Iterative wavefront reconstruction for strong turbulence using Shack-Hartmann wavefront sensor measurements.

An iterative wavefront reconstruction method using Shack-Hartmann wavefront sensor (SHWFS) measurements is presented in this paper. A new cost function for the wavefront reconstruction problem is derived and the solution is obtained iteratively using the gradient descent method. The proposed method aims to effectively handle the scintillated SHWFS measurements and to provide simpler and accurate ways to achieve branch-point-tolerant wavefront reconstruction suitable for adaptive optics compensation of strong turbulence. Simulated iterative wavefront reconstruction results show the effectiveness of the proposed method. A laboratory optical testbed is also presented to show the experimental implementation of the proposed method.

Signal-to-noise ratio limitations for intensity correlation imaging.

Intensity correlation imaging (ICI) is a concept which has been considered for the task of providing images of satellites in geosynchronous orbit using ground-based equipment. This concept is based on the intensity interferometer principle first developed by Hanbury Brown and Twiss. It is the objective of this paper to establish that a sun-lit geosynchronous satellite is too faint a target object to allow intensity interferometry to be used in developing image information about it-at least not in a reasonable time and with a reasonable amount of equipment. An analytic treatment of the basic phenomena is presented. This is an analysis of one aspect of the statistics of the very high frequency random variations of a very narrow portion of the optical spectra of the incoherent (black-body like-actually reflected sunlight) radiation from the satellite, an analysis showing that the covariance of this radiation as measured by a pair of ground-based telescopes is directly proportional to the square of the magnitude of one component of the Fourier transform of the image of the satellite-the component being the one for a spatial frequency whose value is determined by the separation of the two telescopes. This analysis establishes the magnitude of the covariance. A second portion of the analysis considers shot-noise effects. It is shown that even with much less than one photodetection event (pde) per signal integration time an unbiased estimate of the covariance of the optical field's random variations can be developed. Also, a result is developed for the standard deviation to be associated with the estimated value of the covariance. From these results an expression is developed for what may be called the signal-to-noise ratio to be associated with an estimate of the covariance. This signal-to-noise ratio, it turns out, does not depend on the measurement's integration time, Δt (in seconds), or on the optical spectral bandwidth, Δν (in Hertz), utilized-so long as ΔtΔν≫1, which condition it would be hard to violate. It is estimated that for a D=3.16 m diameter satellite, with a pair of D=1.0 m diameter telescopes (which value of D probably represents an upper limit on allowable aperture diameter since the telescope aperture must be much too small to even resolve the size of the satellite) at least N=2.55×10(16) separate pairs of (one integration time, pde count) measurement values must be collected to achieve just a 10 dB signal-to-noise ratio. Working with 10 pairs of telescopes (all with the same separation), and with 10 nearly adjacent and each very narrow spectral bands extracted from the light collected by each of the telescope-so that for each measurement integration time there would be 100 pairs of measurement values available-and with an integration time as short as Δt=1 ns, it would take T=2.55×10(5) s or about 71 h to collect the data for just a single spatial frequency component of the image of the satellite. It is on this basis that it is concluded that the ICI concept does not seem likely to be able to provide a timely responsive capability for the imaging of geosynchronous satellites.

Light propagation through anisotropic turbulence.

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς(2-α).