” is the most unfortunate one. Rather than to illustrate and explain it does one thing: confuses. In the European literature it is called CIRCLE OF DIFFUSION or SCATTER - this is exactly what it is. Also f x number (for example f8) is incorrect. Correct is f/number.

Excellent write-up, Bob. Thank you for finally writing an authoritative source I can link to instead of trying to explain this myself over and over.

For those still thinking that depth of field is an intrinsic property of the lens, what you are thinking of isn't depth of field. What you are thinking of is called depth of focus. If you think of the cone of light projected by a lens onto the sensor, the depth of focus is how far you can get from the tip of the cone before the diameter of the cone is big enough to be considered out of focus. Depth of focus is intrinsic to the lens, and independent of the sensor/media size.

If you never enlarged your pictures (i.e. viewed the slide or negative with the naked eye), then depth of field would be proportional to depth of focus and sensor size wouldn't be a factor (distance to subject would be a factor, but in most of these discussions we're assuming the subject distance remains constant). But the instant you enlarge the picture, the two become different in proportion to the enlargement factor. If you're enlarging to a fixed size (e.g. 4x6 print), then the enlargement factor is dependent on sensor size, and so the depth of field changes with sensor size.

I have one comment, and a question for Bob Atkins or anyone else who knows.

Comment: the final formula you give is, as mentioned, for fixed aperture ratio fn. Putting the factor fn back and adjusting focal length F and circle of confusion in proportion to the image size (sensor or film frame size) in order to get the same angular field of view and the same sharpness in prints of same size gives a simple guideline:

1) At intermediate distances, the DOF in a print of the same size of a photo taken at the same distance with same angular field of view is proportional to (aperture ratio)/(focal length).

2) since focal length varies in proportion to image size, so does the aperture ratio needed to achieve a given DOF.

So to keep the same DOF you go about one stop larger for the shift from 35mm to the common DSLR formats. To maintain a given shallow DOF for work like portraits, a 135/2 lens could be replaced by a 85/1.4, and an 85/1.8 by a 50/1.2, so it is sort of doable: smaller digital formats like the 4/3" system might struggle to produce a decent substitute for the traditional portrait lenses.

Question: is there a simple way to understand how the degree of background blur for objects well outside the depth of field changes with sensor size and aperture ratio? You mentioned that it is not predicted by your DOF formula. If one adjusts the aperture ratio to keep the same DOF with different image sizes, can one say if the degree of background blur increases, decreases or stays the same with decreasing image size?

Distant background blur is a function of the physical size of the aperture, which is usually pretty much the same as the actual physical diameter of the front element for prime lenses used wide open. The larger the diameter, the more background blur you get.

Background blur should be greater for DLSRs with small sensors because the image has to be enlarged more (and thus the blur is enlarged more) to get to a given print size compared to full frame sensors or 35mm film.

I don't think the smaller image capture area - and therefore greater magnification should be taken into consideration for background blur. Yes, there will be increased blur from the greater magnification - but that is true for your subject as well!

Everyone who still has no clue what that all means in practical terms should have a look here: http://www.outsight.com/hyperfocal.html#math. I found especially the depth of field calculators extremely useful ...

„3. 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“ <br> <br>first i was confused, because i thought the dof can’t change just from cropping, since what i see in the center remains the same… <br>reading your discussion with michael, i learned that it’s because of enlargement/print/circle of confusion… <br>but there is still one point i’m curious about: when i enlarge a photo, according to the mathematical approximations, the plane in focus keeps its sharpness, while the other areas get even more unsharp, thus reducing the dof… <br>but yet, when looking at enlargements of the same picture, the “feel” of dof will often stay about the same (at least i think so)… <br>maybe the phrase "not unacceptably less sharp than the sharpest part of the image" is the key to this, since even the best media will blur the focused areas from physical resolution to some extent… so, when enlarging the picture, the plane in focus will get blurred with the same ratio like the unsharp areas, and the dof (with above definition) should stay the same… <br>if this assumption of mine is correct, this means that the mathematical approximations work only in the case that the blurring of the focused areas will be less than i can spot with my eye on the final (rather small size?) print… <br>ok, i’m not a pro and i don’t have the means of working with medium or large format cameras, but some negatives from my old nikkormat show grain when enlarged to standard 10x15cm, which has a more or less slight, but visible effect on the sharpness and therefore i can’t see your above mentioned point 3 working on further enlargements of them… (maybe I should mention that i have a) quite good eyesight for close up details, and b) only cheap lenses for that cam, but also think of (quality) grainy b+w images or huge poster size prints)... <br>this means that in this case (which for me is the most common one) i still disagree with point 3. <br>so unless the approximations consider the effect/visibility of blurring the (sharpest) reference plane through the medium/grain, i find them not too useful for myself… <br> <br>umm… can anybody still follow me? am I just wrong somewhere? <br>and isn’t there also some effect from lens to media distance, which results in different dof for different format cameras, but would of course not apply to enlarging? <br><br>comments from medium/large formatters very welcome!

Michael - I can't seem to follow your argument and I really don't know quite what you are trying to say. Let me say what I am trying to say.

• You take a 50mm lens.
• You put it on a 35mm film camera and take a shot.
• You put it on a 10D and take a shot. Same distance from your subject.
• You now make a print from the 10D image.
• You now make a print from the 35mm negative, exactly the same size with exactly the same view - obviously you need to crop the 35mm negative to do this since 35mm film the lens has a wider field of view.
• So now you have two prints of exactly the same size and exactly the same field of view (angular coverage).
• They both show the SAME depth of field.

Just out of curiousity, does the 1.6x multiplier affect the DOF in the viewfinder? With my 10D and 50/1.4 lens, it seems that I end up with much less DOF in the resulting photo than I actually saw in my viewfinder. For example, the following image (1.4, 1/45s, ISO 3200) was definitely NOT this blurry when I was composing the shot:

I'm new to photography (SLRs) and I'm not sure if this is a digital-only thing but I would like to know why the image I am seeing in the viewfinder is not the image that is recorded. I've been disappointed by many of my photos because the DOF is much more shallow than the image I originally composed.

Any feedback would be appreciated, or useful tips on how to anticipate the DOF without actually seeing it in the viewfinder.

The answer is: "There is no answer".

The question is whether to use film or digital. So many people want to believe that since a decent DSLR can produce an acceptable 8X10, and that, is as much as most customers will pay for, digital is just as good as film. It is. It is not. Each has it's limitations, and accepting one format blindly, only diminishes the resources available to the photographer.

This article by itself is a valuable resource, but as part of the series about choosing and using a digital camera is by far the best information I have found on the subject.

I think something must happen to many people who making a living capturing images. Like other kinds of work, profit eventually takes precedent over quality. I salute those who make quality their 1st priority.

To Pete Kazmier:

To see what the depth of field will look like in the final photo, press your SLR camera's "Depth Of Field Preview" button. This button is usually located on the right side of the lens (camera viewed from the front), conveniently near to where your left index finger will be when gripping the camera

Normally, when you look through the viewfinder of an SLR camera, the aperture is kept wide open at all times. This gives you a nice, bright image. It makes composition easy. But of course having an always-open aperture doesn't show what the depth of field will look like as you change the aperture (f-stop).

Therefore, to see the DOF of your chosen aperture, press the DOF Preview button on your camera. The image (usually) gets darker since (usually) your aperture is less than full-open -- less light gets to the viewfinder. As the name indicates, this lets you preview the DOF that will be in the final photo.

(And don't worry about the image being darker while the DOF Preview button is pressed. If the camera is set to Automatic mode or to Aperture Priority mode, it will compensate by leaving the shutter open for a longer time, to gather more light.)

If you check out Norman Koren's page on DOF in the links below, you'll find a simple derivation for calculating the CoC from the DOF scale markings on a lens.

Bob Atkin's 17mm lens, for example, appears to have DOF scale markings based on a 30 micron CoC.

Regarding Pete Kazmier's question about the difficulty in judging DOF in the viewfinder, I believe the difficulty arises from the difference in apparent magnification between the viewfinder and the final image. The apparent magnification is much less in the viewfinder, so the DOF appears larger than it does in the final image. It's particularly hard to judge DOF on DSLR's which typically have much smaller viewfinder images than film SLRs. The viewfinder image in my Canon A-1 is about twice as large as that of my Canon 10D! The smaller viewfinder image makes it difficult to judge focus, period, much less DOF.

I myself use a non-SLR digital camera, albeit a Canon G5 with a maximum aperture of f/2.0 I find that it is possible to achieve some background blur with the lens all the way open, though it is of course impossible to tell from the LCD preview (with this camera, it is best to forget they even tried to put in an optical viewfinder.)

It seems like it wouldn't be that hard to write some soft- or firmware to give me an on-demand overlay of the region of "good" focus, which would correspond to the same range that used to be printed on lenses by the f/stop. Apply a quick and dirtly calculation of the very local (pixel-to-pixel) contrast, smooth, and overlay on the preview image. Maybe this is too much to ask from the current DIGIC, but I expect it on my G9 someday. Hey, then my little LCD would be even better than a high-magnification, low-brightness digital SLR viewfinder for evaluating depth of field! If anyone out there has already written this firmware, I would be happy to beta-test.

PS for Pete Kazmier's question: DOF preview isn't going to help you when you are getting shallower DOF in the final image than you expect. As mentioned before, the viewfinder shows the image for a fully open lens, and you can only increase DOF by stopping down, not decrease it.

Excellent piece of work.

My sole comment is a bit irreverent perhaps, but I would be careful of discussing how a Canon FD lens performs on a 10D :-)

I think you need a different set of example photos...

I have noticed the discrepancy between the DOF in the view finder and the DOF on the captured image in EOS 10D, just as Pete Kazmier mentioned.

I was shooting with 50mm f/1.8 at 1.8 so that there is no need to use the DOF preview button. When focus on a close object at about 2 feet and check the blur in the background, the captured image has much SHALLOWER DOF than seen in the view finder. The difference is so pronounced, there is no mistake about it!

I suspect the cause might be a mask placed some where between the mirror and the view finder that reduced the effective apture at the view finder, which results in deeper DOF.

This is a quite significant flaw, which partly defeats the main advantage of SLR that you see exactly what you will capture.

One explanation I have heard and read explaining why you do not get the same depth of field on finished photos/files as in the viewfinder is that modern slr(af) viewfinders are designed to be about F 2.8. Check and see with different apertures and what you see in the viewfinder. Am not sure about the technical explanation but my tests confirm that it works. You do not see less deapth of field than what 2,0 -2,8 would give you. Try!

Mats

"One explanation I have heard and read explaining why you do not get the same depth of field on finished photos/files as in the viewfinder is that modern slr(af) viewfinders are designed to be about F 2.8. Check and see with different apertures and what you see in the viewfinder. Am not sure about the technical explanation but my tests confirm that it works. You do not see less deapth of field than what 2,0 -2,8 would give you. Try!

Mats "

Yup! I've noticed this in my eos 300d as well, and my nikon f80, or n65. The camera does NOT show F1.4 or F1.8 if you have the ability for such an aperture. It is as Mats said, *about* f2.8...

As to why it is this way, i have no idea.

Depth of field and hyperfocal distance calculator for your WAP enabled mobile phones.

Well, I'm confused, to my annoyance, as the math isn't hard!

I've set up a spreadsheet which uses the long version of Bob's formula to calculate depth of field for a given distance to the subject and f-number. I wanted to use the "proper" formula so it would work for all values, not be an approximation through a range. For larger distances and f-numbers, my depth of field is coming back negative.

Try it for circle of confusion = 1.85 microns, focal length of lens = 50mm, F/2.8. At distance 30m, the DOF is 122.96m. At distance 40m, it's -119.64m.

Could somebody explain this - or have I just got the formula wrong? I've checked it several times but there could be an idiot mistake in there.

Another DOF page implies that negative numbers mean DOF is approaching infinity, but if this is the case, doesn't that mean there is a flipover value of distance where DOF suddenly drops to zero and reverses?

Thanks for any light shed.

Wow! Quite an explanation. I almost wish this page just showed your four or five summary points, and had a little plus sign you click to display or hide the rest of the article!! :)

To answer the DOF question that was asked ealier, it is because the mirror does not enlarge the image that is made, and when you enlarge the image, the DOF gets shallower.

Do this test, take the image on your screen, downsize it to something around as big as you see in your viewfinder. Does DOF seem bigger? Yes!

Now blow it up to 100%, does DOF seem shallower, Yes!

Here is your answer. As to the physics behind that, I'll leave it to someone else.

So it is established that DOF is the same for the same subject magnification (say a 50mm lens focused at 50cm and 20mm lens focused at 20mm both at the same aperture), but what happens to background blur (bokeh). Is it the same also?

No background blur depends on two things.

Fisrt, lens design matters. The magnitude and nature of the out of focus aberrations contribute to the quality of the "bokeh".

Second the physical aperture of the lens counts. Let's say you have a 25mm lens at f5 and a 50mm lens at f5. The 25mm lens has a physical aperture of (25/5) = 5mm. The 50mm lens has a phyical aperture of (50/5) = 10mm. The magnitude of the distant (infinity) blur when the lens is close focused (i.e. is focused well within the hyperfocal distance) will be twice as much with the larger physical aperture.

Correct me if I'm wrong (and I apologize if this was addressed and I overlooked it) but in discussing circle of confusion for various size prints, aren't you assuming a constant viewing distance? Taking a 5x7 print viewed at arms length as a reference, wouldn't a larger circle of confusion apply if I enlarge that same image to poster size, but view it from across the room or from the other side of the corridor at a mall or theatre lobby? Or in the extreme case, take the image on the theatre screen (projected from 35 mm film) or a billboard along the roadside. The CoC there would be massive, but it's what I see from the balcony, or behind the wheel, that counts. So the C0C boils down to a corresponding angle of the viewer's field of vision. Correct? And that's something to factor in when determining how many pixels you need for a given enlargement. Was that covered?

Yes. See this section of the article:

"...Note also that we have made assumptions about print size, viewing distance and visual acuity in these calculations. These happen to be the "standard" assumptions most camera makers make when calibrating the depth of field scales on their lenses. If we were looking at 4x6 prints from a distance of 6ft, or a 100ft x 150ft billboard from a distance of 3ft, we'd need to make a whole new set of assumptions and we'd calculate totally different values for the circle of confusion and so we'd have a totally different depth of field scale..."

I keep getting into this disucussion with a local camera club. For digital projected images they take a 768pixel maximum (height or width) file and project it to a size of about 50 inches or more. Then a commentator stands about 2 feet from the screen and says that just about every image needs more depth of field, especially close-up and macro images. They sometimes go into telling people to use the DOF scales on their lenses to improve their focus/DOF.

I argue that the DOF scales are based on an 8x10 viewed at around 15-18 inches away and not for a 60x40 enlargement viewed from 24 inches away. No one seems to want to hear that. Besides, 768 pixels blown up to 50 inches is around 15 dpi. I don't think the images should be judged from 2 feet away. Am I missing something obvious?

I have thought about building large format DOF adapter for my HDV digital camera. While there are several 35mm DOF adapters available, I haven't found any mid-to-large format adapter.

The basic idea is, using larger diameter of lens and larger ground glass, to achieve larger image (read: more details and more light). I suppose, in that way I can get better picture and (maybe) shallower DOF in this type of adapter than existing adapters using 35mm lens and 36x24 ground glass picture.

I want to use the focal distance of "normal view" (50mm eq) at larger format (lets say, min. twice bigger than 35mm film, ie. 70x50mm, but it can go up 127x102 (5x4'), I suppose). It can't be bigger because ground glass must be shaked or rotated in order to clean out grain from picture.

My questions is - does larger format lens have impact on DOF (measured to the eq. of 35mm, with larger ground glass) - which mid(large) format lens may be suitable for this type of project

Thanks for any respod,

Great discussion. I have been trying to understand DOF/sensor size better and wanted to see how this correlates with shutter times.

Does the shallower DOF imply that full frame cameras are "faster"?

Lets say we are comparing a Canon 5D at F/4 and a Canon 40D at F/4, both being used with an effective focal length of 80mm. Because the 5D setup has a shallower DOF, shouldnt you should be able to use a smaller shutter time compared to the 40D?

I found a sensor size-DOF calculator here -http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm.

Based on this calculator, a 5D at F/2 will have the same DOF as a 40D at F/1.2.

For instance lets say that you needed the following exposure times in the 40D for a certain shot

1/200 sec at F/2.0

1/320 sec at F/1.2

Due to the shallower DOF, the 5D should only need a 1/320 sec exposure time at F/2, to get the same shot?

Am I missing something here?

Circles of confusion:

For some reason I do believe that I will have the same amount of depth of field at F/8 (or any comparable aperture and at the same distance) in the following scenarios: 1. My Pentax Optio S5i, built-in zoom lens set to 5.8mm which is like 35mm on a full-frame film or digiital.

2. My Rebel XT, with Canon Ef-s 10-22 mm, lens set to 22 mm, which is like 35mm on full-frame film or digital camera.

3. My Canon Ef 24-70mm, lens set to 35mm on a full-frame digital or film camera.

I find it really hard to believe, that the sensor has some inherent and intrinsic properties that can actually alter the depth of field in a given situation.

Wow what a great and very in depth explanation. I have been considering changing from my crop factor 40D and making the plunge into full frame digital for my wedding and family business, this will definitely help me make up my mind.

Mubeen,

The way I understand it, with a cropped sensor, you need to be further away from the subject for the same field of view as you would with a full frame sensor.

DOF increases the further the subject is away from the camera.

Therefore, with a FF sensor, you move closer to the subject for the same field of view, shortening the DOF.

Perhaps my understanding is wrong.