Path-integrated Turbulence Research Articles

Measuring atmospheric turbulence strength based on differential imaging of light column

We propose and experimentally evaluate a novel approach to measure atmospheric turbulence, in which imaging of light column technology is integrated into a differential motion method. In the approach, a large acquisition scene of the light column and a narrow field of view of one pixel of the charge-coupled device respectively allow high temporal and spatial resolutions, which offer the possibility of path-integrated turbulence strength measurement with multiple paths. In addition, we describe the measurement principle of the approach. Lastly, comparative experiment is performed to verify the feasibility of the approach.

Stellar scintillation and the atmosphere’s vertical turbulence profile

The relationship between stellar scintillation in the strong-focusing regime and the atmosphere’s vertical turbulence profile is investigated with numerical simulation. For two distinct atmospheric profiles, the irradiance variance at a point on a telescope aperture is evaluated as a function of the weighted path-integrated turbulence (i.e., Rytov variance). Additionally, we compute the aperture-averaged irradiance variance and the log-amplitude correlation across the aperture as functions of the Rytov variance. For one atmospheric profile, scintillation is dominated by turbulence in the tropopause; for the other, scintillation arises from turbulence in both the tropopause and the lower troposphere. The numerical results indicate that (1) stellar scintillation depends on the actual profile of atmospheric turbulence and not just on its weighted integral and (2) in the strong-focusing regime the irradiance variance is determined primarily by an optical wave’s coherence length as it passes through the tropopause.

Two-color correlation of atmospheric scintillation

We present the results of measurements of the correlation of scintillations of two colors of light made in the turbulent atmosphere. In strong path-integrated turbulence the correlation is below that predicted by the weak-turbulence theory. A phenomological theoretical approach is used to account for saturation effects. This simple theory provides a reasonable approximation to the correlation data. Thus, we conclude that saturation effects reduce the two-color correlation of atmospheric scintillation.

Aperture averaging of optical scintillations in the turbulent atmosphere

We have developed approximate expressions for the aperture-averaging factor of optical scintillation in the turbulent atmosphere. For large apertures and weak path-integrated turbulence with a small inner scale, the variance of signal fluctuations is proportional to the -7/3 power of the ratio of the aperture diameter to the Fresnel zone size. If the inner scale is large, the variance is proportional to the -7/3 power of the ratio of the aperture diameter to the inner scale. In strong path-integrated turbulence, two scales develop. That portion of the variance associated with the smaller scale is proportional to the -2 power of the ratio of the aperture diameter to the phase coherence length. That portion of the variance associated with the larger scale is proportional to the -7/3 power of the ratio of the aperture diameter to the scattering disk. These simple approximations are within a factor of 2 of the measurements.

Wander of an optical beam in the turbulent atmosphere

A simple, analytic, geometrical optics expression for the variance of the beam displacements caused by propagation through weak refractive turbulence described by the Kolmogorov spectrum is presented. The analytical formula includes the effect of the divergence or convergence of the initial beam. The formula is compared with numerical results obtained from a more complicated expression including effects of diffraction and strong path-integrated turbulence. The simple geometrical optics expression holds for apertures larger than the Fresnel zone size and larger than the ratio of the square of the Fresnel zone to the phase coherence length.

Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere

Irradiance statistics were simultaneously measured with five apertures of four different sizes and also with five different bandwidths under conditions of strong path-integrated turbulence to determine aperture size and bandwidth requirements. The probability density function and the second and third moments are considered. Good measurements of these statistics can be made with detector apertures near the wave coherence length and with bandwidths near the ratio of the transverse wind velocity to the wave coherence length under these conditions.