Getting Technical: Depth of Field

As a photographer, one of the most important things you need to consider when composing a photograph is your depth of field; that is, how much of your image will actually be in focus. 


Image courtesy of Wikipedia

Proper selection of depth of field can have a significant impact on your final image. Is your subject fully in focus? Is your background busy and distracting? Is there enough isolation between the two to make your subject stand out? I won't go much into the artistic applications of depth of field in this post since artistry is always so subjective, but I do want to discuss the technical aspects of it, and how your choice of camera and composition will impact it.


The equation approximately defining the depth of field for a camera is:

Depth of Field = 2D2AC/F2

Where D is the distance your camera is focused to, A is your aperture setting, F is your camera’s focal length, and C is a constant that I’ll come back to in a bit. It's important to note that this is approximate because this equation doesn’t hold at macro distances and it assumes that the image plane and the lens are parallel. But for everyday photography that doesn’t involve macro or tilt lenses, this equation holds reasonably well. Breaking this equation down, you can see that there are two main things driving your depth of field: your choice of lens, and how you’re composing your photo.


Your choice of lens is always a key part in carefully crafting a photo. Based on this equation your lens’s focal length and aperture will both impact your depth of field. Longer focal lengths will decrease your depth of field, and faster apertures, which are numerically smaller, will decrease your depth of field as well. But in the equation, depth of field is proportional to the inverse of focal length squared, while it’s only proportional to the aperture. That means that your depth of field is always going to be more dependent on your focal length than your aperture; increasing your focal length will have a bigger impact on your depth of field than using a faster aperture. You can always change your aperture to change your depth of field, but if you’re looking to make a bigger change you may be better off changing your focal length instead.




Where your camera is relative to your subject will impact your photos in a variety of ways. It will determine your perspective relative to your subject and how compressed it is, it will change how much background you have in your final scene, but the thing we care about here is that it will impact your depth of field. The closer you are to your subject, the shallower your depth of field will be. Get too close and your subject may not be entirely in focus. Get too far away, and the background may be distracting. Looking back at the equation, we see that depth of field is proportional to the square of the focus distance so, just like focal length, it will have a larger impact on depth of field than aperture will. This is why portrait photographers will often try to get as close to your subject as they can: they're looking to separate them from the background. Likewise, landscape photographers prefer their subjects to be very far away so as much of the scene is in focus as possible.


What's interesting here is the interplay between focal length and focus distance. If you're looking to achieve a shallow depth of field you'll want to opt for a longer focal length and a shorter focus distance. A problem arises though because these two factors act in direct opposition to each other since they both impact your field of view. Choose a focal length that's too long and you'll have to stand too far away from your subject to really see the benefit. Choose a focus distance that's too close and you'll need a shorter lens to fit your subject in the frame.


This relationship benefits larger format cameras in terms of minimizing depth of field since they inherently have a wider field of view for a given focal length*. This allows you to focus more closely for a given focal length while still keeping your subject in the frame, which reduces your depth of field. In this instance though, what you're witnessing is a property of the lens, not the image sensor. A larger sensor isn't actually producing a shallower depth of field, it's just allowing a lens to produce it by letting it focus closer to your subject.



Most everything we've talked about up until this point has been about your lens and where it is relative to your subject. But remember that constant in the depth of field equation? It’s called the Circle of Confusion. This value isn’t as easily quantifiable as things like focal length, aperture, or focus distance, but, mathematically speaking, it’s just as important as your choice of aperture so it needs to be considered. In essence, the Circle of Confusion is the smallest circle that one would normally expect the human eye to be able to discern from a point. But what makes this especially interesting is that it depends entirely on your camera’s image sensor, be it digital or film; your choice of lens or composition do not impact the Circle of Confusion at all. Larger formats theoretically have larger circles of confusion, and thus for any fixed combination of focal length, aperture, and focus distance a larger format camera should inherently have a larger depth of field.


Now...I know what you’re thinking right now, because I thought it too. “How can the size of my sensor impact how much of my image is in focus?” I couldn’t wrap my mind around it, so I did what any photography nerd would do: I set up a rig to test it.

Doing Photography nerd things....

This is my test rig, a 300mm lens mounted to a tripod focused on a fixed depth of field measuring target. I ran most of my tests at a focus distance of 9 feet, which is just above the 8 foot minimum focus distance, but I also ran some at 6 feet** and 12 feet. I swapped in multiple bodies with sensors of different sizes and resolutions and took images of the target to compare the results. I tested this with my Nikon D750, which is a full frame camera with a resolution of 24 megapixels, my Nikon D7200, which is a 1.5x crop camera the same 24 megapixel resolution, and with my Nikon D3100, which is a 1.5x crop camera with a resolution of only 13 megapixels. 


300mm f/4, D750 @ f4, 6ft focus distance. Notice the subtle green and purple color shifts.

Looking at these test shots, especially at the faster apertures, pay close attention to the purple and green fringing. They’re the result of spherochromatism and they indicate that an area is out of focus; purple in the foreground, green in the background. I chose this lens specifically because it’s an older lens that doesn’t correct this as well as some of my newer ones, so it highlights the depth of field quite nicely***.

I have to admit that this is not the result I was expecting. Theoretically speaking, relying purely on the equation above and the "accepted" vales of the Circle of Confusion for different sized sensor formats, I was expecting to see a difference between the full frame camera and the two crop-sensor cameras, but instead the largest difference I see is between the two crop-sensor cameras. This would seem to indicate that image resolution plays a bigger role here than sensor size. There is a slight difference between the D7200 and the D750, but it's less pronounced than the difference between the D7200 and the D3100, which is contrary to what the math indicated.

I have an entire set of photos with different combinations of camera body, focus distance, and aperture, but I'm not going to bother showing them here because they all basically say the same thing as the three I showed above: your choice of image sensor just just barely matters to your depth of field, and even then only if you look really hard. But, by a huge margin, it's still your choice of lens and your composition driving your depth of field.




If you step into any photography forum on the Internet and post a comment that your sensor size directly impacts your depth of field independent of composition, you will almost undoubtedly start a flame war. The problem with this assertion is that, while technically true as I've shown here, it relies on nebulous numbers are difficult to quantify and seems to play so small a role compared to other factors that it is a borderline non-difference.

Ultimately, I think this little experiment has just prompted me to do more digging; I was expecting a different result based on some published math, so now I have a real desire to better understand that math, and how exactly you go about determining the Circle of Confusion for a digital sensor.

* Conversely, larger format lenses also tend to be slower, but as we've seen aperture has a smaller impact than focal length.

** I used a macro extension to allow "closer than minimum" focus.

*** Plus it has a tripod foot, so I could swap camera bodies without moving the lens relative to my test subject.