Depth of Field Definitive(ish)
An attempt to explain WHY we get Depth of Field
On the last page I gave you a Photographers perspective on Depth of Field. This is the view expressed in most books and magazines that address the subject, it’s not that they are wrong, it’s just that some of the criteria used to to explain Depth of Field are actually irrelevant. Here is a bold statement.
Scale Ratio is the ONLY thing that effects Depth of Field
Why is it that our lenses can’t focus everything? Well it’s just Scale Ratio and Geometry. The Geometry we can’t alter the Scale Ratio we can (and do all the time).
Let’s go back and look at the definition of Scale Ratio. The Scale Ratio is simply the size of your sensor compared to the size of the subject you are photographing expressed as a ratio, something to 1, the 1 being the size of your sensor which, of course, is a fixed size, the something is how many times your sensor would fit into your subject.
The higher the ratio the wider the Depth of Field, the lower the ratio the narrower the Depth of Field (We’ll see WHY later).
Focal length is often used as a variable when defining Depth of Field, it’s not that this is wrong, it’s just that it’s irrelevant.
Suppose you take a shot framing a building from 100 feet away with a 500 mm lens at f8, you would get a reasonable Depth of Field. Now take a 50 mm lens and frame the same shot again at f8, you have to be closer (around 10 feet away), the point being is that the Depth of Field would be exactly the same!!. The focal length of the the lens is irrelevant the ONLY thing that matters is the Scale Ratio, how many times the building is compared to the size of your sensor. The only thing that altering the focal length of the lens actually alters is how far away from the subject you are.
A more extreme example is when we move close to the subject and Depth of Field becomes a real issue. If you fit your 500mm lens with the aperture at f8 onto a set of bellows and frame a subject Life Size, that is a Scale Ratio of 1:1 the Depth of Field will be tiny (0.08cm), change the lens for a 50mm lens at f8 and reframe to get the same Life Sized image on your sensor and the Depth of Field will be exactly the same, at a Scale Ratio of 1:1 the Depth of Field is always 0.08cm at f8. Again the only thing that alters is how far away from the subject you are, with the 50mm lens you will be around 2 Inches, with the 500mm lens around 7 feet!!
That’s the effect let’s take a look at the why.
To see why Scale Ratio alters Depth of Field we have to go back and look at the light as it falls on the subject. As the light hits the subject it is diffused, bounces off in all directions, some of which come our way towards our lens, the light does not come off the subject as parallel beams, each beam of light is a slightly diverging cone of light. We are talking a tiny divergence measured in micrometers or even Pico meters. If you can visualise it think of a ' cloud of light ' coming from your subject.
Your lenses job is to focus these diverging beams back into a point source again, it focuses these beams onto your sensor, and we get a clear image. Your lens has a plane of focus either side of which the image projected by the lens gets progressively less sharp.
This is where the geometry comes in. If you imagine these cones of light from a distant object they are coming to the lens at pretty much the same angle, virtually parallel to each other and the lens can focus them all onto a flat plane that is your sensor. They will all be within the bounds of acceptable focus.
What happens when you move closer (decrease Scale Ratio) is that you increase the angle of these beams relative to each other, as the angle gets steeper the cones of light get less and less parallel to each other the closer you get, the result is your lens can no longer focus all the rays onto the same plane (your sensor). Points of light that are behind the plane of focus will focus behind the sensor plane, those that are in front of the plane of focus will focus in front of your sensor. On these cones the sensor is seeing the cone of light before or after it is focused which is WHY it’s blurry. As I said it's just geometry. The term used is Acceptable Angle those rays within the acceptable angle will be focused on the sensor plane, those outside will not, the further they are from the Acceptable Angle the more diffused (blurred) they will be.
The Effect of Aperture
Why does making the aperture smaller increase Depth of Field? Well we're back to Scale Ratio again, this time the scale is a ratio between Aperture size and Sensor size. As the sensor size is fixed we only have to worry about the aperture size. The aperture is (usually) smaller than the sensor so we have a negative ratio (<1:1), which has the effect of increasing the lenses overall Scale Ratio (the higher the Scale Ratio the greater the Depth of Field), the smaller the aperture the the more it increases the overall Scale Ratio the lens is seeing, when close to our subject the more of the diverging rays will fall into the Acceptable Angle. In the distant view the rays are parallel and the effect of Aperture is minimal other than controlling the light, as we move closer and lower the Scale Ratio the effect of Aperture gets more pronounced.
As Aperture is independent of the original Scale Ratio and can be altered separately, mitigating the effects of the Scale Ratio, keeping it as a separate variable is valid.
I find just using Scale Ratio when I want to visualise Depth of Field is easier for me than all the other ways that involve loads of variables that are irrelevant to what is happening.
Using Scale Ratio explains WHY a camera with a small sensor will always have more Depth of Field than a camera with a large sensor, WHY a wide angle lens has more Depth of Field than a telephoto lens. Knowing WHY opens the door to understanding.