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Analytical expressions for the crosscovariance (time-of-flight velocimeter, LTV) and for the power spectrum (laser Doppler velocimeter, LDV) are presented based on the assumption of all apertures having a Gaussian transmission function. The objects are simulated at solid targets having lateral spatial correlation, i.e. giving rise to partially developed speckle. The case of fully developed speckle can thus be simulated by having zero correlation length. For both systems and either target the relative width of the crosscovariance (LTV) and power spectrum (LDV) is calculated analytically based on the entire optical system and expressed as a function of the number of modes in the detection system. It is shown that the LTV will give in general a lower variance for the velocity estimate but that spatial correlations of the target are most detrimental to the LTV system. Besides, the decorrelation effects for measurement on curved surfaces are considered and it is shown that both systems will suffer equally in the case of a multimode system but the LTV system will be superior to an LDV system in case of a single mode system. The basic difference between the performance of the two systems stems from the inherent difference in bandwidth.
Harold T. Yura,Steen Gruner Hanson, andLars Lading
"Comparison between the time-of-flight velocimeter and the laser Doppler velocimeter for measurements on solid surfaces", Proc. SPIE 2729, Optical Velocimetry, (13 February 1996); https://doi.org/10.1117/12.232995
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Harold T. Yura, Steen Gruner Hanson, Lars Lading, "Comparison between the time-of-flight velocimeter and the laser Doppler velocimeter for measurements on solid surfaces," Proc. SPIE 2729, Optical Velocimetry, (13 February 1996); https://doi.org/10.1117/12.232995