In the velocity measurement using spatial filter, the parallel-slit forms a kind of narrow-band-pass spatial filter, and its selectivity is defined by the ratio of center frequency to frequency width about spatial frequency characteristics. And it is desirable that the selectivity is as large as possible.
In this paper, from the above point of view, the problem of the narrow-band-pass optimal spatial filter is considered.
The optimal problem is to maximize the selectiviy for the fixed slit-number N, with which the frequency width is defined like a standard deviation of frequency characteristics.
It is shown that this problem is equivalent to minimizing the quadratic from about a certain matrix A, and its solution is the eigen vector corresponding to the minimum eigen value of matrix A.
Besides, the change of the selectivity is discussed when the random error exists in realizing the weighting function as a spatial filter.