# Why is the area in focus in front of the focus distance narrower than behind it?

I guess the title and the picture explain my question well.

• Please provide a link to the page or article from which you sourced that image. Feb 27, 2017 at 12:26
• A comment on most of the provided answers: it's partly a measure of our subjective impression of in/out of focus. Every traced ray is following a straight line (after the last lens element), so what matters, as in the provided links in some answers, is whether we're interested in keeping nearer or more distant objects in better focus. Feb 27, 2017 at 12:35

Why is the area in focus in front of the focus distance narrower than behind it?

It isn't. Not always. Just usually for landscape shooters using wider lenses aiming somewhere not that close. :) The 1/3-2/3 proportion rule is basically a rule of thumb that does not apply in all cases.

The larger your aperture, longer your lens, or closer your shooting distance (i.e., thinner the depth of field), the more that proportion will actually range closer to 50/50 (think: hyperfocal distance).

• At hyperfocal distances the ratio approaches 1:∞. At distances approaching unity (macro) the ratio approaches 1:1 Feb 27, 2017 at 18:54

Depth of field is all about angles and being able to tell a difference between them. As things get further away, the angles change less and less. If you move forward 1m at a distance of 2m, you may change the angle by 30 degrees. If you move 1m closer at a distance of 2000m, the angle hardly changes at all.

The proportion of near and far DoF is this same principle, but "compacted" around the plane of best focus.

• Accepted that DoF is about angles in terms of the minute angles at which blur is perceived as a point. But 30°? Do you mean 30 arc seconds? Feb 27, 2017 at 12:12
• @MichaelClark "if you move 1 meter forward at 2 meters, you may change an angle by 30 degrees." It is most assuredly not 30 seconds of arc. My comment makes a point about the geometry of relative distances, and then connects that to depth of field, as DoF is this essential geometry on a small scale. The angles relevant to DoF itself are more on the scale of micro-radians in most cases. Feb 27, 2017 at 18:10
• The only angles that matter with regard to DoF are those that are just on either side of what can be differentiated by human vision. As I am sure you are aware, an arcsecond is a more precise unit of measurement than a micro-radian by about a factor of 5. Feb 27, 2017 at 18:51
• Please consult wikipedia for the definition of analogy. Feb 28, 2017 at 0:16
• When both analogies use angles that are different by a factor of about 360 it can get confusing exactly what you are attempting to communicate. Feb 28, 2017 at 0:58

Why is the area in focus in front of the focus distance narrower than behind it?

It isn't aways.

In fact it very rarely is exactly a 1:2 ratio as depicted in your illustration. The rule of thumb you have cited is only approximate. For every focal length and aperture there is only one precise focus distance where the ratio between front and rear Depth of Field is exactly 1:2.

The ratio of the DoF in front of the point of focus to the DoF behind the point of focus will be different for every focus distance when using the same lens and aperture setting (assuming the other conditions are also the same: magnification/display size, viewing distance, assumptions about the viewer's vision, etc.).

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.

For example, using a 300mm telephoto lens with a maximum magnification of only .24X and a MFD of 59 inches the DoF calculates to 1:1 within the limits of rounding the distance to one one-hundredth of an inch. With a FF camera and a 300mm lens at f/4 the DoF will be 0.09 inches in front of the focus distance and 0.09 inches behind the focus distance with standard display and viewing conditions. In reality the near DoF will be microscopically smaller than the rear DoF. This difference is not perceptible and utterly meaningless, though. One has to increase focus distance to 133 inches before the near DoF at 0.54 inches is smaller to two significant digits than the rear DoF at 0.55 inches.

With a 30mm lens at f/4 the 1:2 ratio is achieved at a focus distance of 92 inches. At the macro focus distance for a 30mm lens of 2.3622 inches the ratio is 1:1. With a focus distance of 287 inches (just short of the hyperfocal distance) the ratio is 1:61.4 with a near DoF of 141.2 inches and a far DoF of 8674.3 inches.

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. For why this is the case, please see:

• That level of precision is all well and good if you're measuring precision of acutance at different focus distances only a few microns apart with something like the OLAF system. Well, at least if you remember to put the cover plate in front of the sensor on the test bench it is. It's not really needed when all one wants to know is how far in front of and behind the point of focus things will look acceptably sharp when looking at an image displayed at a specific size, viewed from a specific distance, by a person with a specific visual acuity. Feb 27, 2017 at 18:46
• "It is not well defined because the distance between the hyperfocal plane and "infinity" depends on what "infinity" is. If infinity is 1e20 meters or 1e99 meters matters." You're obviously not using the same definition of hyperfocal distance as I. Since the hyperfocal distance is the focus distance at which the rear DoF extends to infinity, if one redefines infinity then one must also recalculate the hyperfocal distance based upon the changed definition. Again, this is significant for precise scientific measurement, but not so much for typical photo viewing. Feb 27, 2017 at 19:03
• It all depends on whether your goal is to measure, oops, I mean view microscopic pinholes or to calculate blur that is acceptable until it can be perceived by a viewer. The two are related but don't necessarily require the same level of precision. Further, are we talking about ray tracing lenses that are theoretically perfect according to their design parameters or are we talking about measuring manufactured lenses that vary to one degree or another from that design? You seem to keep switching back and forth. Feb 28, 2017 at 1:07
• Dude, we've been using it for decades before a pixel had anything to do with taking a photo. And yes, film is similarly limited by the size of the chemical grains in the emulsion. But as was the case then and is still the case now for the vast majority of camera/lens combinations in use the resolution limits of the lens are most often the limiting factor, not the resolution and/or pixel pitch of the sensor. At the upper end of the pyramid sensors are sometimes out-resolving lenses, but there are a lot more 18-55mm f/3.5-5.6 and 50mm f/1.8 lenses on entry level interchangeable lens cameras... Feb 28, 2017 at 1:41
• Yes. Because back in the dark ages we were taught that we had to account for print size and viewing distance as well as film format, focal length, and aperture. If shooting 135 film we knew that a 16x20 print would have half the indicated DoF as a chart calculated for an 8x10 print would. The reason most shooters today can't get the results they want from a DoF calculation is because they don't realize they're using CoC needed for an 8x10 but when they're pixel peeping a 20 MB file on a 23" HD monitor that they're looking at a piece of a 54x36 inch print! Feb 28, 2017 at 2:16

You are right, the DOF behind the subject is larger than the DOF before it, but the difference can be very small. That the distance behind is larger can be seen if you look at the formulas for DOF (from mhohner.de: Optical formulas):

Front DOF = cFd^2 / (f^2+cFd)
Rear DOF = cFd^2 / (f^2-cFd)

f is the focal length
d is the focus (or subject) distance
F is the F number of the lens (2.8, 4, 5.6 etc)
c is the circle of confusion (usually around 0.03mm)

You see that the denominator for the rear DOF (f^2-cFd) is always smaller than the denominator for the front DOF (f^2+cFd), which makes the rear DOF larger.

To understand lenses and how they image, you need to know that the lens projects an image of the outside world on the surface of film or digital sensor. Upon close examination you will discover that this image is comprised of countless circles of light. These circles are called circles of confusion because their boundaries are indistinct and they are jumbled end-to-end alongside countless neighboring circles.

We deem an image to be sharp when these image forming circles are so tiny we can’t perceive them as disks. Instead we see a tiny point of light that is not discernable as a disk. This works out to be ½ millimeter viewed from a distance of 500mm. In other words, smaller is better.

Light rays from the subject play on the surface of the lens. As they pass through the lens, the shape of the lens alters their path. They are caused to bend inward (refract). We can trace out this path; it resembles two ice-cream cones set pointy end to pointy end. When we focus, we are adjusting the position of the surface of the digital sensor (or film) as it relates to the lens, so the apex of this cone of light just kisses the light sensitive surface. If achieved, tiny circles result. If the surface is not exactly at the apex of this cone, the circles will be not so small. Sharpness of image is dependent on these circles remaining small.

Now the back-focus (distance lens to image plane) is a variable based on subject distance. If the object is at infinity (as far as the eye can see), the back-focus is at its shortest. We measure the back-focus length when imaging an object at infinity. If the object is closer, the back-focus distance is elongated. The closer the object, the longer the back-focus. At unity (life-size) the back-focus is elongated to twice the focal length. If the object is just shy of infinity, the back-focus is only slightly elongated.

What I am trying to tell you is this: Subject distance dictates the length of the back focus. As you move closer and closer to the subject, the magnitude of the back-focus elongation increases. The bottom line is -- objects far from the camera have nearly the same back focus distance over an extended range. Conversely, objects close to the camera have expanded back-focus, and this distance changes radically with distance changes. It is these back-focus changes that change the size of the circle of confusion. The result is: Depth-of-field extends approximately 2/3 forward and 1/3 back towards the camera from the point focused upon.