Spatial filtering velocimetry revisited: exact short-time detecting schemes from arbitrarily small-size reticles

Spatial filtering velocimetry was proposed in 1963 by Ator as a velocity-sensing technique for aerial camera-control systems. The total intensity of a moving surface is observed through a set of parallel-slit reticles, resulting in a narrow-band temporal signal whose frequency is directly proportional to the image velocity. However, even despite its historical importance and inherent technical advantages, the mathematical formulation of this technique is only valid when infinite-length observation in both space and time is possible, which causes significant errors in most applications where a small receptive window and high resolution in both axes are desired. In this study, we apply a novel mathematical technique, the weighted integral method, to solve this problem, and obtain exact sensing schemes and algorithms for finite (arbitrarily small but non-zero) size reticles and short-time estimation. Practical considerations for utilizing these schemes are also explored both theoretically and experimentally.