A new device is described with which screws of any length can be calibrated rapidly for both periodic and cumulative errors in terms of interference fringes. It can also be used to plot correction cams to remove fixed errors of translation or rotation, and to monitor the operation of an engine while ruling diffraction gratings or scales, correcting by automatic feedback differences between the actual carriage position and its proper position as shown by an optical interference field. This so-called “Commensurator,” whose name arises from its function of overcoming the incommensurability of the wavelength of the light used for calibration and the lead of a screw with English or metric threads, consists principally of a screw drive system, eight-figure dials, and a generator, geared together in ratios that can be controlled to one part in 10<sup>8</sup>. Fringes produced by a Michelson interferometer mounted on the ruling engine (or having one mirror moved by the nut of the screw being calibrated) are changed photoelectrically to a wave train that measures translation to within 0.1 microinch. A second wave train of almost identical average frequency is produced by the Commensurator generator to measure screw rotation, and the two trains are continuously compared by means of a phase-sensitive amplifier and motor to within 1/100 cycle or fringe. Any error in carriage translation appears as a lag or lead which produces a torque in the motor until synchronism is re-established by a relative shift of the two wave trains, and thus makes possible automatic plotting of the screw error curve on a moving chart. Corrections for changes in barometric pressure or in temperature can be introduced during operation. By means of this device the variations in lead of a screw having 14 inches of nut motion have been recorded to the nearest 0.2 micro-inch in eight hours. When the error signals of the Commensurator are fed back directly to the corrector mechanism of a ruling engine, transient as well as fixed errors of run and period can be automatically compensated for. If the fringe system is lost, it can be re-established from the Commensurator record, so that controlled ruling of gratings wider than any available coherent fringe-field appears possible. During any period in which fringe control is not exerted the engine operates in the orthodox manner.
GEORGE R. HARRISON and JAMES E. ARCHER, "Interferometric Calibration of Precision Screws and Control of Ruling Engines," J. Opt. Soc. Am. 41, 495-502 (1951)