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I'm aware that a teleconverter will reduce the amount of light reaching the film or sensor in a camera, and as such you hear people banding around things like "With a 2x teleconverter this 300mm f/2.8 becomes a 600mm f/5.6".

Given the aperture isn't physically any different, I wonder how that affects depth of field (and associated effects like bokeh). It would make sense that the depth of field remains the same, and the image is merely cropped.

Is it just another one of these things that people say, that may be convenient for exposure calculations, or is there actually a change in the image produced?

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TL;DR version: Teleconverters don't affect depth of field at any given distance. They literally transform your 300 f/2.8 lens into a 600 f/5.6 lens. Any 600 f/5.6 lens, teleconverted or not, will have the same depth of field as a 300 f/2.8 lens.

There's a lot of confusion about the relationship between depth of field, aperture, f-stop, and focal length. In reality, it's all very simple:

Depth of field is determined by focal distance and the apparent size of the front element of the lens.

By apparent diameter, I mean the width of the area of the front element that isn't blocked by the aperture.

You can actually see how big this apparent diameter is, by looking at the front of a lens while it's detached and the aperture is held open.

The relationship between f-stop, focal length, and apparent lens diameter is as follows:

(Size of aperture in mm) = (Focal length in mm) ÷ (f-stop)

For example:

  • The apparent diameter of a 210mm lens set to f/4.5 is 47mm,
  • The apparent diameter of a 70mm lens set to f/4.5 is 15.5mm,
  • The apparent diameter of a 70mm lens set to f/8 is 8.75mm,
  • And the apparent diameter of an 18mm lens set to f/3.5 is a paltry 5.1mm.

Now, back to depth of field. Depth of field is the distance in front of and behind the focused distance that is still "acceptably" in focus. Since the level of acceptable blur differs from person to person, a better way to analyze depth of field is through the circle of confusion.

Here's a handy picture from the Wikipedia page on Circle of Confusion: A diagram explaining the circle of confusion

The circle of confusion is the area on the sensor that is hit by light from a single point. If you're in front of or behind the plane of focus, then your circle of confusion gets bigger. At the plane of focus, the circle of confusion is (ideally, but never in practice) zero.

How quickly your circle of confusion grows as you move away from the plane of focus is a factor of one thing only: The angle between the widest converging lines (the edge of your apparent lens size). Now, this means a few things:

  • If you are focused 10 times further away, you have to go roughly 10 times further from the plane of focus to get the same change in your circle of confusion
  • Two lenses focused at the same distance, with the same apparent size, will result in the same change in your circle of confusion (and therefore the same depth of field.)

Conversely, this also debunks several commonly held beliefs about depth of field:

  • Two lenses at the same f-stop do not necessarily have the same depth of field. The longer lens will have a shorter depth of field, because it has a bigger apparent size. (Sorry, Matt.)
  • Teleconverters, cropping, and smaller sensors do not have any effect on depth of field at a given apparent size (f-stop and focal length).

Take two pictures: one with a 35mm f/1.8, and one with a 210mm f/11. Now, crop the 35mm image to have the same field of view as the other image. They will have almost exactly the same depth of field. Here you go: alt text

  • Firstly, no need to apologise - I was talking about two lenses with the same focal length not two lenses with different focal lengths. Secondly your statement that a telecoverter doesn't affect depth of field could be a little misleading in this case as the question is "does a 300 f/2.8 with a 2x converter have the DOF of a 600 f/2.8 or a 600 f/5.6" so it does affect DOF in the sense that the relative aperture size changed. – Matt Grum Nov 17 '10 at 13:13
  • And the answer is that a 300 f/2.8 with a 2x converter acts EXACTLY like a 600 f/5.6 - in both light gathering ability and in depth of field. – Evan Krall Nov 17 '10 at 17:09
  • Excellent answer. Thanks for bringing CoC into the mix. It should be noted that CoC is affected by the imaging medium, which is why most DOF calculations involve the minimum CoC of the imaging medium in addition to focal length and aperture. This is not really a factor for reductions or direct prints at native resolution, but it is an important factor for enlargements. You can find formulas here: en.wikipedia.org/wiki/Depth_of_field (under DOF Formulas.) – jrista Nov 17 '10 at 20:49
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    It should also be noted that, according to Leslie D. Strobel, in his book "View camera technique", around page 150 or so, he provides strong evidence and some math indicating that cropping DOES affect the amount of DOF present in a final image. While physically DOF as projected by a lens does not change, the perception of the viewer of a final image should not be ignored when calculating DOF. Read more here: books.google.com/… – jrista Nov 17 '10 at 20:55
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The depth of field is that of a F/5.6 lens in the example you state.

Yes, the aperture has not physically changed. However, the ratio of aperture to focal-length has increased.

Therefore, light rays reaching the sensor will be less oblique. That results in increased depth-of-field.

  • By that logic, you get less depth of field by cropping an existing image? – Rowland Shaw Nov 16 '10 at 19:05
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    @Rowland - No. Cropping does not affect the angle at which light enters the lens because it does not increase focal-length. It is the same when mounting a lens on cameras with different sensor sizes, you get a 'cropped' field-of-view but you didn't change focal-length. – Itai Nov 16 '10 at 19:42
  • But there is going to be the same field of view in the centre portion of a shot at 300mm compared to a 600mm lens – Rowland Shaw Nov 16 '10 at 19:57
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    @Rowland - Depth-of-field can be defined by aperture size and focal-length alone. How much you crop changes the field-of-view in the picture (not the lens') but has no effect on depth-of-field. If you need more explanations then I suggest you look up how depth-of-field works. Otherwise it may end up a very long discussion here :) – Itai Nov 16 '10 at 20:10
  • Cropping does affect the apparent DOF, though. If you take a full-frame image that is mostly in-focus in the center, and blurred along the top and bottom edges, cropping WILL introduce a change in the dof that is apparent in the image (assuming the cropped version and FF version are scaled to the same size). Sensor does play a specific role in DOF calculations as well, from the standpoint of CoC. A smaller pixel allows for finer CoC, which affects DOF when enlarging for print. Most official DOF formulas take into account CoC (which is a function of imaging medium) as well length & aperture. – jrista Nov 17 '10 at 20:39
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Can't add anything to Itai's excellent succinct explanation of what's going on, however I'll introduce a proof by Reductio ad Absurdum:

Suppose that using a teleconverter extended the focal length and as a result let in less light but without affecting the depth of field. As well as making a 600 f/5.6 a manufacturer could take an existing a 300 f/2.8 design and incorporate some teleconverter optics but in the same body. They would then be able to offer two versions of the 600mm lens that behave exactly the same exposure wise but one would have the DOF of a 600 f/5.6 and one would have the DOF of a 600 f/2.8.

They could also replace the 300 f/2.8 with a 150 f/1.4 with incorporated telecoverter, and be able to offer 3 versions of the 600 with different DOF et cetera et cetera.

Eventually you arrive at a lens with infintesimally small depth of field but still behaving like a 5.6, which is clearly absurd, thus the original proposition (that the DOF is unchanged by a telecoverter) must be false.

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    Your assumptions are not purely theoretical. Real-life telephoto lenses have a negative group at the back that behaves much like a teleconverter. – Edgar Bonet Nov 16 '10 at 15:04
  • yep, it behaves exactly like a telecoverter in fact, hence the name "tele" "converter", it allows a standard lens to have a focal length longer than the physical length which is the defining feature of a telephoto lens – Matt Grum Nov 16 '10 at 16:26
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    Your argument is invalid, specifically "one would have the DOF of a 600 f/5.6 and one would have the DOF of a 600 f/2.8." In reality, one would have the DOF of a 600 f/5.6, and the other would have the DOF of a 300 f/2.8. Here's the secret: A 300 f/2.8 has the same depth of field as a 600 f/5.6, NOT a 600 f/2.8 – Evan Krall Nov 17 '10 at 19:20
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    @Evan Krall you seem to have missed the point of Reductio ad Absurdum, my point was that assume the premise then you have one lens with the DOF of a 600 f/2.8 and one lens with the DOF of a 600 f/5.6, as this is absurd Ye premise must be false. I'm in agreement with the other answers to this question! – Matt Grum Nov 17 '10 at 22:39
  • sorry guys but when i use a DOF calculator a 300mm f2.8 is not exactly like a 600mm f5.6. the number don´t match.... – user17481 Mar 1 '13 at 11:56
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Depth of field is determined by the focusing distance and physical aperture size (nicely explained by Evan Krall). Adding a teleconverter does not change the physical aperture size; you are simply magnifying the image already projected by the lens, and the focal length and f-number increase together in proportion.

Because the physical aperture size is unchanged, depth of field is unchanged for a given focusing distance.

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A teleconverter is simply spreading out the picture of the lens, like a magnifying glass. It does only change the frame by cropping (faking a higher focus distance) and the illumination level by using an equal amount of light for a bigger amount of pixels. It doesn't alter anything else from the original shot, e.g. the DoF or focus distance.

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I'll answer two questions, the one you asked and the one you also should have asked. I'll also cover various different scenarios (same subject distance without cropping, same subject distance with cropping, and same framing).

How does a teleconverter affect depth of field?

Let's take a look at this. Depth of field is:

DoF = 2 * x_d^2 * N * C / f^2

where f is the focal length, C is the circle of confusion, N is the aperture number, and x_d is the subject distance. If the subject distance stays constant, and you don't decide that due to less cropping C should be increased, a doubling of focal length will double the aperture number as well but C stays constant. Thus, depth of field will be halved by the teleconverter. (If you increase C due to less cropping needed, the depth of field would stay constant.)

However, sometimes you want to keep equal framing. Then, a doubling of focal length will correspond to a doubling of subject distance. Thus, x_d^2 / f^2 stays constant and C stays constant too. However, a doubling of focal length will double N, and thus, depth of field will be doubled with equal framing.

So, TL;DR: it depends on whether you maintain equal framing by changing subject distance (different DoF), whether you crop (same DoF) or whether you just accept a longer focal length gets you a different picture (different DoF, but in the other direction).

You should also have asked:

How does a teleconverter affect background blur?

This is easier. Background blur disc size (assuming background at infinity) is:

b = f * m_s / N = (f/N) * m_s

The aperture opening, f/N is maintained by a teleconverter. m_s is subject magnification, i.e. subject size on the sensor divided by its actual size. If you keep equal framing, m_s stays constant and thus, with equal framing, background blur disc size is constant.

However, if you don't keep equal framing, the 2x teleconverter doubles m_s. Thus, you will get more background blur.

But, if you keep the subject distance the same, and have cropped the original image by 2x, and decide that you no longer need cropping due to the teleconverter, then m_s is doubled by the teleconverter but due to less cropping, the width/height/diagonal of the actually used sensor piece are doubled as well, so blur disc size as a percentage of the actually used sensor piece diagonal stays the same.

So, TL;DR: it depends here again whether you maintain equal framing by changing subject distance (same blur), whether you crop (same blur) or whether you just accept a longer focal length gets you a different picture (different blur).

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The accepted answer is very definitive. It is also wrong. Let's first state what is correct here:

TL;DR version: Teleconverters don't affect depth of field at any given distance.

Wrong.

They literally transform your 300 f/2.8 lens into a 600 f/5.6 lens.

Correct.

Any 600 f/5.6 lens, teleconverted or not, will have the same depth of field as a 300 f/2.8 lens.

Wrong.

Depth of field is determined by focal distance and the apparent size of the front element of the lens.

Partly right, partly wrong. The scene geometry and its relation to depth of field is determined by the apparent size of the entrance pupil of the lens. The entrance pupil is the apparent size of the aperture as seen when looking into the front lens.

Its diameter can be determined by dividing the focal length through the aperture number.

And here we get to the fundamental mistake in the accepted answer: the answer assumes that the scene geometry is the only factor to depth of field. It isn't. Depth of field is defined as the distance where you can detect unsharpness, and unsharpness is defined via the "circle of confusion" criteria. If you use the same projection medium (the same film or the same sensor) and look at the results at a scale where the media's resolution defines the circle of confusion, the magnification of the scene rendition is very relevant to the resulting depth of field.

If you use the same lens with the same settings on a 40MP full frame sensor, its depth of field will be (assuming the lens produces pixel-level sharpness) will be half of what you get on a 10MP full frame sensor but the same as what you'd get on a 10MP crop factor 2 sensor. Ignoring the pixelation, partial images will be indistinguishable.

An in-flange teleconverter in a similar vein retains the image geometry: crops will be indistinguishable as long as you ignore the pixelation. It is, however, the pixelation which defines the circle of confusion, so with a 2x teleconverter, you'll usually get half the depth of field because the pixel as the main contributor to the circle of confusion now covers a finer grid over the original scene.

In contrast to depth of field, quantifying background blur in terms of the pixel size seems non-sensical since its scale is relevant more in relation to the scale of subject features or the frame size. The relation to the subject features is not changed by the teleconverter, in relation to the frame, its extent doubles which means that the blurriness in relation to the finished image is expanded.

In short: things are complex and less than intuitive, but they are so already before adding the teleconverter into the equation. Because of this complexity, you need to specify very carefully the values you are asking about since they are often colloquially used sort-of interchangeably but behave in quite different manners when looking at scene geometry, image geometry, and the resolution of the medium.

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You are confused:

Given the aperture isn't physically any different, I wonder how that affects depth of field (and associated effects like bokeh). It would make sense that the depth of field remains the same, and the image is merely cropped.

Cropping an image only retains the same depth of field when done physically on a print, resulting in a smaller piece of paper, viewed in the same manner as the original paper. As soon as you employ any kind of enlargement in order to better see details, the depth of field (defined via the spread disk of unsharpness becoming discernible under scrutiny) becomes smaller. The only exception is when there is already an absolute limiting factor visible, like film grain or pixel size.

A flange-side teleconverter does not change the size of the entrance pupil and thus works with the same scene but with a smaller crop distributed across the sensor. That gives it less light per pixel (thus double the aperture number) but due to more sensor pixels half the size of the "circle of confusion" and thus half the depth of field. Unless the optical quality of the lens was already at its limit and the additional pixels are unable to provide any additional information.

A filter-side teleconverter is a different deal since it does scale up the size of the entrance pupil and thus usually maintains the same aperture number. So the depth of field then gets smaller both by the smaller crop resolved on the same sensor as well as by the larger entrance pupil looking at the scene.

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