Circle of Confusion (CoC) is generally used in two ways.
So the Depth of Field calculation on the sensor is based on lens parameters (focal length, aperture, and focus distance), and then is ALSO based on sensor size and its viewing enlargement to 8x10 inches. The lens focuses at only one distance, and what the eye sees is the importance. How much we must enlarge that sensor sized lens image to view it at 8x10 inches, when we can then probably see some of that out-of-focus blur that the lens might create. The enlargement required depends on the sensor size. The smaller the sensor, the greater enlargement that is required. We enlarge the original small sensor size or film size into a larger view (standard is an 8x10 inch print) to be able to see and judge the details, including focus blur and depth of field. Larger images will appear to have less DOF, and smaller image will appear better.
In regard to blurring the background, this calculator (on previous page) also computes CoC at the background distance. It is shown as Background x CoC which is a multipler of the actual CoC limit (c on the sensor) seen at the Background distance. A larger multiplier means greater relative blur. Normal Depth of Field computes the distance limits where the blur becomes as large as the maximum permissible CoC limit. Background CoC is reported in the calculator as "X times CoC", meaning actual CoC there is X times size of that maximum acceptable CoC limit entered for DOF. This is a relative scale of blurring there at the background distance, relative to the just-acceptable CoC at the limit of DOF. CoC is a mathematical hypothetical zero size point, but which is now computed to be blurred larger. However, blur and CoC are vague things, which does not worry calculators at all, but depending on contrast, our eyes can see it as vague unsure variable result.
The numerical CoC limit = (sensor diagonal mm / a constant often about 1500) which for 35 mm film size sensors, CoC is about 0.03 mm diameter. A sensor diagonal half this size would have a CoC limit half this size. Because a smaller sensor image must be enlarged more to view at the same size (the DOF calculation assumes the standard 8x10 inch print), in which case the two images enlarged to the same viewing size will have the same enlarged CoC size then. That enlarged size is judged to be about the limit of human eye perception. Everything about computing DOF is about this standard 8x10 final viewing size from 10 inches (due to CoC). This standard viewing size is of fundamental primary importance to Depth of Field calculations (regardless if anyone is aware of the convention). The idea is that blurring is much easier to see when enlarged, but difficult to perceive in a small image.
So in this vague situation, knowing the computed DOF numbers is not particularly important. What is important is knowing when greater depth of field is likely needed, and what to do about it generally. (See So What To Do about Depth of Field?).
Resolution: For a crop factor 1.5x sensor, the CoC diameter is 0.02 mm. If this is compared to the distance between the lines in a resolution chart, then that diameter distance theoretically represents 1/0.02 = 50 line pairs per mm maximum possible resolution (on the sensor) at the limits of that DOF span. This is NOT the maximum resolution, instead the opposite, it is the resolution at the DOF limits. Limits meaning less resolution is detectably blurred, but more is acceptably sharp when viewing the enlarged print. If at the background distance, 5X CoC for example is 5x0.02 which is 0.1 mm distance, 1/0.1 representing 10 line pairs per mm maximum resolution at that distance. Lenses today can typically resolve 80 to 120 line pairs per mm (a few maybe a bit more).
DOF is computed from the limit of maximum permissible CoC (which CoC is computed from sensor size). The concept is that if the background were located exactly at the computed far limit of DOF, the blur diameter there would be exactly equal to CoC (maximum permissible CoC x 1x). So it is not sharply focused there, but is at the limit where we say the distance becomes out of DOF bounds. For example, the sites DOF calculator, in its initial default case B, 200 mm f/4 at 24 feet, the DOF zone span is 0.668 feet, which extends 0.339 feet behind focus. If we say the background is only 0.339 feet behind the focus point, the Background CoC necessarily computes exactly 1x CoC, or the CoC diameter. Should the background be closer than the far DOF limit, then the CoC will be less than 1x (and will be within the DOF range). The background CoC is shown as a multiplier of this limit, and a larger multiple is a multiplied greater blur. The Background Distance is input here as the distance Behind The Subject, not from the camera. It assumes the subject still stands where it was (with respect to background), but the longer lens steps back.
CoC Size: The chart shows CoC size, which in DOF calculations, the specified CoC limit is computed as on the sensor size. Except we don't view the sensor, instead the CoC concept is designed to be enlarged to viewing size, where we do judge DOF. So one goal here is to point out the important concept is that the actual perceptible Depth of Field limits we see are due to the Enlarged CoC size after the image is enlarged to final viewing size, which by convention, the CoC divisors and values all compute for an assumed 8x10 inch print (203.2×254 mm) viewed at 10 inches (25 cm). The perceptible DOF situation absolutely depends on viewing enlargement. The bigger we enlarge it, the easier and better we can detect the blur. So you should know that the convention is that DOF is routinely computed for a 8x10 inch print size. Viewing DOF in smaller than the conventional 8x10 will look better than calculated, and viewing it larger will look less sharp (at distance limits). You can change print size here, but this is not a DOF calculator. If you have a different viewing size, the DOF calculator on previous page has an option to compute for it.
This calculator possibly might be informative in some degree about the basic concepts, but its main point is to show that the CoC calculator convention is to compute for an enlargement to 8x10 inches. Due to that, your actual enlargement different than 8x10 may not match your computed DOF result and expectation very well. But in practice, we don't often use a DOF calculator anyway, other than very special cases or more usually, as a learning experience. We quickly learn to "just know" what to do. See a section below: So What To Do about Depth of Field?
The easy workaround is that if using a calculator, and if your enlargement is to be 2x 8x10 size, then for better accuracy, double the CoC that your calculator uses for your sensor. If the enlargement is to half of 8x10 size, then cut your CoC to half (and other enlargement ratios like 10% from 8x10 size will work the same way). The bottom line is that the enlarged CoC in your print size is simply your sensors regular CoC times the enlargement. Except DOF calculators already assume the enlargement will be to 8x10 inch size, its an old convention from early days. This can be just a simple adjustment if you want it more precise.
The chart Show Dimensions option can show either just the Sensor dimensions, or also the Enlarged standard final viewing size dimensions for DOF comparisons. But only a 4:5 sensor format will fit the conventional 8x10 inch print shape, so how should a standard comparison of DOF compute it?
The calculator Print Enlargement option computes the Method of computing the enlargement to compare on the DOF conventional 8x10 inch print size. This enlargement enlarges the visible CoC too, which is Enlarged CoC value = Sensor CoC x enlargement.
Fitting the diagonal is not a prefect solution, it means the enlarged image dimensions don't exactly fit the paper shape (except for 4:5 sensors). Some cropping is always required to match the print size anyway, due to shape differences, but (except for square or wide panoramic film) the diagonal method will be pretty close.
The chart Enlarged Image Area is shown as the percentage of the enlarged image area that will fit on the 8x10 inch print at this enlargement of the diagonal. The 8x10 inch print shape is aspect ratio 1.25:1 and its size is 254×203.2 mm. Enlarged widths greater than 254 will be cropped. Heights less than 203.2 will be underfilled 4% (4:3) to 11% (3:2) or 12% (1:1). Cropping attention is always needed when printing. Arguing in support of the method of matching diagonals, the diagonal is the full view of the lens diameter, and it relates better to the actual overall size of the shape. The diagonal method is not practical for printing, but important for CoC considerations, because most important, then the enlarged CoC is the always the same enlarged size on the print, computing Depth of Field to the same standards (based what the human eye can see). If your goals are not 8x10, the DOF calculator on the previous page can specify a different size.
The Snellen eye test chart: The smallest blur dot that the normal human eye can perceive is difficult to determine precisely, but see Wikipedia about the visual acuity of the optometrists standard 6/6 or 20/20 Snellen eye charts (20/20 is feet and 6/6 is the metric measure, and 6 meters is 19.7 feet). Line 8 is readable for 20/20 vision, and three lines above it (line 5) is twice size marked 20/40, meaning normal 20/20 vision could read it at 40 feet, but it is the largest you can read at 20 feet, you have 20/40 vision (or 6/12 vision). The big E top line is 20/200, meaning 20/20 can read it at 200 feet. The chart is dimensioned in angular size. The big E example here is the special 5x5 Snellen font. In the Snellen chart text line representing 6/6 or 20/20 vision (line 8), each letter is viewed at the distance subtending an angle of 5 minutes. A letter E (also like B or F or R or P) has three horizontal lines and two spaces, and these 5 features (lines and spaces both when possible) are 1 minute of arc each (on the 20/20 line, as shown in that Snellen chart at the proper distance).
The Snellen chart's letters are designed to be fully recognizable or not, but the Depth of Field CoC limit is instead to be just perceptibly present, or not. I calculate enlarged CoC limit is 3 minutes of angle if viewed at 10 inches (CoC diameter viewed on a standard 8x10 inch print). I'm arguing with myself here, as 3 minutes is pretty large, and human vision is often said to perceive 1 minute size, but it is what it is. An image at the 10 inches standard viewing distance and standard 8x10 enlargement size, the 1442 0.22557 mm enlarged CoC value computes 3.05 minutes. The 1500 0.21685 mm CoC value is 2.93 minutes. Depth of Field calculates the scene distance limits where the standard enlarged and viewed hypothetical "point" of zero size is blurred enough to reach this CoC size limit believed to then be perceptible to normal human vision.
It has been said that this DOF standard CoC value (diagonal / 1500) represents 20/60 vision, at least it is three times larger than the 1 minute angle that a 20/20 eye is said to see. It is difficult for me to imagine 20/60 vision to be a reasonable goal argument for a sharp photograph, but in this situation, it is a size limit number of out-of-focus blurring, not a concept about 20/60 vision. It is obvious that 1 minute of 20/20 vision is too small to be a practical limit for DOF CoC (if 1 minute represents sharpest normal vision). The 20/60 sounds pretty large, but it does match the math (in a different way). The DOF CoC is computing the enlarged blurred size of a hypothetical zero diameter point, not any visible detail. And the math says you can multiply your CoC divisor by 3 (4500 instead of 1500) to compute CoC 1/3 size, to be approximately 1 minute in the standard enlargement. The DOF calculator on the previous page here will allow doing that, but that is quite extreme, and I seriously doubt you would like being so restricted. But these are different concepts, and my own notion about how to resolve this difference is that 1 minute size is said to be the smallest that a human eye can resolve (can actually see as a spot). 20/20 is how a good human eye can reliably identify a text letter size of 5 minutes size. DOF blur is an overall blur, Not any actual physical spot we can see, so the 3 minutes seems a compromise between these two results. But 20/60 vision is an entirely different subject than detecting a fuzzy area. No doubt the CoC goal must have been 3 minutes, but whatever the reasoning may be about determining the visibility of blurring, photographers should understand that this 3 minutes is obviously the judgment of authorities about what becomes perceptible blur for Depth of Field (seen by the human eye in the standard 8x10 inch enlargement viewed at 10 inches). There is no perceivable difference the blurriness of 0.0299 and 0.301 mm, but math can draw a hard line at 0.03 mm between those numbers.
One note puzzling to me is that the 1972 Kodak pamphlet Optical Formulas and Their Application on page 5 suggests CoC = Focal Length / 1720, which they say is 2 minutes of size. There was a 1720 CoC divisor in an early hundred year old standard, but today the divisor of sensor diagonal is 1500 or 1442. The term Focal Length took me by surprise there, because CoC is defined as sensor diagonal / 1442 or 1500. However the meaning possibly might be that a "Normal" lens (meaning a "Normal" field of view) is considered to be a focal length of approximately the sensor diagonal (so in a way it might match as equivalent). But then these words imply using a long lens of 10x focal length would use a CoC 10x larger, which does match image viewing enlargement, but there is no sensor size base stated. I can't make much sense of that, but it doesn't seem modern. The (35 mm film diagonal of 43.267 mm / this 1720) is 0.025 mm, which was the CoC suggested by Zeiss back around that time (dividing diagonal by 1730), and it is 2.5 minutes. But today, the idea is diagonal/1500 = 0.0288 mm, which is often used as 0.03 mm ( /1442), and it is 3 minutes of angle.
Not all users realize this Depth of Field significance of the enlargement of sensor size to viewing enlargement, but it is a basic concept of DOF. There are some arbitrary factors, but the more we enlarge it, the easier and better any blurriness is seen. The DOF calculation assumes the standard viewing size is 8x10 inches (203×254 mm, diagonal 325.28 mm), viewed at 10 inches (25 cm). Metric A4 print size is also close to this viewing size.
Focal length and f/stop and distance compute the diameter of a blurred "point" of original zero size in the lens onto the sensor. That CoC limit is computed from the sensor diagonal, corresponding to the enlargement needed to reach a standard 8x10 inch viewing size where the eye will see it.
Things affecting Depth of Field precision:
The rest is just math. But in practice, we really don't need much precision, or actually even any numbers, just knowing what to do about Depth of Field is the useful skill. See So What To Do about Depth of Field?
CoC Divisor: The maximum permissible CoC limit in DOF calculations (DOF computes what distance is declared blurred and what is not). CoC is defined as sensor diagonal mm / a divisor representing enlargement to a standard viewing size.) The CoC that we can view has been enlarged in the final print size. So two factors, sensor diagonal size and a standard divisor representing degree of enlargement to a standard viewing size to evaluate Depth of Field (the standard for DOF computing is CoC representing a standard 8x10 inch print viewed at 10 inches or 25 cm distance). The significance is that the CoC for the sensor size is enlarged for us to see in the viewed print. This limit defines the minimum detectable blur computed with Depth of Field (in that enlarged standard print size).
Both human vision and blurriness are difficult to specify, but the sure thing is that CoC to represent human acuity (after enlargement to 8x10 inch print size) is today conventionally said to be diagonal / 1500 on the sensor. However, we commonly use CoC of 0.03 mm for 35 mm film size, which mathematically corresponds to a 1442 divisor. So the default divisor here is 1442, but you can specify 1500 if preferred. 1500 and 1442 are only 4% difference, not much difference. A larger divisor computes a smaller CoC limit, which more critically reduces the acceptable DOF span, and vice versa. Smaller film must be enlarged more, so it necessarily computes a smaller CoC limit. Our habits of guessing distances in the field make great precision unlikely.
I doubt it was anyone’s plan to use 1442 as a divisor, but use of the 0.03 mm decision (for 35 mm film and 1x sensors) is very clear. My notion is that it might just be the result of rounding CoC of 0.0288 to 0.03 for 35 mm film, but the 0.03 mm result does necessarily require a 1442 divisor. It’s not all that critical, but you can use 1500 if you think it's important. If comparing DOF numbers from a different DOF calculator, make sure you realize any difference in sensor size or CoC used, because those are factors to compute DOF (as are f/stop and focus distance, and enlargement size if offered).
Depth of Field is all about the degree of enlargement of the small sensor image when we see it at larger viewing size. The more we enlarge it, the better we can see it to detect any blur at a distance away from the focus point. Depth of Field is sharp enough until we can see and detect the blur. The purpose of CoC is to compute the DOF visible due to degree of enlargement. If comparing computed DOF results with other calculators, DOF is always the same formula, surely everyone has that right. But if a result difference, make sure the CoC and Sensor Size used are the same values, because other DOF calculators don't seem to actually compute the CoC as frame diagonal size divided by a standard divisor. They typically don't mention divisor, or even actual sensor size for many camera models). In examining their CoC for the various frame size choices, calculators seemingly just used some CoC values they found somewhere, which is a little crude, because then any corresponding divisor necessarily varies with frame size. Then CoC is Not the concept of a standard divisor based on enlargement size, but seems just some assorted values. For example, when comparing calculators for CoC size, a leading calculator site shows CoC values which when examined with sensor size, correspond to divisors in the range of 1150 to 1760 (frame diagonal / CoC, which is a confusion). But digital sensors were typically near 1442 (speaking specifically of those only including the digital sensors from 1x to 2.7x crop factor. 6 cm film varied the most.) There was still the question of what should CoC actually be, so my site instead takes a purist view, and actually computes the frame diagonal size as precisely as it can be specified, and uses the one same divisor to compute CoC for all formats of frame sizes, all with a consistent divisor. The Wikipedia CoC list has these same frame values still varying 9% in the corresponding divisor, but some calculators are not that close.
The specific reason for choosing 1442 here is simply because that CoC result is what we often see. DOF calculators commonly use CoC for 35 mm film stated as 0.03 mm. Awhile back in not too distant times, the Zeiss optical company specified the "modern" CoC divisor to be 1500. Many sources now repeat it as 1500 as the classic wisdom, but most DOF sources seem not to actually compute their CoC values. 1500 computes 35 mm CoC as 0.0288 mm, usually seen as 0.03 mm, or maybe 0.029 mm. Zeiss is in Germany, but the Japanese camera market adopted the value 0.03 mm for 35 mm film (possibly just rounding? Blurring is rather vague, but I suspect it was a larger decision than just rounding.) But 0.03 mm is the value we commonly see today from the manufacturers (for 35 mm film size, 1x crop factor). The diagonal of 35 mm film frame is 43.267 mm (from the 36×24 mm frame), and to get the CoC result of 0.03 mm, the corresponding divisor has to be 43.267 / 0.03 = 1442.2. Hence, 1442 is the divisor actually being used to have ever gotten 0.03 mm. I choose for the calculator to do the actual diagonal and divisor computation, and to get this same familiar value, it seemed best to use 1442 to conform. Feel free to change the calculator to use 1500 if you prefer it. It's just perhaps a 4% change in CoC and DOF span. But blurring is a vague concept, not very critical, and other factors like our approximations for distance and focal length and sensor size, and our unconcern about specific enlarged viewing size seem much larger issues. DOF is computed from CoC which was as standard estimated to apply to 8x10 inch prints viewed at a distance of 25 cm (10 inches).
DOF calculations for full frame 35 mm cameras typically use 0.03 mm for CoC, and APS-C size DSLR cameras often use 0.02 mm (due to enlargement of crop factor). A compact camera or smart phone might have CoC = 0.004 to 0.007 mm (since much more enlargement is necessary). Other values have been used in the past. CoC size in pixels is also shown in this sites calculator, which might be judged before enlargement. However, Depth of Field is a little bit arbitrary, blurry is a vague concept.
Viewing Size Dimension is about the relative enlargement of your viewed image. The standard size for DOF calculation is 8x10 inches. 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 more, then we need to start with a smaller CoC (to prevent the eye from being able to perceive it). Regardless of your intended viewing conditions, standard DOF calculations always assume viewing a standard 8x10 print size. It also applies to the same 8x10 inch size viewed on the monitor screen too. This field is to describe a different image size that you may choose to view, to better account for the effect of your enlargement on the Depth of Field calculation.
The CoC used in the calculator (previous page) is shown in bold if and when modified by the Viewing Size not being the standard 8x10 inches (203x254 mm standard). Because, CoC is the largest allowable blur, to still not be perceptible by our eye. If we're going to view an image enlarged bigger, then maximum permissible CoC at the sensor has to be smaller (to not exceed what our eye can perceive). Or vice versa. If divisor is unchanged, the calculator uses CoC = sensor diagonal / 1442, which is the standard CoC values used by other DOF calculators (0.03 mm for full frame size, for example).
Macro: Depth of Field calculators are Not accurate for macro situations. Macro calculations are inaccurate because at the very close distances, we don't know extended focal length, and maybe not f/stop reduction, and likely not the location of the front nodal point of the lens to know accurate working distance. At the close focus point, these are large factors. Accuracy depends on knowing the numbers. Macro procedures instead compute 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. For DOF calculators, known focal lengths at distances of at least a few feet (magnifications less than 0.1) will be usable in lens calculations.
Yes, I know we can compute much finer precision than the eye can ever see. So yes, I know that computing DOF distances to four significant digits is an unusual thing to do. It's more a two digit concept, if that. :) But humor me, it may be wishful, but I do it just to be able to enter some results back in to check the calculation consistency. For example, the initial default case with 23.4x15.6mm sensor shows 200 mm f/4 DOF far limit is 24.34 feet. Then entering a background distance of 0.34 behind the 24 foot focus (as 0.34 background here, not 24.34) must compute Background CoC there as 1x CoC (showing concept), because it is at the DOF limit of exactly 1x CoC which is the definition of DOF. Or entering -0.33 in front does the same, same reason. Just 0.3 misses the exact 1x CoC value by a little (it is actually 0.33874 behind). The math distinguishes tiny differences, the eye not so much. So 4 or 5 significant digits helps the beauty of the math, but our eye won't see the same precision. The real world is that our sensor sizes and crop factors and focal length numbers are slightly rounded values. APS-size sensors are slightly smaller than 24x16 mm, and their crop factors are slightly different than the often seen 1.5 or 1.6. This little difference affects CoC size, which can slightly skew calculated results in a small way, but the concept should still be clear.
I doubt anyone ever uses a DOF calculator in routine situations. We can't be bothered to stop to actually measure all the distance limits. We can't even accurately set the lens focus to numbers like 11.0 feet. Depth of Field is Extremely Important, but the calculator can be a learning tool, maybe to help learn concept and expectations. What we do need to routinely know and use is how to increase (or decrease) Depth of Field (how to choose settings that give the best try for the situation).
When you compute DOF limits, you are specifying that the CoC at those limits will be someone's notion about the size of maximum acceptable blur that a standard enlargement will show. Meaning any more blur would be unacceptable. But there's virtually no difference just either side of that line, and that's not the same meaning as "sharp". The focused point is always sharpest. If focusing at your situations hyperfocal distance, the DOF span is from infinity to a half of hyperfocal. That does not actually mean "sharp", focusing at 8 feet is not the same as focusing at infinity. Instead those limits ensure the blur at infinity and at half of hyperfocal will be limited to the maximum permissible CoC diameter still considered to be acceptable blur. And this indeed might often be acceptable, but you should realize it is a compromise, and maybe there are times you may want a more critical calculation. And our enlargements are of variable size.
If interested, you can increase the CoC Divisor higher than 1442, and that will compute more critical DOF limits. This will not then match standard DOF, but if you want it tighter, you can.
For example, if you double the 1442 divisor to 2884, that reduces CoC to half diameter (the maximum allowable blur is now half the blur, so to speak), and it will compute new DOF limits accordingly, half the span of previously, suitable for printing twice the standard 8x10 inch print size. This doubled divisor also doubles the new hyperfocal distance, which then will recompute infinity to half of the new hyperfocal with blur at half of the previous CoC. You'll like that part, except the new DOF span will be substantially less span. But it can be a guide, and increasing the divisor is the way to implement it. This change does not affect what the lens does, or what you can see, but it does compute new numbers.
Other Divisors can be considered, increasing 10% (to 1586) or 20% (to 1730), and the acceptable CoC will be the same percentage smaller diameter blur, with proportionally smaller new DOF span (see next page). Definitions of "sharp" have been a little bit arbitrary, and the resolution of a typical eye is a bit vague, and again, viewing enlargement is a big factor too.
However, in usual practice, we don't do precise DOF calculations. We can realize when a scene needs greater depth, and know to stop down more than usual. We know a scene with very wide range (very both near and very far objects) will need a shorter lens well stopped down, and hyperfocal may be a very good thing to know then. Greater focus distance also helps depth of field. Our experience learns about what we should expect, and we know what we need to do as best try.
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 of practical use in the field, other than to learn an idea of Depth of Field concepts. However, we certainly do need to know the basic concept. We need to recognize when a scene needs greater Depth of Field, and we do need to know what to do about it. It should become second nature to you.
The first three lens properties above are normally the way we adjust for better DOF. Normally all we know when first seeing the scene is that this one is deep (for its distance) and will need a lot of DOF, so we learn how to maximize DOF without having specific numbers. If an adjustable camera providing the control we need, we can learn to always routinely first look and become aware that our scene situation needs more depth of field. Then we can give it our best try, all we've got. We likely don't have the choice of changing our camera and sensor size, but some biggies that we can learn to do are:
In the DOF formulas, focused distance and focal length are squared, which has larger effect on DOF span than does f/stop or CoC. The results are not linear, but while stopping down f/stop is good, and most convenient to avoid changing image framing, stopping down only one stop has relatively smaller effect on DOF. A useful tip is that increasing both distance and focal length by the same multiplier has opposite effects, so generally remaining same depth of field AND same field of view (if all else is the same, speaking of at the subject), but then a modestly distant background has less of both field of view and depth of field (see previous page).
In the math, a larger sensor (because it needs less enlargement to print an 8x10 inch print) computes a larger acceptable CoC limit (proportional to the sensors diagonal dimension), which increases DOF range. So in the math, with all else the same (i.e., with same focal length and distance), the smaller sensor has smaller CoC which creates less DOF due to its greater enlargement required. But in practice, what we routinely see on the cell phones and compacts is the opposite due to the tiny sensor's necessarily much shorter lens (required for a comparable view), often only 4 or 5 mm focal length on compacts and phones. The small sensor size is detrimental to DOF, but the necessary very short lens focal length more than compensates (focal length gets squared, but CoC does not).
Old-timers may remember the tiny Kodak Disc film, or 110 film size. These had quality issues being so small, prohibiting very much print enlargement from film. Compact and phone digital camera sensors have no film grain (enlargement really hurts film grain), but they are about half the dimension of Kodak Disc film, and 1/4 the dimension of 110 film size. DSLR cameras and lenses are significantly larger because some users prefer a larger sensor. A larger sensor reduces the viewing enlargement required, therefore allowable CoC is computed to be larger. Depth of Field calculations are about the degree of enlargement required to provide the standard viewing size, because enlargement determines how well we can see the detail.
Many tend to ignore sensor size today, but it's still important. My notion of film size in the past is that:
The practice of guessing at distances in the field does not contribute precision to our DOF numbers. However, the concept survives anyway. Regardless if we know any numbers or not, our skill in photography needs us to recognize the situations that need greater depth of field (or faster shutter speeds, etc). We need to look, and see, and think about what we’re doing. When we recognize we need greater depth of field, calculating is not a big help. Giving it properties with more depth of field is the big help. Give it what you can when you see you will need it. The calculator is more a learning tool, rarely used in practice. Depth of field is more about what our capabilities are able to do. When we realize the situation needs unusual depth of field, then we do what we can to improve it. We automatically do what we can do when we realize we need it. The common actions are these:
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. Example, a cropfactor 1x FX 50 mm lens at f/22 computes Hyperfocal as 12.25 feet. Enter 12.25 focus, and the DOF calculator will reach infinity. But enter 12.0 feet, and it reaches "only" 592 feet. These results will be indistinguishable (even if you could set focus to exactly 12.25 feet). Exact numbers are not always as significant as they might appear. :) We don’t know the focal length or the sensor size precisely. In practice, we probably guess at the distance, and the actual guess might be 11 feet, which computes DOF to 107 feet. And we might then show it full screen size on our wide screen monitor, which might be about twice the size of the computed standard 8x10 inch print size. So, your DOF results may vary a little, but it is very good to know the concepts (which I would argue are more important than the exact details). When you realize your scene needs greater depth of field, then give it what you’ve got.
Depth of Field "numbers" are just approximations, not to taken exactly literally. DOF is not actually sharp from one limit to the other. 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, our eye becomes able to perceive seeing it (depending on our enlargement of it). 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 (feet = meters x 3.28). This scales to other similar ratios, like 0.025 mm CoC viewed at 25 cm is familiar. For DOF to be judged in a standard way, that was standardized as perceiving 0.025 mm of film 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 the sensor size to the enlarged print 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.
Is the divisor 1442? You probably won't see mention of the number 1442 anywhere, but I didn't make it up, it is simply what it must be if consistency is a goal. Maximum permissible CoC dimension is about the degree of enlargement of sensor size to final print size, and this judgment is contained in the definition CoC = Sensor diagonal mm / divisor. This is a little arbitrary, about what we think our eye can perceive in the print. It did have different values in the early days of film and lens development. Lietz (the first 35 mm Leica, about 1925) used CoC = 1/30 mm, also called 1/770 inch, which is 0.033 mm, which computes a 1300 divisor (11% less than 1442). The Zeiss optical company (long ago, in East Germany before WWII) later published using /1730 (20% greater than 1442, 0.025 mm CoC). Then the Zeiss company in recent times reduced it to /1500 (4% greater than 1442, 0.0288 mm) — both slightly more strict than 0.03 mm (for 35 mm film size) which computes 1442. But today, it is most common (for Japanese cameras) to say full frame CoC is 0.03 CoC, which could just be rounding, but which actually computes the divisor 1442 as being the standard value today. Many DOF calculators today use 0.03 mm CoC for 35 mm film, which necessarily computes the CoC divisor of 1442. That standard 0.03 mm might be thought of as a 1500 value rounded up, but to get 0.03 mm, the 35 mm film diagonal is 43.26662 mm, divided by 0.03 mm is 1442.2. Using 0.03 mm CoC concept with Crop Factors is used as CoC = 0.03/Crop Factor, since both CoC and Crop Factor involve the sensor diagonal. If you don't like 1442, then try 1500 (0.0288 mm CoC for full frame), but it will not agree precisely with most other DOF calculators then. Blurriness is a vague thing, hard to verify in results. The CoC diameter is a scaling factor to scale the blur to what our eye can perceive at this standard 8x10 enlargement. The CoC number is the sensor diagonal / divisor (often 1442, and 0.03 mm CoC in full frame 35mm).
Wikipedia quotes work in 1829 and 1832 calculating Circle of Confusion, so that name comes from a different era. They had microscope and telescope 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 COMPUTED diameter of the blurred circle of an out of focus point source). Camera sensor size creates a factor of enlargement to view it. 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, or CoC = 0.02 mm for smaller APS sensors (because the smaller sensor requires half again greater enlargement to view it).
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.
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 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 permissible CoC value was choosen 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.
If you crop your image significantly before enlarging it, that's the equivalent of a smaller sensor, with less DOF.
If you will view a different size image or print, you can use the Viewing Size parameter to describe your size, and it will calculate DOF based on that instead of the standard 8x10 inch print (203x254 mm).
The Hyperfocal distance is a special idea of DOF. Wikipedia finds "hyperfocal" in work printed in 1867. It is sometimes used for landscape photography with wide angle short lenses, when we want an extreme DOF range, extending to infinity, and also back to a near foreground object (to add interest and emphasize depth). For example, an APS-C sensor (1.5x crop factor) with 18 mm lens at f/16 computes Hyperfocal distance as about 3.4 feet (depending on precise sensor dimensions). There are two ways to define hyperfocal, and what that means is this:
However if Infinity or half of hyperfocal are inappropriate distances for your subject range (like a group photo in the school), hyperfocal would be a poor plan that time. Then, focus on your subject instead (into its depth a bit). The focus distance is the sharpest point in your photo. For example, even if your hyperfocal is say 6 feet, but your subject is at 20 feet, and there really isn't anything much closer, then probably you should focus at 20 feet instead. Infinity is still OK there, focus anywhere beyond hyperfocal will reach infinity (better even). But if you do have something important at 3 feet, and at infinity, then the idea is to focus at hyperfocal at 6 feet, for DOF from 3 feet to infinity. Focusing at 6 feet won't be the sharpest possible focus for 20 feet, or for infinity, or for 3 feet, but 20 is well within DOF limits of 3 feet to infinity.
See the The Hyperfocal chart and calculator on the previous DOF page. The chart for your sensor size is all you would ever need to be able to use Hyperfocal.
Hyperfocal focus does not mean the infinity and the closest point are fully sharp, they are not. Instead it's just some definition of "the maximum limit of sharpness deemed acceptable". You might not always agree. The actual focus point is always the sharpest point, which can help the actual subject there. Or possibly focus at some intermediate point might be important. But it is good to know that if focus is at any distance greater than the Hyperfocal distance, DOF limit will reach to infinity. Focal length and f/stop and sensor size changes hyperfocal.
Again, a wide angle lens with a short focal length, stopped down well like to f/16, will reduce hyperfocal and increase the DOF range tremendously. That's often a big plus.
However, while hyperfocal is a strong concept, there is a caution. It may not always be the best choice, because the DOF limits are maximum limits of acceptability. Let's say maybe hyperfocal comes out as say 12 feet. Then focusing at 12 feet then will extend DOF to infinity, and back to 6 feet. Perfect if that's your goal, however focusing at 12 feet is NOT the same as focusing at infinity or at 6 feet. Actual focused distance is always the sharpest point.
Or (in this case) focusing instead at infinity will reach back to hyperfocal at 12 feet, within perceived acceptable limits. Is one end (12 feet or infinity) more important to your picture? It is a choice, but there are choices.
Or maybe in many cases, even if hyperfocal is 12 feet, but there is really nothing really close this time, focusing on something out in the zone, like perhaps around 50 feet, is often a better compromise. For example, in the calculator, with sensor 1.5 Crop factor, 24 mm lens at f/8. Hyperfocal is about 12 feet. Background distance at 99999 shows CoC at infinity is about 1.0x the CoC limit, which is what DOF range means. CoC of 0.02 mm diameter roughly means only 1/0.02 = 50 line pairs per mm maximum resolution. But focusing at 50 feet is only 0.237x CoC at this 99999 infinity (sharper, 1/(0.02x0.237) is 210 line pairs per mm), and DOF extends back to 10 feet (which is not 6 feet, but maybe it is enough?) This could matter sometimes.
The best general plan is to always center the DOF range around the subject. Focusing on the subject more or less does that (but see Fraction of DOF in front of subject) below. Hyperfocal is a major principle, but can be used a few ways. One way is when you really need extreme DOF from infinity back to half of hyperfocal. Another way is any focus past hyperfocal will reach to infinity, and the further past it is sharper at infinity. Stop and consider if one end is the most important.
Subject distance is a factor of DOF, but it does not affect hyperfocal distance. But subject distance at hyperfocal is a big effect.
Hyperfocal varies with the square of focal length ratio. Doubling focal length gives 4x hyperfocal distance, or 10x focal length gives 100x hyperfocal. And one half of focal length gives 1/4 hyperfocal distance. Hyperfocal distance is not affected by focus distance.
Stopping down two stops more gives half of hyperfocal distance (stopping down one more stop is 0.707 x hyperfocal).
So, doubling focal length AND stopping down four more stops is the same hyperfocal distance.
In our calculator example on previous page about standing back with longer lens to better blur the background, the longer lens blurs the background more. But at an "equivalent" subject distance, for the same planned Field of View (to create the same picture) and at the same f/stop, the subject DOF range is the same overall span. And then stopping down the longer lens a bit more increases the DOF at the subject, but leaves the background DOF still less (if background is sufficiently distant to separate these two zones). Both results can be good goals.
These are basic ideas which have been known for maybe 150 years. The alternative of simply focusing on the near side of the subject zone typically wastes much of the depth of field range in the empty space out in front of the focus point, where there may be nothing of interest. Focusing more into the depth centers and maximizes the DOF range, generally more useful. We hear it said about moderate distance scenes (not including infinity) that focusing at a point 1/3 of the way into the depth range works for this, which is often near true, maybe a little crude, better than knowing nothing, but some situations do vary from that 1/3 depth (below). Close and macro focus situations are closer to the middle at 1/2 way in, and don't include infinity.
The crude distance marking today on our lenses make it hard to set a specific focus distance. If your lens only has a mark at 10 and at 5 feet, setting 6.117 feet won't be easy. But we can approximate it to about 6, at least between 5 and 10. It's all a little vague anyway. Sometimes it might be easy to focus on something at an estimated 6 feet, and then shift your camera aim to the real subject.
Every Depth of Field calculator should show hyperfocal focus distance.
Many prime lenses have a DOF calculator built into them. Speaking of prime lenses (i.e. those lenses that are not zoom lenses) which normally have marks at the distance scale showing the depth of field range at the critical aperture f/stops. In the old days (before zoom lenses), this easy way was the standard procedure to handle DOF. However, this tremendous feature is becoming a lost art today. Zoom lenses cannot mark this for their many focal lengths. Also todays faster AF-S focusing rates can put the marks pretty close together. These 85 mm and 105 mm lenses are AF-S, but it still gives a DOF clue. (the "dots" are the focus mark correction for infrared.)
For example of hyperfocal distance, at right is an older 50 mm FX lens, with focus adjusted to place the f/22 DOF mark at the middle of the infinity mark, which then actually focuses at about 12 feet, and the other f/22 DOF mark predicts depth of field from about six feet to infinity (assuming we do stop down to f/22). This places the focus at about 12 feet. The DOF calculator says this example (FX, 50 mm, f/22, 12.3 feet) DOF range is 6.1 feet to infinity.
Or another case, one not including infinity. If we instead focus this 50 mm lens at 7 feet, then the FX f/11 marks suggest DOF from about 5.5 to 10 feet (at f/11, which is about 1/3 back in this case). The idea of the markings (which appear on prime lenses, zooms are too complex to mark) is to indicate the extents of the DOF range. And done because it can be very helpful. Sometimes f/22 is the best idea, sometimes it is not. f/22 causes a little more diffraction, but it can also create a lot more depth of field. There are ifs and buts... The sensor size Never affects the attached focal length, however, the focal length chosen to frame the image right on that sensor does depend on sensor size, and depth of field certainly depends on focal length.
The newer internal focusing lenses focus very fast (much less rotation needed). The photos of the 105 mm lens and the 85 mm lens show tick marks to mark f/32 or f/16 DOF, but there is no room to show more. And their distance scales are too compressed to be very readable.
Those DOF end point extremes will 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 permissible limit specified. Focus is always 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. What you specifically need to know are the factors to increase DOF (stopping down, a shorter lens, and longer distance).
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 of your subject 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. Instead, consciously focus a bit more into the depth of 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 true if up focusing pretty close. That focus point may not be where the subject is, and that subject will always be sharpest if you actually focus on it (so there are trade offs).
Regardless, hyperfocal becomes interesting.
Still, regardless if 1/3 in front is always very accurate or not, (and since we don't measure any distances anyway), it is a generalization sometimes halfway close, perhaps better than not knowing anything. It will never be more than 1/2 in front, but can be well less than 1/3. What is important is for the photographer to realize that depth of field is a zone, and that often (regardless of exact details), it's a good plan to realize we can center that zone on the important scene area, instead of just always focusing on the first object in front (which likely wastes all of the DOF in front of it). Focusing back into the scene a bit can often help to center the focused zone.
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 compute the hyperfocal number, 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).
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 Field of View with around a one foot zone of DOF (again, speaking about the conventional 8x10 inch print viewed at 10 inches).
Depth of Field is NOT an exact number. The entire concept depends on arbitrary judgment of how much blur the eye can detect, which depends on sensor size, enlargement of that sensor size, and also viewing distance. Depth of Field is computed based on the Circle of Confusion (CoC), which is the criteria judged to define the maximum acceptable blur circle (to be small, not quite perceptible) due to being out of focus. CoC is measured on the sensor, and is typically defined as sensor diagonal / 1442 today. The diameter of the smallest possible theoretical point after it is defocused is seen as a larger blur circle (because it focuses in front of, or behind, the sensor plane). CoC is the maximum permissible diameter of this blur circle, judged to still be imperceptible in our vision after enlargement to an assumed standard viewing enlargement of 8x10 inches. If the blurred area is too small for us to perceive it, then we imagine it is not blurred. Enlargement of viewing size is a big factor of perception. But 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.
This CoC diameter is on the sensor, the lens is where the geometry is. But then it is enlarged to our viewing size, and the DOF computation (based on CoC) is when it is enlarged to 8x10 inch print viewing size, then anything larger is perceived by the eye. DOF computes the distance limits defined by this hypothetical maximum permissible CoC limit. Distances outside that span are blurred. Distances inside this span are considered sharp enough.
The DOF Standard of Viewing is in an enlargement of an 8x10 inch print (near A4 size) when viewed at a distance of 10 inches (25 cm). You should know that DOF calculators use a CoC based on sensor size (typically sensor diagonal dimension / 1442), which assumes this standard enlargement, regardless if you assume it or not. If you view an image larger than 8x10 inches, DOF will appear less than you calculated. If you view an image smaller than 8x10 inches, DOF should appear better than you calculated. Based on what our human eye can resolve, DOF is calculated for the enlargement of the sensor size image to a standard 8x10 inch print.
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.
Depth of Field is an angular size concept, and the math is 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 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 (page top above, 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 Three, Examples about background