Depth of Field / Senor Size

[iND]

Please try to explain why larger sensors will have a greater depth of field at the same lens/aperture/distance


Example 55mm/f2.8/10ft


Canon 5D (full frame) depth of field = 1.69 ft


Canon 50D (1.6) depth of field = 1.07 ft


Why does sensor size change the physics?

[DavidEccleston]

They don't. With equal settings and distance, the DOF will be identical, but the images will be framed differently.


To get the same framing with a crop camera as a full 35mm sensor camera, you will need to increase your distance. DOF increases with focus distance, therefore crop cameras will have a DOF 1.6 times greater than full frame for the same framing and aperture.


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[tkerr]

Sensor and, pixel size and density, effect the image scale and field of view. Smaller sensor has less area.

[Daniel Browning]

Please try to explain why larger sensors will have a greater depth of field at the same lens/aperture/distance

Because of reproduction magnification (AKA "enlargement ratio").


For example, let's say 135mm on full frame shows the entire head of a portrait and the eyes and nose are both in focus. Now switch the camera to 1.6X crop without changing focal length, f-number, or subject distance. You can no longer see the entire head -- just from the eyebrows to the chin. And now the eyes and nose are 1.6X larger. With that larger size, it's apparent that the front of the nose is actually slightly outside the depth of field.


Now, what if you had cropped the full frame image to match the same angle of view (eyebrows to chin) as the 1.6X image? Then the DOF would go back to being the same -- but only if the limiting resolution was the same. For example, the 20D and 5D2 have the same 8 MP if they are cropped to the same angle of view -- so in that case they would have the same DOF. But if you compared the 5D2 cropped to the 7D, it is possible to see thinner DOF on the 7D due to higher limiting resolution.


Hope that helps.

[Trondster]

Well - this depends a lot regarding what you call "depth of field" and "in focus" - that is calculated from the CoC (Circle of Confusion) or "how large can a blur be while still being regarded as sharp". The "depth" of the DOF in inches is thus highly dependent on what you accept as sharp - and for digital images - how large a blur can be in percent of the image, and still be regarded as "sharp". If you want a 100% crop of a 20+Mpx camera to be "sharp", you have to have a much smaller CoC than the standard tables and calculators use.


From what most people would regard as "the same DOF", the depth of what you would call "sharp" in relation to the width of the picture does not change when you crop in or use the same lens on different cameras with different sensor sizes. So - if you took the same lens at the same focus distance, and shot two shots - one with a full frame camera and one with a 1.6x crop camera, you would get two images with "the same DOF". You would get the same exact image (apart from the resolution) as the crop camera, if you took the image from the full frame camera and cropped in. Try it yourself. Take an image with thin DOF, resize it to 800x600 and view. Crop the original image in, resize to 800x600 and compare the two. The images both have the "same DOF" - not in absolute measurement in inches/cm, but in relation to the size of the picture.


So - what is that about larger sensor cameras having less DOF? That would happen if you shoot two images with the same effective focal length, the same focus distance and the same aperture numbers (f numbers.)


DOF is easiest described as being dependent on focus distance, effective focal length and absolute aperture. (Some say (effective) focal length does not add into the equation, but it is so much simpler to compare two images shot with the same effective focal length and thus the exact same viewing angle.)


The absolute aperture in mm is found by dividing the focal length with the f number.


Thus, if you take a 135/2, the absolute aperture is 135mm / 2 ~= 68mm.


If you take a 85/1.2, the absolute aperture is 85mm / 1.2 ~= 71mm.


Thus - these two lenses have just about the same absolute aperture (given that f-numbers such as "f/1.2" and "f/2" are rounded numbers anyway), and should thus at the same focus distance and effective focal length give the same DOF.


Lo and behold - if you put a 85/2 on a 1.6x crop camera, the effective focal length is 85mm * 1.6 = 136mm. Thus - if you shoot the same image with a 85/1.2 at full aperture on a 1.6crop camera and with a 135/2 at full aperture on a full frame camera, you should get the exact same image, with the exact same viewing angle and the exact same DOF. (Try it!)


And this is the point - both images are shot (at the same focus distance) at an effective focal length of ~135mm, giving the same angle of view and exact same picture and DOF (because of the same absolute aperture), but the crop camera needs to shoot this at an aperture number of f/1.2, while the full frame camera can shoot this at an aperture number of f/2. Thus - if you shoot two pictures at the same focus distance, and the same effective focal length, the camera with the smaller sensor (and thus the larger crop factor) needs to shoot at a larger aperture measured in f numbers (although the absolute aperture is the same) to get the same DOF.


If you shot with the same aperture number in this example - 135mm @f/2 with the full frame camera and 85mm @f/2 with the crop camera, the full frame camera would get thinner DOF.


It is easy to calculate which focal length would need which aperture number to match a crop camera with a full frame camera, with the same DOF and the same focal length - just divide both the desired focal length and aperture number with the crop factor. Thus, to match a 135mm f/2 on a full frame camera, you need a 135/1.6 mm f/ 2/1.6 = 85mm f/1.2 on a 1.6x crop camera. To get the same on a 2x crop factor camera, you need a 67.5mm f/1 lens.


But, you may ask, wouldn't that mean that you could shoot any thin DOF with a smaller sensor camera - you just need a larger aperture in f-numbers. Well - here is the tricky part - it's quite difficult, for not to say impossible, to make lenses with a very very small aperture number. If you put an 85/1.2 on a full format camera, you need a 50mm f/0.7 to match that on a crop camera - as far as I know - there exists only one if these, made by Zeiss for NASA, and later famously used by Stanley Kubrick to film a movie lit by candle lights only. (Very bright candle lights, but still..)


To match the DOF and effective focal length on a 85/1.2 on a full format camera, a x2 micro Four Thirds camera would need a 42.5mm f/0.6 lens. Now it really gets tricky.


And, if you want a compact camera with a crop factor of say 5.6, like the 1/2.3" sensor in the Canon PowerShot SX130 IS, you would need a 135/5.6 mm f/ 2/5.6 = 24.1mm (that is has) lens with an aperture number of 2/5.6 = f/0.36. That it has not - and such a lens would much likely be very impossible to create.





Fun fact: When you take a fixed aperture lens (like 70-200, 24-105, 24-70 etc) and shoot it at max aperture on different sensor size cameras, matching the zoom to keep the same effective focal length, this phenomenon is very visible.


Fun fact II: When you shoot with any current zoom lenses, the absolute aperture is larger (and thus has the smallest DOF) at the longest focal length, even though the aperture number is the same or increases a bit. A 70-200 f/2.8 has an absolute aperture of 70/2.8 = 25mm at the smallest focal length and 200/2.8 = 71.4mm at the largest focal length. A 70-300 4-5.6 has 70/4 = 17.5 at 70mm and 300/5.6 = 53.6mm at 300mm. Therefore - smaller dof at the long end of the zoom.


Fun fact III: If you had a zoom lens with the exact same absolute aperture, say like a hypothetical 70-200 f/2-5.7, the absolute aperture would be the same at all focal lengths, and thus the DOF would be exact the same no matter which sensor size camera fitted to the lens, if you always shot it at max aperture.





A lengthy post, with a subject that is very hard to wrap ones head around, but there you go - DOF and sensor size explained.








Edit: Mind you - all of this is regarding comparing DOF at the same focus distance. At shorter focus distances, the DOF becomes thinner, and at longer focus distances, the DOF becomes thicker.


I am not entering any discussion as to how you can compare DOF at different absolute apertures vs different focus distances - that depends a lot regarding how you define DOF - is it the amount of blur of a distant object relative to the size of the blurred object (if so, some entertaining musings at The Luminous Landscape are actually correct), or is it the amount of blur of a distant object regarding to the percentage of the frame. Or whatever. What I have written above, however, is quite correct, but, as I stated, hard to wrap ones head around.





Edit II: If you shoot the same subject with the same lens, but with different cameras with different sensor sizes, changing the distance to the subject (and still focusing correctly on the subject), so that the size of the subject is the same, then the DOF will be smaller on the camera with the same sensor. Although the absolute aperture (and here, the aperture number as well) stays the same, the focus distance changes, and thus the DOF changes. But, the framing, the relative size of objects behind and in front of the subject etc also change, and thus it is much simpler to compare DOF when shooting at the same focus distance.

[neuroanatomist]

Four factors affect depth of field (the part of an image that is 'acceptably sharp')

• circle of confusion
• iris diahragm
• focal length
• subject distance

To simplify a bit, depth of field tables/calculators use a standard value for circle of confusion (CoC) for each sensor size. DoF is directly proportional to CoC. FF sensors have a larger CoC, therefore they have a deeper DoF when you hold everything else constant. The common and useful proposition that larger sensors have shallower DoF applies to a shot framed identically. To do that with the same lens and f-number on a smaller sensor, you'd need to move further from the subject. That 'outweighs' the effect of CoC, and so when you take the same picture (i.e. same subject framing) with the same lens/aperture on a FF camera vs. crop camera, the DoF is shallower in FF.

[TucsonTRD]

• circle of confusion

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That's what I'm running in every time this topic comes up. I don't try to fight it anymore. I just make photos using the settings I desire on the camera I have in hands at the time. Whether I want a small or large DoF, it doesn't really matter to me what I would do differently if I were using a FF camera.


Braden