A Machine for Synthesizing Two-Dimensional Fourier Series in the Determination of Crystal Structures

Abstract

An electromechanical analog machine is described which performs a two-dimensional Fourier synthesis for use primarily in x-ray crystal structure calculations, ρ(xy)=Σ lim hΣ lim kFhkocos2π(hx+ky).The analog to a term in this summation is obtained through the use of a pair of selsyns as a synchro-variable transformer somewhat similar to its use in servomechanisms. ρ(xy)hk is represented by the output voltage, Fhko by the input voltage, and 2πhx and 2πky are the angles of rotation of the primary and secondary rotors respectively. A system of crossed shaft and cascading gear trains turns the rotors to the appropriate angles for each selection of point (x, y) in the unit cell. The present machine handles h and k values up through 8, but provision is made for future extension through 16. Computations are shown for two known structures to indicate the results obtainable with the machine.