1.1. Diffraction image ►

Ray, on the other hand, is simply a straight line with the origin at the point-source, that remains perpendicular to the wavefront. While rays are useful in presenting geometrical aspects of optical phenomena, they represent only a tiny fraction of the total energy propagating through the energy field. Furthermore, it is only their geometric properties that are considered in imaging. Therefore, ray (or geometric) optics has no direct ties with physical properties of the energy field.

The wavefront, while itself a geometric category, is more directly related to the underlying physics. It identifies the location of in-phase wave sources, making it the basis for calculations determining the properties of wave interactions. Hence, the significance of the wavefront is in that its form directly determines quality of optical imaging in a telescope. Obviously, form of the wavefront and geometric properties of the rays are directly inter-related, but the ray geometry remains only loosely related to the interactions taking place within the energy field. The most striking example is that of a spherical wavefront, whose rays all meet in a single point. At the same time, the actual physical image formed by waves emerging from the wavefront is a bright spot surrounded by a series of fading rings. How is this taking place?

According to Huygens' principle, every wavefront point is a source of secondary wavelets. This constitutes a micro-structure of energy field propagation, with the energy advancing in the direction of the wavefront, but also spreading out in other directions. However, principal wavefronts form in the direction determined by extending straight lines from the point source. This results from the wavelength of light being very long compared to the density of wave sources. Waves moving in other directions generate phase difference, but always much smaller than a full phase, needed to form another effective wavefront (FIG. 1, right).

In order to form the image of a point-source, portion of the energy field created by a faraway point-source needs to be brought together, creating a point of high energy concentration - a point-source image. For this, the waves need to arrive at such a point in the same state of propagation - or phase - which, in turn, requires that optical paths from all wavefront points are identical. The more difference in optical paths, the less efficient wave interference, resulting in deterioration and, ultimately, disintegration of the point-image. Obviously, a single ideal wavefront shape for the purpose of optical imaging is a sphere, with every point on it at an identical separation from the center of curvature. Waves from spherical wavefront arriving at its center of curvature - or focus - all meet in phase, for the maximally efficient energy concentration into a point-image.

However, this point-image is not a point of light, but an extended pattern of intensity distribution (Inset A). The reason are residual wave interactions around the point of convergence, the concept introduced by Fresnel. This effect is known as diffraction of light. As a result, the light energy directed toward focal point is spread into a pattern, setting a limit to image contrast and resolution. Physical size of diffraction pattern is inversely proportional to the telescope's relative aperture 1/F, with the first minima (Airy disc) radius given by rAD=1.22λF, λ being the wavelength of light, and F the focal ratio F=ƒ/D, ƒ and D being the telescope focal length and diameter, respectively.

The effect on image quality is not directly related to the physical size of the pattern, rather to its angular size, as subtended on the sky, and the object itself, through the pupil (aperture) center. Its radius is given by αAD=1.22λ/D, in radians. Angular size of diffraction pattern (i.e. of the point-source image) in a telescope sets direct limit to its theoretical resolution and maximum useful magnification.

1.1. Diffraction image ►

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