Errors in compensating for image oscillation by means of a gyroscopic head

Gyroscopic systems can be used to compensate the shifts of an image on motion picture film due to oscillations of the camera. The major task of such correcting systems is the measurement of the natural oscillations of the motion picture camera and the appropriate compensating rotations of the optical elements based on these measurements, so as to cancel the motions of the camera itself. This paper analyzes the error occurring when compensating for image oscillations as a function of the camera system parameters by introducing the concept of a compensation function. This function is expressed as the ratio of the function describing the harmonic motion of the gyroscope to a similar function for the harmonic oscillations of the camera. The theoretical treatment is illustrated using the transfer function of the gyroscopic compensation system manufactured by the Arnold and Richter company. The compensation function is plotted in turn as a function of the frequency of the harmonic oscillations of the image for various values of the time constant, t, in the transfer function of the correcting system.