Relationship between the f -number and the ruling frequency for a better discrimination of optical surfaces with the classical Ronchi test

Abstract

We present a criterion to properly choose the ruling frequency during the testing process of concave mirrors using the classical Ronchi test. It is known that when the number of lines per inch (ruling frequency) is low, the Ronchi test loses sensitivity; this fact implies that it is not qualitatively possible to determine the real surface shape; only an approximation would be obtained. In addition, if a higher ruling frequency is used, the ronchigram would be exposed to diffractive effects, making it even more difficult to identify the patterns for the real surface shape. We have found that by mathematically relating the f-number of the surface and the ruling spacing, the detection range of the Ronchi test can be improved. This allows us to know the shape of the patterns with the best certainty corresponding to a given optical surface. We have analyzed the behavior of real ronchigrams produced for two different parabolic mirrors to demonstrate this fact. In addition, real ronchigrams obtained from primary mirrors of telescopes that support the use of this criterion are shown.