Methods and apparatus are provided for measuring distance from an instrument origin to each of a plurality of points in an environment. Laser pulses are emitted along a measurement axis at successive displacements about the origin. The emission time of each pulse is time-shifted relative to a fixed rate. The time shift corresponds to an index of a repetitive sequential pattern. Received pulses are detected at respective arrival times. For each received pulse: a current apparent distance is determined, a measured delta distance is calculated, a range interval is assigned by comparing measured delta distance with an expected delta distance synchronized with the index of the latest emitted pulse, the current apparent distance is defined to be a true measured distance for any received pulse assigned to a first time interval, otherwise the current apparent distance is defined to be a false measured distance.