Depth of Field, Focal Length, and Sensor Sizes

[Flammel]

I don't get this:

The article on sensor sizes seems contradicts the articles on depth of field and focal length.

The sensor article says that since larger sensors require you to move closer to the subject or use a longer focal length for the subject to fill the same portion of the frame, a smaller aperture would be needed: Larger sensors have shallow depth of field.

However the articles on DOF and focal length say that focal length does not change depth of field significantly if the subject occupies the same amount of frame: large and small sensors would have the same DOF if the subject occupies the same amount of frame.

Also, you could argue that a cropped sensor is just that: a cropped version of the image that would have been taken by a full frame sensor. Since cropping a picture does not change depth of field, why would the use of a smaller sensor?

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[Colin Southern]

A FF sensor produces a tighter DoF that's equal to an aperture increase of approx 1 stop (over a typical crop-factor camera)

When thinking about crop-factor cameras, it's also important to remember that although the image circle is cropped (thus cropping the field of view), the final (printed / displayed) image has the same physical dimensions as one from a FF camera, which needs to be taken into account. eg you wouldn't print a shot 12 x 8" from a FF camera, but only print one taken from a crop-factor camera 6 x 4".

[eNo]

Play around with the DOF calculator at http://www.dofmaster.com/dofjs.html and see if this starts making some sense.

[arith]

The dof is relating to the lens and is the same whatever the sensor size; or I thought. But it would be mystical if it was otherwise.

[PopsPhotos]

The numerical value of the lens' focal length is calculated as if it is to be used on a standard 35mm format. If only part of the image the lens throws to the back of the camera is being used, the focal length of the lens is effectively different. For this reason, you have to calculate the effective focal length of a particular lens lens for the sensor (film) size in your camera.

Lens made specifically for small sensor cameras are marked truly, when mounted on a small sensor camera. If you put one of those on a 35mm frame sensor (film) camera, they will not project across the entire field of the sensor, giving you vignetting. Thus the focal length marked on that lens is not true when used on that camera.

I don't know if this makes sense to you, but it does to me. I remember using some tele boosters designed for a camera I did not own on a camera I did own. I got vignetting with those attachments, which made for some interesting darkroom sessions.

Pops

[will_c]

Well I think this is more or less right...

Typically over distances of metres to tens of metres DOF is approximately inversely proportional to the square of magnification (all else being equal), so if you decrease the magnification by a factor of m then you increase the DOF by a factor of m-squared, regardless of whether this is achieved by increasing the distance or reducing the focal length.

On a full frame camera, an image of a subject taken with a with a 50mm lens will have a larger DOF than an image of the same subject taken from the same position with an 80mm lens, the difference being a factor of 80/50 squared, i.e. 1.6 squared. If one then crops the 50mm version by 1.6 in each dimension to get the same field of view as the 80mm version and makes a print of the same size from each, then the cropped 50mm image will have to be magnified by 1.6 relative to the 80mm image in the printing process, so its out of focus circles of confusion will be magnified relatively by a factor of 1.6 as well. This partially cancels out the greater DOF that it had in the first place, but not completely (i.e. you end up with 1.6 squared divided by 1.6). The end result is that the DOF of the cropped 50 is greater than that of the straight 80 by approximately the cropping factor (1.6).

Thus smaller sensor cameras have greater DOF when taking the same picture with the same aperture as larger sensor cameras.

DOF is also approximately proportional to relative aperture (e.g. go from F2 to F4 to get twice the DOF).

Will

[Dave Humphries]

I don't get this:

The article on sensor sizes seems contradicts the articles on depth of field and focal length.

The sensor article says that since larger sensors require you to move closer to the subject or use a longer focal length for the subject to fill the same portion of the frame, a smaller aperture would be needed: Larger sensors have shallow depth of field.

However the articles on DOF and focal length say that focal length does not change depth of field significantly if the subject occupies the same amount of frame: large and small sensors would have the same DOF if the subject occupies the same amount of frame.

Also, you could argue that a cropped sensor is just that: a cropped version of the image that would have been taken by a full frame sensor. Since cropping a picture does not change depth of field, why would the use of a smaller sensor?

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Hi Flammel,

While I have not been back and re-read all three tutorials, one important thing that you haven't mentioned in your post, is what aperture we are talking about, since this clearly will have an effect on DoF.

Numerically equal apertures (e.g. "f/8") DO NOT result in the same DoF when you compare between full frame and any other sized sensor. Just as we commonly multiply the focal length the manufacturer states by the sensor crop factor to obtain an idea of the field of view to expect, we must also multiply the aperture value by the crop factor, in order to get the DoF expectation correct.

Thus f/8 on my Nikon D5000 (cf 1.5) will give me the same DoF as f/12 on FF full frame camera.
This is why the compact and bridge cameras have such amazing DoF; the crop factor on my Fuji S6500 is about 4.7, so the lens may say "f/8", but in 35mm terms, I would need f37.6 on a FF camera.

Two caveats to that statements;
a) I haven't played with any DoF calculators, but these may well be effectively doing this conversion 'unseen', and
b) I haven't thought too hard about a FF lens used on a crop factor camera

That said, it is true - I just don't have the mental capacity or time to prove it

EDIT, I see Will has also posted while I have been composing this - I think we're saying the same thing in a different way

Cheers,

[Flammel]

That wasn't my question, really.

I asked:

Does focal length change depth of field if the subject occupies the same portion of the image? (ie. if you move forward/back)

If you use the same exact focal length on a full frame camera as on a cropped sensor camera, would you get the same depth of field?

I'm assuming that all other values, including aperture, are not changed.

What I don't get is this: assuming that a cropped sensor gives you the equivalent of cropping the final image (assuming cropped res. = res. of cropped sensor, pixel size remains constant), how would a larger sensor have a shallower depth of field? Depth of field is a function of the lens. A cropped sensor just uses a smaller portion of the image circle.

So, to say that larger sensors have a smaller depth of field must mean: to achieve the same image as a full frame camera, an otherwise identical cropped sensor must use a wider focal length. Thus, the argument is that longer focal lengths give you a shallower depth of field.

So, the original question: Does focal length affect depth of field?

The article on focal length reads:

"
Note that I did not mention focal length as influencing depth of field. Even though telephoto lenses appear to create a much shallower depth of field, this is mainly because they are often used to make the subject appear bigger when one is unable to get closer. If the subject occupies the same fraction of the viewfinder (constant magnification) for both a telephoto and a wide angle lens, the total depth of field is virtually* constant with focal length! This would of course require you to either get much closer with a wide angle lens or much further with a telephoto lens, as demonstrated.........."

So: Does sensor size directly affect depth of field?

[rpcrowe]

If you are shooting from the same distance with the same focal length lens (I am talking about the actual focal length of the lens, not the equivalent focal length) with both a 1.6x crop camera and a full frame camera; the depth of field of the full frame camera will be greater than the DOF of the 1.6x camera.

Full Frame: 50mm lens using f/2.8 focused at 1.5 meters will provide a .15 meter DOF

1.6x: 50mm lens using f/2.8 focused at 1.5 meters will provide a .09 meter DOF

The reason that the DOF of the full frame camera is greater than the DOF of the 1.6x camera is that you do not need to enlarge the image from the full frame camera as greatly to achieve print size than you need to enlarge the 1.6x image.

There is actually only one lens to subject distance in which the points of the image is in total focus and that is at 1.5 meters for the above calculation. Nearer and farther from 1.5 meters, the points will form circles. These circles are called "circles of confusion" the larger the circle; the less in focus the point will seem. Acceptable circle of confusion is when a point, after being enlarged still seems to be in focus when viewed from arm length distance.

Obviously, the larger the blow-up, the sharper the original points need to be. The acceptable circle of confusion for a full frame camera is .03mm while the 1.6x original image needs to be sharper to make the Same size blow-up. The circle of confusion for a 1.6x camera is .019mm.

Therefore the original image from a 1.6x camera needs to be sharper than the original image from a full-frame camera when both are enlarged to the same size.

TWO FACTORS COME INTO PLAY:

We will usually not shoot a full frame camera from the exact same distance as we would shoot a 1.6x camera and/or we will usually use a longer focal length lens on the full frame camera in order to fill the frame with the image.

If we shoot a portrait with a 1.6x camera using a 50mm lens and fill the frame with the subject, we would need to use an 80mm lens to fill the frame at the same distance if we were using a full frame camera.

Full Frame: 80mm lens using f/2.8 focused at 1.5 meters gives a .06 meter DOF
1.6x crop: 50mm lens using f/2.8 focused at 1.5 meters gives a .09 meter DOF

Therefore, we can say in this case that the 1.6x camera provides a greater depth of field.

What if we don't have an 80mm lens for our full frame camera? We would simply have to move in closer with the 50mm lens to fill the frame than we would with the 1.6x camera. The depth of field in this case would also be greater for the 1.6x camera since you are shooting from a further distance.

So, the answer to the question "Does a full-frame camera give less depth of field than a 1.6x camera is "YES! and NO!" IT DEPENDS HOW YOU LOOK AT THE EQUATION...

[Flammel]

Okay, see this is what I mean: Isn't depth of field a function of the lens? Doesn't the aperture determine the depth of field?

If depth of field is determined by the aperture, how does the camera body influence the depth of field?

[McQ]

Okay, see this is what I mean: Isn't depth of field a function of the lens? Doesn't the aperture determine the depth of field?

If depth of field is determined by the aperture, how does the camera body influence the depth of field?

The two* main factors controlling depth of field are aperture and subject magnification. Aperture is pretty straightforward: larger apertures (smaller f/number's) decrease depth of field. Magnification is where it gets more complicated, because it's actually comprised of two parameters at once: subject distance AND focal length. However, the net result is that higher magnification decreased depth of field for a given aperture.

Yes, focal length does not affect depth of field, but only if the magnification is kept constant. If you stay at the same distance from your subject, using a longer focal length will decrease the depth of field (because this increases subject magnification). This is where sensor size comes into play. At the same subject distance, a larger sensor necessitates that you use a longer focal length in order to produce the same composition. However, this causes the depth of field to decrease, so you also have to use a smaller aperture in order to produce a similar-looking image (both in terms of DoF and composition).

I think a big source of confusion is with the meaning of the word "magnification"; this isn't how big the subject appears in the image, but how much they have been enlarged in absolute terms (on your sensor itself). A larger sensor needs to magnify a subject more in order for the light from this subject to fill the sensor area.

*of course, one's definition of the circle of confusion also affects DoF, but for relative comparisons this value is fixed and standard, so it's irrelevant for the above discussion. Focal length also comes into play a little, but only for extremes of magnification.

[rick55]

I think I'm getting a little confused now.

I agree with McQ and rpcrowe that DOF is different for FF and compact sensors, but perhaps I'm confused about magnification.

I think of magnification as correcting for CoC working backwards from the print. So say I pick the old metric of 0.01" on a 4x6 print. It doesn't matter for this discussion what CoC I choose for the print, or what print size. The data from a 35mm (i.e., full frame) sensor has to be enlarged 4.35 times (6 * 25.4 / 35) to become a 4x6 print. Working backwards, to have a CoC on the print of 0.01", that now has to be 0.0023" on the sensor. A 22mm (compact) sensor has to be enlarged 6.93 times. That means a CoC of 0.0014" on the sensor to get the same 0.01" CoC at the print. And of course, that's a ratio of 1.6.

So for the same CoC where it matters, on the print, you need a 1.6x smaller CoC on a compact sensor. Therefore, your depth of field is shallower for a compact sensor for the same focal length and aperture. The DOF calculators will show you how much. Or you need to use a 1.6 times smaller CoC in running DOF calculations if you expect to get the same results on a print.

Cheers;
Rick

[arith]

That is a lot clearer then.

[McQ]

So for the same CoC where it matters, on the print, you need a 1.6x smaller CoC on a compact sensor. Therefore, your depth of field is shallower for a compact sensor for the same focal length and aperture.

There's a lot of angles to look at this from that are all correct. Your CoC/magnification observations are yet another way.

For those that might see this more clearly with a formula:

Magnification is just the distance from lens to sensor, divided by the distance to the subject from the lens.

M = f/(s-f)
where: M=magnification, f = focal length and s = subject distance

[atlantean]

Well, to be honest, do the understanding and calculation of the DOF, crop factor, etc,... help a photographer take a so-called "perfect" shot?
Personally, i would rather use all the calculators as a sort of "learning apparatus". After all, the human eye is the final judge of all photos ever taken. Imo, the brain should follow the heart to take a good photo.

[rick55]

Well, to be honest, do the understanding and calculation of the DOF, crop factor, etc,... help a photographer take a so-called "perfect" shot?

Calculation of DOF, or having DOF marks on a lens, helps a photographer control another aspect of the shot, just like controlling the exposure. If the photographer isn't predicting the DOF, they aren't defining whether the foreground/background is sharp, they're letting it happen.

Personally, i would rather use all the calculators as a sort of "learning apparatus". After all, the human eye is the final judge of all photos ever taken. Imo, the brain should follow the heart to take a good photo.

They are certainly learning tools. And the human eye is the judge of the result, but it seems to me there are two choices: 1) either calculate or learn to estimate DOF, or 2) take combinations of exposures (e.g., 2.8 @ 1/1000, 4 @ 1/500, 5.6 @ 1/250, 8 @ 1/125) of each shot and see in postprocessing which one has the DOF you want. I think the former will give more reliable results.

Cheers;
Rick

[calexe]

Hello! I'm new here. Hope to give some useful contribution.
1.

Well, to be honest, do the understanding and calculation of the DOF, crop factor, etc,... help a photographer take a so-called "perfect" shot?
good photo.

Yes, for sure. DoF is a key factor for composition. You might need to know what DoF is needed in order to get what you want in focus. You are shooting in a tridimensional world. Shoot a portrait from 0.8m with f/2 on a 50mm lens with an 1.5-1.6 crop camera and you'l get merely 2 cm of DoF. This means hopefully only eyes in focus. If this what you wanted - it is ok, otherwise...
Further, especially in action photo, you might not have the chance to shoot a 2nd photo. If you prepare in advance, including DoF in your thinking, then this would make the difference between having THE PICTURE or having nothing .

2.

Personally, i would rather use all the calculators as a sort of "learning apparatus". After all, the human eye is the final judge of all photos ever taken. Imo, the brain should follow the heart to take a good photo.

No need to learn calculations or to use tables as far as you can multiply by 1 and by 10. . See here how to do it. You may ignore the mathematics in the article and memorize only the final conclusions. Hope it helps.

[carregwen]

Hello! I'm new here. Hope to give some useful contribution.
1.

Yes, for sure. DoF is a key factor for composition. You might need to know what DoF is needed in order to get what you want in focus. You are shooting in a tridimensional world. Shoot a portrait from 0.8m with f/2 on a 50mm lens with an 1.5-1.6 crop camera and you'l get merely 2 cm of DoF. This means hopefully only eyes in focus. If this what you wanted - it is ok, otherwise...
Further, especially in action photo, you might not have the chance to shoot a 2nd photo. If you prepare in advance, including DoF in your thinking, then this would make the difference between having THE PICTURE or having nothing .

2.

No need to learn calculations or to use tables as far as you can multiply by 1 and by 10. . See here how to do it. You may ignore the mathematics in the article and memorize only the final conclusions. Hope it helps.

You could be a useful person to have around! Welcome to here, we look forward to your images, and your math skills!

Some nice images on your website for the tours.

[New Daddy]

Play around with the DOF calculator at http://www.dofmaster.com/dofjs.html and see if this starts making some sense.

This is an old thread, but I'm bumping it up, because I had the same question but the important concepts have already been discussed here.

I think McQ really nailed it. It is also consistent with Wikipedia's DOF entry (http://en.wikipedia.org/wiki/Depth_of_field), which addresses the topic from many angles (no pun intended).

One thing I'd like to point out is the DOF calculator mentioned above (It happens to be the first google result when you do a search on "dof calculator"). I've used it many times too, but after all, I think the calculator is very misleading. At the same focal length (in absolute mm, not in 35mm equivalent), same aperture and same subject distance, the depth of field

Below is from Wikipedia on depth of field. It also says that if the focal length and subject distance are the same, the DOF in different sensor size will depend on the size of the final print. The two sensor will have the same DOF if the final images are not magnified. The smaller sensor will have LARGER DOF only if its final image is magnified to match that of a larger sensor (the second bullet point below). The DOF Master at the above link assumes that this will be the case (i.e., the final images will be magnified to result in the same size regardless of the sensor size) without saying as much on the web page. It took me a while to figure out their assumptions.

Same focal length for both formats
Many small-format digital SLR camera systems allow using many of the same lenses on both full-frame and “cropped format” cameras.

• If, for the same focal length setting, the subject distance is adjusted to provide the same field of view at the subject, at the same f-number and final-image size, the smaller format has greater DOF, as with the “same picture” comparison above.
• If pictures are taken from the same distance using the same f-number, same focal length, and the final images are the same size, the smaller format has less DOF.
• If pictures taken from the same subject distance using the same focal length, are given the same enlargement, both final images will have the same DOF. The pictures from the two formats will differ because of the different angles of view.
• If the larger format is cropped to the captured area of the smaller format, the final images will have the same angle of view, have been given the same enlargement, and have the same DOF.

[Colin Southern]

I cannot remember ever having used a DOF calculator in shooting an image...

I can't ever recall shooting one at F16 and cursing that it couldn't be F15.65 because that's what a calculator said would give me an ideal DoF either ...