Characteristics of a polynomial representation of atmospheric phase distortions

A hypothesis of "frozen" turbulence in separate horizontal layers of the atmosphere and an allowance for the external turbulence scale are used to find the matrix of the moments of the coefficients of the expansion of a wavefront on an aperture in terms of the Zernike polynomials. It is shown that the aperture has an averaging effect on lower-order aberrations and that it causes a deterioration in the precision of representation of the wavefront by a finite number of such polynomials with coefficients averaged over the measurement time. An example is given of a calculation of the characteristic time of the "frozen" phase distribution over the aperture.