DOF & DX Crop Factor

[frankie_frank1]

A 100mm lens in 35mm format will be 150mm in Nikon APS-C format, with the same

aperture. What about the DOF? Does it also has 1.5X factor?

[leslie_cheung]

The simple answer is DOF stays the same.

[rainer_t]

http://www.bobatkins.com/photography/technical/digitaldof.html

[leslie_cheung]

Nevermind my answer above. This DOF business is rather complicated. Follow this link to

read about it. http://www.photo.net/learn/optics/dofdigital/

[mendel_leisk]

Look at it this way: the lens produces an image, the body crops the image. That's all it does.

[tonybeach]

To be precise, the lens is a 100mm lens regardless of format, and optically it will behave the same -- what changes is the FOV. If you move back with a smaller format to get the same FOV then you will have more DOF at the same aperture, but if you use a different focal length and keep the same FOV then the DOF will be the same in either format.

[robert meier]

A 100mm lens in 35mm format will remain 100mm in Nikon APS-C format. DOF will also remain the same.

[leonard_evens]

I don't know why you should accept my answer to your question rather than one of the different answers above, but my answer is actually correct.

 

Let me explain. DOF is determined by three factors, the format size, which determines the maximum acceptable circle of confusion you will use, the focal length and the relative aperture. Roughly speaking it is inversely proportional to the coc. If you choose a smaller format by a linear factor of 1.5, you have to enlarge more by the same factor. Hence, you have to decrease the coc by a factor of 1.5. So, if you keep the focal length and aperture the same, you increase the DOF roughly by a factor of 1.5.

 

However, it can get a bit more complicated than that. When you increase the enlargement factor, you also increase the effect of diffraction. So you decrease the f-number of the smallest usable relative aperture (i.e., increase the aperture)). At the same time, you have to use a smaller f-number (i.e. larger aperture) at the other extreme to limit DOF as much as possible because of the effect described in the previous paragraph. That means that the range of usable apertures remains essentially the same when you go to the smaller format. But it is shifted down to larger apertures at both ends by about 1.17 stops.

[radfordneal]

There's a very easy way of seeing how out-of-focus things not in the plane of focus will be. (Note that I've avoided the term "depth of field", which in my opinion just brings in ambiguous ideas about how much in focus is "in focus enough".)

 

Let's assume that the lens has just one element - the complications of real lenses with many elements aren't relevant here. So the f-stop is the focal length divided by the diameter of this element - eg, a 100mm f/4 lens has a 25mm diameter element. And if you use this f/4 lens at an f-stop of f/8, it effectively has only a 12.5mm element.

 

A perfect lens focuses a point of light located on the plane of focus to a point on the film/sensor. Points of light elsewhere produce a circle (or ellipse) of light on the film/sensor. How big is this circle? It depends only on the size of the lens element (as long as the distance is much greater than the focal length).

 

Here's why. Let's look at a point behind the plane of focus (in front of the plane of focus is similar but slightly harder to explain). All the light from this point that enters the lens will end up on the film/sensor (remember, we're assuming a simple lens here). On the way to the lens, this light will pass through the plane of focus. The lens doesn't know whether a ray of light coming from the plane of focus originates there, or from an object behind. So each ray passing through the plane of focus ends up on the point on the film/sensor that images that point on the plane of focus. It's easy to see that the rays of light from a point of light behind the plane of focus that make it to the lens will form a circle (or ellipse) as they pass through the plane of focus. So the image of this out-of-focus point is a circle (or ellipse). How big a circle? If the distance to the plane of focus is much bigger than the focal length of the lens, the size of the circle will be proportional to how big the lens element is (ie, to the focal length divided by f-stop). (The circle also gets bigger the further the point is from the plane of focus, of course.)

 

So in figuring out how out-of-focus something is going to be when taking a picture with one camera/lens or another, you just have to look at the focal length divided by f-stop. So an APS-C format DSLR (1.5 "crop factor") with a 24mm lens used at f/2 will have the same degree of blurring of out-of-focus objects as a full-format 35mm SLR on which (to get the same field-of-view) you've mounted a 36mm lens, if you use that lens at f/3. In both cases, the effective diameter of the lens is 12mm.

[richard_driscoll]

A simple way to look at DOF (ignoring diffraction) is as follows. The formula are approximate but good enough for most purposes I find.

 

The hyperfocal distance is given by:

 

H = F^2/(f * c)

 

Where F is the focal length, f is the f stop and c is diameter of the circle of confusion.

 

For a focussed distance of D, the near and far limits of focus are given by:

 

D1 = HD/(H+D) and D2 = HD/(H-D).

 

(Note that if H=D then D2 is infinite and D1=H/2 as we'd expect from the definition of hyperfocal distance).

 

For 35 mm full frame the circle of confusion is often taken to be 0.03 mm so for a DX camera it should be 0.03/1.5 = 0.02 mm.

 

In moving from full frame to a DX format the focal length needs to be reduced by a factor if 1.5 for the same angle of view but the square factor in the first formula means that the hyperfocal distance is reduced by a factor of 1.5, increasing DOF.

 

If we put a full frame lens on a DX camera the depth of field scale will not be correct since the required circle of confusion is reduced. From the first formula you can see that the f stop needs to be made smaller by a factor of 1.5.

 

Since f numbers are in a series with a common factor of sqrt(2) or 1.41 and since 1.41 is pretty close to 1.5, then a rule of thumb is that if you put a full frame lens on a DX camera you need to use the DOF marks corresponding to 1 f stop larger. For example if the lens is set to f/5.6 use the f/4 markings.

 

SUMMARY

We could summarise the answer to Frankie's original question like this. A 100 mm lens designed for full frame on a DX camera gives about the same angle of view as a 150 mm lens on a full frame camera and at the same f stop gives more depth of field than the 150mm lens on the full frame camera, the advantage being equivalent to about one f stop. However the depth of field scale will be in error by about one f stop.

[johnw63]

Hmmmmm.

 

I think things get complicated when you want to get the same FoV. As far as I know, the lens optics do not change. How light moves through the lens does not change. Assuming the film plane and sensor plane are at the same distance from the lens mount, the point of focus should not change. Therefore, the DoF should not change...unless you start MOVING things to duplicate the FoV on the sensor as compared to the film. Light does not bend differently when it's target is a sensor of any size vs a spot on film.

 

So, perhaps the question should be, "How does the DoF change when I attempt to duplicate the scene on a Nikon DSLR that I saw in my film SLR ? "

[richard_driscoll]

I can answer John's question.

You duplicate the scene you saw through the viewfinder of your film SLR by using a lens of shorter focal length. The reduction is by a factor of 1.5. For the same f stop the DOF will be greater with the DX camera. To get the same DOF use a larger f stop (smaller f number), increased by a factor of 1.5, which is about 1 stop.

 

This should hold good for objects not too close, say about 10 focal lengths or more away.

[pete_s.]

As usual most people get this wrong and think the dof is the same. It's not and Leonard Evens as well as the dof article by Bob Atkins got it right. It's not complicated at all. You just have to realize that in the definition of dof lies what is sharp to the eye. Basically people forget how the circle of confusion limit is defined, hence the confusion.

[pete_s.]

Oh, a few other actually answered the OP's question. Sorry about that.

[briany]

Leonard Evans, I love the pretension: "but my answer is actually correct." Correct, except where it's, umm, too simplistic and wrong in many instances. Read Bob Atkin's article, but for middle distances, depth of field is proportional to the circle of confusion, and inversely proportional to the Square of the focal length. Regarding John Williamson's statement of the question above, when you're going for an equal framing (angle of view), and equal perspective (camera/object positioning), the depth of field is greater for digital (from Bob's article, we can see it's 1.5x as much). While this may somehow surprise Leonard, it's pretty obvious to anyone who's used a camera phone, which hardly even needs to focus due to it's massive DoF, or to anyone who has shot with a digicam and been frustrated that they couldn't achieve a pleasing background blur on a photo.

[lex_jenkins]

And now you know why it's called circle of confusion.

[ed_farmer]

Huuuuummmmmm . . . .

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I have been away for a few years, but it seems like this discussion just comes up over and over again, year after year . . .

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If the answer was "it stays the same": a 50mm lens would have the same DOF on a Minox, a Nikon FE, an RB-67 and a 4x5 Wisner. However, we all know that this is not true. So, why would it be the same on FF and APS-C sensors?

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In the end, DOF is related only to magnification at the film plane. Go ahead and tell me that I am wrong, but then go back and do the math.

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The short answer is that the OP had it right in the practical sense. A 100mm lens on an APS-C camera will have roughly the same DOF as a 150 on a FF.

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Ed

[briany]

Ed, you had it right, right up until the end - a shot with a 100mm on DX will have the same framing and perspective as the same shot from the same place with a 150mm on FF, but the magnification on the FF frame will be larger (same subject size, 1.5x image size), so less DOF by a factor of 1.5x. Again, it's all laid out at http://www.bobatkins.com/photography/technical/digitaldof.html