Temporal properties of the Zernike expansion coefficients of turbulence-induced phase aberrations for aperture and source motion

Abstract

Zernike polynomials are often used to analyze turbulence-induced optical phase aberrations. Previous investigations have examined the spatial and temporal characteristics of the expansion coefficients of the turbulence-induced optical phase with respect to these polynomials. The results of these investigations are valid only for certain geometries and atmospheric models and do not take into account the effects of relative motion between the sensor and the object of interest. We introduce a generalized analysis geometry and use this aperture-and-source geometry with conventional methods to arrive at a general expression for the inter- aperture cross correlation of the Zernike coefficients. Aperture-and-source motion considerations are introduced to derive an expression for the temporal cross correlation and cross power spectra of these expansion coefficients. Temporal correlation and spectrum results are presented for several low-order Zernike modes, given certain aperture-and-source motions.