A network telescope is a portion of routed IP address space in which little or no legitimate traffic exists. Monitoring unexpected traffic arriving at a network telescope provides the opportunity to view remote network security events such as various forms of flooding denial-of-service attacks, infection of hosts by Internet worms, and network scanning. In this paper, we examine the effects of the scope and locality of network telescopes on accurate measurement of both pandemic incidents (the spread of an Internet worm) and endemic incidents (denial-of-service attacks) on the Internet. In particular, we study the relationship between the size of the network telescope and its ability to detect network events, characterize its precision in determining event duration and rate, and discuss practical considerations in the deployment of network telescopes.