2-POINT ESTIMATES OF THE SPECTRAL DENSITY-FUNCTION WITH FINITE SEPARATION AND VOLUME

The spatial and temporal variation of a fluctuating quantity can often be described with sufficient accuracy as a sum of independent modes, whose powers are given by a function S(k) for each frequency. Many diagnostics are restricted to making measurements at two points, so that a determination of S(k) by spatial Fourier transformation is not possible. Nevertheless, in the limit of point measurements with infinitesimal separation, the mean wave number kBAR and the rms deviation sigma about the mean can be exactly determined by repeated measurements of the phase difference between the tips. If the separation is finite, the method can be extended in such a way that the correct results are obtained for any separation as long as S(k) is Gaussian. For other spectral shapes, the error in the measurement of kBAR may be of the order of sigma, and the fractional error in the measurement of sigma may be substantial. A finite measurement volume reduces the sensitivity to short wavelength modes. Under certain assumptions, the measured values can be adjusted to yield better estimates of kBAR and sigma.