Comparing Depth of Field of Two Lenses

There is a Depth of Field (DOF) calculator below (about mid page), but which was not really done for general purpose. It does do that too, but there's already a very good one at DofMaster, so there was no need for another doing the same thing. And I shirk at the work to provide sensor size and Circle of Confusion (CoC) for every camera model known to man. :)

So the DOF calculator below is a little different, in that it also adds a few new features.

- It also computes
**CoC at the Background distance**behind the subject , to indicate the amount of blurring there, a concern when wanting to blur and hide the background. It's a calculated way to compare and judge the degree of blurring there. In addition, it also shows Field of View there, both at subject and at background, indicating how much of that background your choices must include. The best way to hide the background is to not show much of it, which is calculated here. - The calculator compares numerical situations of Depth of Field of
**two lens**. Specifically, instead of reaching for a 50 mm f/1.8 lens to blur the background, it suggests a better way with better results, by standing back with a longer lens (greater DOF on subject, but also greater blurring at background). Not only can the background be blurred better, but the longer lens only shows the best small selected part of what is seen. This technique is nothing new, it has always been well known to pros, and suggesting its consideration is the point of this article. Using f/1.8 on photo work they hope to sell seems not their best choice. This calculator is an interactive comparison of two lens choices, allowing making decisions about how to blur the background. - There is a viewing enlargement factor, called
**Largest Print Dimension**here, to be a more accurate DOF guide related to the actual size of your image that you will view. The DOF that we view depends on the total enlargement of the sensor image, because more enlargement magnifies the blur that we can perceive (which is what DOF is about). Standard DOF calculations assume an 8x10 inch print viewed at 10 inches. The "Largest Dimension" (here) of an 8x10 print is the 10, so 10 is the default here too. Video screens show pixels directly (instead of inches), but simply measuring the apparent viewed inches on the screen provides enlargement detail for that screen use. But inches count when printing on paper. Do realize that the standard for DOF calculations is an 8x10 inch print viewed from ten inches. That's what other calculators show (determined by choice of CoC), and 10 inches is the default here too, but that may not be your situation, and you can change the enlargement.

- Sensor size can be hard to determine, but the calculator offers four possible ways to easily specify or compute your sensor size, which determines Circle of Confusion, which is the basis of Depth of Field calculations. Entering actual precise sensor size is the best plan, but just entering Crop Factor can be very close too.
- Calculators should use the exact precise f/stops instead of just the approximated nominal marked numbers (e.g., f/11.3137 instead of f/11). This one does, and most do, but there are exceptions.

This is quite difficult for a **compact camera**. The sensor is so small that their lens is necessarily very short, which ensures a great depth of field. Setting a wide aperture may not be a choice, but choosing more dim lighting can help. The best chance to blur the background some with a compact camera is to zoom in greatly, and then stand back as necessary, but stand as close as that zoom can allow (not closer than about 5 feet for a portrait). Choose a background that is very much more distant, hopefully a few hundred feet.

We should realize that both focal length and subject distance are Depth of Field (DOF) factors. We can use them both for our goal. My notion of a portrait at f/1.8 is that there will of course be DOF problems, usually about the hardest possible way to make a good picture, and the last thing I want if I can prevent it. Notions may vary, but studio portraits likely work at f/8 or f/11 (again, the usual goal is that the work will sell). Studio flashes are made big to allow those apertures. We like the sharpness of depth of field.

The defaults shown in the DOF calculator below initially compares a 50 mm f/1.8 portrait at 6 feet with a 200 mm f/4 at 24 feet, both using a DX APS DSLR camera. It assumes the background we want blurred is 40 feet behind the subject (try other distances too, the longer lens usually wins). Pros would more likely use maybe a 200 mm at f/4 for this purpose (of hiding the background). Or 100 mm at f/2.8 can be better too. The 200 mm is 200/50 = 4x longer than 50 mm, therefore the two subject fields of view are the same size if the 200 mm lens stands back at 6x4 = 24 feet.

And if both lens with distances adjusted to be the same field of view at the subject are also at the same aperture, then they have the Same DOF range too (at the subject) - the adage about the "same image has same DOF", etc. (at the subject, it does). But where we stand does affect the perspective, and the background is certainly NOT the same then... in the long lens, most of the wide background is zoomed out and gone missing, but what's left is even more blurred focus (assuming that is a plus here). This standing back at greater distance is little problem to do outdoors, and it possibly need not be that extreme. If both could use the same f/1.8 then, the depth of field at the subject is the Same, both 0.29 feet of DOF (which is only 3.5 inches - from nose to hair may be more than that). DOF does not describe the sharpest necessarily, instead it defines the maximum blur that we can accept. But we don't have to use the same aperture, the 200 mm lens at 24 feet can use say f/4, which has 0.66 feet of DOF (8 inches). That's still not much, but it's sure a lot better, more than twice as much DOF. But it is even more blur at the background.

Qualification: This adage is a rule of thumb that the "same image" (meaning "same size subject image") at same f/stop will have the same depth of field. It is true when the shorter lens subject distance is less than about 1/5 of its Hyperfocal distance (then DOF is same within 4%, and normally well less). At reasonable subject distances, this is generally quite true except wide angle lenses need shorter subject distance. There are multiple parameters affecting the result, but try it, you'll find a lot you like. Proper portrait perspective is generally considered to need a longer lens anyway. FWIW, regardless of lens focal length, a subject distance less than 6 or 7 feet is simply too short for proper portrait perspective. 8 or 10 feet is even better. Stand back a bit, don't get the camera up in their face.

And the overwhelming advantage is even much better yet: We said this Field of View (FOV) at the subject would be the same in either situation (about 2.9x1.9 feet, about right for head and shoulders). But the background field at 40 feet of the 50 mm lens is 22 feet wide. 22 feet of stuff you want blurred away. However, the field of view of the 200 mm lens is only 8 feet wide at 40 feet (behind the subject). So most of the objectionable junk you want to blur is simply missing, simply gone, removed in the best possible way. And better, you can surely move the camera slightly to one side to choose to align the best 8 feet of background decently enough, probably even if it were not blurred. But in fact, it is blurred at 200 mm. Probably blurred more (perhaps a bit less if background is near), but 1) the subject DOF is so much better, and 2) there is much less of the background even showing. And 3) usually the background that is visible is blurred even more.

So again, it's like this. Two lenses, one longer and standing back at equivalent distance to have the same field of view at the subject. If at the same f/stop, then they have the same depth of field at the subject. Assuming the background is not real close behind subject: The long lens is further from the background, so the background is still blurred quite well. A very big deal is that long lens also has a much smaller view of that background, so we can move a slight step sideways to choose a nice small spot to show, one which does not distract. And another very big deal, then the longer lens can be stopped down a couple of stops more to improve the subject DOF considerably. This does reduce the background blurriness some, but it's still more blurred than the short lens. What's not to like? The only downside is we need to bring the longer lens, and have room to stand back.

It should be obvious that this is a really big deal to know. There are three properties offered by the longer lens: Greater DOF at subject, a much smaller area of background to select and be seen, and greater blur on the background. There are many numerical combinations where the longer lens is simply better. And a few more where a property or two is still worth consideration. If you also find f/1.8 distasteful, there is this better way.

So the calculator below computes the sensor CoC at both subject and background distances, to make this point.

concerned with CoC at the Background

Here we go. **Identify your camera sensor size** by entering either actual Sensor Size or Film Size or Crop Factor or even a final CoC value. Any of those can calculate sensor size. CoC also determines a sensor size, because CoC is about the standard enlargement of sensor size. Full frame 35 mm cameras often use 0.03 mm for CoC, and APS cameras often use 0.02 mm. A compact camera or smart phone might have CoC = 0.004 to 0.007 (much more enlargement is necessary). This is from CoC = Sensor Diagonal / 1442 (these are standard definitions, but are somewhat arbitrary too). Sensor size can be hard to know, but it can be computed from Crop Factor. You can see how to determine your Crop Factor.

It's hard to beat precise actual sensor size specifications though.

Film or Sensor Size dropdown box: I have NOT researched every possible cameras sensor size (virtually none). The film sizes there are known good, but the digital sensor sizes are approximations, ballpark, because actuals can instead depend on the specific camera models chip. Especially the compact and phone sizes like 1/1.8" CCD are possibly vague (actual sensor sizes are instead described as specifications of XxY mm). The approximated sensor size used is shown in results. The film sizes are known good, but other than for film, I suggest the Crop Factor option may be more accurate (if actual sensor size is not known).

Megapixels is unimportant here, only used to compute image size (pixels). It does NOT affect Depth of Field or Field of View. Megapixels is only for you to see and confirm that computed sensor size is about correct, which does affect CoC and FOV. Many camera numbers are approximations, so a size difference of several pixels is probable and not a big deal, if not too far off.

Aspect Ratio computes image dimension in pixels, image diagonal, and also Field of View (**except** direct Sensor Size or Film Size instead uses actual sensor shape for Aspect ratio).

It will be appreciated if you would please report (Here) any problems with the calculator, or with any aspect of this or any page.

If you see results of NaN, it's an error meaning an input is Not A Number (periods are OK, but don't use commas).

DOF is Depth of Field, CoC is Circle of Confusion, FOV is Field of View, and BG is background.

The next page has photo examples of these initial default cases.

When feet/meters is changed, the checked Convert checkbox will convert previous numbers to keep the same distances. Otherwise that feet/meters change will leave distance values numerically unchanged (but feet and meters are different distances).

**BG CoC** is the computed CoC at the BackGround distance. It is shown as "X times CoC", meaning X times size of that acceptable CoC entered (probably diagonal / divisor mm). It is a relative scale of blurring. The DOF concept implies that if the background were exactly at the computed far limit of DOF, the blur diameter there would be exactly equal to CoC (1X CoC). A larger multiple is a multiplied greater blur.

**Largest Print Dimension** is about the relative enlargement of your viewed image.
An example is the "largest dimension" of 8x10 is 10. When we enlarge the viewed image, we enlarge the CoC too, so it's easier to see the blur then, which becomes no longer a suitable indictor. The DOF concept is all about **the CoC we can perceive, when enlarged from the sensor size we use**. If we are going to enlarge our view, then we need to start with a smaller CoC. Standard DOF calculations assume viewing a standard 8x10 print size from 10 inches, which is the 10 inch default here (254 mm). This feature is to describe a different image size that you may view, to account for the effect of your enlargement on the Depth of Field calculation.

CoC is computed as (sensor diagonal mm / 1442), default unless CoC or Divisor is directly specified.

However, note that you can specify any CoC limit directly. Yes, it will then compute and show a sensor diagonal size based on (CoC x Divisor), but that sensor size is just for reference, and is not further used. It does Not affect DOF now, since CoC has already been specified directly. The DOF formula computes with only CoC, focal length, f/stop, and focus distance. Sensor size is not in the DOF formula, except that it should have of course defined CoC. So, bottom line, you need to know what you're doing if you specify CoC directly. Just because you saw someplace use 0.03 CoC, this does NOT mean that is a proper number for your camera and its sensor size.

If comparing results with other calculators numbers, make sure the CoC and/or Sensor Size used is the same value. The DOF numbers here agree perfectly with DofMaster, Canon Europe, Bob Atkins, PhotoPills when we use CoC Divisor 1442 to match their fixed 0.03 and 0.02 mm CoC for FX and DX. However one major site does show different results. I don't know why it doesn't agree with anyone, it doesn't say what they're doing, but something seems off there.

My notion is that the CoC 1442 divisor was a film era number, and 1500 is considered more modern now, as a slightly tighter limit in sharpness (Wikipedia and others think that now). I used 1500 here at first, however, 1442 still seems clearly the norm on the internet, so I went with the flow. CoC is a little arbitrary, and you can use either above. There's not much difference, being 0.03 or 0.029 mm CoC for full frame 35mm, perhaps a 4% change in DOF calculations. Other factors like focal length and distance seem a larger issue.

Rounding: Note that numerically, real world APS sensors are slightly smaller than 24x16 mm, and their crop factors are actually slightly larger than 1.5 or 1.6. Just for example, the Nikon D5300 DSLR camera manual provides specifications:

6000x4000 pixels

24.2 million pixels

1.5 crop factor

23.5 x 15.6 sensor

Depth of Field calculators are not accurate for macro situations. Macro calculations are inaccurate because we don't know extended focal length, and maybe not f/stop reduction, and probably not the location of the front nodal point of the lens to know distance. At the close focus point, these are large factors. Accuracy depends on knowing the numbers. Macro instead computes DOF from measured magnification. Macro 1:1 means the object image is the same size on the sensor as the object in real life, true regardless of sensor size. Distances of at least a few feet will be most accurate in any lens calculation.

Circle of Confusion (CoC) is theoretically zero diameter (a point) at the focus point. But this blur circle grows larger when not in focus, and the DOF range is calculated to not exceed the standard limit (sensor diagonal/1442) of acceptable CoC. CoC (and therefore Depth of Field) definitely also depends on the current enlarged viewing size, which is magnification of the DOF blur. We should know that standard CoC is considered to view as acceptable sharpness in the **standard 8x10 inch enlarged print viewed at 10 inches**.

Depth of Field (DOF) is certainly not ONLY about aperture. DOF is an extremely important basic of photography, however IMO, exact DOF calculators may not be great practical use, other than to get a rough idea. But we certainly do need to know the concept. We need to know this, it should be second nature to you.

- Shorter focal length
- Stopped down aperture
- Greater subject distance
- Larger camera sensor
****** - Showing the image smaller

- Longer focal length
- Wider open aperture
- Closer subject distance
- Smaller camera sensor
- Showing the image larger

****** The three lens properties above cause the CoC (blurred diameter) in the sensor image. Then the DOF that we perceive relates to how large we enlarge that CoC to view it. We do think of cameras with smaller sensors giving greater DOF, **which might appear to be the opposite of just said above**. And they certainly do that, a little cell phone may not even adjust focus, yet it is in adequate focus about everywhere. But that is only because the field of view of a tiny sensor is drastically cropped (compared to a larger sensor). Therefore it must use a very short lens to achieve the same normal wider view (Crop Factor). That shorter lens certainly does increase DOF drastically. But even if we could use the Same lens (and ignore the crop), then the smaller sensor image still must be enlarged more (to view at same size), which reduces DOF. In the math, a larger sensor computes a larger acceptable CoC limit, which increases DOF.

- One thing DOF is NOT is an absolute value computed to a few decimal places. DOF is instead a vague approximation of a vague range of perhaps acceptable focus.
- We focus at only one specific distance. Therefore all other distances are NOT in best focus. As the degree of out of focus increases away from the focus point, tiny points in our image grow larger, and appear as larger blobs instead of as the tiniest points. At some point, we become aware of seeing that. The diameter of this out-of-focus blob (one from what should have been the tiniest point) is called
**Circle of Confusion**(CoC). We can calculate that actual CoC diameter on the camera sensor image, when at a distance away from the actual focus point. But then we also enlarge that image when we view it. This magnifies any blur, to be easier to perceive it.Statistical tests have said the average resolution of our eye is to perceive 6 mm of detail at 6 meters distance, called 6/6 vision in Europe, or 20/20 vision in the US ( x 3.28). This scales to other similar ratios, like 0.025 mm at 25 cm is familiar. For DOF in our photos, that was judged as perceiving 0.025 mm of detail on an 8x10 inch print when viewed at 25 cm (ten inches). This size print represents substantial enlargement of the small sensor image, so CoC limits at the sensor must be divided by the enlargement factor (from sensor size). Eyes do vary, but someone established this ballpark number, used for DOF as the limit of acceptable CoC diameter (that blurriness limit that we still call sharp). So this 8x10 print viewed at 10 inches is our standard for calculating the DOF blur that will be created. Today, this judgment is contained in the CoC = Sensor diagonal mm / divisor definition. History has used /1730 and then /1000 and /1442 and /1500, and likely others. The number is hard to verify results. The DOF formula details the geometry involved in the lens, and one factor is the CoC value which is determined by sensor size, for the purpose to scale it to what our eye can perceive at this standard 8x10 enlargement. The CoC number is defined as sensor diagonal / divisor (often 1442), but which is the CoC diameter as perceived in the standard 8x10 enlargement. It will vary in other enlargement scales.

The Depth of Field is the computed distance zone around the focus point, the span where the CoC remains less than our arbitrary limit for the size of CoC, considered to be in focus. The image is only focused at one distance, and

**gradually degrades**away from that point. Focus just outside the DOF calculation will be hardly different than the focus just inside the DOF calculation. For example, maybe the DOF limit computes 20 feet. But then you probably cannot detect much difference a couple of feet either side of 20 feet, but the exact focus point will be better. DOF is NOT at all magic numbers, it's just where the math precisely computes the CoC size crossed an arbitrary threshold size boundary. The boundary is very vague to our eyes. Sharpest focus is at the one distance where we actually focus. Depth of Field is a vague concept.

- If we can see these blurred blobs in the results, that's normally considered bad, when that distance is not in focus well enough. If only slightly out of focus, it may not enough for us to even notice it, much less object about it. Which is good, and while standards vary, DOF is a way to judge it. The exact calculated numbers are rarely important (just a simple guide). But the zone of DOF we perceive is certainly really important, and the big thing to know is what the controls are, and to know how to adjust it. With a little experience, we know what to expect, and this works pretty well.
The name Circle of Confusion is from another era, and Wikipedia quotes work in 1829 and 1832 calculating Circle of Confusion. They had microscope and telescope and binocular lenses then, but this was before cameras or film. Still same concept, but maybe if invented today, we might pick a simpler name for CoC (it is the diameter of the blurred circle of an out of focus point source). Camera sensor size is a factor of enlargement. Older work used CoC = (sensor diagonal / 1730), or 0.025 mm for 35 mm film. Today, we often use the computation (sensor diagonal mm / 1442) for acceptable maximum CoC in the final standard print size. These are often rounded numbers, or CoC = 0.03 mm for full frame 35 mm sensors, and CoC = 0.02 mm for smaller APS sensors (because the smaller sensor requires half again greater enlargement).

CoC is arbitrary, and professional level might prefer it smaller, with larger safety factor. Our CoC number choice does not affect the image in any way, it only affects how we might judge it, or plan it. It is an arbitrary notion about when out of focus is judged to become too noticeable. And DOF very definitely also depends on how large you enlarge the image to view it.

- What makes DOF even more arbitrary is that the larger we enlarge and view the image, the more noticeable becomes the blur blob of CoC. View it too small, and we may not even notice it. The standard of viewing DOF is considered to be an 8x10 inch print viewed from 10 inches. That's about a 9x enlargement of 35 mm film (CoC 0.03 mm), and so the CoC we see then is the 0.03 mm x 9 = 0.27 mm in this print. We enlarge our smaller digital sensors even more to see 8x10, so allowable CoC has to be smaller. Every sensor size has a different CoC (from sensor diagonal mm / divisor) - because we assume to enlarge each to the standard 8x10 inch print to judge it. DOF is a different number after enlargement, BUT the standard maximum CoC value was chosen to be acceptable when viewing this standard print size. Today, we view first on the computer screen, or even a cell phone. But we view different sizes, and this also affects the acceptable CoC goal. There is NOT just one number for DOF of a situation.
But, you can use the Largest Print Size parameter above to describe a print size (specify the largest dimension, like 20 for a 16x20 print), and it will calculate DOF based on that instead of the standard 8x10 inch print.

- The
**Hyperfocal distance**is a special idea of DOF, sometimes used for landscape photography with wide angle lenses, when we want an extreme DOF range, extending to infinity, and also back to a rather near foreground subject. For example, an APS-C sensor with 24 mm lens at f/16 computes Hyperfocal distance as 6.1 feet. Then**actually focusing at hyperfocal distance means that DOF extends to infinity, and back to half of hyperfocal distance**. It can be extreme, and shorter lenses can do much more of that than longer lenses. Crude distance marking today on our zoom lenses make it really hard to set a specific focus distance, but you can just focus on something at 6 feet, and then use that focus for your landscape.Those end point extremes will of course Not be as sharply focused as the actual focus point, but they will still satisfy the standard CoC specified. Do realize that DOF just means barely tolerable limits, where the CoC has grown to the maximum limit specified. Focus is always of course sharpest at the exact focused distance. Focus is not necessarily perfect if inside DOF, instead it is assumed unacceptable if outside DOF, but there is no sharp dividing line. If you want really sharp images, include ample safety factor for DOF; pay attention to enlargement size, stopping down at least one more f/stop, and if really important, focus on the important spot that needs to be sharp.

- Your DOF calculations may not exactly be realized particularly close in practice, due to your own degree of enlargement, and your viewing distance, and your own eyes, or an inaccurately specified sensor size, and how accurately you guess the actual distances. It is just a large ballpark. You'll have to decide for yourself if your images are as sharp as you want, and then you need to know the factors to increase DOF.
A couple of tricks are to plan on having sufficient DOF with ample safety factor, and then learn to center that DOF around your subject depth. If DOF is limited, don't focus on the nose if you want the ears sharp too. Repeat this to yourself: Focusing on the closest point wastes the half of the DOF range in front of that point (where there is nothing). Instead, you can plan to better center the DOF zone around your subject.

To do that centering, we hear about the simple (rough) guide of focusing 1/3 of the way into the scene depth (1/3 of scene in front of focus point, and 2/3 behind). If we think that 1/3 of the DOF range is in front of subject, then it makes sense to focus 1/3 into the scene, instead of at front point, and instead of half way back. There is no good argument for the front point, and half way is only true if up pretty close, near minimum focus distance. So 1/3 may not be exact, but often better. That focus point may not be where the subject is, and of course that subject will always be sharpest if you actually focus on it (so there are trade offs). But 1/3 can sometimes be true enough, often not greatly wrong, and can be a better rough guide than knowing nothing.

Regardless, hyperfocal becomes interesting:

- Specifically, 33% DOF in front of focus is
**very closely true**when focused at 1/3 of hyperfocal distance. This 1/3 guide is dead on then, if focused at 1/3 of hyperfocal. Then 50 mm at f/8 is roughly near 18 feet DX, or 12 feet FX, probably common ballpark situations? - Focusing at closer than 1/3 of hyperfocal is more than 33% in front, up to 50% at closeup extremes. Like about 40% in front if at 1/5 of hyperfocal. That's near 33%.
- For 1:1 macro, DOF is near zero, but what there is will be 50% in front.
- Focusing at further than 1/3 of hyperfocal will be less than 33% in front. Like about 25% in front at 1/2 of hyperfocal. That's near 33%.
- Maximum DOF occurs when focused at hyperfocal, and then we know DOF does extend from infinity back to half of hyperfocal. So it might be a surprise that this is 0% in front, only because the infinity behind is so much larger. Math involving infinity is awkward. :) But 1/3 into the scene has no meaning if infinity is involved.

Situations will vary, and the DOF in front of focus might be from 0% to 50% (at extremes). Otherwise, 1/3 is not the worst guess (we are not actually measuring distances anyway). Generally, short lenses have closer hyperfocal, and stopping down any lens brings hyperfocal back closer to us (and brings a short lens back very near). That's a lot to know. Frankly, in practice, we never know what hyperfocal number is, so we just soon learn the general idea of what we need to do when DOF is important. Stopping down some, and focusing somewhat into the scene depth can usually help considerably. Just standing closer with a shorter lens can help DOF, and as discussed here, standing back with a longer lens can reduce DOF range (specifically, will be same DOF at the subject with same f/stop, but greatly different at the background).

- Specifically, 33% DOF in front of focus is

For portraits at around 8 or 10 feet, I think a good tip is to focus on the near eye, after ensuring ample DOF, like f/8. IMO, f/1.8 is never the best try, and this article is about an alternative. For full frame portraits, I like about 120 mm at around 10 feet. For DX or APS crop cameras, that would be about 80 mm around 10 feet. Ten feet is very good portrait perspective, and at f/8, that's about a 2x3 foot FOV with around a one foot zone of DOF (again, of course speaking about the standard 8x10 inch print viewed at 10 inches).

Depth of Field is NOT an exact number. Depth of Field is computed based on the Circle of Confusion (CoC), which is the arbitrary criteria defining the maximum acceptable blur circle (to be small, not quite perceptible) due to being out of focus. CoC is the diameter of the smallest possible theoretical point after it is defocused to be seen as a larger blur circle (because it focuses in front of, or behind, the sensor plane - then causing a larger out of focus circle on that plane). CoC is the maximum permissible diameter of this blur circle, arbitrarily still judged to be imperceptible in our vision (also assuming a standard viewing enlargement). If the blurred circle is too small for us to perceive it, then we imagine it's not blurred.

Carl Friedrich Gauss 1777-1855 was a most brilliant mathematician (in a class with Newton) who did many amazing great things, one of which was to formulate optical theory (1840) that is still used today. He founded the renown optics factory in 1846, which in 1945 came to be in Jena, East Germany. Coc is computed from the film or sensor diagonal dimension. Gauss thought the eye's criteria of visibility of focus blur ought to be a CoC of (frame diagonal divided by 1730, in mm, which computes 0.025 mm today for 35mm film). But today, CoC of diagonal divided by 1442 is common universal (0.03 mm for 35mm film). But it's still an arbitrary guess about blur, about what our eyes see after enlargement. Blur diameter cannot be precisely defined... kinda depends. And so a CoC limit is somewhat arbitrary, there's been a few choices. CoC is just a rough guess attempting to measure focus blur, which makes DOF numbers be a vague thing.

The **DOF standard of viewing** calculations is in an enlargement of an 8x10 inch print (near A4 size) when viewed at 10 inches (25 cm). Viewing the enlargement size is an important factor in what we see, and in CoC and the Depth of Field calculations. This viewing enlargement factor makes small sensor diagonal be an important factor of DOF. It's the reason smaller sensors have a smaller CoC, and larger sensors have a larger CoC (sensor size requires enlargement of CoC). But standard DOF calculations assume a standard 8x10 inch print is viewed. So this affects viewing a smaller print or a larger print:

Computing on the diagonal attempts to equalize for different sensor or print shapes, but many vague assumptions are included. You should include a safety factor, especially for large prints, one extra f/stop for safety.

DOF is an angular size concept, and the math is all very precise, EXCEPT for the main factor of CoC, which is rather vague and arbitrary. So there are no hard answers about Depth of Field. And since Depth of Field GRADUALLY changes with distance, there is of course no sharp line at the computed limit. There will be virtually no difference seen slightly either side of the computed limit. Numerical Depth of Field is at very best, an extremely rough guide.

Depth of Field is a fundamentally important principle of photography. However using it is MUCH LESS ABOUT any computed numbers, and VERY MUCH MORE ABOUT understanding how to use the factors that increase or decrease it (f/stop, distance, focal length, and sensor size). Normal situations are not much concern, but sometimes we're aware we want a lot of depth of field, or don't want much of it, and we should know how to control that, to do what we can.

Continued - Part Two, Examples