Optical phase under deep turbulence conditions

Abstract

The Markov approximation for waves in random media specifies that, under strong scintillation conditions, the optical field of unbounded waves has a normal probability distribution with zero mean. Using the coherence function provided by the Markov approximation, we calculate statistics of the phase of the optical field that accounts for the presence of multiple phase dislocations. We also develop and test a Monte Carlo model that generates the phase samples obeying these statistics. In contrast to numerous phase models described in the literature, this model generates discontinuous phase samples that contain optical vortices.

Influence of bandwidth error on the performance of adaptive optics systems for uncooperative beacons: plane wave and spherical wave analysis

“…It can be obtained by assuming that the uncorrected or residual phase increments obey Gaussian statistics 16 . When this condition is not satisfied, i.e., after propagation through very extended turbulence volume which can induce uniform statistics of phase increments 17 , the extended Marechal approximation in the form stated in Eq. ( 7) is no longer valid.…”

Zernike decomposition of aberrations in strong atmospheric turbulence

“…There are elegant approaches for the statistics of the phase and corresponding Monte-Carlo realizations in the limit of strong turbulence; see for example, Ref. 24. However, such an approach is limited to strong turbulence, has not been fully validated for moderate turbulence, and does not easily provide the Zernike variances that would be useful for a designer of an adaptive-optical system.…”

“…The simulation approach is most useful in the case of strong scintillation (Rytov variance greater than 0.3), where no analytic or numerical expressions have been verified to be accurate for treatment of detailed phase statistics. "Deep turbulence" is also mentioned here as in other papers, 24 and refers to moderate-to-strong scintillation conditions in which turbulence is relatively "weak" as measured by D/r0, i.e., D/r0 < 10, where D is the aperture diameter and r0 is Fried's (spherical-wave) coherence parameter. 3 The scope of this paper is limited to the computation of Zernike variances as might be needed by a designer of an adaptive optics system for setting the actuator spacing and stroke needed for a continuous-facesheet deformable mirror.…”

“…Theoretical treatments of non-Kolmogorov turbulence are found in the literature. [17][18][19][20][21][22][23][24] This work quantifies the impact of strong turbulence on the distribution of the strength of the Zernike aberrations for the design of adaptive optic systems and includes a study of sensitivity to non-Kolmogorov spectral exponents and anisotropic turbulence in a circular aperture. The approach is to use numerical integrals where applicable, and then to verify and extend the results with a wave-optics simulation that has received significant past validation.…”