- A new method of calculating the optical transfer function (OTF) for image blur caused by arbitrary motion is introduced. Previous methods, except for a few specific types of motion, were numerical rather than analytical. This new method makes it possible to obtain analytical expressions for the OTF deriving from any kind of motion by means of the statistical moments of the motion function. Analytical OTF expressions are derived for linear, quadratic, and exponential motion and for high- and low-frequency vibration. A comparison of image degradation is presented for linear and exponential motion and high-frequency vibration of the same blur extent. The method can be implemented in real-time restoration of images blurred by arbitrary motion and in image motion degradation analysis.