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It has been mentioned at a few places that a larger sensor results in images with a shallower depth of field. Example image:

APS-C Canon 30D left, FF Canon 5D right, same lens, same composition, both f/2.8

APS-C Canon 30D left, FF Canon 5D right, same lens, same composition, both f/2.8

I understand how sensor size would relate to, for example, field of view, but the relationship with depth of field does not seem straightforward.

It actually seems contradictory - I have more wells on my sensor, and I am able to focus on less number of points.

What is the reason for this effect?

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See this question and its answers photo.stackexchange.com/questions/10079. The relationship is actually pretty direct. –  mattdm May 16 '11 at 13:36
    
agreed with Matt. Looks duplicate to me. –  epoon May 25 '13 at 2:59
    
It's not correct to say that the same lens has been used here. In your example the lens has been zoomed in (focal length has been changed). This is very important when we talk about DOF. –  Sunny Reborn Pony Aug 19 at 8:50

6 Answers 6

up vote 28 down vote accepted

Firstly, the number of wells on the sensor has no bearing on where you can focus or 'how much' you can focus on. Out of focus light is still light hitting the sensor.

Simply put, you have shallower depth of field with a full-frame sensor because you have to get closer to the subject (or zoom in) in order to fill the frame. Note that in your example it says same composition: the camera has been moved or the focal length changed in order to fill the frame with the bottle.

To put it another way, if you fix a tripod in place and take a shot with an APS-C camera with the bottle filling the frame, then take the same shot in exactly the same position with a full-frame camera, you will have more space around the bottle. So you will either need to zoom in or move the camera closer to achieve the same shot where the bottle fills the frame, either of which will alter the depth of field,

See this excellent summary of sensor sizes and their effects.

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-1 full frame sensors do inherently have less depth of field, it's not to do with getting closer, in that example the camera was not moved in order to fill the frame with the bottle - I know 'cos I shot it! –  Matt Grum May 16 '11 at 13:33
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Right. I don't mean you have to move the camera closer (or zoom in) in order to get a shallower DoF, I mean you have to move closer (or zoom in) to fill the frame which results in shallower DoF. –  ElendilTheTall May 16 '11 at 13:52
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Yeah I changed focal length, as far as I'm concerned zooming counts as using the same lens (others seem to disagree) –  Matt Grum May 16 '11 at 18:09
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When you are zooming you are changing the focal length - and it is focal length that is the critical aspect here. Whether you do it by swapping one prime lens for another or by zooming a zoom lens is irrelevant. –  Staale S May 18 '11 at 8:21
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This is wrong answer. DOF changes because the circle of confusion changes. –  epoon May 25 '13 at 10:39

Without moving the camera you will get shallower depth of field when using a larger sensor whilst maintaining aperture ratio and field of view (whilst maintaining the same final output size). I.e. if you keep the same settings but zoom the FF camera to match the angle of view (yielding an equivalent composition).

Depth of field is a function of the physical size of the aperture. A 75mm f/4.0 lens on a full frame camera has a physical aperture that is 75/4 i.e. 18.75mm, whereas a 50mm f/4.0 lens on a 1.5x crop camera has a physical aperture that is 50/4, 12.5mm

From this it is easy to work out what equivalent aperture you'd need to get the same depth of field with both cameras/lenses, to get a physical aperture of 18.75mm with a 50mm lens it would have to be f/2.6 (50/18.75) which is more than a whole stop faster!

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well, I thought same composition meant same aperture.. –  Lazer May 16 '11 at 13:43
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@Lazer composition usually refers to the position/orientation of objects in the frame, not to camera settings such as aperture or shutter speed. –  Matt Grum May 16 '11 at 13:46
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@MattGrum - "physical size of the aperture"! That is exactly the variable influencing the DoF, and not the f#, which is a relative figure. +1. –  ysap May 16 '11 at 17:16
    
Might want to change "without moving the camera". To achieve the same framing when changing from a smaller to a larger sensor but maintaining lens and aperture (as stated in the quote in the question), you would indeed need to move the camera closer since you now have a wider FoV...and thats ultimately what changes DoF. –  jrista May 16 '11 at 17:57
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@jrista Of course you have to have to scale to the same output size when comparing sensors, otherwise if you compare a P&S with a DSLR you wind up comparing a 6"x4" to a postage stamp. It just doesn't make sense! There is exactly the same number of factors in play when comparing sensors and changing focal length and when comparing sensors by changing focal length: one. But changing focal length yields images that look roughly the same and have the same perspective, so that's clearly the right choice to me. –  Matt Grum May 16 '11 at 21:22

maybe the clearest way to explain this is: if you compare it to a cropped (aps-c) sensor, shooting the same thing from the same point, to get the same result (framing) on full frame you need a longer focal length; as a matter of fact, longer lenses give a shallower depth of field.

edit(more accurate, more annoying): so it's uncorrect and misleading to say a bigger sensor leads to a shallower depth of field, at least directly, no way this could actually happen.

Depth of field really depends on focal lenght and f-number ONLY; on every possible sensor (or film) the same lens (same settings) will give the same depth of field. If we assume every camera we put this given lens on has the right mount to fit it and the same distance between the lens and the focal plane to get focus right, all we get comparing all possible sensor/film formats is different cropped parts of the same projected image circle.

UPDATE: Here's an update to tell my commenters (and everybody interested) why I didn't account for CoC in relation to sensor size in my answer above. Most people who may read this already know probably more than me about this subject and may find stupid to read something they already know; keep in mind I'm just trying to put this in perspective.

For those who don't know, a Circle of Confusion is one among infinite dots of light a lens projects on its focal plane, in our case the part of a camera where a sensor or some film is. The closest this dot gets to a point (which has no size, but our dot is never a point because lenses are not perfect), the sharper the image (in that area), and vice versa. (A rough definition just to introduce newcomers to the subject, experts please don't waste time criticizing this).

I think we can agree the maximum permissible CoC is a value used to determine with mathematical certainty what is in focus and what is not; it serves the purpose of "drawing a line" (as actually there is a smooth transition between in focus and not in focus), and it may well be adjusted according to the print size you want to achieve, as a larger print would make this transition more evident and, at some level, one would notice that some areas, appearing to be in focus looking at a smaller print of the same image, are actually out of focus.

Applying formulas in which one element is the CoC to determine DOF is an analytic process, so it's a way to understand what's going on, not changing things (i.e. the image a lens is projecting on a focal plane). The fact that CoCs exist and that one needs to decide what's the right CoC size to produce a sharp image of a given size is not changing the way a lens works across different sensors/film formats.

If you want to get a large print, I understand it may be needed to consider a different acceptable sharpness. In my answer above I assume (and I declared I do) the focal plane is always the same, that's what's happening in modern DSLRs we're talking about: the different rendition of a lens on different bodies is just a matter of cropping.

an ugly oversimplified drawing sometimes helps that's it

making two print of the same size from the two different sensors will give varying results depending on the resolution of the two sensors.

if we assume pixel density is the same for both sensors and we print at a fixed resolution, the prints from the smaller sensor will look exactly like the larger ones, just cropped.

if again we assume pixel density is the same and we print at a fixed size, the prints from the smaller sensor will look like enlarged crops of the larger ones, at a lower quality.

if we simply and more correctly to the purpose of our analysis assume both have enough pixels to print a fixed size we want without noticeable loss in quality, what we get in prints from the smaller sensor is like a cropped enlargement of the print from the bigger sensor, so we can indeed see a difference in depth of field, that is, we see more detail so it's easier to spot slightly out-of-focus areas. This we could have accounted for if we decided to put a larger CoC in the formula when, while shooting, we calculated the DOF. Who's so rough a photographer not to do so? ;-)

However, I'm not really mocking anyone. I'm just saying, long story short: if you do big prints you might want to squeeze a bit more DOF out of your aperture selecting a higher f-number, so some part of the image around the line separating out of focus and in focus will be sharp enough to be considered fully in focus also in enlargements. That's it.

The same lens with the same aperture settings (at the same focal length if it's a zoom) will always give the same result. CoC is not a physical variable like those I just mentioned which really changes light coming out of the lens and into you camera, it's a parameter used to determine mathematically if something is in focus.

You can't say DOF is a function of sensor size (among others) because larger sensors are used for large prints and in large prints you see out of focus areas that in small prints you don't see. First because to call this an indirect relation is an euphemisms, then because this is accounting for detail at the expenses of sheer exactness. Maybe I'm missing on... more than something.

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+1: That pretty much sums it up. –  DragonLord May 16 '11 at 15:17
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Quantitatively, the depth of field formulas depend on a "maximum allowable circle of confusion," which basically depends on what you consider to be "acceptably sharp." Some people impose the same allowable CoC in all circumstances (sort of a quality metric for lenses), in which case this answer is correct. Others, including myself, believe this "acceptable sharpness" criterion only makes sense in the context of a finished work, e.g. a print. In that case, the maximum allowable CoC depends on the degree of enlargement, which in turn depends on sensor size. –  coneslayer May 16 '11 at 16:23
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I always assume the same final output size (in which you do get shallower DOF with the larger sensor) as it's not like people print images from P&S cameras a tenth of the size as those from DSLRs, no people tend to print/view images the same size regardless of how large the sensor is! –  Matt Grum May 16 '11 at 18:26
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@Matt: Me too, and I thought that was pretty well accepted, but see photo.stackexchange.com/questions/11291/… for a dissenting opinion. –  coneslayer May 16 '11 at 18:59
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+1 for "If we simply and more correctly to the purpose of our analysis assume both have enough pixels to print a fixed size we want without noticeable loss in quality, what we get in prints from the smaller sensor is like a cropped enlargement of the print from the bigger sensor, so we can indeed see a difference in depth of field, that is, we see more detail so it's easier to spot slightly out-of-focus areas." A smaller sensor or a crop from the large sensor have exactly the same effect of increasing apparent DoF when enlarged. –  mattdm May 17 '11 at 15:12

Why does a bigger sensor lead to a shallower depth of field?

In simple terms: It doesn't.

If you used exactly the same lens, and only changed the sensor size, you would not get a shallower depth of field with the larger sensor.

It's only when you change other variables to compensate for the different sensor size that you may get a change in depth of field.

In the case of the example images you posted, the photographer actually moved the camera! He presumably did this to compensate for the change in sensor size, so that the main subject filled approximately the same portion of the frame. However, clearly when you move the camera, it changes the perspective and relative distances between objects - in this case, with the camera further from the subjects it will have more depth of field.

Of course, if he hadn't either moved the camera, or changed the focal length (via zooming or changing lenses), then the shot taken from the smaller sensor would look "cropped", only showing a portion of the image the larger sensor shows. But in all other respects the technical aspects of the photo would be the same, only cropped.

So the reason a lot of things change according to sensor size is not actually due to the sensor size, but due to what you do to compensate for the sensor size, whether that be by choosing a different camera location, lens, or zoom level. In the case of this example, it was choosing a different camera locations - specifically, changing the camera to subject distance.

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Depth of Field is a function of many variables, one of them being the distance to subject. In the example shot you posted, the left-hand side was taken with a Canon 30D, which has an APS-C cropped sensor (24mm), while the right-hand side was taken with a Canon 5D, which has a Full Frame sensor (35mm). Both photographs were taken with the same lens at the same aperture.

The reason DoF changed between the 30D and 5D is because to maintain framing, or the size of the subject relative to the size of the image, you have to get the 5D closer. This is because the 5D has a wider Field of View for any given lens than the 30D. The closer you focus to a subject, the thinner your Depth of Field will be.

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Depth of field is determined by only two factors. They are magnification ratio and fstop. By magnification i mean final prit size versus object size. larger sensors require less magnification to get to a particular print size thus appear to have greater depth of field, but if magnified to the same ratio as the smaller sensor, will prove that that the circle of confusion is based ONLY on the fstop.

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Your answer does not add new insights and this question was already answered with great details. You should avoid these king of answers. –  Itay Gal May 24 '13 at 18:10

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