How to Understand Depth of Field
Getting Focused
When you focus your camera lens on a subject, there's only one exact plane that's truly in focus. Everything in front of or behind that specific plane is going to be blurry to some extent. But there's some amount of distance in front of and behind the focal plane where the amount of blur is too small to be noticeable, so objects inside those distances still "appear" sharp. This zone of apparent sharpness is called "Depth of Field."
The Pinhole Camera
The first depth of field concept to master starts with understanding a pinhole camera. That might seem strange, but a pinhole camera is unique in that it HAS NO LENS, so no light is being bent (refracted) to achieve focus. With a pinhole camera, everything is equally in focus. There is no zone of apparent sharpness that gets more blurry on either side. A pinhole camera works best when the distance from the pinhole to the sensor is 100 times the diameter of the pinhole. That's an fstop of f100, since by definition fstop equals the distance from the lens (or pinhole in this case) to the sensor divided by the diameter of the aperture (a pinhole in this case). An aperture any bigger than f100 and you'd need a lens to help focus the light. An aperture any smaller than f100 starts to make the image ever more hazy due to light diffracting at the edges of the pinhole and mixing with the light that's passing straight through the hole.
Now lets make the pinhole bigger and add a lens to focus the light onto the sensor. The lens truly focuses on a subject at only one specific distance. The light coming from a point on that subject hits all over the surface of the lens and the lens refracts that light into a cone where the exact tip of the cone converges on the camera's sensor. That's what it means to be in focus. Any point closer or farther away than the subject also has its light bent into a cone by the lens, but the tips of those cones don't end up converging exactly at the sensor, they converge behind or in front of the sensor, so they show up as blurry circles on the sensor itself rather than sharp points. The diameter of the aperture determines the base size of those cones. A wider cone still focuses the subject itself to an exact point on the sensor. That doesn't change. It's still in focus. But the wider cones for points in front of and behind the subject now create larger circles of blur where they cross the sensor. As the diameter of the aperture gets larger (e.g. f2.8 is a larger diameter than f8), the size of the blur on the sensor for any object not in exact focus also gets larger. As the diameter of the aperture gets smaller (e.g. f11 is a smaller diameter than f4), the size of the blur on the sensor for any object not in exact focus also gets smaller.
The main practical point of this first concept is this: if you stay at the same distance to the subject you're focusing on and use the same focal length lens (no zooming in or out), you can alter the depth of field just by changing the diameter of the aperture. Lower fnumbers mean larger diameter apertures, larger cones, bigger circles of blur at the sensor for objects not in focus, and thus shallower depth of field since those out of focus objects get more blurry. Higher fnumbers mean smaller diameter apertures, smaller cones, smaller circles of blur at the sensor for objects not in focus, and thus greater depth of field since those out of focus objects stay sharper. Of course, when you change the aperture, you'll need to compensate for the increase or decrease in amount of light getting through the lens to the sensor by changing either the shutter speed or ISO sensitivity setting if you want to keep the overall exposure the same. Putting your camera in "Aperture Priority" mode lets you manually choose the fstop and have the camera figure out what to do with the other two settings to get a proper exposure.
Maximum Acceptable Blur Size
The second concept has to due with the blur size. Part of quantifying Depth of Field as being a specific distance in front of and behind your subject is deciding how big those circles of blur on the sensor can get before they become "noticeable" to the human eye. The traditional value is based on people viewing an 8x10 print from a foot away and determining what looks "sharp" to them. That method results in a traditional maximum acceptable blur size of .03mm on 35mm film (what we now call a "Full Frame" sensor, which is actually 24mm x 36mm in size). The technical name for this maximum acceptable blur size is "Circle of Confusion." Yes, it seems confusing at first, but remember it's just a generally agreed upon value for how big the diameter of the blur can get before it's deemed to be "noticeably" out of focus to the human eye.
Now that we've quantified the maximum acceptable blur size on the sensor, we need to look more closely at those camera side cones for out of focus distances in front of and behind our subject. Let's keep the focal length of the lens we're using fixed for this discussion (no zooming in or out). Then, for a given aperture diameter, there's one specific distance in front of the subject that will have a cone on the camera side of the lens that ends up creating exactly that "Circle of Confusion" size blur on the sensor. That distance on the subject side is called the Depth of Field "Near Limit." Anything closer than the Near Limit will have a camera side cone that creates a blur on the sensor larger than the Circle of Confusion and is considered to be outside the Depth of Field. Also, for a given aperture diameter, there's one specific distance behind the subject that has a camera side cone that results in a blur size on the sensor that equals the "Circle of Confusion" value. That distance on the subject side is called the Depth of Field "Far Limit." Anything farther away than the Far Limit will create a blur on the sensor larger than the Circle of Confusion and is considered to be outside the Depth of Field. The subject side distance from the Near Limit to the Far Limit quantifies the total Depth of Field. It is specific to the subject distance, focal length of lens, and diameter of the aperture (fstop).
Near the Sensor on the Camera Side
The third concept is unfortunately skipped in most Depth of Field explanations (probably because it feels so confusing to try to explain). But here it goes. For the Near Limit and Far Limit distances on the subject side of the lens, there are precise corresponding distances on the camera side of the lens. There's a distance behind the sensor where the focusing cones converge to points for objects that are at the subject side's Near Limit. Likewise, there's a distance in front of the sensor where the focusing cones converge to points for objects that are at the subject side's Far Limit. The camera side distance between these two planes (one behind the sensor, the other in front of the sensor) is called "Depth of Focus." This can be confusing, especially since the terms are often mistakenly used interchangeably! But just remember, there's "Depth of Field" on the subject side of the lens and there's an exact corresponding "Depth of Focus" on the camera side of the lens.
Here's the big point to take in: The camera side "Depth of Focus" total distance stays constant in size for a given fstop value, regardless of subject distance or even focal length of lens. You can zoom in and out or get physically closer or farther away and as long as you keep the working fstop value the same, the size of the camera side Depth of Focus stays the same. It's a tiny distance, but it's constant. It stays constant because the factors that determine its size are the Circle of Confusion value, which doesn't change, and the angles of the focusing cones, which stay the same so long as the fstop stays the same. Here are some actual camera side Depth of Focus ranges for a .03mm Circle of Confusion (Full Frame sensor):
f2
 0.12mm

f2.8
 0.17mm

f4
 0.24mm

f5.6
 0.37mm

f8
 0.48mm

f11
 0.66mm

f16
 0.96mm

Also, the camera side focal plane (where the sensor is positioned) is always directly in the middle of these Depth of Focus ranges. You can visualize focusing at a specific distance on the subject side of the lens, which sets the exact distance from the lens to the sensor on the camera side of the lens, and then changing the camera side Depth of Focus range around the sensor to these different values just by changing the fstop. The focus point itself isn't changing. The infocus planes on the subject side and camera side are not changing. It's just the size of the focusing cones that are changing, and those cone size changes either shrink or expand the camera side Depth of Focus in a very orderly fashion which is pretty easy to visualize. However, on the subject side of the lens, the corresponding variations in the Depth of Field have an additional complicating twist which we'll address next.
Subject Distances and Camera Side Focal Planes
The fourth depth of field concept to master involves understanding what's going on with the focal planes on the camera side of the lens as you focus on subjects at different distances. The first one to understand is the infinity focus point. Let's consider a 50mm lens on a traditional full frame DSLR. When you focus that lens at a star, or the moon, the lens bends the light into a cone that converges to a point that's 50mm from the lens. That's actually what defines the "focal length" of a lens (where it converges parallel incoming light rays, which is basically what you get when you focus on a very distant subject). Now, if a very distant subject has a focal plane on the camera side that's 50mm from the lens, how far from the lens do you think the focal plane will be for a subject that's just 100 yards away? The answer is 50.027mm. That's right, on the subject side of the lens you've gone all the way from focusing on a star, or the moon, to focusing on something just 100 yards away, but on the camera side of the lens the focal plane has only moved 0.027mm farther away from the infinity focus point! Here's a scale model of the camera side focal plane distances corresponding to different subject side distances for a 50mm lens:
A change in focus distance for far away subjects has a very small corresponding camera side focal plane change, but as subjects get closer, the camera side focal plane distances start to spread out more and more.
Now let's use the scale model of the camera side focal planes for different subject distances together with a scale model of the camera side Depth of Focus ranges for different fstop values. Pick a subject focus distance, say 12 feet. Pick an fstop, say f4. Next, position the f4 Depth of Focus range so it's center is at the 12 foot subject distance mark. Now you're focused on a subject 12 feet in front of the lens, and you can easily visualize how the fixed size camera side Depth of Focus range encompasses a specific set of subject side distances. Those subject side distances that are encompassed by the Depth of Focus range define the Depth of Field for f4 at 12 feet. This is hopefully an "Ah Ha" moment. Slide that f4 Depth of Focus range to a different subject distance and see how it will encompass a different set of subject distances. This is a scale model of what's going on inside your camera as you vary your fstop and focus at different subject distances. Focus on a subject 100 yards away. See how the Depth of Focus range now encompasses huge distances? Now keep the fstop the same and focus on a subject 10 feet away. See how the Depth of Focus range now encompasses much smaller distances?
The main practical point of the fourth concept is this: if you keep the focal length of the lens the same (no zooming in or out) and keep the fstop the same, then physically moving farther away from a subject significantly increases your Depth of Field. Physically moving closer to a subject significantly decreases your depth of field. The scale model can help you see intuitively why this is true.
What Happens with Changing Focal Length
The final point is just a minor extension of what you've already seen. Here's a scale model of the camera side focal planes for subjects at different distances, but with the addition of different focal length lenses. The Depth of Focus range for each fstop stays the same regardless of the focal length of the lens, but you can see that the camera side focal plane distances for corresponding subject side distances are very different.
For example, when you "zoom in" by using a 100mm lens versus a 50mm lens, you end up with a completely different spread of camera side focal planes for the same set of subject side distances. Visualize the f4 Depth of Focus range centered at 16 feet with a 50mm lens versus that same f4 Depth of Focus range centered at 16 feet with a 100mm lens. The subject side distances that get encompassed change significantly. That's why you get shallower depth of field when you stand still and zoom in (as long as the fstop stays the same). But you also have a different amount of the scene filling the frame, so overall it's a very different image. If you physically move from 16 feet to 32 feet, then zoom in by using a 100mm lens versus a 50mm lens, you will actually frame the same scene. Now what happens to the subject side distances that are encompassed by the f4 Depth of Focus range? They end up being almost identical!
The final practical point is this: "moving closer or farther away" by zooming in or out gives you nearly the identical Depth of Field as actually physically moving closer or farther away and leaving the lens focal length the same. As long as the same scene fills the frame (or more technically, the subject is the same size on the sensor), then the Depth of Field will be nearly identical. There's some difference because the Depth of Focus range for a given fstop will encompass a different proportion of subject side distances in front versus behind the focal plane depending on the lens focal length. You can see on the scale model that the shorter focal length lens will have the Depth of Focus range encompassing more subject side distance on the far side of the subject and encompassing less subject side distance on the near side of the subject. The longer focal length lens will have a more even distribution. One last tidbit: For a given fstop, slide the Depth of Focus range so its edge is touching the infinity focus point. There you have a visualization of the "Hyperfocal Distance." That's the most depth of field you can get, from a Near Point all the way to Infinity.
This Depth of Field explanation includes the idea of the camera side "Depth of Focus" ranges together with scale models of the camera side focal planes for subjects at various distances. Hopefully this has provided an intuitive approach to understanding what's going on behind scenes with Depth of Field tables, calculators, and lens scales.
Epiphany?
Which concept helped you gain insight into WHY Depth of Field behaves the way it does?
© 2016 Brad Funkhouser
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