Ok - you reduce the number of versions of the same image getting to the film which lessens the photons hitting it. That's cool. But how does that really cause the depth of field increase?
For the long explanation, see here:
http://www.normankoren.com/Tutorials/MTF6.html
Here is the short version,
There is only ONE distance from the lens that is perfectly focused. That would be S above. The light passing through the lens and aperture is perfectly focused on the film/sensor plane. That is true regardless of the aperture used.
Now look at the light rays for the object at Sr and Sf. Because of their shift behind or in front of S, their light does not hit the film/sensor plane where all the light intersects again into a single point. If you look at the red/green lines, and imagine them being in the shape of cones, the cone for the red lines is truncated by the film/sensor plane before it comes to a point, so you get a circle on the film/sensor instead of a point. The green cone comes to a point in front of the film/sensor plane and then starts a new expanding cone as it continues toward the film/sensor plane. It too gets truncated by the film/sensor plane and creates a circle. This is what is referred to as the Circle of Confusion. The larger the circle of confusion, the more out of focus something will be.
If "a" is reduced, or you "stop down", then the angle between the sides of the cones are reduced. Thus at the point of truncation for each cone, the circle of light created on the film/sensor plane gets smaller. The objects from which the light is coming get sharper. There is a limit to this effect though.
Light has that pesky nature that allows it to act like particles traveling in a straight line (as the diagram above shows), but it also acts like a wave at the same time. When waves pass through an opening, they tend to spread out on the far side of the opening. Check out the next image and you will see what I am talking about.
With a big opening, the diffraction is reduced. The wave tends to stay close to its original shape. With a small opening, diffraction increases and the wave spreads to the sides much more.
So what you have are the two natures of light working against each other. A large opening reduces diffraction but increases the circle of confusion for objects that are not right on the focal plane. We get what is called a shallow depth of field. A small opening may reduce the circle of confusion and thus render objects further from the focal plane as sharper, but now diffraction starts to become a problem as we continue reducing the size of the opening. For every lens, there tends to be a "sweet spot" in terms of getting the best sharpness by reducing the circle of confusion but not losing sharpness because of diffraction. As a ROUGH rule of thumb, that spot will generally be in the middle of the aperture range for the lens, but not necessarily. Much depends on the internal optics of the lens.
We often speak of the DOF as the range where everything is in focus, but that is not really correct. There is only ONE plane where everything is perfectly focused. As we move in front of or behind that plane, we start to lose focus no matter what, but changing the aperture allows us to control the degree of out of focus by manipulating the circle of confusion and minimizing the effect of diffraction.
If you get into Macro photography, then diffraction can really become an issue that you have to pay attention to. But for most other realms of photography, we can usually ignore it and just pay attention to what we normally think of as DOF where everything is "in focus" or close to it.
Did that help?
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