How aperture affects depth of field

Michael Fryd

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In another thread, a beginner photographer was having trouble understanding why aperture affects depth of field. A few people had tried to explain it, but he was having trouble with the math.

I thought I would put up a few diagrams, which hopefully will make things a little clearer without any need for math.

.

To keep things simple. Let's assume we are taking a photo of three points, which are at various distances from the lens. A purple point, a blue point, and a yellow point.

Light from each point spreads out in all directions, however, we only care about those rays of light that reach the lens. Let's look at a diagram showing some of those rays.

cb4f0be558c34be5bb24e4bd91be20c2.jpg.png

Notice that when the rays hit the lens, they change direction. This is the purpose of a lens.

In this example, the lens is focused on the blue point. Notice that all of the rays from the blue point converge at a single point on the sensor.

The yellow point is further away. Note that all the rays from the yellow point converge in front of the sensor, and then start to diverge. By the time they reach the sensor, they spread out. Thus they are spread out when they hit the sensor. If the yellow point had been further from the lens, the amount of spread would have been larger.

The purple point is closer to the sensor. Those rays hit the sensor before they have a chance to converge. They are also spread out over a small area of the sensor. If the blue point had been even closer to the sensor, the amount of spread would have been larger.

.

The yellow and blue points are not in perfect focus. Their images get spread out over a small circle on the sensor. The size of this circle (the amount of blurriness) is called the "Circle of Confusion", which is abbreviated as "CoC".

The human eye is not a microscope, nor is it perfect. If the CoC is small enough, the human eye won't notice the blurriness, and the corresponding point will look like it is in focus.

Remember, the CoC gets bigger as we move away from the focus distance. There is a range of distances around the focus distance where the CoC is small enough that everything looks to be in focus. This range is the depth of field.

.

Smaller apertures tend to increase the depth of field range. With a smaller aperture we get a "deeper" depth of field.



Let's look to see how the aperture reduces the size of the CoC.



473173beea944f2b96518116a94bef9d.jpg.png



In the above diagram we have added an aperture. This is a hole that blocks some of the light. Notice that rays of light that were blocked are towards the edges of the lens. If you look carefully at the diagram, you will see that with the outer rays blocked, the spread of the remaining rays is smaller in size. A smaller spread is a smaller CoC. A smaller CoC means the the point looks sharper.

If the purple point was previously just outside the depth of field, the CoC reduction from the smaller aperture may be enough to bring it within the depth of field.

Thus a smaller aperture yields a deeper depth of field, as the smaller aperture blocks the outer rays, reducing the blurriness.
 
Excellent illustration.

This should be a standard to explain the basic.
 
Nice but the OP got lost somewhere else. Here is his last post with my comments:
I'm having trouble with this explanation. I should not have thought about it.

No, with a longer lens, more light will be let in, but that light will decrease in intensity as it travels to the sensor, with the square of the distance
No, this is focused light. In fact, it increases its intensity as it travels (well, this applies for the cone corresponding to any point on the object side).
If the more light is admitted to the sensor, what is meant by decreasing intensity? In my mind more light = more intensity

The intensity of the light reaching the sensor will be the same in each case.
I guess you are talking about shooting the same object with different FL’s? Or the same one but from a farther distance with a longer lens? Eventually, the images projected will be equally bright, indeed, but the longer lens in the second scenario would receive lower intensity at the front element because the object is farther away. The focusing increases that intensity, and eventually you get the same brightness.
This is just my reading comprehension, but I'm not following the explanation. This seems to negate the statement above.
 
Small correction:

The yellow and purple points are not in perfect focus.

Very clear diagrams. Should be easy to understand for anybody. When it gets complicated (and not quite intuitive?) is when you add different focal lengths and subject distances and want to compare DoF in each case.

 
The simplest diagrams I've seen that illustrate the effect of aperture are something like the following...

7e9614275821412e8d0a6fe00ae00e09.jpg

From left-to-right, light passes through a lens that's also the aperture, is refracted to the focus point (green dot) and diverges beyond that point.

The human visual system perceives slightly imperfect focus as being acceptably sharp. At some point the amount of defocus is enough that we see the detail as blurred. The range of distance within which details look acceptably in focus (the space between the red vertical lines) is the depth of field.



4df7e2a7588b4c68b5e8172ec8fe443d.jpg

When light passes through a smaller aperture, it's refracted along a shallower path to the focus point and diverges along a similarly shallow path beyond the focus point. As a result, there's a greater distance before and after the focus point within which details in slightly imperfect focus are seen as being sharp enough. Depth of field is greater.

--
Bill Ferris Photography
Flagstaff, AZ
 
In another thread, a beginner photographer was having trouble understanding why aperture affects depth of field. A few people had tried to explain it, but he was having trouble with the math.

I thought I would put up a few diagrams, which hopefully will make things a little clearer without any need for math.

.

To keep things simple. Let's assume we are taking a photo of three points, which are at various distances from the lens. A purple point, a blue point, and a yellow point.

Light from each point spreads out in all directions, however, we only care about those rays of light that reach the lens. Let's look at a diagram showing some of those rays.

cb4f0be558c34be5bb24e4bd91be20c2.jpg.png

Notice that when the rays hit the lens, they change direction. This is the purpose of a lens.

In this example, the lens is focused on the blue point. Notice that all of the rays from the blue point converge at a single point on the sensor.

The yellow point is further away. Note that all the rays from the yellow point converge in front of the sensor, and then start to diverge. By the time they reach the sensor, they spread out. Thus they are spread out when they hit the sensor. If the yellow point had been further from the lens, the amount of spread would have been larger.

The purple point is closer to the sensor. Those rays hit the sensor before they have a chance to converge. They are also spread out over a small area of the sensor. If the blue point had been even closer to the sensor, the amount of spread would have been larger.

.

The yellow and blue points are not in perfect focus. Their images get spread out over a small circle on the sensor. The size of this circle (the amount of blurriness) is called the "Circle of Confusion", which is abbreviated as "CoC".

The human eye is not a microscope, nor is it perfect. If the CoC is small enough, the human eye won't notice the blurriness, and the corresponding point will look like it is in focus.

Remember, the CoC gets bigger as we move away from the focus distance. There is a range of distances around the focus distance where the CoC is small enough that everything looks to be in focus. This range is the depth of field.

.

Smaller apertures tend to increase the depth of field range. With a smaller aperture we get a "deeper" depth of field.

Let's look to see how the aperture reduces the size of the CoC.

473173beea944f2b96518116a94bef9d.jpg.png

In the above diagram we have added an aperture. This is a hole that blocks some of the light. Notice that rays of light that were blocked are towards the edges of the lens. If you look carefully at the diagram, you will see that with the outer rays blocked, the spread of the remaining rays is smaller in size. A smaller spread is a smaller CoC. A smaller CoC means the the point looks sharper.

If the purple point was previously just outside the depth of field, the CoC reduction from the smaller aperture may be enough to bring it within the depth of field.

Thus a smaller aperture yields a deeper depth of field, as the smaller aperture blocks the outer rays, reducing the blurriness.
This is by far the best and easiest to understand explanation of how aperture affects DOF that I have seen anywhere.

Thank you 🙂
 
The simplest diagrams I've seen that illustrate the effect of aperture are something like the following...

7e9614275821412e8d0a6fe00ae00e09.jpg

From left-to-right, light passes through a lens that's also the aperture, is refracted to the focus point (green dot) and diverges beyond that point.

The human visual system perceives slightly imperfect focus as being acceptably sharp. At some point the amount of defocus is enough that we see the detail as blurred. The range of distance within which details look acceptably in focus (the space between the red vertical lines) is the depth of field.

4df7e2a7588b4c68b5e8172ec8fe443d.jpg

When light passes through a smaller aperture, it's refracted along a shallower path to the focus point and diverges along a similarly shallow path beyond the focus point. As a result, there's a greater distance before and after the focus point within which details in slightly imperfect focus are seen as being sharp enough. Depth of field is greater.
Simple as that. Nicely done.
 
The simplest diagrams I've seen that illustrate the effect of aperture are something like the following...

7e9614275821412e8d0a6fe00ae00e09.jpg

From left-to-right, light passes through a lens that's also the aperture, is refracted to the focus point (green dot) and diverges beyond that point.

The human visual system perceives slightly imperfect focus as being acceptably sharp. At some point the amount of defocus is enough that we see the detail as blurred. The range of distance within which details look acceptably in focus (the space between the red vertical lines) is the depth of field.

4df7e2a7588b4c68b5e8172ec8fe443d.jpg

When light passes through a smaller aperture, it's refracted along a shallower path to the focus point and diverges along a similarly shallow path beyond the focus point. As a result, there's a greater distance before and after the focus point within which details in slightly imperfect focus are seen as being sharp enough. Depth of field is greater.
It may have different meaning in Japanese :-) but the way it is drawn, it shows tolerance to defocusing, not DOF.
 
Here is a more to scale simulator. In particular, you can see that the DOF behind the plane of focus is deeper.
 
The simplest diagrams I've seen that illustrate the effect of aperture are something like the following...

7e9614275821412e8d0a6fe00ae00e09.jpg

From left-to-right, light passes through a lens that's also the aperture, is refracted to the focus point (green dot) and diverges beyond that point.

The human visual system perceives slightly imperfect focus as being acceptably sharp. At some point the amount of defocus is enough that we see the detail as blurred. The range of distance within which details look acceptably in focus (the space between the red vertical lines) is the depth of field.

4df7e2a7588b4c68b5e8172ec8fe443d.jpg

When light passes through a smaller aperture, it's refracted along a shallower path to the focus point and diverges along a similarly shallow path beyond the focus point. As a result, there's a greater distance before and after the focus point within which details in slightly imperfect focus are seen as being sharp enough. Depth of field is greater.
It may have different meaning in Japanese :-)
Hopefully not something offensive :)
...but the way it is drawn, it shows tolerance to defocusing, not DOF.
With depth of field being a perceived quality determined, in part, by a circle of confusion - the diameter of the largest detail that appears acceptably sharp - isn't a range of tolerable defocus a reasonable indicator of depth of field? If there's a wider range of acceptable sharpness within the image projected on the glass plate, film, or sensor, would that not translate to greater depth of field?

If not, it would be interesting to see an example of a situation in which that quality would correlate with depth of field becoming more shallow.

I'm trying to keep in mind that we're looking for a simple, understandable way to convey in a broad sense how aperture affects depth of field in the Beginner's Questions forum. I think Michael's off to a good start but am looking for opportunities to simplify even more to arrive at something that, while not technically precise, is accurate enough.

--
Bill Ferris Photography
Flagstaff, AZ
 
This demonstrates what happens when you move the sensor forth and back or when you defocus the lens by just moving it and your target is at infinity. It doesn't hint at the properties of lenses to image objects farther away closer to the lens. In other words, the lens equation is not demonstrated. You do not see how objects at different distances are imaged, which is the whole point.
 
The simplest diagrams I've seen that illustrate the effect of aperture are something like the following...

7e9614275821412e8d0a6fe00ae00e09.jpg

From left-to-right, light passes through a lens that's also the aperture, is refracted to the focus point (green dot) and diverges beyond that point.

The human visual system perceives slightly imperfect focus as being acceptably sharp. At some point the amount of defocus is enough that we see the detail as blurred. The range of distance within which details look acceptably in focus (the space between the red vertical lines) is the depth of field.

4df7e2a7588b4c68b5e8172ec8fe443d.jpg

When light passes through a smaller aperture, it's refracted along a shallower path to the focus point and diverges along a similarly shallow path beyond the focus point. As a result, there's a greater distance before and after the focus point within which details in slightly imperfect focus are seen as being sharp enough. Depth of field is greater.
It may have different meaning in Japanese :-)
Hopefully not something offensive :)
...but the way it is drawn, it shows tolerance to defocusing, not DOF.
With depth of field being a perceived quality determined, in part, by a circle of confusion - the diameter of the largest detail that appears acceptably sharp - isn't a range of tolerable defocus a reasonable indicator of depth of field?
A different concept for a different purpose. It is called depth of focus: https://en.wikipedia.org/wiki/Depth_of_focus
 
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If anyone happens to have fairly bad eyesight and wears glasses, you can simulate the affect aperture has with your eyes. Form a circle with your thumb and first finger and look through the hole at an object that is not clear to your eyes, then slowly close that circle down to as small as possible and watch the blurry object get clearer as the hole you are looking through gets smaller. Same effect. Also, fancy rifle peep sights have variable aperture openings to be able to close down so you can see the front sight and the distant target both clearly.
 
The simplest diagrams I've seen that illustrate the effect of aperture are something like the following...

7e9614275821412e8d0a6fe00ae00e09.jpg

From left-to-right, light passes through a lens that's also the aperture, is refracted to the focus point (green dot) and diverges beyond that point.

The human visual system perceives slightly imperfect focus as being acceptably sharp. At some point the amount of defocus is enough that we see the detail as blurred. The range of distance within which details look acceptably in focus (the space between the red vertical lines) is the depth of field.

4df7e2a7588b4c68b5e8172ec8fe443d.jpg

When light passes through a smaller aperture, it's refracted along a shallower path to the focus point and diverges along a similarly shallow path beyond the focus point. As a result, there's a greater distance before and after the focus point within which details in slightly imperfect focus are seen as being sharp enough. Depth of field is greater.
It may have different meaning in Japanese :-) but the way it is drawn, it shows tolerance to defocusing, not DOF.
But that's the same thing.
 
If anyone happens to have fairly bad eyesight and wears glasses, you can simulate the affect aperture has with your eyes. Form a circle with your thumb and first finger and look through the hole at an object that is not clear to your eyes, then slowly close that circle down to as small as possible and watch the blurry object get clearer as the hole you are looking through gets smaller. Same effect. Also, fancy rifle peep sights have variable aperture openings to be able to close down so you can see the front sight and the distant target both clearly.
Not quite. You are actually forming a pinhole camera. Pinhole cameras "focus" on everything from zero to infinity because it is a geometric projection.

You can actually buy pinhole glasses that have opaque "lenses" covered in tiny holes that employ the effect.
 
If anyone happens to have fairly bad eyesight and wears glasses, you can simulate the affect aperture has with your eyes. Form a circle with your thumb and first finger and look through the hole at an object that is not clear to your eyes, then slowly close that circle down to as small as possible and watch the blurry object get clearer as the hole you are looking through gets smaller. Same effect. Also, fancy rifle peep sights have variable aperture openings to be able to close down so you can see the front sight and the distant target both clearly.
Not quite. You are actually forming a pinhole camera. Pinhole cameras "focus" on everything from zero to infinity because it is a geometric projection.

You can actually buy pinhole glasses that have opaque "lenses" covered in tiny holes that employ the effect.
Your eye is still there. Bob is right.
 
Small correction:

The yellow and purple points are not in perfect focus.

...
Thank you for the catching this typo. Unfortunately, I don't know how to change it at this point.
 

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