Fig. 183.—Airy’s Diffraction Pattern.
The relation of the diffraction pattern as disclosed in the moments of best seeing to its theoretical form is a very interesting one. The diffraction through a theoretically perfect objective was worked out many years ago by Sir George Airy who calculated the exact distribution of the light in the central disc and the surrounding rings.
This is shown from the centre outwards in Fig. 183, in which the ordinates of the curve represent relative intensities while the abscissæ represent to an arbitrary scale the distances from the axis. It will be at once noticed that the star image, brilliant at its centre, sinks, first rapidly and then more slowly, to a minimum and then very gradually rises to the maximum of the first bright ring, then as slowly sinks again to increase for the second ring and so on.
Fig. 184.—Diffraction Solid for a Star.
For unity brightness in the centre of the star disc the maximum brightness of the first ring is 0.017, of the second 0.004 and the third 0.0016. The rings are equidistant and the star disc has a radius substantially equal to the distance between rings. One’s vision does not follow down to zero the intensities of the rings or of the margin of the disc, so that the latter has an apparent diameter materially less than the diameter to the first diffraction minimum, and the rings themselves look sharper and thinner than the figure would show, even were the horizontal scale much diminished. The eye does not descend in the presence of bright areas to its final threshold of perception.
One gains a somewhat vivid idea of the situation by passing to three dimensions as in Fig. 184, the “diffraction solid” for a star, a conception due to M. André (Mem. de l’Acad. de Lyon 30, 49). Here the solid represents in volume the whole light received and the height taken at any point, the intensity at that point.
A cross section at any point shows the apparent diameter of the disc, its distance to the apex the remaining intensity, and the volume above the section the remaining total light. Substantially 85% of the total light belongs to the central cone, for the theoretical distribution.
Granting that the eye can distinguish from the background of the sky, in presence of a bright point, only light above a certain intensity, one readily sees why the discs of faint stars look small, and why shade glasses are sometimes useful in wiping out the marginal intensities of the solid. There are physiological factors that alter profoundly the appearance of the actual star image, despite the fact that the theoretical diffraction image for the aperture is independent of the star’s magnitude.