Pinhole Imaging

The most basic method for finding the direction of light is shadowing. Even the amoeba can tell that the side of its body facing a strong light source is warmer (or more chemically stimulated) than the side facing away, and turn toward (or away from) the light. X-ray and gamma-ray astronomers once used detectors that were in principle only slightly more sophisticated than the amoeba's simple shadowing.

However, the flood of light can be converted into an image with a simple pinhole camera. Any closed box or room (i.e., a camera in Latin) with a small aperture (apertura = "opening") can serve as an image-forming device. Rays of light from outside objects enter the aperture and continue in straight lines to the opposite side. On the image surface, light from each source thus has a well-defined location: the angular positions of the light sources have been mapped onto (x, y)

Figure 1.1 At the back of a pinhole camera, light sources at different angular positions in front of it are mapped onto locations in the image. The intensity of the light at each point in the image depends on the flux entering the camera from the light sources outside it.

locations on a surface. The organized pattern of light intensities is an image.

The feature that distinguishes an image from illumination is the spatial organization of intensities in the image. The amoeba senses the total illumination without knowing where the light comes from, but in a camera the light is sorted into location by its direction of origin. As beings with eyes, we are so used to knowing the angular positions of light sources that it tends to be difficult for us to imagine light without knowing what direction it came from.

Let us now examine the properties of the images formed by a pinhole camera. A pinhole camera consists of a light-tight box. At the center of one end is the aperture and at the other end is a surface on which light falls. (Important to remember: pinhole cameras can be any shape and size, and the receiving surface need not be flat. The camera still works, but the math is more complicated.) Light from many sources falls on the front of the camera, and a tiny fraction of it enters the aperture. Light that enters crosses the interior and falls on the receiving surface.

Inside a camera, we define the line between the aperture and the point that lies directly "under" the aperture as the optical axis. This point is the point on the receiving surface that is closest to the aperture—a distance called the focal length—and light reaching this point arrives perpendicular to the receiving surface. If we point the camera at a source of light—that is, align the optical axis of the camera with the direction of the source—then the image of the source lies on the receiving surface and on the optical axis.

Now consider the location of a source at an angular distance i) (theta) from the optical axis. The angle t) is measured at the aperture of the camera, and the image of this source forms some height, h, from the optical axis:

where F is the focal length. The greater the angular distance a source lies from the optical axis, the greater the linear distance its image lies from the optical axis.

Pinhole cameras can easily cover off-axis angles of 45° to 60°, so that the whole image spans a 90° to 120° angle. The rectilinear mapping of source position to image location has some interesting consequences. An array of sources that lies on a straight line in front of a camera will lie on a straight line on the image. In addition, the images of sources that lie on a great circle on the celestial sphere will lie along a straight line on the image. In terrestrial imaging, the sides of buildings are rendered as straight lines, and in astronomical imaging, horizons, equators, and longitude circles are rendered as straight lines. Images in the pinhole camera are said to be both rectilinear and free of distortion.

As imaging devices, pinhole cameras collect too few photons to be practical. If the aperture is enlarged to make the image brighter, light from different sources overlaps, and the image is blurred. If the aperture is too small, diffraction caused by the wave properties of light degrades the image. For practical imaging, light must be collected over a large area and focused into an image.

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