Technically, why is the out of focus area blurred more when using a bigger aperture?

Question

I'm wondering, technically, why and how does the out of focus areas blur more when using a bigger aperture. I think it'd help a lot if I presented a problem that's been driving me nuts for a long time:

I've read that the f-number of the human eye varies from about f/8.3 in very bright light to about f/2.1 in the dark. But from what I've tested, I always see out-of-focus areas with the same amount of blur.

Which leads me to ask: how does this aperture thing work, why does it create a blur from the technical point of view, and does it also apply to eyes, or is it just a "failure" in the camera lenses we've come to like and never wanted to "fix"?

Answer 1

I'm going to crib from my answer to an earlier question on aperture:

When the aperture is very small, the admitted light is highly "collimated", which is a fancy way of saying "all the rays are nicely parallel to each other". This results in a sharp focus for all the light that comes in. When the aperture is more open, only the rays which closely match the focus point are collimated — which means that whatever you've focused on is sharp, but farther or closer parts of the scene will be increasingly blurry.

Basically, the smaller the aperture, the more restricted-to-exactly-in-focus the light is. A bigger aperture lets in more light, but the "price" is that it's less controlled.

The following diagram from Wikimedia may help:

On the left, the wide aperture results in only the center, focused ♡ card rendered sharply. The more-narrow aperture on the right excludes the less-collimated light from the out-of-focus ♠ and ♣ cards, resulting in a sharper image overall.

Remember, the red/green/blue dotted lines in the diagram trace the outside of a cone of light rays. The more-focused light is also included in the image made with the wider aperture on the left, but the image sensor (or film) can't tell which was which, so the result is more blur except for the rays which happen to be precisely at the focal point.

This surely happens with the human eye as a lens as well. I think it's just really hard to control your experiment, since you can't actually snap a picture to compare side by side. In the time between evening and midday — or even in the half hour it takes your eyes to acclimate to a dark room — you lose the perfect memory of how much blur there was. This is further complicated by the fact that your brain is working very hard to correct all defects from the eyes and present a mental model of the entire world in perfect focus. (That's what the brain part of the human vision system does.)

It's very hard to look at just one spot; your eye flicks around subconsciously, and builds a perfect image from one which is really only sharp in the center. This adds another huge complication — not only is the lens of the eye a relatively simple system with a lot of aberrations, the sensor is irregular. Or rather, it's highly specialized. The central area is called the fovea, and that's only about 1mm in diameter — and the most sharp part, the foveola, is only 0.2mm. That's where really sharp vision comes from. But this area doesn't contain any rods (the cells sensitive to dim light), so this sharp area is not involved at all when you're in dim light. This makes a simple comparison with camera systems basically impossible.

On top of that, there's another flaw in your basic assumptions — the idea that the human eye sees the same amount of motion blur no matter the amount of light. Actually, the input is actually integrated over time, and the amount of time does increase in lower light levels. And, "exposure" is actually controlled in another way: the sensitivity is boosted in the darkness — the effective equivalent of auto-ISO.

So, to get to the direct question: it's the nature of optics, and so it also applies to our eyes. But our eyes are a different kind of system than a camera and lens. The human vision system features a simple lens, a complicated sensor, very complicated instantaneous post-processing, and an incredibly complicated storage and retrieval system. A camera generally uses a sophisticated lens, a comparatively straightforward sensor matrix, and comparatively straightforward post-processing (until computational photography comes into its own — whether Lytro succeeds this year or someone else five years from now). And the memory system is bit-for-bit perfect — not like human memory in the least.

Whether this difference is something we "like" and don't want to fix is a matter of interpretation. Certainly the idea of depth of field is in our artistic/visual vocabulary as a society; whether it will stay that way in a hundred years is a matter of speculation. My guess is yes, even as technology changes.

A camera with a different type of sensor, like that used in the Lytro can actually record the direction of the incoming rays of light. This additional data allows these cameras to create an entirely-sharp image even with a very large aperture. But that's not how the Lytro company is selling it: instead, their gimmick is images where you can click to change the calculated point of focus on the fly. That they chose this route rather than the all-

Answer 2

Why the wide aperture blurs the background more

Let me start with Wikipedia figure:

Above we have a wide open aperture. Only point 2 is in focus. Points 1 and 3 are out of focus. Due to wide aperture, the rays coming from them through different parts of the lens intersect the screen 5 (a film or a digital sensor) in different points. We may also tell that these rays form a point (intersect) before (red) or beyond (green) the screen. The corresponding cones of light intersect with the screen and form an ellipse-like image on the screen. Wider aperture allows for wider cone of light (so it allows to collect more light and blurs more).

Effectively, an out-of-focus point produces a circle of confusion. This is what we can call blur or bokeh.

For smaller aperture below, the rays too far from the center are cut off, so the circle of out-of-focus point is smaller.

If the circle of confusion is smaller than film grain or sensor subpixel, we cannot tell if it is out of focus at all, and then the point appears as in focus even if it is not. So with finite aperture, there is a range of distances which all appear as in focus. The depth of this range is called the depth of field (DoF). It is bigger for smaller apertures.

If the aperture is really, really small, then only the central rays can pass, and we have an infinite depth of field no matter what. Every point, close or far away, is represented as a point on the image. This is how pinhole camera works. Adjustable aperture allows to have anything in between.

How it looks like

At smaller aperture f/32:

At larger aperture f/5, an out-of-focus background is blured more:

(images are again from Wikipedia)

Answer 3

Light rays arriving from the focused subject are refracted when passing through the lens and hit the sensor (film). Rays originating from a single point form a cone which base is the open circle in the lens. The bigger the aperture, the bigger the base of the cone. Then, a secondary cone is formed and the rays meet again at the focal point.

Rays originating from subjects that are in different distance from the lens form cones of different lengths (heights, to be more accurate). For longer cones (objects beyond the focused subject), the secondary cones are shorter. For shorter cones (objects in front of it), the secondary cone is longer. The length of the secondary cone is determined by the length of the primary cone.

Because of that, when the light from a point on the non-focused object approaches the sensor, the image is a small circle, rather than a single point (it is really more of an ellipse but lets neglect that).

When the aperture gets larger, the base of the two cones get larger, and hence their head angle. Because the length remains unchanged, the image circle gets bigger. This is why you get more blur when the aperture is wider.

For reference, and a schematic that really explains all the mambo-jumbo above, read this article.

Answer 4

The other answers incorrectly associate the blur effect with some lens properties. You don't have to assume anything about how the image is formed by the lens or even that a lens exists.

The scene simply looks slightly different from different locations across the aperture.

As you can see in the picture, if you choose to keep the red object in the same position for each aperture point, there is no way the green object can stay in the same position. This creates blur, because the final image combines all those individual views.

This means that theoretically (and ignoring diffraction) the only case when where everything can be in focus is pinhole, creating the image from a single point. In the real life a small but not pointlike aperture is better, because of diffraction and increased amount of light, but that's another question.

Pursuing the subject further, "who" actually selects what is in focus?

Why the red object and not the green one? The geometry only determines that they cannot be both in focus and the amount of defocus depends on the aperture and this is the fundamental reason of the DOF effect.

How actually the final image is combined from partial views? This depends on the "blue box" device. In the real life, the "blue box" is of course lens. Until now, we pretended we don't know anything about how the image is combined in order to show that the out-of-focus phenomenon emerges from geometry and not from the lens properties.

But it does not have to be lens. Instead, we might place thousands of pinhole image recorders across the aperture surface and acquire thousands of individual images. Then, by simply overlaying those images we get the same DOF effect - depending purely on the aperture. And unlike lens, we might then overlay the same images differently, keeping the green object stationary (which would blur the red one, obviously).

Answer 5

When light hits the sensor it creates a spot the same shape as the aperture but at size dependant on real world distance of the source object from the plane of focus. If the aperture is a circle you get a circle, if the aperture is square you get a square. The bigger the aperture, the bigger the shape, thus it will overlap more with neighbouring shapes and give you more blur.

As you get close to the focal plane the size of the shape projected into the sensor is so small it's indistinguishable from a dot. These distances define the depth if field.

Your eye works in exactly the same way, but I wouldn't trust what you're seeing as the brain does a crazy amount of processing! You only see detail within a tiny spot in the centre of each eye. Your brain moves each eye around very quickly to "scan" the scene and pieces it all together without you ever knowing!

Answer 6

Look at it this way. With a small enough aperture, you don't even need a lens! That is called a pinhole camera.

A lens focuses objects at a particular distance, because it works by bending light.

A pinhole (at least an ideal one) works by mapping points of light from different angles to corresponding angles on the film, irrespective of distance. (Real pinholes have limitations. Too small a pinhole will simply scatter light due to diffraction.)

An aperture in front of a lens brings in some of the characteristics of the pinhole. The smaller you make the aperture, the more you effectively turn your camera into a pinhole camera. This brings in the advantage of wide depth-of-field focus, but also some of the disadvantages of the pinhole: less light gathering power, diffraction artifacts at very high f stop numbers.

Answer 7

This is not technical explanation, but it is experiment. Following text is copied from Ben Long's book Complete digital photography:

If you are nearsighted enough to need glasses, try this quick little depth-of-field experiment. Take off your glasses and curl up your index finger against your thumb. You should be able to curl your finger tight enough to create a tiny little hole in the curve of your index finger. If you look through the hole without your glasses, you will probably find that everything is in focus. This hole is a very tiny aper-ture, and therefore provides very deep depth of field—deep enough, in fact, that it can correct your vision. On the downside, it doesn’t let a lot of light through, so unless you’re in bright daylight, you might not be able to see anything well enough to determine if it’s in focus. The next time you’re con-fused about how aperture relates to depth of field, remember this test

I tried this, and it really works. Try to look at some text which is about 100m away from you. I'm wearing short-sighted glasses.

Answer 8

The blur is greater because the impulse response of the optical system is modified adversely by using a larger aperture. However, if the aperture is made smaller (nominally f/11 or f/16 in some lenses) then the degradation due to diffraction effects becomes more dominant. So there is an optimal aperture, which is somewhere between an ideal impulse response and the diffraction limitations of a lens.

The point spread function is the optical transfer function, which is the Fourier Transform of the optical impulse response function.

The MTF (modulation transfer function) is similar to the OTF, except that it ignores phase. In non-coherent photography applications they can be considered quite similar.

Essentially the OTF, MTF, point spread function, describe the responsiveness of the optical system.

When a lens is wide open, the path of the light has more variability in the path, so that off the exact focus point, it has a greater point spread function which as it convolves with the image becomes the blur.

Below is an answer I recently provided to a similar question. https://physics.stackexchange.com/questions/83303/why-does-aperture-size-affect-depth-of-field-in-photography

Depth of field is a perception phenomenon which factors in the HVS (human visual system). It is really a game of "how much blur can we have until it becomes objectionable?" There is only one "plane" (usually really a segment of a sphere) which is in focus. At that point the imaging system performs in accordance with losses such as atmospherics and the MTF (modulation transfer function) of the lens.

As an object moves off that plane, it immediately becomes "out of focus" and there is a point spread function which describes a growing disk which is in some circles (no pun intended) called the "circle of confusion."

Smaller apertures employing central portions of the lens, have the light taking a shorter (and more consistent) path through the lens. This helps reduce the point spread function which describes the circle of confusion (and not always a circle). The point spread function of an optics system is also called the impulse response.

The resultant image is one which is the convolution of the target image and the point spread function. At least for non-coherent imaging. So the perception of the depth of field is linear with the f-stop and focal length.

Unfortunately, depth of field has it limits, and a very very small aperture will not provide nearly infinite depth of field, because diffraction plays a greater role, in blurring the image, as the aperture gets smaller.

So what really happens with depth of field is that objects are not really in focus off the focused plane, but rather the blur is considered negligible. Think of it this way: a thumbnail photo might look clear, but if expanded to be an 8x10" photo, it may be unacceptably fuzzy. So acceptable depth of field is a determination of the effect of the impact of an off focused image on the observer, given the optical system (atmospherics, lens, sensor/film, and rendering/printing process) and the perception perspective (how big is the viewed image).

In practical application, a so-called hyper-focal setting on a lens, may give an acceptable image of a scene when viewed on a small format display or print, but when expended or enlarged, will yield a more fuzzy appearance as it is in reality not completely in focus through the "depth of field."

Comments are welcome, and perhaps I can rewrite both answers to be more universal to address this common question.