[This page was converted from the Gemini version
at gemini://gemini.ctrl-c.club/~lars_the_bear/hyperfocal.gmi]
This article describes and compares two different methods for optimizing depth-of-field in traditional landscape photography, where both near and distant objects are expected to be in reasonable focus. The use of hyperfocal distance has the benefit of long usage, and is well-understood. Merklinger's method is less widely used, but is much easier to apply in the field.
In this article I've assumed a basic familiarity with photographic concepts such as aperture, exposure, and focus. I haven't presented any of the mathematical analysis, only the results, because the math is well-established and easy to find elsewhere on the Web.
The problem, in essence, is to find camera settings -- lens selection, aperture, etc. -- that will allow both near and distant objects to be in focus. To have objects sharp over a wide distance range is often desirable in landscape photography, because subjects close to the camera give a sense of depth and scale to the image, which might be lacking if the whole scene is distant.
The diagram below shows a typical situation, and one that will be used to illustrate the rest of this article.
The classic depth-of-field problem.
A common approach to photographing this kind scene is to focus on the distant mountains -- which are usually "at infinity" so far as photography is concerned, and hope that the foreground will take care of itself. If one uses a small-ish aperture -- f/8 or smaller -- and a wide-ish angle lens, very often everything will work out fine (see below for an explanation why this is). However, having the nearest subject at only 5m from the camera is a challenge with this hit-and-miss approach.
The traditional best-practice method for dealing with the challenge illustrated above is to make use of hyperfocal distance. Hyperfocal distance is defined in two, somewhat related ways; both will be important in the discussion that follows, so I will quote both.
1. Hyperfocal distance is the closet point at which, if a lens is focused, objects at infinity are acceptably sharp. When so focused, the range of acceptable sharpness extends back from the focus distance to a point half the focus distance from the camera (see the diagram below).
2. Hyperfocal distance is the distance from the camera at which objects just become acceptably sharp, when a lens is focused at infinity.
The first of these formulations of hyperfocal distance is the one that most photographers know about, and is illustrated below.
Hyperfocal distance as it is traditionally employed in landscape photography -- focusing at the hyperfocal distance ensures a depth-of-field from half the hyperfocal distance to infinity.
There are a few points to note about hyperfocal distance.
First, I'm being sloppy when using terms like "distance from the camera". It's reasonable to ask what part of the camera; but for landscape photography where the scene depth runs to miles, this isn't a significant objection.
Second, these two definitions give distances which differ only by a focal length and, again, that difference is irrelevant in landscape work.
Third, it's reasonable to ask what "acceptable focus" means. A lens has at best one plane of perfect focus -- only objects at one exact horizontal distance from the lens axis can ever be truly in focus. The uncertainty in how to specify acceptable focus leads to significant contention, and is a point that I will take up again later.
Fourth, the point of focus is a surprisingly short distance into the scene. It strikes many photographers as counter-intuitive that, in a scene where distant objects may be miles away, the hyperfocal method tells them to set the focus at, say, ten metres. The diagram above does not really show how peculiar this situation really is, because I can't draw it to scale. No other diagram I've seen of hyperfocal distance does any better -- there's an intractable problem of scale here. But the hyperfocal distance really is generally as short as the math tells us it is.
Fifth, and this is a direct consequence of the previous point, the distant objects are typically at the far boundary of the zone of acceptable focus. Your distant mountains will just be sharp, according to the definition of sharpness you've adopted (see below). The point of best focus is, of course, the hyperfocal distance and, very likely, there's nothing in particular of interest at that distance. That's just a statistical matter -- if your scene extends from (say) five metres to five miles, odds are that there's nothing much going on at the exact point of focus.
When comparing with Merklinger's method, this last point is particularly significant, because Merklinger would have us focus on the distant objects, which will therefore be at the point of best focus. The hyperfocal method generally offers sharpest focus in the foreground regions of the scene. More on this, somewhat controversial, claim later.
The hyperfocal method turns on being able to define what "acceptable focus" means. Only objects at one distance (broadly) are in perfect focus; everything else will be out of focus, to some extent. The notion of "circle of confusion" is an attempt to objectify the subjective notion of acceptable focus. The circle of confusion is (broadly) how close two features can be, before they can no longer be resolved as separate features. This is, in principle, an objective measure because it depends on the resolution of the film emulsion or digital sensor.
However, in modern practice these resolutions are generally higher than the resolution of the human eye, when frames are printed at common sizes. Therefore, most photographers have adopted a conventional circle of confusion of 0.02mm, which is derived from the resolving ability of the human eye when looking at a regular print at arm's length. Many computer programs or smartphone apps that provide hyperfocal calculations purport to be able to use a circle of confusion that is tailored to a specific camera; but how they can do that with no knowledge of how the images will be post-processed and presented, I really couldn't say. The conventional figure of 0.02mm is pretty arbitrary, to be honest, but it is well established. All the calculations used in this article are based on this figure.
For the record, hyperfocal distance is calculated using the following expression:
H = ( l * l / (c * f) ) + l
where "H" is the hyperfocal distance, "l" is the focal length of the lens, "c" is the circle of confusion, "f" is the f-number (5.6, 8, 11...). Be aware that if you specify the focal length in millimetres, the hyperfocal distance will also be in millimetres. Note that the "+l" term in this expression may usually be omitted as it is small, and it is this small term that forms the (small) difference between the two different definitions of hyperfocal distance I gave earlier.
There are similar expressions for working out the nearest and furthest points of focus, but I'm not going to give them, as they are well-known -- just do a Web search for 'depth of field formulae.'
So far as this article is concerned, his method for dealing with scenes that extend to infinity (or, at least, for miles) can be expressed very simply:
Focus on the most distant object in the scene, and set an aperture whose diameter is equivalent to the "disk of confusion". The disk of confusion is the smallest distance between objects in the scene that need to be resolved.
When this method is applied, I will refer to the aperture selected as the "Merklinger aperture" for simplicity. I should point out that Merklinger's treatise deals with more situations than simply maximizing depth-of-field, and is mathematically rigorous.
Merklinger's method replaces the notion of 'circle of confusion' with what he calls a 'disk of confusion'. The difference is that Merklinger is concerned with features in the world, rather than in the resulting image. A disk of confusion is no less arbitrary than a circle of confusion, and does not have the benefit of fifty years of practical experience to back up the conventional values used.
In principle the disk of confusion does not depend on the way that the image is post-processed and displayed, provided that the resolution of the camera sensor, printer, etc., are adequate (and they probably are with modern equipment). In practice, images are often displayed at less than life-size, and a feature that could be resolved in life might only be resolved using a magnifying glass in a printed image. So there is a risk that the method might be too conservative -- that it might force the use of a smaller aperture than is really needed. However, as I will show, in practice this does not seem to be the case, at least with values of disk of confusion commonly used.
In practice, photographers using Merklinger's method seem to have settled on a disk of confusion of 5mm-6mm, rather as many who use hyperfocal distance have settled on a circle of confusion of 0.02mm. 6mm is sufficient to distinguish individual blades of grass, or two facial moles from one another, or texture lines in a rock. However, if the nearest subject is very close, setting a lower value of disk of confusion might be appropriate.
The tables below show the aperture that needs to be set for two different disks of confusion values: 2mm-4mm and 5mm-6mm. The reason there are ranges here is because in practice we can't set an arbitrary f-stop: we're limited to the values provided by lens and camera manufacturers. Consequently, it doesn't make any difference whether the disk of confusion adopted is 5mm or 6mm -- the calculated aperture rounds up to the same f-stop (we need to round the f-number up, rather than down, because we want to err on the side of a smaller aperture and increased depth of field. Probably.)
Focal length Merklinger aperture Nearest point of acceptable focus 18 mm f/4 4.0m 27 mm f/5.6 6.5m 35 mm f/8 7.7m 50 mm f/11 11m
Above: Merklinger's aperture for a disk of confusion of 5mm-6mm, for various lens focal lengths. With this aperture, and the lens focused at infinity, then features 5mm (or so) or larger will be distinguishable. The nearest point of acceptable focus according to the conventional depth-of-field formula is shown for comparison.
Focal length Merklinger aperture Nearest point of acceptable focus 18 mm f/8 2.0m 27 mm f/11 3.3m 35 mm f/16 3.9m 50 mm f/22 5.7m
Above: Merklinger's aperture for a disk of confusion of 2mm-4mm, for various lens focal lengths. With this aperture, and the lens focused at infinity, then features 2mm (or so) or larger will be distinguishable. The nearest point of acceptable focus according to the conventional depth-of-field formula is shown for comparison.
These tables tell us, for example, that if we want to use a 27mm lens, and will accept a 6mm disk of confusion, then we should set f/5.6 (or smaller aperture) and focus at infinity. Conventional depth-of-field formulae tell us that the point of nearest acceptable focus is 4m at this point. We can't find out the point of nearest focus using Merklinger's method, but we can determine that features at least as large as 6mm will be resolvable.
An interesting, and coincidental, feature of the 6mm disk of confusion is that the point of nearest focus is, within a metre, the same as the f-number. So in a sense, Merklinger's method does give us a way to estimate the point of nearest focus. Sadly, there's no simple correspondence (that I could find) between f-number and the near point with any other disk of confusion. However, I've calculated the point of nearest focus easily enough because it is by definition the same as the hyperfocal distance with the lens focused at infinity (see Definition 1 above.)
Merklinger's method is extremely simple to apply in the field -- you don't need to calculate anything, you just need to remember a handful of numbers. If you're content to work with a 5mm-6mm disk of confusion, you just have to remember one f-number for each lens: f/4 for 18mm, f/5.6 for 27mm, f/8 for 35mm, f/11 for 50mm, and so on. Of course you can use an aperture smaller than any of these, so long as conditions allow.
Note: these lens focal lengths are the real focal lengths, not SLR-equivalent focal lengths. Broadly, a 35mm lens on a camera with an APC-S sensor will have an angle of view roughly the same as a 50mm lens on a full-frame sensor. This fact is completely irrelevant to Merklinger's method -- we use the focal length engraved on the lens.
With the 6mm disk of confusion value, we need also to remember not to have in the scene anything closer in metres than the f-number; again, this is an easy rule of thumb to remember.
If we focus at the hyperfocal distance, then objects at infinity will always (just) be in focus. So with the hyperfocal method we need to consider particularly how the near point (point of closest focus) varies with aperture. This is illustrated for a range of lens focal lengths in the
graph below.
Graph of variation of nearest point of focus with aperture.
This graph shows how the point of nearest focus varies with aperture, when focused at the hyperfocal distance, for various lens focal lengths. Notice that to be sharp at 5m, an aperture of f/8 will suffice for any of the lenses. However, the 18mm lens should be sharp from about 5m to infinity for <i>any</i> aperture setting. It's hard to take an out-of-focus landscape shot with lens if you set the focus manually to something reasonably close to the hyperfocal distance (which, of course, varies with aperture). For all other lenses, more care is required
With this method, even with the closest object in the scene only 5m away, most lenses will offer a range of apertures that will keep the whole scene sharp. In fact, any lens with a focal length up to 35mm will be sharp from about 5m to infinity with any aperture setting f/5.6 or smaller.
How does this compare with the Merklinger method? Using the 6mm disk of confusion value, looking at the table above we see that we should focus at infinity, and set an aperture of f/4 for the 18mm lens, f/5.6 for the 27mm, and f/8 for the 35mm. Using the hyperfocal distance, these settings give near focus points of 4m, 6.5m, and 7.7m respectively. With this method, only the 18mm lens will put the 5m object in the zone of focus. However, the other lenses only put the near point a few metres away, which might matter little in practice -- since we don't know how comparable the circle of confusion and disk of confusion are.
What the hyperfocal method gives us, however, is the knowledge that we could open up to f/2.8 with the 18mm lens, rather than the f/4 offered by Merklinger, and still have the 5m object in the focus zone. So, arguably, the hyperfocal method gives is a bit of extra flexibility where keeping near objects sharp is concerned. This is hardly a surprise -- we would be focusing only 10m-20m into the scene with this method.
Focusing with the Merklinger method is trivial -- in practice we focus (automatically or manually) on the most distant point of the scene, or just set manual focus to the infinity stop, or as near as the lens will get to it. Focusing on distant objects, rather than infinity, is probably a little better in landscape work, because this will tend to move the near point a bit closer to the camera. In practice, however, it's unlikely to make a discernible distance.
Focusing at the hyperfocal length, however, is a different matter, particularly if your lens does not have a distance scale, or the scale is not particularly precise (not unusual). It's worth thinking about how the near and far focus points will be affected by errors in focus. As an example, for the 35mm lens at f/5.6, the following graphs show the variation in near and far points. The vertical dotted line in each graph shows the hyperfocal point -- the place we ought to be focusing.
Graph showing variation of nearest and further points of focus with aperture.
The graph above shows how the nearest and furthest points of focus vary with focus point, with aperture f/5.6 and a 35mm lens. The hyperfocal distance with this configuration is 10.98m (dashed vertical line). The crucial point here is how rapidly the far point collapses if the lens is focused too close: focusing even at 10m (about 1m too close) reduces the far point to 100m</i>
The near point varies only slightly with focus distance -- in fact it varies less than the focus distance error in this case: focusing five metres too far into the scene only moves the near point one metre away. However, the far point is a different story. Focusing too far into the scene does not move the far point back (as it is already at infinity), but focusing too close has a dramatic effect on the far point. Focusing even one metre too close reduces the far point from infinity to only about 100m. This could well ruin the shot. Most likely your lens or camera will not allow focus to be manually set with a precision of one metre, so you'd have to compensate for this error (as photographers generally do).
One stop down (smaller aperture) will nearly always fix the problem with far point when focus distance is uncertain, and will bring the near point closer, too. But this won't help when the lens is already fully stopped down, or there isn't enough light to stop down further. In addition, some lenses will lose sharpness owing to diffraction at smaller aperture than f/11 or so.
The Merklinger method is unaffected by focus position errors, because focus and the far point are always at infinity.
Because there is no long-standing convention about how to choose the disk of confusion in Merklinger's method, it's interesting to see how the near focus point varies as different values are chosen. Because the Merklinger method always has sharp focus at infinity, we don't need to consider the far point. The results for a 27mm lens are shown below.
Graph of how the near point varies with disk of confusion.
The graph above shows how the near point varies with the chosen disk of confusion in Merklinger's method. This graph is for a 27mm lens and, although the gradient of the line is different for other lenses, it is always a straight line.
As we might expect, the larger we choose the disk of confusion, and thus the larger the aperture, the near point moves further away and depth-of-field decreases. The relationship between near point and disk of confusion is a linear one so, although choosing 'wrongly' will affect which near objects are sharp (as it should) it won't affect it disproportionately, in the way that focus position errors do with the far point using the hyperfocal method.
It's worth bearing in mind that a disk of confusion of 1mm is probably not achievable with any common lens -- common lenses won't stop down to 1mm diameter.
It's worth wondering how much any of this complexity is actually necessary. Suppose we just set f/8 and focus at infinity? Of course distant objects will be sharp, so we need to consider only the near point.
Variation of near point when focused at infinity.
With aperture at f/8 and focus at infinity, objects as close as 16m are sharp, with any lens up to 50mm. For more wide-angle lenses, the near point is even closer
This combination, f/8-infinity, will produce good results for a range of lens focal lengths, and very good results for wide-angle lenses, and requires no calculation or even a lot of thinking. What's more, the f/8 aperture is likely to correspond to a workable shutter speed in a whole range of lighting conditions in a way that f/16, for example, won't.
What we have to be careful not to do, in landscape work at least, is to set f/8 and focus on the nearest object in the scene, if that object is only 5m away. We'll get away with it with lenses 27mm or shorter; but for 35mm and up the far point will be less than 30m away.
The key difference between the hyperfocal and Merklinger methods is that the hyperfocal method tends to emphasise sharp focus for near objects, whilst Merklinger favours distant objects. Since we have chosen a circle of confusion or disk of confusion, the methods should, in principle, produce comparable focus results, because in both cases both near and far objects will be 'in focus' within the criteria chosen of in-focus-ness. However, because we can't focus exactly at a particular point (hyperfocal method), and because we don't really have much experience of choosing a disk of confusion (Merklinger method), the near/far object distinction may well be relevant in the field.
So which to use? As always, it depends on the circumstances.
In the end the choice of method might come down to a simple question: which is more important -- confidence in close focus or confidence in distant focus? In practice, in landscape photography distant objects are often unsharp anyway, owing to atmospheric haze. Close objects, however, are usual capable of sharp focus.
In really demanding situations, where the nearest subject is only a few metres from the camera, then there's probably no alternative to using the hyperfocal distance calculation. This is particularly true if the foreground is clear and well lit, and the background dark or hazy. However, some care needs to be taken to ensure that you don't set the focus point too close. In most other situations, Merklinger's method is likely to produce perfectly decent results, with a whole lot less math.
[ Last updated Tue 22 Feb 19:28:25 GMT 2022 ]