Characteristic parameters of adaptive optical imaging system in oceanic turbulence

Since recently one is interested in underwater communications, imaging, sensing and lidar appeared, it is important to study characteristic parameters of the adaptive optical imaging system in oceanic turbulence. Until now, the characteristic parameters of the adaptive optical imaging system in atmospheric turbulence have investigated widely and in depth, but those in oceanic turbulence have been examined seldom. It is known that the atmospheric turbulence is induced by the temperature fluctuation. However, the oceanic turbulence is induced by both the temperature fluctuation and the salinity fluctuation. The temperature and salinity spectra have similar ''bumped'' profiles, with bumps occurring at different wave numbers. Thus, the behavior of light propagation in oceanic turbulence is very different from that in atmospheric turbulence. In this paper, the influence of oceanic turbulence on characteristic parameters (i.e., strehl ratio, Greenwood time constant, and isoplanatic>) of the adaptive optical imaging system is studied. The approximate analytical expression of the Strehl ratio for the short-exposure imaging case is derived. It is demonstrated by the numerical calculation method that this Strehl ratio approximate expression is accurate enough except the near field when DG/r0=1 (where DG is the pupil diameter of the optical system, r0 is the seeing parameter in oceanic turbulence), and the relative error maximum of this Strehl ratio approximate expression in the far field is much smaller than that in the near field. In addition, the analytical expressions of the Greenwood time constant and the isoplanatic> in oceanic turbulence are also obtained in this paper. It is shown that the values of the three characteristic parameters (i.e., Strehl ratio, the Greenwood time constant and the isoplanatic>) decrease when salinity-induced optical turbulence dominates gradually. The Strehl ratio, the Greenwood time constant and the isoplanatic> also decrease as the rate of dissipation of kinetic energy per unit mass of seawater decreases or the rate of dissipation of mean-squared temperature increases. It is known that the isoplanatic> at wavelength λ=0.5 μm are roughly 7-10 μrad for a nearly vertical path from Earth to space in atmospheric turbulence. However, it is shown in this paper that the isoplanatic> may be on the order of μrad after 100 m propagation distance in oceanic turbulence. Therefore, the influence of oceanic turbulence on the isoplanatic> is very large. The results obtained in this paper will be useful in the applications of adaptive optics imaging systems involving oceanic turbulence channels.