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Depth of Field: An Investigation

Introduction

The control over the Depth of Field in an image is one of the more important tools in the photographer's arsenal, since a photo of a subject taken with a large or long depth of field will look quite different from a photo taken with a small or shallow depth of field.

You might wonder why anyone would want to deliberately throw objects in a photograph out of focus. One of the main reasons for narrowing the depth of field is subject isolation. Reducing the depth of field immediately draws the viewer's attention to the subject of your photo, and away from any distracting elements in the background. You might like to do this if you're shooting a portrait of somebody, or perhaps a photo of a bee on a flower.

A cropped portion of this photo demonstrates subject isolation using a shallow depth of field.

Interestingly, use of a shallow depth of field is also used to achieve certain effects in cinematography. In horror films, for example, we are often treated to a shot of the next victim of the serial killer filmed with a shallow depth of field, while the killer approaches as a blurred shadow from behind.

Of course, some types of photography are much more suited to a much longer depth of field - often when there is no particular subject, or while shooting landscapes or seascapes where the scene itself is the subject.

Bokeh is the term that photographers will use to describe the background and foreground blur that accompanies photos taken with a shallow depth of field. It is derived from an (apparently deliberate) mis-spelling of the Japanese word boke, which quite simply means "blur". While subjective, common consensus is that a flat, smooth blur without any discernible edges is preferable.

Parameters that affect Depth of Field

All other things being equal, there are three physical parameters that will alter the depth of field of a scene. In no particular order, these are the subject distance, lens aperture and, most contentiously, the lens focal length. If any of these three are changed without changing the other two, the depth of field of any resulting photograph will change.

It is important to note that while you may not have the opportunity to change all three parameters when composing a photograph, you should be able to change at least one, and often two, regardless of whether you use an advanced SLR camera, or an inexpensive compact digital camera.

While the user of an SLR has the ability to change lenses to obtain longer focal lengths, the easiest way to increase or decrease the focal length of a lens is through the use of a zoom lens, which by definition is a lens which has the ability to move through a range of focal lengths. Most compact digital cameras are also fitted with a zoom lens (notable exceptions like the Ricoh GR and Sigma DP1 are equipped with a fixed focal lengh or prime lens).

Unfortunately for compact digital camera users, for the sake of miniaturisation and sumplicity, camera manufacturers have increasingly started removing the manual controls from their cameras, especially the lower end and ultra compact models. For example, until the release of the Digital IXUS 980IS, none of Canon's ultra compact IXUS line of cameras had full manual controls. However, most advanced compact cameras and all SLRs will have both full manual control, and (in the case of some advanced compacts) an aperture priority mode which sets an appropriate shutter speed for the aperture setting specified by the user. If your compact digital has one of these, you're in luck, although you may need to find the user manual.

Subject distance, of course, needs very little explanation - being the distance between the camera and the object that you are focussing it on. Counter-intuitively, It can also often be the one parameter of the three that you can't change - for example, if you're shooting a bird in a tree or an animal/insect that will run away if you approach it.

The Acceptable Circle of Confusion

As much as we would like to think otherwise, the human eye is not a perfect lens with an infinite amount of resolution. In fact, the resolution of the human eye has been measured to be approximately 50 cycles per degree^[1]. Roughly translated, this means that the eye can resolve two separate point light sources 0.35mm apart, at a distance of 1 metre. If two point light sources are closer than 0.35mm together, they will appear to be one, single point light source when viewed at 1m with the naked eye.

In their article covering Depth of Field, Canon states that they use an Acceptable Circle of Confusion of 0.17mm at normal reading distance^[2]. Given the figure of 0.35mm at 1m stated before, we can see that Canon are using a very reasonable figure of 50cm for their definition of normal reading distance.

However, this value is not the Acceptable Circle of Confusion that Canon uses when deeming whether a lens is in focus or not. While someone shooting 35mm Velvia slides through an old film camera has the option of looking at their image at the size at which it was captured by the camera, mostly images are enlarged to a size larger than the standard 24x36mm size of 135 film prior to viewing. This has the effect of enlarging any imperfections in the original film.

When you have film developed, the standard output size unless you opt for enlargements is a 4x6 inch (10x15cm) print. This is the size that you will get if when you get those 36 prints back in the envelope from the mini-lab or department store. Not so coincidentally, this is the same size as the little pockets in a standard photo album.

The other standard sized print is the 5x7 inch (13x18cm) print. This is the size of a standard "desktop photo frame" print. This is approximately a 5x enlargement of the original 135 format slide (or 25 times the area, since both length and width are 5 times their original size). Interestingly, Canon use a 5x7 inch print as their standard for determining focus - that is, a point light source must have a Acceptable Circle of Confusion of no greater than 0.17mm at normal reading distance when projected at a size of 5x7 inches. Dividing this figure by 5 means that the diameter of the Acceptable Circle of Confusion at the film plane of the camera must be 0.034mm or less for a point to be deemed in focus. For reasons known only to themselves, Canon round this figure up to 0.035mm.

Of course, the world doesn't revolve around 35mm Canon cameras. In fact, at the time of writing, Canon only made three 35mm SLR camera models - the film EOS-1v, and the "full frame" digital EOS 1Ds Mark III and the EOS 5D Mark II. The table below lists the circles of confusion used in different formats, and by different manufacturers. While the exact values aren't important, it's interesting to note that Canon settled on a different value for the Acceptable Circle of Confusion than the other manufacturers for 35mm format. Note also that the circles of confusion for digital cameras with smaller, "cropped" sensors are necessarily smaller since their images need to be enlarged further to achieve the same sized print.

Depth of Field

Now, while this obviously isn't the case, let us assume that we have a perfect lens attached to our hypothetical camera. This means that when the lens is focused on a single point light source, it will project it as a single point light source onto the film plane of the camera (albeit inverted, as with all convergent lenses).

Depth of field and the Acceptable Circle of Confusion.

The yellow vertical line shows the position of the focal plane, while the green vertical line shows the position of the film plane.

In the example diagram, the lens is focused on the white point source, which is therefore sitting on the focal plane. As the incident light from this light source hit the lens, they are refracted, and merge at a single point on the film plane.

The blue point light source shows the extent that the depth of field extends into the foreground of the scene captured by the lens. Just as with the point on the focal plane, once light rays from this point light source are refracted by the lens, they converge at a single point, albeit this time behind the film plane.

Similarly, the red point light source shows the distance that the depth of field extends into the background behind the focal plane. Once again, the incident light rays from the point light source are refracted by the lens into a single point, this time in front of the film plane. The light then continues in a straight line, with the rays diverging from that point onwards.

The magenta coloured segment of the film plane in the diagram shows the diameter of the Acceptable Circle of Confusion. As shown in the diagram, point light sources at the nearest and furthest extremes of the depth of field are not focused as a single point as they pass through the film plane, but instead throw image circles with an identical diameter to the Acceptable Circle of Confusion, meaning that they will still appear to be a single point light source.

While not shown on the diagram, it is evident that any point light source between the nearest and furthest extremes of the depth of field will project an image circle with a diameter smaller than the Acceptable Circle of Confusion, and that the diameter of this circle will decrease as the point source approaches either side of the focal plane. All such points will therefore also appear to be in focus.

It is important to note that the focal plane is not situated at the midpoint between the nearest and furthest extremes of the Depth of Field. In fact, it will always be closer to the nearest extreme than the furthest, meaning that in any photograph, a greater extent of the background will be in focus compared to the foreground.

The Hyperfocal Distance

Before explaining why the Hyperfocal distance exists, the definition of the focal length of a lens should be revisited. The focal length of a lens is defined as the distance from the centre of the lens to the focal point, when the lens is focused on an object at infinite distance.

The obvious question that arises from this definition is that there is no object that we can focus a lens on (even one as sophisticated as the Hubble Space Telescope) that is infinitely far away. While this is true, there becomes a point where an object sufficiently far away from the lens is treated as being "infinitely far" away. While this distance depends on the focal length of the lens (a 16mm Wide Angle lens will reach "infinite focus" at a point much closer than a 600mm Telephoto), any lens that is focused on the Moon, which is over 380,000km away, is likely to be at infinite focus.

Looking at the Depth of Field diagram in the previous section, it can be seen that as a lens focuses on an object progressively further away from its minimum focus distance (the minimum distance at which the lens can still refract incident light to focus it on a single point), the distance between the lens and the point of focus decreases. As the subject distance increases, the distance between the lens and the focal point will approach the lens focal length.

At some stage, these two points will be sufficiently close that regardless of how much further objects in the background happen to be from the primary object of focus, they will not create an image circle on the film plane that has a diameter larger than the Acceptable Circle of Confusion. If the lens is focused on an object positioned precisely on the Hyperfocal distance, any light rays hitting the lens perfectly perpendicular to the film plane (and thus going through a point at the focal length of the lens) will create an image circle with a diameter identical to that of the Acceptable Circle of Confusion.

It should be noted that the hyperfocal distance is dependent on both aperture and focal length, if the diameter of the Acceptable Circle of Confusion remains constant. For any particular lens, the Hyperfocal distance increases at a rate proportional to diameter of the aperture, and at a rate proportional to the square of the lens focal length.

How Subject Distance affects on Depth of Field

At a constant aperture and using a constant focal length, the Depth of Field of a scene will narrow as subject distance approaches the Minimum Focus Distance of the lens (that is, the shortest distance from the film plane that a lens can focus on any subject). Given the same conditions, the depth of field will lengthen as the subject distance moves toward the Hyperfocal distance for the lens. As the subject moves beyond the Hyperfocal distance, the Depth of Field begins to decrease again. In fact, once past the Hyperfocal distance, as a subject/point of focus approaches infinity, the nearest bound of the Depth of Field will approach the Hyperfocal distance.

Subject distance also affects the position of the subject within the Depth of Field. As subject distance decreases, the the subject's position within the Depth of Field approaches the midpoint of the nearest and furthest extent of the Depth of Field. Conversely, when subject distance increases, the proportion of the Depth of Field in front of the subject, compared to that behind it, will decrease.

How Aperture affects Depth of Field

Decreasing the aperture also decreases the angle of refraction.

At the same focal length and the same subject distance, the Depth of Field of a scene will narrow as aperture diameter increases (smaller f-stop value) and lengthen as the aperture diameter decrases. As shown in the diagram, as the aperture diaphragm closes, the light from a point source is diffracted at a shallower angle in order for the point light source to remain in focus.

While the diagram only shows the path taken by light projected from a point source in focus, closing the aperture diaphragm effectively reduces the refracted angle of all light being captured by the lens regardless of whether it is in focus. If we now revisit the diagram demonstrating the boundaries of the Depth of Field in this earlier section, you should note that the cones of light projected from the point light sources on the boundaries of the Depth of Field will be diffracted at a shallower angle should the effective aperture be reduced.

Given that the diameter of the Acceptable Circle of Confusion will not change, it is evident that the image circles thrown by the point light sources previously at the boundaries of the Depth of Field at the wider aperture will now have a smaller diameter than the Acceptable Circle of Confusion. This means that these points now lie within the boundaries of the Depth of Field, which have both shifted further away from the focal plane in their respective directions.

How Focal Length affects Depth of Field

At the same subject distance and aperture f-stop, the Depth of Field of a scene will narrow as the focal length increases, and lengthen as the focal length decreases. In practice, this works out quite well in most cases, since landscape photographers, who generally use "wider" lenses with short focal lengths generally want the maximum amount of depth of field, while telephoto lenses, used to frame subjects at longer distances, are often used by photographers who want subject isolation. Macro photographers, who often use lenses with longer focal lengths at relatively short subject distances, often find they have too little depth of field, meaning they have to use smaller apertures and flash strobes to compensate for the lack of available light.

For very short subject distances, the depth of field, being already significantly reduced due to the subject distance, becomes essentially independent of the lens focal length^[3]. At moderate to large distances, the size of the depth of field is a function of the Hyperfocal distance which, as discussed earlier in this section is proportional to the square of the lens focal length.

Recently, especially amongst reviews and advertising for compact digital cameras, there has been a tendency to express the range of a camera's lens in 35mm equivalent focal length. Along a similar line, users of "cropped" DSLRs talk of a focal length multiplier when mounting a lens of any given focal length onto their cameras. These values relate to the field of view of the camera relative to the "standard" of 135 format film or in more recent times, a "full frame" digital camera. When reading these figures, it is important to note that while these "equivalent focal lengths" provide an accurate description of the framing of any photo, they do not in any way affect the Depth of Field of any scene.

This is where the bad news starts for compact digital camera users and to a much lesser extent, users of "cropped" DSLRs. For example, the Canon PowerShot G10 is advertised as having a 28-140mm "35mm Equivalent" zoom. In reality, the lens has a focal range of 6.1 - 30.5mm, which is a range that would be extremely wide if mounted on a 35mm SLR, "Full Frame" DSLR or even a "cropped" DSLR. This essentially means that unless an extremely short subject distance at the longer end of the zoom is used, it will be difficult to obtain subject isolation, and basically impossible at even moderate subject distances.

Unfortunately for users of compact digital cameras, unless some unforseen exception in the Laws of Physics (and Optics, in particular) is found, this is one disadvantage that will not be bridged by the ongoing march of technology. While camera manufacturers cram an ever increasing amount of megapixels into their camera sensors, the Laws of Optics dictate that a lens of a certain focal length and aperture will have a minimum diameter.

Related Discussion

In the section discussing the Parameters that affect Depth of Field, it was mentioned that the relationship between lens focal length and Depth of Field was contentious. In fact, you don't have to look far on the internet to find many articles stating that the Depth of Field is independent of focal length. An example is this article on popular Photography site, The Luminous Landscape. You might wonder why I've referenced it here given that it seems to completely contradict what has been stated above. In fact, both that article and this one are both correct.

How is this so? As it turns out, the author of that article has stated that if the subject size remains constant within the frame and that the aperture remains constant, then the depth of field is identical at any focal length. If you look into this statement more closely, you will realise that maintaining the same subject size at different focal lengths requires you to change the subject distance. For example, if you were shooting an apple using a 20mm lens, you would need to be physically much closer to the subject than if you were using a 200mm lens. As mentioned earlier in the article, reducing the subject distance reduces the Depth of Field. As it turns out, it seems that the amount that the Depth of Field is reduced by moving closer to the subject is essentially equal to the amount that the Depth of Field is increased by using a lens with a much shorter focal length.

This leads us into another common assertion that a larger format camera will have a narrower Depth of Field than any camera with a smaller format at the same focal length, aperture and framing. While true, the statement is misleading because it suggests that larger-format cameras inherently have a shallower deep of field than smaller format cameras.

In fact, this isn't the case and at the same subject distance, aperture and focal length, a camera of any format will have an identical Depth of Field. Due to the restricted field of view of smaller format cameras compared to those of a larger format, a photographer needs to move a larger format camera closer to the subject to achieve the same framing which, as we now know, reduces the Depth of Field.

Citations

• ^[1] The Image Processing Handbook, John C Russ, 2006.
• ^[2] Canon Professional Network - Depth of Field, Canon Europe, 2009
• ^[3] Wikipedia - Depth of Field, 16 May, 2009