Surface Tolerance
In 1879 the English physicist, Lord Rayleigh, showed that for practically perfect image formation all of the light emanating from a point in an object (or from a star) must, after reflection or refraction, meet in a point in the focal plane after traversing paths that do not differ by more than one quarter of a wave length of light. This tolerance is known as the Rayleigh limit.
Experience has shown, however, that images quite reasonably approaching the same degree of perfection will be obtained if the difference in light path does not exceed twice the Rayleigh limit, or one half of a wave length. (The wave length of this was similarly demonstrated by A. W. Everest, who originated the unique "doughnut" curves for testing the paraboloid. A mathematical discussion of his methods is given by Mr. Everest in the book Amateur Telescope Making Advanced.
yellow-green light, which we may adopt as a standard, is 1/45,000", or 0.000022".)
In the case of reflection, the light travels twice through the space in front of the mirror. Therefore, the departure of the mirror's surface from a true paraboloid may not exceed a quarter wave in order to meet the more tolerant half-wave limit. To this end, the difference between sphere and paraboloid (distance PS, Fig. 37) must be reduced to this amount, or to 0.0000055".
The 6-inch f/8 mirror must therefore be corrected (under or over) to within 55/114, or approximately 0.045", of the value of r2/R, so that corrections of between 0.05" and 0.14" are tolerable. But because of the probable error of observation, it is prudent to have the measured correction lie within 0.07" and 0.11". A mirror corrected to the exact value of r2/R, with a smooth, regular-appearing curve, will perform within the Rayleigh limit, and the finest possible definition will be realized.
next- error of observation |
|
