Power spectra requirements for wave-front-compensative systems*

The phase degradation of an optical wave front distorted by turbulence in the propagation medium may be corrected in a piecewise-linear fashion by using an array of small circular mirrors. An option in the correction scheme is to compensate for overall tilt separately. We have evaluated power spectra and variances of the piston and tilt motions of the mirror segments as well as the motion of the overall tilt corrector. The form of the spectra for any propagation medium is an aperture integral of the product of the phase-difference power spectrum, describing the medium, and a generalized transfer function, representing the aperture and its segments. In the case of low-power atmospheric propagation, the necessary propagation results are linear in turbulence strength; hence the path may be sectioned into a large number of thin slices. A set of standard curves is found to represent a generalized slice, and the differential contributions may be summed to represent any propagation path. The standard curves, further modeled in terms of power-law dependencies, are practical for use on a desk calculator.