Fourier-based layout for grating function structure in spatial filtering velocimetry

Optical spatial filtering velocimetry (SFV) has been used for several decades for velocity measurements. Since the 1990s, charge-coupled device (CCD) line sensors have been used for the realization of spatial filtering systems by the inherent implementation of grating functions using a specialized clock regime. Another approach is the realization of optical SFV systems by utilizing array detectors (CCD or CMOS) with software-implemented grating functions, especially for two-dimensional velocity measurements. Choosing a suitable grating function for the observed scene can be an obstacle when using SFV, and relies on the experience of the user. With this in mind, this contribution presents an overview of how to assemble an optical spatial filtering system. After a general description of signal generation in spatial filtering systems, a straightforward approach to identifying matching harmonic grating functions by using Fourier analysis is presented. This approach has particular advantages for observed scenes with a periodically structured pattern, which were problematic when using SFV in connection with a fixed grating function. Matching periods of harmonic grating functions can be found as peaks in the spectral density distribution of the imaged scene. Once a matching grating function has been found, the signal processing can be made with SFV, which is simpler than calculating the cross-correlation of full frames and is suitable for real-time application. Criteria for the layout of an array-detector-based spatial filtering velocimeter are then discussed. (paper)