Do smaller sensor cameras have more Depth of Field?

Short Answer

Yes, and No.

Full frame bodies tend to offer a wider range of Depth of Field. Both full frame and crop tend to offer the same limit on deep Depth of Field, but the range for full frame extends further into shallow Depth of Field. This means that any depth of field you can get with a crop can be matched by a full frame. However, full frame can usually get Depth of Field shallower than a crop body.

Medium Answer

It depends on how you want to compare. If you structure the comparison carefully you can show the Crop Bodies have more, less, or the same Depth of Field.

At the same Angle of View and same Aperture diameter, they have the same Depth of Field.

At the same Angle of View and same f/stop, the crop body has more Depth of Field.

At the same focal length and same f/stop the crop body has less Depth of Field

Long Answer

Let's start by taking a look at the question "Do smaller sensor cameras have a narrower angle of view?"

The answer to that is that if you insist on comparing at the same focal length, then yes they do. However, most photographers will choose a shorter focal length for a smaller sensor camera and end up with the same angle of view as a full frame.

If you are shooting your full frame with a 50mm lens you get a 46° angle of view. If you switch to a 2X crop body, you can switch to a 25mm lens and get that same 46° angle of view.

In terms of Depth of Field, given the same subject, same angle of view, same aperture diameter, and same shutter speed, you get essentially the same image, independent of sensor size.

By "essentially the same" I mean the same framing, same Depth of Field, same motion blur, same overall image noise and same diffraction bluring.

What this means is that if your crop body sensor is set to the same angle of view, aperture diameter, and shutter, you're going to get the same results as a full frame body.

Keep in mind, I said "aperture diameter" not "f/stop". The f/stop is the ratio of the focal length to the aperture diameter. For instance "f/4" means the aperture diameter is the focal length ("f') divided by 4. For a 100mm lens, f/4 is a 25mm aperture diameter. For a 50mm lens f/4 is a 12.5mm aperture diameter.

Consider a full frame camera with a 50mm lens at f/4. On a 2X crop body, you would need a 25mm lens at f/2 to get that same aperture diameter. On the crop body you probably will want to set the ISO two stops lower in response to the bigger f/stop.

It's interesting to note that at f/2 you get four times the light per unit area than at f/4. With a 2X crop body, the sensor is 1/4 the size of a full frame sensor. These two balance out, and you end up getting the same total light captured from a full frame at f/4 and a 2X crop at f/2.

Now if you insist on shooting your crop body at the same focal length and same f/stop as the full frame, you will get different results. Most noticeably, the crop body will give you a much tighter framing, as if you had "cropped" the full frame image (hence the term "crop body"). You will also have shallower Depth of Field

However, if you shoot your crop body at the same angle of view, and same aperture diameter as the full frame, you get the same results.

An advantage of a full frame camera, is that at any particular angle of view, you typically have the option of wider aperture diameters.

If you are shooting your full frame with a 50mm lens at f/1.8, your 2X crop body would need a 25mm lens at f/0.9. That's not a lens stocked at your local Best Buy. If your are shooting your full frame with a 50mm lens at f/1.2, then your 2X crop needs a 25mm f/0.6 lens. Even an online camera superstore doesn't stock that lens.

The bottom line is that full frame cameras give you the option of shallower Depth of Field. However, any Depth of Field you can get with a crop body, you likely will be able to match with a full frame.

Diffraction Limits

While it may seem that crop bodies offer the option of deeper Depth of Field, this isn't usually the case. It's true that crop bodies generally allow you to choose smaller aperture diameters, but diffraction issues tend be the limiting factor for Depth of Field, and those kick in at the same point for both full frame and crop bodies.

Remember, Depth of Field refers to range of distances where the image is sharp enough that a typical human viewer sees them as being in focus. Diffraction issues add blur to the image. At large aperture diameters, the blur is small enough that it isn't significant. As you move to smaller aperture diameters, the blur becomes more significant. At some point the diffraction blur is enough that nothing appears to be in sharp focus. At that point, a Depth of Field calculator might tell you that there is deep depth of field, but that's ignoring diffraction. The resulting image will not be sharp.

Is defraction affected by focal length?
If I'm using a 55-300mm lens on a crop sensor body at a given f stop, say f11, will defraction be any worse at 300mm than at 55mm?

Diffraction in micrometers is a function of f-stop. It's also a function of aperture in mm and focal length in mm, but those effects are combined in the f-stop calculation.

Thanks for the response. Just to clarify, are you saying that the images won't appear any more blurred at 300mm at a given f-stop than at 50mm, at least not on account of diffraction becuase that's already factored into the f-stop calculation?

My images at 300mm aren't as sharp as I would like so, if I've understood you correctly and we can rule out defraction as the cause, it must either be down to the characteristics of the lens or poor technique on my part. I'll work on addressing the latter :-)

It the f-stop remains the same as the lens is zoomed in or out, then the diffraction at the sensor will remain the same. Most wide-ratio zoom lenses aren't as sharp at their longest focal lengths as at shorter ones.

In terms of the final print, the diffraction is the same if you have the same angle of view and same aperture diameter.

A full frame camera with a 200mm lens at f/32, will yield a print with the same amount of diffraction blur as an 8X crop body with a 25mm lens at f/4.

Personally, I am more concerned with the magnitude of the diffraction in the context of the image, rather than the magnitude of the diffraction as measured against the physical sensor. But then, I tend to care more about the results than the implementation details.

I think you are talking about diffraction measured in object space. I was talking about diffraction measured in image space. In image space, diffraction is determined by f-stop. No need for complicated formulations.

Consider a 50mm lens at f/32. We put that lens on a full frame camera and take a photo. Then we move that lens to a 4X crop body, and take another photo (also 50mm at f/32).

If we look at a square millimeter of either sensor, we will see the same amount of diffraction. However, if we make an 8x10 print of both images, the one from the crop body will have more visible softening from diffraction. Obviously, the two prints will have different framing. The print from the crop body will appear "zoomed in" compared to the print from the full frame body.

So, if you are measuring diffraction on the sensor (something I would refer to as an implementation detail) then sensor size is not a factor. If you are comparing how diffraction affects the final image, then both f/stop and sensor size are factors.

Right. I was separating diffraction from equivalency. I think they are best understood separately.

Aaaah! The old DoF thread revived :-) I love DoF threads.

You can match the DoF of a crop image (same FOV) with full frame only if you have a 1.5x longer focal length in full frame and can stop it down one stop more. I'm sure that's not always possible, given the present lens portfolio, when you shoot a crop image @ f/22 or f/32! Yes, yes, diffraction...

Sorry, just being argumentive, couldn't resist after my mod-induced but self-constructed cold turkey kick off from that other site (some say 'sight'), hope the mods here will allow :-)

It is unfortunate that OP contains a bit of the FF vs. m43 comments.

OK, that shows my preoccupation with (Nikon) DX vs FX. But I think shrinking the DX format to m43 in this discussion calls the FX (full frame) lens to go to an even smaller aperture. So my main argument still stands.

It's not a question about equivalency, it's a question about whether your concern is how diffraction affects the final image, or implementation details of the camera being used.

From the perspective of the final image, at the same angle of view, with f/8 on an 8X crop body you will see much more diffraction in your final print than with f/8 on a full frame.

You are correct in that if you are looking at only a small section of the sensor, they will be the same.

I would think a beginner would be more concerned with how diffraction will affect their final images, than how it affects an intermediate step along the way.

Sort of.

First of all, a full frame can always match the depth of field of a crop body by using the same focal length, same f/stop, and cropping the resulting image. But that's not always desirable as you lose resolution.

In terms of matching the depth of field of a crop body (without resorting to cropping the image) we need to look at the limiting factors. Let's assume we have selected focal lengths that give us the same angle of view on our crop body and our full frame camera. On the shallow end, the limiting factor is usually maximum aperture diameter. With common, commercially available lenses, the larger sensor usually wins out, as you are more likely to have a wider aperture diameter available.

On the other end (deep depth of field), the limiting factor is usually diffraction. But this is depending on how we define depth of field.

The definition I am using, is that the depth of field is the range of subject distances where objects are sharp enough that, under typical viewing conditions, they appear to the unaided human eye to be in focus. This is not the definition used by typical Depth of Field calculators. They tend to use a definition like: "the range of distances that are still acceptably sharp, considering only focus issues, and ignoring diffraction, and other issues."

If we wanted to have a technical discussion about the contribution that aperture makes to depth of field, then the Depth of Field calculators are correct. If we want to have a conversation about how the resulting image will look, then we need to take diffraction into account.

At some point, the loss of sharpness due to diffraction is so great, that nothing in the image appears sharp. At that point, I would say the depth of field is zero. Stopping down further reduces sharpness, and doesn't increase depth of field.

Getting back to whether or not crop bodies offer deeper depth of field, my answer is "no". With a crop body, you can usually stop down past the point where nothing is sharp. Full frame bodies usually also let you stop down past that point. While it is generally true that crop bodies let you go further past that point, that decreases sharpness, and does not increase depth of field.

The summary is that full frames generally allow you to choose shallower depth of field. Both full frame and crop bodies are generally equally limited by diffraction when it comes to deep depth of field. That limit is the same, independent of sensor size.

edit: no delete option? T_T

It's rare that someone posts technical details about DOF, especially including format changes, that are actually correct, but the OP is correct. Amazing.

Perhaps this is a bit off topic, but I am really curious about diffraction correction. The Canon DPP4 software includes an option for DC. The function really seems to work based on my testing at f/20 and beyond. I have read this is based on "deconvolution" algorithms, but I have no idea how that works. I would think diffraction is a physical property that cannot be altered.

In the absence of noise, and with sampling above the Nyquist frequency, if the blurring function is known, it can be at least partially removed. If you want to get the phase right, it's computationally expensive. But you can see substantial improvement even with less-than-optimal algorithms. For round apertures, the blurring effect of diffraction is well understood and predictable.

As to how it works, you could transform the image to the frequency domain, perform corrections and then transform it back, or you could just convolve the image with an appropriate kernel.

en.wikipedia.org/wiki/Convolution