Diffraction

For people learning diffraction the first time, the various viewpoints presented in this chapter may be overwhelming and the main conclusions can be lost in the detail. Several elements are crucial for this discussion, however, so let's look at them at the beginning:

1. Diffraction is caused by the wave nature of light. Because light cannot be localized, images are necessarily fuzzy. The quantum mechanical concept of the photon as a particle does not help fix its position.

2. Diffraction is a consequence of a limited aperture. It is an angular blurring that is independent of the focusing power of the instrument.

3. Diffraction is not just a phenomenon observable in the rings. The spread of the central spot is caused by diffraction.

4. Quasi-static light and dark regions exist because diffraction can be modeled as a standing wave, with the aperture providing the boundaries.

5. A limit exists to optical quality that is difficult to exceed.

Once readers have a working knowledge of diffraction, the star test is more easily understood. Diffraction itself is not often explained well, and many people believe a kind of folklore about what it is and what causes it. Authors either sidestep diffraction entirely, or they take the too-easy refuge of mathematics. The scarcity of introductory instructions is unfortunate, because the concepts underlying diffraction are not all that difficult to understand. More importantly, some of these ideas are the most beautiful and fundamental in physics. Diffraction touches on notions as varied as the limits of what is knowable and concept of the particle.

Diffraction is much more than the process that generates rings around a stellar image. While it is true that diffraction makes these rings, it is possible to shade the edges of the aperture to make such ringing arbitrarily small. Diffraction, though, still blurs the central spot. Images without rings still display diffraction. Literally, diffraction means a "breaking up" of a wavefront, which is disturbed by passage of the wave near an obscuring body.

Say that we were in a universe where light consisted of infinitely tiny particles that could be traced from the star, through the telescope, and finally to the eye. Diffraction would not exist in such a world. Either the particles continue undisturbed beyond the obscuring body, or they hit and are stopped. Close approach would make no difference. The region outside the illuminated cone near focus, where you wouldn't normally expect light, is called the geometric shadow.

When optical designers ray trace optics, they are using the "light-as-particles" assumption that light will go only where geometry allows. The concept of light moving in particles is called "ray optics." In ray tracing the system, they are assuming that light will go through the optics as if it were a tiny elastic sphere, smacking into optical surfaces, deflected according to empirical rules of refraction and reflection. Surprisingly, this ballistic model will predict the course of light fairly well. To first order, it does a fine job.

Unfortunately, the behavior of light has other characteristics not explained by modeling light as a particle. Light seems to be able to turn corners. By itself, this feature is not too surprising. Any enterprising 17th century physicist could have postulated, for example, that a particle of light has some finite size. As it brushes near a surface, it could be pushed back into the lit region. But experiments done near straight edges showed that light was deflected into the shadows of the obscuration. Instead of banging its shoulders into the obscuring body and being thrown into the lit region, the light ray seemed to be grabbing the edge of the aperture and swinging around. Strangely, some of the shadow also seemed to bleed into the lit region.

Some angles of deflection are preferred. Moving away from the position of best focus, the illumination dims as expected. But here's the strange behavior—it then starts to brighten again. With higher and higher angles, the illumination goes through many such oscillations, which cause the familiar diffraction rings around stars. A theory postulating light as particles has no way of understanding such behavior, except by supposing a defect in the optics. At focus, one doesn't expect light to be anywhere except at a dazzling point in the center.

The eventual explanation came by saying that light did not resemble particles as much as waves. Many of these effects can be observed in a puddle—or other shallow pool of water—by watching the behavior of the water waves in the surface. Lay a piece of wood across part of the puddle so that it interferes with the steady course of waves, and start a wave by dropping a pebble on one side of the pool. Notice that as the wave passes the end of the wood, it curls around into the protected region. This is diffraction.

Water waves are very interesting, but they don't immediately seem to relate to optical quality in a telescope. However, we will see how the behavior of a wave near an obstacle or edge results in degradation of the image. Diffraction is the mechanism that produces unavoidable imperfection in telescopes.

In the old light-as-particles model, the image could be perfect as long as the surfaces were perfect. The tiny particles would fly into the telescope, missing all of the obstructions. They would then be perfectly deflected by the optics, always imaged at just the right point. Rays in a perfect instrument either miss the telescope entirely or are placed in an infinitesimal blur circle. We could carefully inspect the image of exceptional instruments and indeed see a tiny replica of the star. Nearby, we might also observe an even smaller planetary image.

Unfortunately, the real world of optics doesn't permit infinite precision. Waves are not localized. It's much like finger-painting while wearing mittens— drawing fine lines or dots is impossible with such pudgy fingers. People have often thought that diffraction could be suppressed by obscuring or diffusing the edge. However, diffraction originates because wave energy exists in a finite, restricted aperture. The aperture is always in our optical system, so modifying the edge shapes the course of how waves are broken up, not the fact that they will be disturbed. We can shove diffraction effects around like a child rearranging vegetables on a dinner plate, but we are unable to make them go away.

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