Analytical solution of excess fractions method in absolute distance interferometry

摘要

A universal method for precision lenght measurements, called "excess fractions" was proposed at the end of the 18th century for the precise calibration of gauges. In this method, the interferometer compares an unknown gauge with the number of known wavelengths. The array of Φ_i; which consists of the remainders of an integer number of wavelengths in the length of the gauges, was obtained and analyzed. For the measurement of gauge lengths that were small enough, the integer number of wavelengths can be found heuristically. With the development of lasers technique, the possibility of applying this idea to the measurement of large distances, such as the distance to the moon, appeared. With the imminent number of wavelengths in the distance, the heuistic solution is not possible. In this paper the solution based on Chinese Remainder Theorem is proposed. The Chinese Remainder Theorem is developed for use in the case, when wavelengths are not mutually prime numbers, and metrological aspects of this solution will be analyzed.