Lens Cameras

The aperture in a pinhole camera is simply a hole: it does nothing to the light that passes through it. Suppose that we place a carefully shaped disk of glass—a lens— in the aperture. Because light passes through glass more slowly than it passes through air, a wavefront encountering glass slows and changes its direction of propagation—that is, the rays of light bend when they pass from air to glass or from glass to air. By shaping the lens so that each ray is bent in direct proportion to its distance from the center of the glass, parallel rays of light from a source will converge until they cross. The rays cross at a point called the focus. After reaching the focus, the rays will continue on diverging paths unless they are intercepted at the focus by a viewing screen, a piece of photographic film, or an electronic detector, such as a CCD chip.

Rays that pass through the center of a lens are called principal rays. Principal rays pass through a lens and exit parallel to their original paths. Since the lens is shaped so that all rays from a given source cross the principal ray at the focus at the receiving surface, all of the rays from a source meet at the focus. A camera equipped with a lens collects all of the light from a star that falls on the lens and concentrates it into a single bright point.

In practice, lenses almost always contain multiple elements made of different types of glass. As light passes through the multiple surfaces and glass types, the wavefront undergoes subtle manipulation. A great deal of art and effort goes into designing optical systems that bring light to an accurate focus.

However complex its internal design, a compound lens acts like an equivalent simple lens. The distance between the location of the equivalent simple lens and the focal plane is the focal length of the lens. Optical designers work hard to

Figure 1.2 The lens of a camera directs rays from a large area to a focal point, resulting in a bright, sharp image. The image of each object falls in exactly the same place that it would in a pinhole camera because the lens directs all rays to converge on the principal rays, which remain parallel to their original paths.

Figure 1.2 The lens of a camera directs rays from a large area to a focal point, resulting in a bright, sharp image. The image of each object falls in exactly the same place that it would in a pinhole camera because the lens directs all rays to converge on the principal rays, which remain parallel to their original paths.

maintain a strict linear relationship between the focal length, F, the tangent of the angular distance from the optical axis, tand, and the ray height, h, from the optical axis:

This is exactly the same rectilinear relationship found in the pinhole camera; that is, under ideal conditions, lens geometry (Equ. 1.4) is the same as pinhole geometry (Equ. 1.3). The lens directs the light from the sources in front of the camera to a tiny point of focus. A camera equipped with a lens forms an image with the same geometric properties as that formed by a pinhole camera, but because the lens admits more light than a pinhole, the image is brighter.

Despite the best efforts of their designers, lenses exhibit aberrations, or departures from perfect imaging. Aberration means that the rays from a point source (such as a star) fail to focus at a common focal point. In spherical aberration, for example, rays at different distances from a principal ray converge ahead of or behind the focus point. Coma and astigmatism are aberrations that affect images away from the optical axis. Lenses also suffer from chromatic aberration, in which rays of different wavelength fail to meet at a common focus. Ordinary camera lenses perform well up to 20° to 30° from the optical axis, but at larger angles the aberrations degrade image quality.

Lenses focus much more light into an image than a pinhole. The ratio between the diameter of the bundle of rays entering the lens and the focal length is called the focal ratio. If a lens has a diameter of 100 millimeters and a focal length of 500 millimeters, its focal ratio is//5.

The smaller the focal ratio, the greater the concentration of light onto the focal surface. Typical pinhole cameras have focal ratios of//500 (i.e., the aperture is V500 of the focal length), but ordinary camera lenses have focal ratios as low as //2. Because the light-gathering area of the//2 lens is 62,500 times greater than the area of the small pinhole, the image formed by the lens is 62,500 times brighter than a pinhole image.

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