Look and think before opening the shutter. The heart and mind are the true lens of the camera.
I think the best way to discover the need for lenses is to analyze a famous lensless camera, the pinhole camera. This is nothing more than a small version of the camera obscura that played such a large role in the history of art and photography. All we need is a light-tight box with a pinhole in the center of one wall and a photographic plate attached to the opposite wall. As shown in Figure 5.1, the formation of an image can be explained with nothing more than ray optics. That is, we assume that light beams move in a straight line, and we perform ray tracing. A ray of light from any point on an object passes through the pinhole and strikes the plate on the opposite wall.
It is obvious from the figure that a point on the object will become a small circle in the image because the pinhole aperture must have some diameter to admit the light. If we make the pinhole smaller, the light reaching the image will be diminished, and the exposure will take longer. If we enlarge the pinhole, the resolution will suffer. At first
it appears that there is no optimum size, and we just have a trade-off between resolution and the time required to expose the plate. But that turns out not to be the case; if we try smaller and smaller pinholes, at some point we find that the resolution actually decreases. The reason for this development is the ubiquitous diffraction phenomenon.
In the limit of very small apertures, the image of a distant point, say a star, becomes a circular disk with faint rings around it. This bright central region, called the Airy disk, is shown on the right side of Figure 5.2. The diameter of the disk measured to the first dark ring is equal to 2.44AN, where A is the wavelength of the light and N is the ratio of focal length to aperture, f/S, defined in Chapter 4 as the F-number. The spot size for a distant point without diffraction is just equal to the aperture diameter S. Therefore, the spot size will increase for both large and small pinholes.
aperture aperture sensor
The optimum pinhole size occurs when the contributions of these two effects are approximately equal. Therefore,
and we conclude that the optimum aperture size is equal to
Since A « 500 nm in the middle of the visible spectrum, we find on average that
for S „ and f measured in millimeters. When opt J
f = 100 mm, the optimum pinhole has diameter Sopt = 0.35 mm. This is approximately the size of a no. 11 needle. A formula attributed to Lord Ray-leigh improves this calculation by the substitution of 3.61 for 2.44 in Equation (5.1).
This derivation is only approximate, and it fails badly for nearby objects. It is clear that light rays from a bright point near the pinhole will diverge through the pinhole to make a spot on the film that is larger than the pinhole. This results in a loss of resolution for nearby objects, and the realization that the optimum size for the pinhole depends on the distance from the pinhole to the object being photographed.
Photography with a pinhole camera requires an exposure time that depends on the F-number (N) of the aperture. From the definition we find that N = 100 mm/0.35 mm or f/286 for this camera with its optimum pinhole size. How does this compare with a typical lens-based camera? A typical aperture setting for outdoor photography is f/ 8, and we have found that every time N doubles, the intensity is cut by a factor of 4. Thus f/8 must be doubled five times to equal approximately f/286, and this indicates about 45 = 1024 times as much light intensity on the image plane as with the pinhole camera. The recommended exposure time for typical (ISO 100) film in hazy sunlight is 1/125 s at f/8. The corresponding exposure for a pinhole camera with the optimum pinhole would be about 8 s.
Thus, a pinhole camera gives at best poorly resolved images and requires very long exposure times as well. It does produce interesting effects, since any focal length is possible and the images show no aberrations or distortion. The long exposure times can also produce unusual effects. For example, during long exposures objects can move quickly through the field of view and leave no trace in the image. In fact, there is a lot of interest in pinhole cameras by hobbyists, but pinhole cameras are toys compared to cameras with lenses.
One other point is worth noting. The ray-tracing approach described above assumes that the rays are unaffected by the pinhole other than the spreading effect of diffraction. This works if the same medium, such as air, fills the camera and the outside space. Suppose instead that the space between the pinhole and the film is filled with water. A ray passing from air to water is subject to refraction, and the path is bent toward the optical axis (a line through the pinhole and normal to the film plane). The unexpected result is a fisheye view of the world. This sensor effect is discussed and illustrated in Chapter 10. An air-filled pinhole camera with a glass window underwater would be the reverse situation and should give a telephoto effect. As far as we know, this arrangement has not been demonstrated.
In summary, here is what lenses do. They permit sharp, high-resolution photos to be made with large apertures. The large apertures mean that adequate exposures can be obtained with high shutter speeds (short exposure times). In addition, the effects of diffraction can be reduced and the region of sharp focus (depth of field) can be controlled. Thus, we see that lenses have transformed a curiosity into an image-making miracle.
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