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Do you still have nagging questions in your mind about lenses, aperatures and exposure? Are you confused about circles of confusion? You might be surprised to discover that even many published textbooks present misleadingly kooky information on the subject of basic lens optics.

Would you like to have a more intuitive grasp of how a lens works?

Try this simple thought experiment:

Imagine two points in space, Point A on a brightly colored object, and Point B, on a white wall.

Point B receives light rays from billions of rays coming from billions of places. Its final color is the sum total of all of the incoming light from each ray.

Point A is a point on a well lit, brightly colored object. (In this case, a bright red chili pepper.) It gives off rays of red light in billions of different directions, but only one of those billions of rays travels from Point A to Point B. Because (in our illustration) only one of the billions of rays reaching Point B is red, there is no chance for a human observer to perceive Point B as having any sort of reddish color to it.

Suppose we could position a lens between Point A and Point B in such a way as to take millions of red rays from Point A — rays never originally destined for Point B — and redirect them so that they could contribute their light to Point B.

Point B still receives billions of rays of light, but now, thanks to the lens, millions of those rays come from Point A. You can imagine that with those proportions in effect, Point B now takes on a reddish color.

Since the same can be said for any point on the object, and since any adjacent points on the object "map" to adjacent (but upside-down and backwards) locations on the screen, the lens is "projecting" an image of the object onto the screen.

Let's set up an aparatus to test this theory.

The lens projects an image of an object onto a screen by gathering rays "never intended for the screen" and bending them back towards the screen until they arrive in such quantities at the surface of the screen that they "outnumber" the other rays coming from all kinds of other sources.

(You can see in my aparatus that I've used a square sheet of opaque cardboard to block many ambient rays, thereby helping the lens rays outnumber the ambient rays, resulting in an apparently brighter projected image. In creating a front and back wall, I'm well on my way toward creating a sealed, light-tight box — also known as a camera.)

An iris reduces the amount of light passing through a lens by reducing the size of the aperature through which that light can pass. Make the lens half as big in area, and half of the rays that were redirected by the lens from Point A to Point B now resume their original paths. They miss Point B completely, and Point B receives half the light it was getting with the larger lens.

And here's the fun part: It dosn't matter what you use to reduce the size of the lens. You can stop down with a fancy many-bladed iris mechanism, or you can even use your hand to cover half of the lens. You won't lose half the picture, just half the light. (By the way, losing half of the light through a lens is defined as losing one f-stop of exposure)

The lens makes all of the rays from Point A converge at Point B. If my lens is round then the incoming cone of rays aimed at Point B has a cricular cross section. If I move my movie screen toward or away from the lens, I'll intercept that cone of incoming rays at a place other than its apex. This will cause my image to go out of focus.

When you look at a blurry photograph, you can actually see the shape of the lens by looking at the bokeh — the shape into which pinpoints of light are spread by the lens of the camera.

Remember, the bundle of rays that travels from object to lens forms an outgoing cone. That same bundle is gathered by the lens and reshaped into an incoming cone whose apex lies in the plane of the screen. Move the screen toward or away from the lens such that you intercept that cone elswhere, and you form a blurry picture in which each point of light from the source object becomes one of many overlapping circles. These circles are what photographers refer to when they discuss bokeh.

While (in a blurry projection) every point from the source image "maps to" a circle, a photograph's bokeh becomes most noticeable in the highlights of the image. It bears very little resemblance to the gaussian blur so often used by digital compositors to suggest shallow depth of field. If the lens itself is not circular (because of the shape of the aperature) then neither will be the bokeh. Additional complications or refinements in the optics of a camera can change the distribution of light intensity across its bokeh. Some people render CG which exhibits bokeh.

Small lenses have small bokeh. They also gather less light, which is why they require that brighter light be supplied to the environment, or sometimes that what light there is be allowed to accumulate (on a recording medium like film) over a longer period of exposure time.

A pinhole camera lens, the smallest lens of all, has virtually no bokeh. It also gathers almost no light, in theory allowing only one ray (in the context of our illustration above) to pass from Point A to Point B. Although it contains no glass, a pinhole camera lens does not operate in a way that is qualitatively different from the way in which a glass lens works. Both kinds of lenses have this in common: they both convey to Point B only that light which originates from Point A, and from no other source. Because a pinhole camera lens operates with so little light, it cannot allow to pass through itself a quantity of rays sufficient to compete with much ambient light at all, and if it is to project a discernable image onto film, it must operate in a light-tight camera and with relatively long exposure times.

I took these pictures with a commercially available high precision wooden pinhole camera, but if you're so inclined, you can make your own simple pinhole camera without too much difficulty. The behavior of a typical CG lens most closely resembles that of a pinhole camera lens.

According to a common misconception, image distortion results from the kind of lens one uses. In many people's minds, a wide-angle lens produces great distortion, while a telephoto lens "flattens images."

In fact the distortion arises from the distance between camera and object, and it becomes most apparent when a distantly-photographed object is unnaturally magnified by a telephoto lens, or when a closely-photographed object is unnaturally reduced by a wide-angle lens.

In the diagrams above, three unit cubes were simultaneously rendered at 4K resolution using a (very wide-angle) 10mm lens on Maya's default film back. All three cubes share common vanishing points (look closely).

The distant cube seems "flatter" than the others because the relative size difference between the front cube face, 100 units away, and the rear cube face, 101 units away, is small. The front cube, by contrast, seems greatly distorted because the front face of the unit cube, at 1 unit away, is twice as close to the camera as is the rear face of the cube, at 2 units away.

Close objects display distortion by virtue of their closeness. People associate distortion with wide-angle lenses because such lenses are commonly used to pleasingly frame close objects. The wide angle lens is not the cause of the distortion.

Distant objects display flatness by virtue of their distance. People associate flatness with telephoto lenses because such lenses are commonly used to pleasingly frame distant objects. The telephoto lens is not the cause of the flatness.

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