Method to Compute Pointing Displacement, Smear, and Jitter Covariances for Optical Payloads

This paper presents a method to assess the pointing and image motion performance of optical payloads in the presence of image displacement (shift), smear, and jitter. The method assumes the motion is a stationary random process over an image exposure interval. Displacement, smear, and jitter covariances are computed from the solution to a Lyapunov differential equation. These covariances parameterize statistical image motion modulation transfer functions (MTFs), and they can be used to verify pointing and image motion MTF requirements. The method in the present paper extends a previous method to include smear, as well as displacement, and hence jitter. The approach in the present paper also leads, as a special case, to a more efficient method to compute the displacement covariance than the previous method. Numerical examples illustrate the proposed method.