Effects of target structure on the performance of laser time-of-flight velocimeter systems

The consequences of partially developed speckle and the effects giving rise to bias errors in velocity determination are discussed with respect to robustness of a classical laser time-of-flight velocimetry (LTV) system. It is demonstrated that surface regimes exist that define the degree of partially developed speckle. These regimes are explored both theoretically and experimentally; surface models are developed to predict the resulting cross covariance from which velocity estimations can be obtained. The surface models describe the behavior of the cross covariance caused by reflection structures and with disparate lateral-roughness scales. In particular, it is shown that it is possible to obtain a twin-Gaussian cross covariance as a result of the presence of partially developed speckle. All models described are compared with experimental observations of the cross covariance for differing surface regimes. The objects are solid targets having lateral spatial correlations in reflection amplitude, height, or both, generally giving rise to partially developed speckle. In almost all cases good agreement with the corresponding theoretical predictions are found. Decorrelation caused by velocity misalignment is shown to shift the peak of the cross covariance significantly, giving a velocity bias. A corresponding theoretical model is developed and verified experimentally. Cross-talk measurements have been performed and compared with a theory developed herein. Both measurements and theory indicate that only spot sizes comparable with or larger than their corresponding separation will lead to a measurable peak shift of the time lag for the maximum of the cross covariance. We conclude that LTV systems will provide accurate velocity estimates under a wide variety of practical conditions.