A roseet scanning pattern is expressed as the vector sum of two counter-rotating vectors. For a Cassegrain system, the scanning pattern is a function of system parameters such as the canted angle, the scanning rate ratio, the configuration of each scanning element, and the distance between them. Using the optical ray tracing method along the direction of the system axis, an algorithm to compute the pattern is derived. This method can be employed to design a scanning-pattern system. By adjusting the system parameters, the desired scanning pattern can be obtained. Finally, by computer simulation with this design algorithm, the results including the effect due to the deflection error are consistent with the experimental observation.