Is the hyperfocal distance calculation outdated?

Question

The hyperfocal distance H is calculated by H = (f^2)/(N*c)+f where f is the focal length, N the f-stop and c the circle of confusion limit. Lets assume we use a fullframe sensor. All those calculators and apps always use the value of 0.03mm for the circle of confusion. Why 0.03mm? The german article on Wikipedia explains it like this:

When viewing an image from an usual viewing distance, the image is viewed with an angle of view of 50° which is an equivalent of 3000 angular minutes. We assume that we will start to notice a blurriness when it exceeds the size of 2 angular minutes which is an equivalent of 1/1500 of the image diagonal. So the blurriness must be kept under the size of 1/1500 of the sensors diagonal. Since a fullframe sensor has an approximate diagonal of 43.2mm, 1/1500*43.2mm gives about 0.03mm.

This made me curious. I think this calculation must come from the ages of analogue photography. Lets say we use a 15mm at F/2.8. Thus the hyperfocal distance is 2.69m. A modern Nikon D850 has a pixel pitch of 4.34 µm. When rays of light converge in front of or just behind the sensor, every circle with a diameter less than 4.34 µm will be recognized as in focus. Dont we have to take the resolution of the sensor in consideration? I dont think we can assume that one will only look at our images with an 50° angle of view.

There are videos out where they promise you to take sharper images by focusing at the hyperfocal distance. Sometimes they tell you to focus at the double hyperfocal distance. In our case we should focus at 2*269m = 5.38m. The image will appear perfectly sharp when viewed with an angle of view of 50° but when calculating the hyperfocal distance with a circle of confusion diameter limit of 4.34 µm, we should focus at 18.53m which is more than 6 times the hyperfocal distance.

In my opinion we dont need to reinvent the hyperfocal distance calculation but I think this is important to know, when using the hyperfocal distance as a guarantee to get the maximum of sharpness in our images.

What do you think about that?

Answer 1

In short:

There are two possible approaches to the sharpness in digital photography:

1. getting the best possible sharpness given the sensor
2. adequate sharpness when the image is viewed

The first approach leads to take into account the size of the sensor sites.

The second is the legacy approach, but it is still relevant, as the view of humans has not evolved.

Answer 2

Hyperfocal distance is a specific application of the concept of depth of field.

There's only one distance that is in sharpest focus. Everything in front of or behind that distance is blurry. The further we move away from the focus distance, the blurrier things get. The questions become: "How blurry is it? Is that within our acceptable limit? How far from the focus distance do things become unacceptably blurry?"

What we call depth of field (DoF) is the range of distances in front of and behind the point of focus that are acceptably blurry so that things still look like they are in focus.

The amount of depth of field depends on two things: total magnification and aperture. Total magnification includes the following factors: focal length, subject/focus distance, enlargement ratio (which is determined by both sensor size and display size), and viewing distance. The visual acuity of the viewer also contributes to what is acceptably sharp enough to appear in focus instead of blurry.

The distribution of the depth of field in front of and behind the focus distance depends on several factors, primarily focal length and focus distance.

The ratio of any given lens changes as the focus distance is changed. Most lenses approach 1:1 at the minimum focus distance. As the focus distance is increased the rear depth of field increases faster than the front depth of field. There is one focus distance at which the ratio will be 1:2, or one-third in front and two-thirds behind the point of focus.

At short focus distances the ratio approaches 1:1. A true macro lens that can project a virtual image on the sensor or film that is the same size as the object for which it is projecting the image achieves a 1:1 ratio. Even lenses that can not achieve macro focus will demonstrate a ratio very near to 1:1 at their minimum focus distance.

At longer focus distances the rear of the depth of field reaches all the way to infinity and thus the ratio between front and rear DoF approaches 1:∞. The shortest focus distance at which the rear DoF reaches infinity is called the hyperfocal distance. The near depth of field will very closely approach one half the focus distance. That is, the nearest edge of the DoF will be halfway between the camera and the focus distance.

We must also remember that hyperfocal distance, like the concept of depth of field upon which it is based, is really just an illusion, albeit a rather persistent one. Only a single distance will be at sharpest focus. What we call depth of field are the areas on either side of the sharpest focus that are blurred so insignificantly that we still see them as sharp. Please note that the hyperfocal distance will vary based upon a change to any of the factors that affect DoF: focal length, aperture, magnification/display size, viewing distance, etc.

All those calculators and apps always use the value of 0.03mm for the circle of confusion. Why 0.03mm?

Because they assume a format (sensor or film) size of 36x24mm and an enlargement to 8x10 inches (or 8x12") viewed from a distance of 10-12 inches by a person with 20/20 vision. Some lens makers assumed the viewer has 20/15 vision and thus they use a CoC of 0.025 mm instead of 0.03 mm.

The image will appear perfectly sharp when viewed with an angle of view of 50° but when calculating the hyperfocal distance with a circle of confusion diameter limit of 4.34 µm, we should focus at 18.53m which is more than 6 times the hyperfocal distance.

Assuming we're using a 96 ppi monitor, such as a 24" FHD (1920x1080) one, when we view an image at 100% (1 image pixel = 1 screen pixel) from a FF camera with 4.34µm pixel pitch, we're enlarging that 46 MP image by a factor that would result in a viewing size of 86x57 inches! Even accounting for the fact that our eyes are probably more than 10-12 inches from our monitor, that's still a much larger magnification ratio that viewing an 8x10" from 12". Blur that is too small to tell apart from a point at standard viewing conditions (8x10" viewed from 12" by a person with 20/20 vision) will be easy to see when enlarged to 86x57!

The more you enlarge an image, the more you magnify the blur and things that look sharp at smaller sizes gradually become more blurry as we increase the magnification.

As the enlargement ratio increases, the depth of field decreases, and thus we must move the focus point progressively further back to keep infinity with the rear depth of field.

For more, please see:

Why did manufacturers stop including DOF scales on lenses?
Is there a 'rule of thumb' that I can use to estimate depth of field while shooting?
How do you determine the acceptable Circle of Confusion for a particular photo?
Find hyperfocal distance for HD (1920x1080) resolution?
Why I am getting different values for depth of field from calculators vs in-camera DoF preview?
As well as this answer to Simple quick DoF estimate method for prime lens

Answer 3

Circle of Confusion (CoC) is NOT a constant. It is computed uniquely for every film or sensor size. CoC = 0.03 mm only applies to 35 mm film size. CoC is judged to be the smallest hypothetical "point" that after enlargement to viewing size is still viewed as a zero-dimension "point" instead of a larger spot that we can see. Standard viewing size is conventionally assumed to be a 8x10 inch print (smaller prints show better DOF, and larger prints show less DOF). Larger sensors are necessarily not enlarged as much (to 8x10 size), which allows the larger CoC limit. Small sensors are necessarily enlarged more (which enlarges this point too), so they must use a smaller CoC to keep it small.

Smaller sensors literally compute less Depth of Field (than larger sensors) from the smaller CoC they must use, however, in usual practice, to still be able to see a usable normal Field of View, they must use shorter lenses. The shorter lens is a larger (squared) effect than CoC, so in practice, their short lens computes greater Depth of Field, but must still be enlarged more to view. If with the SAME lens, smaller sensors compute less Depth of Field.

Technically, to factor sensor size into the Depth of Field calculation, this maximum permissible CoC used for Depth of Field is the sensor diagonal (mm) divided by (for lack of a better name) a standard of Depth of Field Quality factor or value, just called the Divisor. It is a standard used by convention, but there are a few different standards used for this divisor, divisor assumed to be 1500 by Zeiss, and then Japan after WW II started using 0.03 mm for 35 mm, which if computed, requires a 1442 divisor (to get 0.03 mm from the 35 mm film diagonal 43.267).

The diagonal dimension of 35 mm film (and Full Frame digital) is 43.267 mm. So some formulas compute 35 mm CoC as 43.267 / 1500 = 0.288 mm (some call that 0.29), and others (typically starting in Asia) just call it 0.03 mm, which technically is 43.257 / 1442. But this diagonal and CoC number applies only to 35 mm film size (and the same Full Frame digital sensor size).

So larger or smaller film or sensors have different sizes, and different diagonals, and compute different CoC, and different Depth of Field. Any Depth of Field calculator first wants to know sensor size, from which they deliver the CoC value to compute correct Depth of Field (not all calculators use the same divisor value, but 35 mm film size will normally be from 0.288 to 0.03 mm).

CoC and DOF are NOT about resolution of the sensor, but is about the diagonal size of the sensor, ultimately referring to how much viewing enlargement will be required to enlarge this CoC size as seen in the standard 8x10 inch print size.

No, Hyperfocal is in not outdated in any way. Digital changes nothing about the enlargement process. Hyperfocal works exactly like it has always worked, from same DOF formulas, so it too does compute CoC from sensor diagonal. Any Depth of Field calculator surely also shows Hyperfocal, from the same inputs.