DOF confusion on a crop sensor camera

[Siv]

I'm an engineer so I like to over analyze things. I've been thinking about aperture and the relation to depth of field – specifically the difference between a crop and full sensor.

Using those handy online depth of field calculators I find the following where the set-up should give the same subject framing:

• The DOF for a crop sensor is twice as long as that for a full frame for a given aperture and equivalent focal length (e.g. a crop body with a 31mm lens has 15m DOF whereas a full frame with a 50mm lens has a 7.6m DOF where both are 10m from target and f/2.8).
• The DOF for a crop sensor is three times as long as that for a full frame for a given aperture and using the same lens but varying the distance (e.g. a crop body at 16m from the subject has a 9m DOF whereas a full frame at 10m from the subject has a 3m DOF where both have 50mm lenses and the f/1.4).
• To get the same DOF with equivalent focal lengths the crop sensor needs a lens that is 1.5 stops faster (e.g. a crop body with a 31mm lens at f/1.8 has 7m DOF whereas a full frame with a 50mm lens at f/2.8 has a 7m DOF where both are 10m from target)

Now this is where I'm puzzled – it's commonly said that a crop sensor needs the 1.6 multiple applied to lenses when compared to full frame specification (.e.g. a 50mm lens on a crop is equivalent to a 80mm on a full frame) but I have never heard it said that the effective aperture is different too.

So a 32mm f/1.8 lens on a full frame is really a 50mm f2.8 lens on a crop body. So a fast lens is really compromised when used on a crop body since you lose a stop and a half worth of DOF. Is this right?

I'm coming to the conclusion that to get the same photo with a crop as I would get on a full frame camera I need to have a wide lens (there's a limit to how wide I can go) and a faster lens (where the price goes up exponentially). So going from crop to full frame, even though a full frame may be $1k, more expensive it gives your lenses a stop and a half DOF which is probably worth a lot more in equivalent lens cost since narrowing the apperture is free but widening it is expensive!

[ldelacruz]

When I think of aperture I think of light and not necessarily DOF. There are so many variables to DOF.

[ggeen]

I am just tagging this because I'm interested in the discussion. I would THINK that aperture is more a function of the lens and not the sensor. By that I mean, you should get the same DOF of a 50mm f1.8 on a DX and FX sensor. Or at least something close to it.

[zachary]

Originally Posted by Siv

So a 32mm f/1.8 lens on a full frame is really a 50mm f2.8 lens on a crop body. So a fast lens is really compromised when used on a crop body since you lose a stop and a half worth of DOF. Is this right?

I believe thats right, yes. You dont get the same quality of Bokeh on a crop sensor that you do on full frame or film.

I think the opposite is true also. On my 6x6 Bronica, I have a 75mm 2.8 lens, which is probobly like a 50mm 1.4 on 135 because the DOF is RAZOR thin when shooting wide open. Its extremely hard to get your subjet in focus unless I go to F4.

[rockpics]

Glen, an unanalytical and empirical way of thinking about it is this: if you are using a 50 mm lens at f1.8 to make a 3/4 portrait, you will be farther away from the subject with a DX than an FX, therefore, your depth of field will be deeper on the DX.

[ronocnikral]

i think of it kind of like jill.

you are not physically changing the optics. e.g. if you have a 50mm lens, you are not physically making that lens an 85mm or whatever it would be. your exposure is based on your focal length of the lens, aperture opening etc. without physically changing this, e.g. extension tubes, TC's, billows, you aren't messing with optics.

riddle me this...i have a camera with a 80mm lens equal to about 50mm on a "full frame" sensor. How does the physical size of one's sensor/film affect the apparent focal length without physically changing the optics of a lens?

Crop factor - Wikipedia, the free encyclopedia

[ggeen]

Jill, thanks for the consideration. I was thinking more along the lines of using a DX and FX camera with the same lens at the same distance. I did not take into consideration the same framing which would require changing distance. Yes, that would make sense. That is still more a function of the lens -- or its elements -- rather than the sensor.

The smaller sensor caused me to step back to get the same framing. It did not cause the DOF at 10ft to change.

The OP talks about getting the same framing but not about changing distances to the subject but rather changing focal lengths to achieve the same framing at the same focal length. My 50mm has vastly different characteristics than my 85mm. By that I mean, at 10ft, the depth of field is quite different between the two lenses.


[edit]
thanks for the link Connor.

[Siv]

Originally Posted by ggeen

The OP talks about getting the same framing but not about changing distances to the subject but rather changing focal lengths to achieve the same framing at the same focal length.

In my second bullet I do change the distance with the same lens to get the same framing (or at least I think I do) and the DOF on a crop is 3x the DOF on a full frame. To me, that's a big difference!

[ronocnikral]

Originally Posted by Siv

In my second bullet I do change the distance with the same lens to get the same framing (or at least I think I do) and the DOF on a crop is 3x the DOF on a full frame. To me, that's a big difference!

it's not a linear relationship. say i'm 1 mile away from a beautiful mountain with my crop camera. i then switch to my FF camera and compose in the same fashion. will my DOF change 3x??

Depth of field - Wikipedia, the free encyclopedia

I'm coming to the conclusion that to get the same photo with a crop as I would get on a full frame camera I need to have a wide lens (there's a limit to how wide I can go) and a faster lens (where the price goes up exponentially). So going from crop to full frame, even though a full frame may be $1k, more expensive it gives your lenses a stop and a half DOF which is probably worth a lot more in equivalent lens cost since narrowing the apperture is free but widening it is expensive!

wider, yes. lens speed, incorrect. these economics are flawed b/c of the assumption of needing faster lenses on crop bodies. c'est pas vrai.

was that all you wanted to know?

ps, as mentioned earlier, don't think of DOF and aperture as the same. 1) DOF is measured in length, stops are more or less "fictional." 2) DOF is a function of sensor size, aperture size, distance to subject, viewing distance, etc. Stops are a function of aperture f-stop number, shutter speed and sensor/film sensitivity to light.

[ggeen]

Originally Posted by Siv

In my second bullet I do change the distance with the same lens to get the same framing (or at least I think I do) and the DOF on a crop is 3x the DOF on a full frame. To me, that's a big difference!

Yes, you do. You also vary the distance to get the same framing. When you change the distance, you will change the effective DOF.

Same lens, same f/stop, same distance, DX vs. FX sensors being the only difference. That is how I would test whether the sensor changes DOF. You need to increase the number of constants and decrease the number of variables.

I think Connor explains the side effect we know as depth of field in the post above.

[ualymerej]

Originally Posted by ggeen

Yes, you do. You also vary the distance to get the same framing. When you change the distance, you will change the effective DOF.

Same lens, same f/stop, same distance, DX vs. FX sensors being the only difference. That is how I would test whether the sensor changes DOF. You need to increase the number of constants and decrease the number of variables.

I think Connor explains the side effect we know as depth of field in the post above.

Same lens, same f-stop, same distance will give two different frames. I think if we're talking about "apparent" DoF, then you want to at least shoot with the same framing in mind. If you just think about it from a common sense perspective, there's only a couple ways to make the DoF shallower. You can either get closer to the subject and focus closer (which would change your framing), you can make your aperture bigger, or you can get a longer lens and shoot from further away. You could also move the subject further away from the background, but that doesn't involve the camera as much. If the sensor is smaller, you already need to take a few steps back (which changes the focusing distance) or you need a wider lens to get the same framing as a larger sensor. If you reverse the common sense logic I presented earlier, both of these options would result in a deeper DoF. Your only option after that to make the DoF shallower again would be to use a bigger aperture.

You can also think in terms of point and shoots. When you take pictures with a p&s, the DoF is practically infinite; everything looks like it's in focus. You can try standing further back and zooming in; that will draw your subject slightly away from the background, but the shallowest you can get your DoF on a p&s is when you're in macro mode and you're really close to your subject. The sensors in p&s's are tiny in comparison and obviously have much difficulty creating a shallower DoF.

Now, to address why there's no factor for aperture on crop sensors; it's because how the aperture affects the exposure doesn't change. The same amount of light enters the camera and hits the sensor no matter how big the sensor is.

[boldimagery]

Changing your camera sensor doesn't change the optical qualities of the glass. A 50mm is always a 50mm optically speaking. The senor being smaller only see a smaller portion of what the lens is able to produce.

It would be like making a 20x30 and cutting of 1.6 of the total area equally on all sides. Did your DOF change by doing so? You simply cropped the image. That is whats going on with a cropped sensor. In your case a 32mm = 50mm yes in terms of your field of veiw (sort of... ) but it maintains the optical principals of the lens. So, the distortion / perspective you can accomplish with a 32mm lens will have the characteristics of a wide angle this holds true of the ability to reproduce your DOF.

[mmuhlenkamp]

I've linked to this before (it downloads a pdf), but this piece of the Canon EF Lens Work Book has helped explain how different focal lengths affect the image and what the difference between a full frame vs 1.3 crop vs 1.6 crop.

http://software.canon-europe.com/fil..._Book_7_EN.pdf

I don't know exact numbers or ratios (I'm more of a visual person), but when I saw this it really helped me understand the crop factor/focal length issue and how that can affect your image.

[sldi]

if you shoot a subject with a 50mm on full frame then put that lens on a 1.6 crop body you have to move back 1.6 times the original distance to get the same frame. What doesn't move is the subject to background, therefore the effective DOF has to change.

[ronocnikral]

Originally Posted by sldi

if you shoot a subject with a 50mm on full frame then put that lens on a 1.6 crop body you have to move back 1.6 times the original distance to get the same frame.

i've been wondering about this all day. if you have a source which talks about the physics of focal length and composition. another way to put the question, if i compose originally with an 85mm lens, to get the same shot with a 50mm do i have to move my sensor 62.5% of the original distance? i'm not sure, and would truly like to learn...